redacted for privacy - core

AN ABSTRACT OF THE THESIS OF

Devavrata Godbole for the degree of Master of Science in

Electrical amp Computer Engineering presented on October 3 2000 Title

PHASE NOISE MODELS FOR SINGLE-ENDED RING OSCILLATORS

Abstract approved ___ qt- ___

John T Stonick

The tremendous growth of wireless and mobile communications has resulted in placing

of stringent requirements on the channel spacing and by implication on the phase noise

of oscillators typically mandating the use of passive LC oscillators with high quality

factor (Q) However the trend towards large-scale integration and low cost makes it

desirable to implement ring oscillators monolithically using CMOS but they generally

have inferior phase noise performance compared to LC oscillators Currently there is

no tool available for the designer to analyze the effect of oscillator phase noise on the

performance of the communication system Thus an accurate and efficient system level

model for oscillator phase noise which can be used in simulation is of great importance

In this thesis two system level phase noise models accurate at the circuit level namely

Hajimiri Phase Noise model and Digital FIR Filter model for Phase Noise are discussed

and implemented in MATLABs SIMULINK environment to bridge the gap in tools

available for circuit level design and system level design of communication systems

Redacted for Privacy

copyCopyright by Devavrata Godbole

October 3 2000

All rights reserved


by

Devavrata Godbole

A THESIS

submitted to

Oregon State University

in partial fulfillment of the requirements for the

degree of

Master of Science

Presented October 3 2000 Commencement June 2001

Master of Science thesis of Devavrata Godbole presented on October 3 2000

APPROVED

Major Pr essor representmg Electncal amp Computer Engmeermg

of Electrical amp Computer Engineering

I understand that my thesis will become part of the permanent collection of Oregon State University libraries My signature below authorizes release of my thesis to any reader upon request

Devavrata Godbole Author





ACKNOWLEDGMENT

I would like to express my deepest appreciation and thanks to my thesis advisor

Prof John T Stonick for his great enthusiasm in research and invaluable guidance during

my research His passion for teaching and learning has always been a great source of

inspiration for me My appreciation also reaches friends and colleagues I have got to

know during these two years This thesis would not have been completed without their

continuous help and moral support Finally and most importantly I want to express

my sincerest gratitude to my dearest parents for always being there for me No amount

of thanks would be too much for their constant love encouragement and support

dedicate this thesis to them

I

TABLE OF CONTENTS

Page

1 INTRODUCTION 1

11 Definition of Phase Noise and Jitter in Oscillators 1

111 What is Phase Noise 1 112 Units of Oscillator Phase Noise 2 113 What is Jitter 3

12 Importance of Phase Noise Specifications for Communication Systems 4

13 Advantages of Ring Oscillators 6

14 Problem Statement 7

2 HAJIMIRI PHASE NOISE MODEL 10

21 Salient Features 10

22 Explanation 10

23 Conversion of Device Noise to Phase Fluctuations 13

24 Phase-to-Voltage Transformation 16

25 Conversion of Ring Oscillator Device Noise to Phase Noise 16

26 Reducing the Effect of Flicker Noise on Oscillator Phase Noise 19

27 Calculation of Phase Noise Spectrum for Ring Oscillators 23

28 Comparison of Hajimiri Phase Noise Model with SpectreRF PSS Phase Noise Analysis 24

281 Simulation Results for 3-Stage Single-Ended Ring Oscillator Implemented using HP 08J-lm Process having Oscillation Freshyquency 315 MHz 25

282 Simulation Results for 3-Stage Ring Oscillator using HP 08J-lm Process having Oscillation Frequency 500 MHz 29

283 Simulation Results for 3-stage Ring Oscillator using HP 12J-lm Process having Oscillation Frequency 154 MHz 29

29 MATLAB Graphic User Interface (GUI) for Hajimiri Phase Noise Model 31

TABLE OF CONTENTS (Continued)

Page

210 Generation of ISF for the User-Specified Ring Oscillator 33

211 Implementation of Hajimiri Phase Noise Model for Single-Ended Ring Oscillators in SIMULINK 36

2111The SIMULINK Environment 36 2112Hajimiri Phase Noise Model Implementation in SIMULINK 38 2113Improving the Efficiency of Hajimiri Phase Noise Model Impleshy

mented in SIMULINK 39

212 Verification of Fast SIMULINK Method for Hajimiri Phase Noise Model Implementation 40

2121MATLAB Test Simulations 41 2122Simulation for Symmetrical ISF 41 2123Simulation for Non-Symmetrical ISF 42

213 SIMULINK s-Function Implementation of Fast Hajimiri Phase Noise Model 46

3 IMPLEMENTATION OF PHASE NOISE MODEL USING DIGITAL FILshyTER 48

31 Calculating the Phase Disturbance Response from the Oscillators PSD 48

32 MATLAB GUI Designed for the Design of FIR Filter 52

4 LOCAL OSCILLATOR MODEL IMPLEMENTED IN COMMIC 54

5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page

11 Frequency spectrum of an ideal sinusoidal oscillator 1

12 Frequency spectrum of a sinusoidal oscillator having phase noise 2

13 Phase noise measurement 3

14 Jitter 3

15 PLL system 4

16 Generic transreceiver 5

17 Ideal case 6

18 Effect of phase noise on the receive path 8

19 Effect of phase noise on the transmit path 9

110 LC oscillator 9

21 Phase and amplitude response model 11

22 (a) Ideal LC oscillator (b) Impulse injected at the peak (c) Impulse at zero crossing 12

23 Conversion of input noise to output phase noise 13

24 ISF decomposition 14

25 Current noise conversion to excess phase 15

26 Noise in MOSFET 16

27 Conversion of MOSFET device noise to phase disturbance and then to phase noise sidebands 18

28 Non-symmetrical ISF waveform for the oscillator having non-symmetrical rise and fall times 20

29 Symmetrical ISF waveform for the oscillator with scaled PMOS device 21

210 (a) Input Waveform (b) Single-stage circuit (c) Trajectory of the outshyput as the input goes high and C discharges through QN 22

211 Cadence schematic of 3-stage ring oscillator 24

LIST OF FIGURES (Continued)

Figure

212 ISF for 3-Stage ring oscillator obtained using SpectreS and HSPICE simulations 26

213 Phase noise spectrum plot from Hajimiri phase noise model calculated using ISF obtained from SpectreS and HSPICE simulations 27

214 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model 28

215 Thermal noise analysis circuit for HP 08J-lm NMOS process 29

216 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model for 500 MHz oscillation 30

217 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model for 151 MHz oscillation using HP 12J-lm process 31

218 MATLAB Graphic User Interface flow diagram 33

219 3-Stage single-ended ring oscillator with current impulse 35

220 Current Impulse applied at node 1 of ring oscillator 36

221 GUI figure for Hajimiri phase noise model 37

222 Symmetrical ISF plot 43

223 Plot of disturbance in oscillator phase for symmetrical ISF case 43

224 Comparison plot of frequency spectrums of phase disturbance genershyated using the two methods in dBc for symmetrical ISF case 44

225 Non-symmetrical ISF plot 44

226 Plot of disturbance in oscillator phase for non-symmetrical ISF case 45

227 Comparison plot of frequency spectrums of phase disturbance genershyated using the two methods in dBc for non-symmetrical ISF case 45

228 Flow diagram of SIMULINK based fast Hajimiri phase noise model 47

31 Oscillators frequency response 49

32 Generation of oscillators phase disturbance using digital FIR filter 51

33 MATLAB GUI for digital FIR filter design 53


Figure Page

41 Communication IC toolbox 54

42 LO block in simulink 55

43 Selection of Hajimiri phase noise model for LO block 56

44 Selection of digital filter model for LO block 57

45 Mask of LO model 58

46 Hajimiri phase noise model mask 58

47 Digital FIR filter mask 59


1 INTRODUCTION

11 Definition of Phase Noise and Jitter in Oscillators

111 What is Phase Noise

The output of an ideal oscillator with no noise can be expressed as

VLOoutput = Af[wet + cent]

where A is the peak amplitude of the oscillator We is the oscillator frequency and f the

oscillator phase Note that in the case of an ideal oscillator A We and f are all constants

The one-sided frequency of such an ideal oscillator looks as in Fig 11

However in a practical oscillator due to the presence of noise the output is given

by

VLOoutput = A(t)J[wet + cent(t)]

where A(t) and cent(t) represent the fluctuations in peak amplitude and phase of the

oscillator output and are no longer constants As a consequence of the fluctuations in

oscillators phase and amplitude the spectrum of a practical oscillator has skirts close

Frequency

FIGURE 11 Frequency spectrum of an ideal sinusoidal oscillator

2

Frequency

FIGURE 12 Frequency spectrum of a sinusoidal oscillator having phase noise

to the oscillation frequency as shown in Fig 12 The effects of amplitude fluctuations

in an oscillator are generally reduced by some kind of amplitude limiting mechanism

but the phase fluctuations persist indefinitely Therefore the oscillators spectrum is

mainly dominated by the phase fluctuations and as a result an oscillator spectrum having

sidebands as shown in Fig 12 is generally referred to as the phase noise spectrum

112 Units of Oscillator Phase Noise

Conventional units for expressing oscillator phase noise are decibels below the

carrier per Hertz (dBcHz)

~) 10 I Psideband(WO + ~w 1Hz)P PhaseNoise ( W = x og n (11 ) TCarrler

Where Psideband(WO + ~w 1Hz) represents the single sideband power in the oscilshy

lator spectrum at a frequency offset ~w from the carrier The measurement bandwidth

for the sideband power is 1 Hz as shown in Fig 13

3

dB

1Hz Frequency

FIGURE 13 Phase noise measurement

113 What lS Jitter

Fluctuations in amplitude and phase result in uncertainties in the transition inshy

stants of an oscillators periodic time domain waveform Jitter is defined as the time

deviation of a controlled edge from its normal position

There are several ways in which jitter can be measured Two of the most commonly

used measurements of oscillator jitter performance are

1 Absolute or total jitter (OT) It is a measure of clock jitter relative to its source

at various points along a path which the clock travels as it is affected by various

electronic components It is expressed in units of time usually pico-seconds For

a free running oscillator the total clock jitter increases with the measurement

Unit Sometimes the edge Interval is here

Reference I Edg

------y-r r 1 ICI I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

The edges should Somotim (hoodgo ~ ~---=- be here

is here

FIGURE 14 Jitter

4

PLL 1 bullI__P_L_L_2_--

FIGURE 15 PLL system

time-interval This growth in variance occurs because the effect due to phase

disturbances persists indefinitely Therefore the absolute jitter value at time t

seconds includes the jitter effects associated with all the previous transitions

2 Cycle-to-Cycle Jitter It is the instantaneous difference of periods between adjashy

cent oscillator cycles This type of jitter is most difficult to measure and requires

special instrumentation such as timing interval analyzer and other analysis softshy

ware Cycle-to-Cycle jitter estimate is often useful in case of system as shown in

Fig 15 The output of PLLI is the reference for PLL2 If PLL2 cannot lock to

the reference frequency then the cycle-to-cycle jitter measurement of PLLI will

indicate the maximum jitter allowable for PLL2 to lock

12 Importance of Phase Noise Specifications for Commu-nication Systems

In wireless communications frequency spectrum is a valuable commodity Commushy

nications transceivers rely heavily on frequency conversion using local oscillators (LOs)

and therefore the spectral purity of the oscillators in both the transmitter and receiver

is one of the factors limiting the maximum number of available channels and users The

great interest in integrating complete communications systems on a single chip has led

to a new environment for oscillators which has not been explored before To understand

the importance of phase noise in wireless communication systems consider a generic

transceiver shown below in Fig 16 The receiver consists of a low noise amplifier a

band-pass filter and a downconversion mixer The transmitter comprises an upconvershy

5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter

Local Oscillator (LO)

Power Amplifier

Band-Pass Filter

FIGURE 16 Generic transreceiver

sion mixer a band-pass filter and a power amplifier The local oscillator provides the

carrier signal for both the transmitter and the receiver If the LO contains phase noise

then both the upcoverted and the downconverted signals are corrupted

Referring to Fig 17 we note that in the ideal case the signal band of interest in

frequency domain is convolved with an impulse and thus translated to a lower frequency

and a higher frequency with no change in its shape In reality however the desired

signal may be accompanied by a large interferer in an adjacent channel and the local

oscillator exhibits finite phase noise When the desired signal and the interferer are

mixed with the LO output as shown in Fig 18 the downconverted band consists of

two overlapping spectra The result is that the desired signal suffers from significant

noise due to the tail of the interferer Here the end portions of the interferers frequency

spectrum which leak into the adjacent channels have been referred to as the tails of the

interferer This effect is called as reciprocal mixing

As shown in Fig 19 the effect of phase noise on the transmit path is slightly

different Suppose a noiseless receiver is to detect a signal at W2 from a weak transmitter

while a nearby powerful transmitter generates a signal at WI with substantial phase noise

Then the phase noise tail of the transmitter corrupts the desired weak transmitters

6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band

FIGURE 17 Ideal case

signal or it can even completely swamp out the weak transmitters signal The difference

between WI and W2 can be as small as a 200 kHz as in G8M while each of these frequencies

is around 900 MHz or 19 GHz Therefore the output spectrum ofLO must be extremely

sharp In the North American Digital Cellular Standard (NADC) 1854 system the phase

noise power per unit bandwidth must be 115 dB below the carrier power at an offset of

60 kHz from the carrier

13 Advantages of Ring Oscillators

Stringent requirements as mentioned above can be met through the use of LC

oscillators Fig 110 shows an example where a transconductance amplifier with positive

feedback establishes a negative resistance to cancel the loss in the tank and a varactor

diode provides the frequency tuning capability The circuit has a number of drawbacks

for monolithic implementation as follows

1 Both the control and the output signals are single-ended making the circuit senshy

sitive to supply and substrate noise

7

2 The inductor Q in a LC oscillator circuit determines how accurately the oscillator

can tune to certain oscillation frequency As a result the inductor (and varactor)

Q required in low phase noise oscillators is typically greater than 20 prohibiting

the use of integrated inductors as it is not possible to get a Q value greater than

10 for monolithically implemented varactors using the current process technology

Ring oscillators on the other hand require no external components and can be

realized in fully differential form but their phase noise tends to be high because they

lack passive resonant elements Therefore there is huge amount of interest to include

ring oscillators in communications systems but to be able to optimize parameters of

communication systems having ring oscillators it is necessary to have ring oscillator

phase noise models that are accurate at circuit level

14 Problem Statement

It is difficult to analyze the effect of phase noise on the performance of communicashy

tion systems Thus a good system level model that can be used in simulation is desired

In this thesis two different models for generation of phase noise are implemented in

MATLABs SIMULINK environment They are

1 Hajimiri Phase Noise model

2 Digital FIR Filter model

Each of these methods is discussed in detail in the following chapters

8

Actual Case

Wanted UnwantedSignal Signal

t 1--

Downconverted Signals

FIGURE 18 Effect of phase noise on the receive path

9

CD ~ 20 Q) Transmitter Phase Noise

C

~ c 0Q)

E E -20 Adjacent Channel Users u Q)

Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency

FIGURE 19 Effect of phase noise on the transmit path

Frequency _~II1r-- control

C

YOU

FIGURE 110 LC oscillator

10

2 HAJIMIRI PHASE NOISE MODEL

21 Salient Features

There are many models for predicting the phase noise generated in oscillators

[1 2 3 4] Some models are based on time-domain treatments while others like Leeson

model and that proposed by Razavi use a frequency-domain approach to derive a linear

time-invariant models to describe oscillator phase noise

In contrast to the above models the Hajimiri phase noise model uses a linear

time-variant approach for predicting oscillator phase noise Some of its salient features

are

1 It is a physical model that maps electrical noise sources such as device noise to

phase noise It is possible to implement this transistor level accurate phase noise

model in MATLAB for fast and accurate system level phase noise simulations

2 Models implemented at circuit level are slow as simulations take a long time This

is a fast system level model

22 Explanation

For each noise input the disturbance in the amplitude and phase of the oscillator

can be studied by characterizing the behavior of two separate time-variant single-input

single-output systems as shown in Fig 21 As explained in [5] consider the case of an

ideal LC oscillator as shown in Fig 22(a) If an impulse of current is injected at the

time-instant when the oscillators output voltage is at its peak the tank voltage changes

instantaneously as shown in Fig 22(b) resulting in an amplitude change but there is

no change in phase of the oscillator output However application of impulse at the zero

crossing results in some phase-shift but it has minimal effect on the amplitude as shown

in Fig 22(c) It can thus be seen that the resultant change in A(t) and cent(t) in an

11

i(t) ltp(t)

ltp(t)i(t) I -----l~~ hltlgt(tt) ~

o o t

i(t) A(t

A(t)

~

o o t

FIGURE 21 Phase and amplitude response model

oscillator due to noise are time-dependent This is essentially because an oscillator is a

time-variant system

The disturbances in oscillators amplitude die down due to some form of amplitude

restoring mechanism such as automatic gain control (AGe) or due the intrinsic nonshy

linearity of the devices However the excess phase fluctuations do not encounter any

form of restoring mechanism and therefore persist indefinitely For a small area of the

current impulse (injected charge) the resultant phase shift is proportional to the voltage

change 6V and hence to the injected charge 6q Therefore 6rjJ is given by

(21)

The necessary condition for the above equation to hold is 6q laquoqmax Where qmax =

Cnode X Vmax is the maximum charge swing with Vmax being the maximum voltage

swing across the capacitor Cnode where the charge is being injected V max or Vswing is

approximately equal to the supply voltage Vdd in the case of single-ended ring oscillators

The function f(WOT) is the time varying proportionality factor and is called the impulse

sensitivity function (ISF) since it determines the sensitivity of the oscillator to an impulse

input It is a dimensionless amplitude-independent function periodic in 21f that describes

12

(a)

Erfeelor impul slt applied allh e f ern Cllt bsil1g

Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)

FIGURE 22 (a) Ideal LC oscillator (b) Impulse injected at the peak (c) Impulse at zero crossing

how much phase shift results from applying a unit impulse at any point in time The

total phase error at any time-instant t is given by the summation of the all the phase

disturbances that have occurred upto that time-instant because the disturbance in phase

is permanent As a result the equation for oscillator phase disturbance in continuous

time domain is given by [6)

(22)

i(t) represents the input noise current injected into the node of the interest The output

voltage V(t) is related to the phase cent(t) calculated in (22) through a phase modulation

process Thus the complete process through which a noise input becomes a output

perturbation in V(t) can be summarized in the block diagram of Fig23 The complete

process can thus be viewed as a cascade of a LTV system that converts current to phase

with a non-linear system that converts phase to voltage

--

13

f(~t) Ideal integration Phase modulation i(t)

qmax

X t

f ltp (t)

Cos(~t + ltp(t)) V (t)

-00

FIGURE 23 Conversion of input noise to output phase noise

Since the ISF is periodic it can be expanded in a Fourier series as [5]

00

Co f(wot) = 2 +~ COS (nwOT + en) n=l

Where Cn are real valued and en is the phase of the nth harmonic en is not important

in the case of random input noise and is thus neglected here Using the expansion for

f(wot) in the superposition integral and exchanging the order of summation and integral

(23)

The above equation identifies individual contributions of the total cent(t) for an

arbitrary input current i( t) injected into any circuit node in terms of the various Fourier

coefficients of the ISF The equivalent block diagram [7] is shown in Fig 24

Each branch acts as a downconverter and a lowpass filter tuned to an integer

multiple of the oscillator frequency For example the second branch weights the input by

q multiplies it with a tone at Wo and integrates the product As can be seen components

of perturbation in the vicinity of integer multiples of the oscillation frequency play the

most important role in determining cent(t)

23 Conversion of Device Noise to Phase Fluctuations

It is essential to see the effect of small sinusoidal to get an idea of how the various

noise sources affect the oscillator Consider a low frequency sinusoidal perturbation

current i(t) injected into the oscillator at a frequency of t1w laquo Wo i(t) = Iocos(t1wt)

14

Ideal integration

t

f CI Cos(~t +ell

t

f bull

bull bull CnCos(n~t +en)

Phase modulation

i(t) v (t) qmax Cos(~t + ~(t))

FIGURE 24 ISF decomposition

The phase disturbance value is given by (23) as

(24)

The arguments of all the integrals in the above equation are at frequencies higher

than 6w and are significantly attenuated by the averaging nature of the integration

except the term arising from the first integral involving Co Therefore cent(t) is given by [5]

loco locojt cent(t) = -- cos(6wT)dT = 6 szn(6wt) (25) 2qmax -00 2qmax w

As a result there will be an impulse at 6w in the one-sided power spectral density

plot of cent(t) as shown in Fig 25 Now consider a current at a frequency close to the

oscillation frequency given by i(t) = hcos((wo + 6w)t)

15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)

FIGURE 25 Current noise conversion to excess phase

Again going through the integration for cent(t) we find that now all the integration

term except the term arising from Cl get attenuated resulting in two impulses at +~w

and -~w in the power spectral density plot of cent(t) cent(t) is now given by

hCl cent(t) = ~ sm(~wt)2qmax w

More generally applying current i(t) = In cos ((nwo +~w)t) close to at any integer

multiple of oscillation frequency will result in sideband at +~w and -~w in Scent(w)

Therefore in general cent(t) is given by [5J

cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w

FIGURE 26 Noise in MOSFET

24 Phase-to-Voltage Transformation

Computation of power spectral density of the oscillator output voltage requires

conversion of excess phase variations calculated in (26) to output voltage The oscillator

output can be expressed as cos(wot + cent(t)) For small values of cent(t) cos(wot + cent(t))

can be approximated as

eos(wot + cent(t)) = eos(wot)eos(cent(t)) - sin(wot)sin(cent(t)) ~ cos(wot) - cent(t)sin(wot)

Where it is assumed that eos (cent(t)) ~ 1 and sin(cent(t)) ~ cent(t)for small values of cent(t)

Therefore substituting cent(t) from (2 6) we get the expression for PSD of the oscillator

output voltage in dBc as [5J

2In X en PdBc(bW) = ( 4 b )

(2 7) x qmax X W

25 Conversion of Ring Oscillator Device Noise to Phase Noise

The circuit noise in CMOS Ring Oscillator is dominated by the fl icker noise and

thermal noise of MOSFET devices The noise power spectral density spectrum typically

looks as shown in Fig 26

17

Flicker noise dominates at low frequencies and usually falls at -10 dBdecade as

its spectral density is inversely proportional to frequency MOSFET thermal noise or

white noise has a constant spectral density over all frequencies and dominates at higher

frequencies The intersection of J and white noise curves is often called as the J noise

corner Now just as explained for a single frequency current source the low frequency

noise band ~w around DC is influenced by Co term in the integration for cent(t) in (23)

It appears as noise band at ~w in spectrum for phase disturbance Similarly noise band

at ~wo + ~w is influenced by Cl and is downconverted to band at ~w However noise

at ~wo - ~w is also influenced by Cl and results in band at ~w Therefore twice the

power spectral density of cent(t) from (27) should be considered to take into account the

contributions due noise at both the frequency bands ~wo - ~w and ~wo + ~w [8]

Therefore the total single-sideband phase noise spectral density due to one noise source

at an offset frequency of ~w is given by the sum of powers of all the components as

shown in Fig 27 and the final expression is given by

(28)L(~w) =

In the above expression In represents the peak amplitude of the noise voltage It

is convenient to express noise in terms of its power spectral density rather than peak [2 2

amplitude Therefore substituting 2 = -lJ where t6f = 1 gives

(29)L(~w) =

18

1 middot 2 ( ) fNoise

Thermal Noise In ill

1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)

FIGURE 27 Conversion of MOSFET device noise to phase disturbance and then to phase noise sidebands

19

26 Reducing the Effect of Flicker Noise on Oscillator Phase Noise

MOSFET device noise in the 1- region can be described by the equation

Where w1- is the corner frequency of the MOSFET 1- noise The resultant phase

noise spectrum due to this 1- noise is given by

(210)

Thus 1- noise gets converted to p in the oscillators phase noise frequency spectrum

and the frequency at which the white noise power equals the sideband power of noise

arising from 1- noise is termed as the p corner frequency (bwp) Solving for bwp

results in following expression for the p corner frequency of the phase noise spectrum

[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms

Thus the magnitude of noise in the p region of the oscillator spectrum arising

due to MOSFET flicker noise is smaller by a factor equal to c6fms where Co is the DC

value of ISF given by

1 127rCo = - f(x)dx (212)21f 0

Therefore to reduce the effect of flicker noise on the phase noise spectrum it is

necessary to reduce the DC value of ISF Consider ISFs for two different 3-stage ring

oscillators They have the same frequency load capacitance and NMOS devices The

difference is between the width of PMOS devices used in the ring oscillators The

length and width of PMOS device used the first ring oscillator is equal to that of the

NMOS device The ISF for this oscillator is as shown in Fig 28 It has taller and

wider negative lobe than the positive lobe which is short and thinner This is because

of the oscillator output having a fast rising edge and a slow falling edge Thus the

20

Unsymmetrical ISF 04 ----------------------------------------------------

02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

FIGURE 28 Non-symmetrical ISF waveform for the oscillator having non-symmetrical rise and fall times

oscillator is more sensitive during the falling edge and also for a longer time than for

the rising edge As seen from Fig 28 the ISF is non-symmetrical about zero value As

a result the oscillators ISF has a high value of DC resulting in strong upconversion of

low frequency device noise Therefore the phase noise at small frequency offsets from

oscillation frequency is dominated by the presence of MOSFET flicker noise

Now consider the second oscillator whose PMOS device width has been scaled such

that it is 3-times the width of its NMOS device The ISF for such a oscillator is shown

in Fig 29 As can be observed the ISF is symmetrical about zero This is because of

the oscillator having equal rise and fall times

To derive the necessary condition to obtain equal rise and fall times for the ring

oscillator output consider a single stage of a CMOS ring oscillator as shown in Fig 210

It is composed of a PMOS and NMOS device To calculate the rise and fall times of the

output waveform consider an input pulse going from 0 to VDD at time t=O as shown in

Fig 210(a) Assume that just prior to the leading edge of the input pulse (that is at

t=O-) the output voltage equals VDD and capacitor C is charged to this voltage At t =0

21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points

FIGURE 29 Symmetrical ISF waveform for the oscillator with scaled PMOS device

VI rises to VDD causing PMOS Qp to turn off immediately Thus the output voltage

at t=O+ is at VDD (point E as shown in Fig 21O(c)) and NMOS QN is in saturation

region and conducting a large current As C discharges the current of QN remains

constant until Vo = VDD - vt (point F) Beyond point F transistor QN operates in the

triode region The capacitor keeps on discharging until it is fully discharged (point D)

The fall time of the oscillator output waveform (tpHdis given by the time required for

the output voltage to reach V~D falling from VDD The final expression for the time

taken for the capacitor to discharge from VDD to V~D is found to be of the form

08 x C tpHL = K TT

n X VDD

A similar equation can be calculated for oscillators rise time (tPLH) to give

08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)

Operating point at t=O+

I

F E Voo

Operating point Operating point after switching is at t=Oshycomplete

AD ~________~____~~______~

o Voo V Voo Vo

(c)

FIGURE 210 (a) Input Waveform (b) Single-stage circuit (c)Trajectory of the output as the input goes high and C discharges through QN

For the oscillator to have symmetric rise and fall edges it is necessary to have equal

rise and fall times ie tpHL = tpLH Therefore

08 x C 08 x C Kn x VDD Kp X VDD

23

For equal length devices we have

- J-lnWnWp- (213) J-lp

Therefore appropriate scaling of PMOS device as given by (213) ensures that the

oscillator output has symmetric rise and fall edges and hence low DC ISF value

27 Calculation of Phase Noise Spectrum for Ring Oscil-lators

If the above criteria for symmetric oscillator output waveform is met then the only

dominant noise source in the ring oscillator circuit is MOSFET white noise Thus the

flicker noise generated by the MOSFET can be safely ignored and the expression for i~

is given by

(~j)Single-Stage (~j)N + (~j)P

Where

(fb)N = and (fb)P = 4kT x gdsP4kT X gdsN (214)

Where gdsN and gdsP are the transconductance of NMOS and PMOS calculated

when the noise is at its maximum ie when Voutput = V~D As the noise sources are

uncorrelated with each other the total noise for an N-stage ring oscillator is given by N

times that for the single-stage Therefore

2 ) 2 )~ =Nx ~ =Nx( (tlj N -Stages tlj Single-Stage

Substituting (215) in (29) the phase noise spectrum for an N-stage ring oscillator is

given by

(215)

00

xLc n=O (216)L(lw) =

24

FIGURE 211 Cadence schematic of 3-stage ring oscillator

00

N x [4kT gdsN + 4kTmiddot gdsP ] x 2= c~ n=O (217)L(tlw) =

According to Parseval s relation

(218)

Giving

L(tlw) = (N x [4kT gdsN 4kT ~dSP] X 2rms) (219)4 x qmax X tlw

L(tlw) = x [4kT 9dSN + 4kT idsP ] x rms ) (N 2 (2 20)

2 x qmax X tlw

28 Comparison of Hajimiri Phase Noise Model with Spec-treRF PSS Phase Noise Analysis

To verify the validity ofHajimiri phase noise model we compared it with SpecterRF

PSS phase noise results which are known to be very accurate Simulation experiments

were performed on ring oscillators of different stages having transistors of different sizes

The schematic of the ring oscillator used in the simulations is as given in Fig 211

25

281 Simulation Results for 3-Stage Single-Ended Ring Oscilla-tor Implemented using HP O8-Lm Process having Oscillation Frequency 315 MHz

A 3-stage single-ended ring oscillator was simulated for a HP 08jlm process in

HSPICE and in Cadence The PMOS device size was scaled to meet the criteria of

generating an ISF having a low DC value The ISF for the oscillator was obtained

through cadence SpectreS simulations as well as through HSPICE simulations Phase

noise response for the oscillator was then obtained using Hajimiri model and SpectreRF

periodic steady state (PSS) analysis The details are as given below

Ln = Lp = 08jlm Wn = lOjlm Wp = 30jlm and CL = 10pF The oscillation

frequency found using SpectreRF and HSPICE simulations is

SpectreRF (PSS) HSPICE (transient) SpectreS (transient)

31784 MHz 31523 MHz 31756 MHz

Charge pulses of small energy (01 of qmax) were applied at 50 different time-

instants during one oscillation period and the resultant phase disturbance produced at

the oscillator output was measured to give the ISF for the 3-stage ring oscillator The ISF

for the oscillator obtained through SpectreS transient simulations in Cadence as well as

the HSPICE transient analysis simulations are as shown in Fig 212 As can be observed

from the figure ISF calculated using both simulators match up closely indicating that

the ISF calculation is independent of the simulator as long as the models are accurate

After we obtained the ISF the phase noise response for the oscillator was calculated

using (220)

The gmP and gmN indicate the transconductances when the combined noise of

PMOS and NMOS devices is maximal ie when the both the input and output voltages

are at value V~D The transconductance values obtained from HSPICE and SpectreS

simulations are as given in the table There is negligible difference between them

FIGURE 212 ISF for 3-Stage ring oscillator obtained using SpectreS and HSPICE simulations

SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3

The phase noise spectrum for the oscillator using SpectreS and HSPICE simulashy

tions is shown in Fig 213 There is no visible difference between the two-phase noise

spectrums and they exactly overlap over each other

In Fig 214 plots of the phase noise spectrum generated using SpectreRF PSS

phase noise analysis and Hajimiri model phase noise model (ISF generated using HSPICE)

are as shown

The dBc values of phase noise at an offset of 1 MHz for the 2 plots are

SpectreRF (PSS) Hajimiri

-1511 -1512004

As seen from the figure Hajimiri model predicts the phase noise values very close

to values obtained through SpectreRF PSS phase noise analysis The difference between

27

the two was found out to be approximately equal to OldB or 006624 error in dB The

value of I used in Hajimiri model was 23 = 0666 Since I is process dependent further

analysis was performed to determine the I value used by the SpectreRF noise analysis

The circuit used for analysis is as shown in Fig 215

The circuit of Fig 215 was simulated using SpectreS AC noise analysis Since the

noise due to PMOS and NMOS in a single stage of a ring oscillator is maximum when

both in and Vout = 25 V the Vgs = Vds value for the noise analysis performed was

chosen to be 25 V The resistor value is chosen to be 1 mQ so that the voltage drop

across it is negligible and hence value of Vout = Vds ~ 25V The noise generated by

the resistor is turned off and therefore the only noise contributor in the circuit is the

NMOS device The noise analysis was run from frequency 1 kHz to 2 MHz and the input

referred spot noise was found to be 29681e-9 k

Phase Noise Spectrum for 3middotStage Ring Oscillator oo~-------------------------~==~~

I HSPICE I L--------Spec reS----tc--JJ

-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency

FIGURE 213 Phase noise spectrum plot from Hajimiri phase noise model calculated using ISF obtained from SpectreS and HSPICE simulations

28

Phase Noise Spectrum for 3-Stage Ring Oscillator -90 - ----------------- 1

SpectreRF PSS analysis ~ajimiri Phase Nois~model

-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10

FIGURE 214 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model

For a MOSFET device operating in saturation region the input referred thermal

noise spectral density is given by

(221 )

Equating this to the value of thermal noise spectral density from the simulations

Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m

The value of gm is found out to be equal to 1588e-3 Substituting this in above equation

and solving for value ofY as

Y = (29681e-9)2 x Ikr = 0633 (223)

As can be seen the Y value used by the SpectreS is very close to the Y value used in the

Hajimiri model

29

V~lV ~ VdC=2 5V f

25V

NMOS W= lO)lffi L=O8)lffi

V out

FIGURE 215 Thermal noise analysis circuit for HP 08jLm NMOS process

282 Simulation Results for 3-Stage Ring Oscillator using HP O8J-lm Process having Oscillation Frequency 500 MHz

L~ = Lp = 08jLm Wn = 20jLm Wp = 60jLm and CL = 1pF

Oscillation frequency from HSPICE and SpectreRF simulations


500397 MHz 495689 MHz 500001 MHz

The difference in the two phase noise plots at 1MHz offset from the carrier freshy

quency measured in dBc


-13053 -13061

283 Simulation Results for 3-stage Ring Oscillator using HP 12J-lm Process having Oscillation Frequency 154 MHz

Ln = Lp = 12jLm Wn = 20jLm Wp = 60jLm and CL = 1pF

The frequency of oscillation from HSPICE and SpectreRF simulations


154087 MHz 152419 MHz 15384 MHz

30

The phase nOIse plots using SpectreRF PSS phase nOIse analysis and Hajimiri

phase noise model are shown in Fig 217 The difference in the two phase noise plots in

dBc measured at 1 MHz offset is


-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2

Phase Noise Spectrum for 3middotStage Ring Osciliator haling frequnecy = 500MHz -T----- -------------======r=======~==

SpectreRF PSS analysis Hajimiri Phase Noise model

3 4 5 6 7 8 9 10 Frequency

X 10

FIGURE 216 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model for 500 MHz oscillation

31

Comparison plot of Phase Noise spectrum for fO =154MHz using 12um process -40

1--sp~ctreRF ~ss P~ase N~ise A~alysis ~jimiri Phase Noise model -50

7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10

FIGURE 217 Phase noise spectrum using SpectreRF PSS analysis and Hajimiri phase noise model for 151 MHz oscillation using HP 12J-lm process

29 MATLAB Graphic User Interface (GUI) for Hajimiri Phase Noise Model

As seen from the previous section the Hajimiri phase noise model is very accurate

for CMOS ring oscillators As a result we developed a MATLAB based Graphic User

Interface(GUI) program to generate the phase noise spectrum for single-ended ring os-

ciIlators using Hajimiri phase noise model The input parameters for the GUI and the

conditions that they need to satisfy are listed in the table below

32

GUI input parameter Condition

Stages The stages entered should be odd

Supply Voltage or Vee (Volts) Vee value should be positive and

lesser than 6V

NMOS Width or Wn(pm) Wn value should be positive and

lesser than lOOOpm

PMOS Width or Wp(pm) Wp value should be positive and

lesser than lOOOpm

NMOS Length or Ln(pm) Ln value should be positive and

lesser than 100pm

PMOS Length or Lp(pm) Lp value should be positive and

lesser than lOOpm

Load Capacitance or C (pF) Capacitance value should be posishy

tive and lesser than 1pF

When the MATLAB GUI program is called it prompts the user for the above input

parameters If the user input violates any condition as specified above for a particular

input parameter then the field is cleared and an error message is displayed informing

the use of the faulty condition After all the correct parameters have been entered the

ISF for the current oscillator configuration can be plotted using the button labeled Run

HSPICE and Plot ISF and Oscillators Expected Frequency Spectrum The flow of the

GUI program is as shown in Fig 218

33

netlist for the Ring Oscillator as per the user specifications and call the

HSP(CE program

HSPICE

3

Simulate the Ring Oscillator circuit and generate the output files containing the oscillation

frequency and (SF

FIGURE 218 MATLAB Graphic User Interface flow diagram

210 Generation of ISF for the User-Specified Ring Oscil-lator

The most accurate method for ISF calculat ion is to replace the noise sources in

the circuit with impulse sources of small energy and then measure the resultant phase-

shift HSPICE simulations were used to obtain the ISF for the ring oscillator using this

method Three HSPICE netlists for each single-ended ring oscillator are generated using

the PERL script isLgeneration according to the user specifications obtained using the

MATLAB Graphic User Interface (GUI) program osc-parametersm

Check the user inputs and then call the PERL

program to get ISF oscillation frequency

and amptsP and gdsN

MATLABGUI

4 Extract the ISF osci llation

frequency amptsP and gdsN from HSPICE output files

2

Generate the HSPICE

Phase No isc spectrum for the cu rrent Singleshyended Ring Oscillator

34

The first net list does not contain any noise elements and is used for calculation of

the oscillation frequency gdsP and gdsN values The HSPICE simulation for this net list is

run first to obtain the oscillation period which is used for defining the transient analysis

and measure statements in the second net list and third netlist The transient analysis

is run for 11ls The oscillation period is measured after a delay of 100 ns under the

assumption that the ring oscillator frequency is atleast 100 MHz and the oscillator has

thus completed more than 10 cycles giving it enough time to settle down The gdsP and

gdsN values are extracted from the DC operating point analysis performed by HSPICE

for this netlist

The second netlist is used to get the time-instants when the oscillator output

voltage crosses half the supply voltage value during 10th and 30th cycles Since there are

no noise sources in this netlist these values represent time-instants for an ideal oscillator

and are used as reference values for ISF calculation in the third netlist

The third net list is generated for calculation of ISF for the ring oscillator It

contains a Piece Wise Linear (PWL) noise current source defined at node1 as shown

in Fig 219 which injects current impulses are at 50 equidistant time instants of the

oscillator period The impulse is applied during the 10th cycle giving enough time for

the oscillator to stabilize and initial transients to die down The impulse causes a time-

shift in the oscillation and hence a phase-shift The analysis is defined as a sweep analysis

to get 50 different oscillator waveforms for 50 different impulses This enables viewing of

effect of each impulse on the oscillator output independently The resultant time-shift

hence phase-shift in the oscillator output is observed after a gap of 20 cycles to allow the

amplitude disturbance in the oscillator to die down As a result the time-shift observed is

solely due to phase disturbance The time-instant when the output voltage of 30th cycle

crosses value Vee 2 is measured and subtracted from the reference value obtained from

simulation of netlist 2 to give the time-shift Since a single oscillator cycle is equivalent

to 3600 or 21f radians phase shift the resultant phase-shift is given by

t cent = OmiddotZZ p d X 21f Radzans (224)

SC2 ator erw

35

Models llsed ()r PMOS NMOS III O5U111

Node 1 Vee Vee Vee

Vout

FIGURE 219 3-Stage single-ended ring oscillator with current impulse

Where bt = time - instantmeasured30thcycle - time - reerence30thcycle

Since all the stages of the ring oscillator are identical the ISF seen from every other

node to the output is a delayed version of the ISF from node 1 Therefore the ISF for

the ring oscillator can be calculated by application of current impulses at a single node

node 1 in this case Although the unit impulse response is desired applying an actual

impulse with area of 1 Coloumb would drive the oscillator deep into non-linear behavior

Therefore the unit impulse response is obtained by applying impulses with areas 01 of

the maximum charge flowing into the capacitor at each node of the ring oscillator given

by qmax = Vee x Cnode and then scaling accordingly The current pulse-magnitude is

taken to be 1 rnA and the rise-time and fall-time of the pulse are taken to be 10 of the

total pulse-width This is illustrated in Fig 220 The phase shift calculated from (224)

is scaled to give the final phase shift due a unit charge applied at time-instant t as

bt cent final = X 27r Radwns (225)

Osczllator Penod X Total charge applzed

This calculation is performed for all the 50 points at which the impulse was applied

to give the ISF The final GUI figure looks as shown in Fig 221 There are two plots shy

one for ISF and other depicting the oscillator phase noise spectrum

36

q C VTotalCh arg e =PulseArea =~ = Nod max

100 100

I I

~ ~it L Pulse Width Pulse Width = OscillalionPeriod Fall- time = PulseWidth RIse - time = 1000 10

10 ~r-----------------------~~

FIGURE 220 Current Impulse applied at node 1 of ring oscillator

211 Implementation of Hajimiri Phase Noise Model for Single-Ended Ring Oscillators in SIMULINK

2 111 The SIMULINK Environment

SIMULINK is a software package in MATLAB for modeling simulating and anshy

alyzing dynamical systems Its supports linear and non-linear systems modeled in conshy

tinuous time sampled time or a hybrid of the two For modeling SIMULINK provides

a graphical user interface (GUI) for building models as block diagrams using click-and

drag-mouse operations Models can be built from scratch or by modifying existing modshy

els Simulations are interactive so that it is possible to change parameters on the

fly and immediately see the effect SIMULINK users have instant access to all the

MATLAB commands so that the results can be further analyzed and visualized easshy

ily SIMULINK also has a comprehensive block library of sinks sources linear and

non-linear components and connectors Custom blocks can be implemented using the s-

function block in SIMULINK SIMULINK provides an ideal environment for simulation

of wireless systems The effect of parameter change of individual system blocks on the

overall system performance can be accurately and efficiently observed SIMULINK gives

the designer insight into various parameter trade-offs that can lead to optimal system

37

oscparameters_loadHajDI--- r SIngIe-_ 00cIIalltn

Enter Vee (odd)

Enter No 01 Stages (VoH)

Enter Wn 10 Enter Wp 10 (um) (um)

Enter Lp 10Enter Ln 10 (um)(um)

Enter c 10 (PF)

Run Ibpb amp pIollSF - OocIIalora Expactad Fnqunency Spec I 15Fected Osclllolor Frequenc~ speclrum

FIGURE 221 GUI figure for Hajimiri phase noise model

design The Hajimiri phase noise model for single-ended ring oscillator s is implemented

as a s-function block in SIMULINK

38

2112 Hajimiri Phase Noise Model Implementation in SIMULINK

Using Hajimiris method for ISF calculation the phase disturbance at time instant

t is given by the (22) as

cent(t) = rt f(wor) x i(r)dri-oo qmax

Since the SIMULINK simulation is a discrete-time simulation the continuous-time inteshy

gral has to be replaced by discrete-time summation The above equation is approximated

by

cent(t) = (I r(wok) x i(k)) x lT (226) k=O qmax

Where fo(wok) represents the scaled discrete-time periodic ISF i(k) is the circuit noise

and lT represents the discrete-time step of the simulation which is given by Js where

is represents the sampling frequency used for the simulation

As the ISF used in the summation is 50 points long the sampling frequency is

50 times the oscillator frequency The oscillation frequency for the ring oscillator is

typically between 50 MHz-2 GHz Usually for a system level design SIMULINK simshy

ulations will be carried out with sampling frequency anywhere between 10 kHz to 500

kHz as the simulations are for baseband frequencies Consider the worst-case scenario

where SIMULINK simulation is running at 10 kHz and the oscillator is running at 2

GHz Therefore the time-instants at which the phase disturbance values will have to

be calculated will be multiples of SIMULINK time-step = 101Hz = 01 ms but the ISF

sampling frequency is 2GHz x 50 = 100GHz The summation in (226) has to be carshy

ried out in steps dependent on the ISF sampling frequency ie summation time-steps

= l(fs) = 1(100GHz) = lOps So for each simulation time-step the MATLAB sumshy

mation will have to be carried out over degi6~s = 107 points MATLAB summation over

such a huge number of points requires a lot of memory allocation and processor speed

If adequate resources are not available then this phase noise model block will be the

limiting factor for the SIMULINK simulation speed of the Wireless System

39

2113 Improving the Efficiency of Hajimiri Phase Noise Model Im-plemented in SIMULINK

The MATLAB command randn which generates Gaussian Distributed random

numbers is used to model i(k)- circuit noise in the SIMULINK phase disturbance model

Since the discrete-time ISF is 50 points long the phase disturbance value at the

end of first cycle can be represented by the summation over 50 points given by

M M

fo(l) x randn + fo(2) x randn+L L No of cycles=O No of cycles=Ocent(n) = M

fo(50) x randnL No of cycles=O

(227)

Where M represents the total number of complete oscillation cycles

Since the ISF was composed of 50 points in the above equation are 50 different

summations Now since fo(l) f o(2) fo(50) are constants then each summation term

in the above equation can be written as

M M

Yi= L fo(l) x randn = L (228) Noofcycles=O N oofcycles=O

Where Xi = fi x randn Substituting Yi in (227) the equation for phase disturbance

transforms to

cent(n) = (YI + Y2 + Y3 + + Yso) x In X tT (229)

The value of Yi for a particular value of M is evaluated using statistical results namely

If random variable X is defined as X = Xl + X 2 where Xl and X 2 are independent

random variables having a normal distribution then

1 mean(X) = mean(Xd + mean(X2 )

This applies when Xl and X 2 are independent which they are in each call to

MATLAB function randn

40

2Therefore Yi is a random variable having mean=O and a = r x M This random

variable can be generated in MATLAB using the command randn x r i x VM Reshy

placing Yi in (230) the final equation for calculation of phase perturbation at the end

of M oscillator cycles is given as

cent(n) = (rl x randn + r 2 x randn + r3 x randn + + r 50 x randn) x JM x In X tT

(230)

This equation is computationally efficient Only 50 terms need to be evaluated comshy

pared to M cyclesx50 points in (227) Thus the phase noise model implemented in

SIMULINK is no longer the limiting factor for simulation speed However this method

can only be used for calculating phase disturbances for time-instants which are multiples

of the oscillation period Therefore the calculation of phase disturbance at any arbitrary

instant is divided into two parts - calculation of phase disturbance using the fast method

for complete oscillation cycles that can be accommodated with the time-interval and

then the calculation of phase disturbance during the remaining time-interval for the last

incomplete oscillation cycle This new method developed for implementation of Hajimiri

phase noise model in SIMULINK will be called as fast simulink method

212 Verification of Fast SIMULINK Method for Hajimiri Phase Noise Model Implementation

Before implementing the fast method for Hajimiri phase noise model in SIMULINK

it is necessary to prove that the new technique generates phase disturbance having the

same frequency spectrum as obtained through normal simulation technique for the model

Extensive MATLAB simulations were run to validate the new model using ISFs genershy

ated for different 3-stage ring oscillators

41

2121 MATLAB Test Simulations

MATLAB simulations were run for two different types of ISF generated for 3-stage

ring oscillators - 1) Symmetrical ISF 2) Non-symmetrical ISF Disturbance in oscillators

phase or excess phase of the oscillator is calculated using the original equation as given

by (227) and also using the (230) developed for the fast simulink method All the

calculations for disturbance in phase are performed for complete oscillation cycles The

number of oscillator cycles the simulations are run over is 105 The phase disturbance at

the oscillator output generated using the normal method is sampled every 10 complete

oscillation cycles to give total 104 data points Fast simulink method is then used to

calculate the phase disturbance value every 10th cycle over 105 oscillation cycles giving

another set of 104 data points As data points representing the oscillators disturbance

in phase generated using the two separate methods are for the same oscillator they

can compared with each to establish the validity of the new method MATLABs fft

function is used to get the frequency spectrum for the two sets of readings The FFT

for oscillators phase perturbations generated using the two different methods is averaged

over 1000 such simulations and then compared with each other The results are as given

below

2122 Simulation for Symmetrical [SF

Oscillation

cycles

Sampling

Frequency

FFT points FFT avershy

aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42

As can be observed from the comparison plot of Fig 224 and the data represented

in the table the phase disturbance generated using the two methods for the ring oscillator

having a symmetrical ISF tally with each other

2123 Simulation for Non-Symmetrical ISF

Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points

FIGURE 2_22 Symmetrical ISF plot_

Plot of Phase Noise generated using Hajimiri and New method 50

Phase Noise generated using Fast method Phase Noise generated using Hajimiri

40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec

FIGURE 223 Plot of disturbance in oscillator phase for symmetrical ISF case

44

Comparison plot of FFT of Phase Noise generated using Hajimiri Method and Fast method O--------r -----------T-------- shy

FFT using Fast method i FFT usingHajimiri I

-10~

-20

-30 ID 0

~ -40 ilmiddot2 ggt -50

-60

-70

~-----~----60 o 05 15 2 25

Frequency in multiples of 1MHz

FIGURE 2_24 Comparison plot of frequency spectrums of phase disturbance generated using the two methods in dBc for symmetrical ISF case

Unsymmetrical ISF 04

02

0

-020 ilmiddot2 Ol -04

-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points

FIGURE 225 Non-symmetrical ISF plot

45

Plot of Phase Noise generated using Hajimiri amp New Fast method 40 -~------~====~==~========~~====~

Phase Noise generated using Hajimiri Method Phase Noise generated using Fast Method

30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000

FIGURE 226 Plot of disturbance in oscillator phase for non-symmetrical ISF case

Comparison plot of FFT of Phase Noise generated using Hajimiri amp Fast method

0_--------------~~---~~~======~~---shy[-~ FFT using Hajimiri methOd

FFT using Fast method -10shy

-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25


FIGURE 227 Comparison plot of frequency spectrums of phase disturbance generated using the two methods in dBc for non-symmetrical ISF case

46

213 SIMULINK s-Function Implementation of Fast Ha-jimiri Phase Noise Model

From the results presented in the above section it is confirmed that the fast

simulink method for modeling of disturbance in oscillators phase works Therefore we

use it to implement a Hajimiri phase noise model as a s-function block in SIMULINK

An s-function is a SIMULINK descriptor for dynamical system s-functions use

special calling syntax that enables interaction with SIMULINKs equation solver

SIMULINK makes repeated calls during specific stages of simulation to each block in

the model directing it to perform tasks such as computing its outputs updating its

discrete states etc Additional calls are made at the beginning and end of simulation

to perform initialization and termination tasks SIMULINK is real-time simulation enshy

vironment and since the introduced phase disturbance persists indefinitely the value of

phase disturbance calculated in the previous iteration is used as a starting value for the

phase disturbance in the current iteration

The general flow diagram of Hajimiri phase noise model s-function block is as

shown in Fig 228 The fast simulink method developed is used in the s-function to calshy

culate the phase disturbance for complete oscillation cycles during the current time-step

and this value is added to the phase disturbance value calculated for the last incomplete

cycle to give the phase disturbance value at the end of the current time-step

47

Initialize all the outputs to 0 at t = 0

Get the phase disturbance value from previous iteration and use it as the starting value of phase disturbance for the

current iteration

Feedback values

Calculate the phase disturbance for complete oscillation cycles in the current time-step using fast method

Calculate the phase disturbance for the incomplete portion of the last oscillator cycle

Phase disturbance value at the end of current iteration

FIGURE 228 Flow diagram of SIMULINK based fast Hajimiri phase noise model

48

3 IMPLEMENTATION OF PHASE NOISE MODEL USING DIGITAL FILTER

In some cases job of a designer is to choose the right oscillator to optimize the

costperformance ratio of the system To do this it is necessary for the designer to

observe the effect of using different oscillators having different phase noise specifications

on the performance of the whole system The designer may have information about the

phase noise spectrum for the oscillator from the manufacturer or through actual test

measurements To perform system level SNRBER simulations that include the effect

due to phase noise a model that generates phase noise having a spectrum identical to

that specified by the manufacturer or obtained through measurements is needed We

have implemented a system to do this in MATLAB using a white noise generator and

a digital filter The digital filter is implemented as a Finite Impulse Response (FIR)

filter which is designed on the fly using the MATLAB command fir2 As shown in

Fig 31 the user inputs the PSD in dBcHz at several frequency points and the order

of the digital FIR filter

31 Calculating the Phase Disturbance Response from the Oscillators PSD

For system level simulations an important quantity of interest is the phase disshy

turbance This is because the terms sin(cent) and cos(cent) appear in equations for BER of

digital communication systems It is therefore necessary to go through voltage-to-phase

conversion process before designing the digital filter which will model the disturbance in

oscillators phase

As has been discussed before in Section 24 for small values of cent(t) cos(wot+cent(t))


49

Phase Noise specs for the filter

dB

Highest frequency point F=l

1Hz Frequency

FIGURE 31 Oscillators frequency response

cos (wot + cent(t)) = cos(wot)cos(cent(t)) - sin(wot)sin(cent(t)) ~ cos(wot) - cent(t)sin(wot) (31)

Where it is assumed that cos(cent(t)) ~ 1 and sin(cent(t)) ~ cent(t) for small values of cent(t)

Using this narrowband modulation approximation cent(t) at 6w results in a pair of equal

sidebands as illustrated below

Let cent(t) = XIsin(6wt) be the low frequency fluctuation in phase having power

spectral density = yen at frequency 6w It is represented by one-sided frequency specshy

trum having a peak at H (Dw) = Xl Thus Xl is the spectral value of time function

cent(t) Substituting value of cent (t) in (31)

cos(wot + cent(t)) = cos(wot) - XIsin(6wt) x sin(wot) (32)

Therefore

Xl Xlcos(wot + cent(t)) = cos(wot) - TCos(wO + 6w)t - Tcos(wot - 6w)t (33)

(34)

50

Where Al is the PSD value of the oscillators phase noise spectrum at frequency

offset t1w - which is specified by the user Therefore the PSD of cent(t) is specified by

values which are 2 times the square root of the power spectral density spectrum values

specified by the user and the frequency spectrum of cent(t) is specified by a values given

by 2 X PdBc at different frequency offsets from the carrier frequency

(35)

(36)

Lets consider what happens when the disturbance is at DC Let cent(t) = A Then

substituting value of cent(t) in oscillator output equation Vout = cos(wot+cent(t)) after going

through the approximation for small cent(t) we get

cent(t) ~ cos(wot) - cent(t) x sin(wot) = cos(wot) - A x sin(wot) (37)

The PSD of cent(t) is given by

(38)

As phase noise spectrum is specified in dBc the PSD value at zero frequency offset

from the carrier is 0 dBc and therefore H(O) is 1 The frequency response of the digital

filter for frequency offsets from carrier (t1w) gt 0 is calculated using (36)

MATLAB command fir2(NFM) is then used to design Nth order FIR The

vectors F and M specify the frequency and magnitude breakpoints for the filter as specshy

ified by the user F is normalized to be between 0 to 1 with 1 representing the highest

frequency offset from the carrier as shown in Fig 31 The frequency response of the

FIR filter is obtained using the MATLAB command freqz Since the digital filter is

used to model the oscillators phase disturbance the digital filters frequency response

is equivalent to Hltp(t) (w) Using (36) the relationship between phase noise PSD values

and Hltp(t) (w) is given by

(39)

(39) is used to get a comparison plot of PSDs of the digital filter and phase noise

response for the oscillator specified by the user If the filters PSD response is found to

51

Phase Noise output _ _ D_ig_ita_I_FI_~___Rand_n__~r-__________~~I~___ lt_er~r-__~~~

White Noise FIR Filter Generator

dB dB

o o

dB

o

f f f Frequency Frequency Frequency

FIGURE 32 Generation of oscillators phase disturbance using digital FIR filter

be unsatisfactory then the order of the filter is varied until an acceptable filter frequency

response is obtained

The final SIMULINK model implementation is as shown in Fig 32 White noise

having 0 dB PSD is generated by the random number generator randn which has a

flat PSD The noise is then passed through the digital FIR filter As a result the flat

band frequency response of White noise gets shaped by the filter response to give the

required excess phase output having frequency response similar to that of the spectrum

of oscillators phase disturbance

The power of ltJ(t) at the output of the digital filter is 0 dB at DC and has to

be scaled depending upon the carrier power The output of the digital filter is passed

through a constant source SIMULINK block having magnitude equal to the square-root

of carrier power to give the final phase disturbance values to be used in simulations

52

32 MATLAB GUI Designed for the Design of FIR Filter

The Graphic User Interface developed in MATLAB is used to get the PSD values

for the oscillator spectrum from the user needed to design the FIR filter of user specified

order It then plots the computed PSD and specified PSD for comparison The user

can specify 10 different frequency and dBc values The frequency points entered are in

kHz The GUI checks to see that there is a dBc value for every frequency point entered

and vice-versa The dBc values entered should always be negative and frequency points

should always be positive After correct values are entered the user can select the order

of the filter and then check to see if the filter PSD looks satisfactory If not then the

order of the filter can be changed or more data points may be entered until a satisfactory

filter is designed The final GUI is as illustrated in Fig 33

- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1

~ Digital Filter Parameters I I

Digital FIR Alter for Phase NoIse generation

Enter the Order of Filler to be desglned

uata 101015 Frequency offset from carrier (KHz) Magnitude of Osciiiator Ouput Voltage (dBc) ---z- -65 ]

-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-

Power Spectral DensHy Plot of the Designed dlgHal FIR niter and Osclllalor Phue Nolle spectrum

- Dig ilal FIR Filter - User inputi_

5 g -15 _

c f -20 - Ii

FIGURE 33 MATLAB GUI for digital FIR filter design

54

4 LOCAL OSCILLATOR MODEL IMPLEMENTED IN COMMIC

Communication IC Tool-Box or COMMIC is a simulink based tool-box that can be

used to design communication systems COMMICs focus is to tie system level design

and circuit level design together A typical COMMIC implementation is as shown in

Fig 41

Fig 41 lists only a few blocks of the toolbox The Local Oscillator (LO) block

in COMMIC has been implemented using the fast simulink method explained in secshy

tion 213 and using the digital FIR filter as explained in section 31 To observe the

effect of oscillator phase noise on BER of a digital communication system the quantity

of interest is cos(cent(t)) + j sin(cent(t)) This is generated by the LO block as shown in the

Fig 42

Either Hajimiri phase noise model implementation or digital filter implementation

of the model for disturbance in oscillators phase is selected by double-clicking on the LO

block Selecting either method results in the display of MATLAB GUI for that model

as shown in Figs 43 and 44 After the user input parameters have been entered

Source Block 1-------+1

Source block

1) BPSK 2) OAM 3) Pi4DOPSK 4) BFSK 5) OOPSK 6) GMSK 7) MSK

I Channel I

__ J Mixer Final Output after Demodulation scheme

1) Ring resonator Noisy channel Demodulation 2) Diode Mixer 3) Active Mixers

Bit error rate calculation

Local Oscillator Block

FIGURE 41 Communication IC toolbox

55

Real-lmag to LO

Complex Phase_Perturbations_Model

Trigo nometri c Function

FIGURE 42 LO block in simulink

the SIMULINK simulation can be started to get the real-time values for sin(cent (t)) and

cos(cent (t ))

Under the mask the LO block looks as shown in Fig 45 When the Model

Type input for the LO block is selected to Hajimiri the Hajimiri phase noise model

block is activated by making Enablel block in the Fig 45 to have constant value of 1

The digital fil ter model block is disables by making Enable2 to 0 and vice-versa The

Hajimiri phase noise model mask looks is as shown in Fig 46 The digital filter mask

is shown in Fig 4 7

56

---------------shy ~ ----shy -Osc_phase_nolse_modeJ

Hajimiri Model

Phase_Pertllbations_Model

Enter NO of Stagn Entor Vee (odd) (Von)

Entor Wn 10 Entor Wp 10 CUm) (um)

Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ

_ It tSF OIdIa Expec rnqcy Spectrum I

FIGURE 43 Selection of Hajimiri phase noise model for LO block

57

Digital Filter

Phase Perturbations_Model

Tri~~~~~~trlc

FIGURE 44 Selection of digital filter model for LO block

- -

58

~- -~

- Oscphase_nolse_modeJlPhase Perturbatlons_ModeJ _so ~ _ middottw400~ 1 l - l~ ~_4gtlaquo ~_ ~ gt ~- t _ _ JYih~i ~ _JO

Hajimiri Model for Phase Noise in Single-ended Ring Oscillators

Enable 1

Enable2

FIGURE 45 Mask of LO model

signal1 signal2 signal3rt Hsigna14

- ~ 1I I Ollsimu5 DemlD(r lshy1 S-FlJ1dion

FIGURE 46 Hajimiri phase nOIse model mask

59

)----+1 PhaseNoise model FIRRlter

Digital FIR Fi~er Block

FIGURE 47 Digital FIR filter mask

60

5 CONCLUSIONS

1 Hajimiri phase noise model for single-ended ring oscillators is accurate

2 The Hajimiri phase noise model s-function block implemented in MATLABs

SIMULINK environment using the fast algorithm is accurate and efficient

3 The digital FIR filter block implemented in SIMULINK can used to model the

oscillator phase disturbance accurately

4 The LO s-function block implemented in SIMULINK is capable of generating phase

disturbance values accurately using either Hajimiri phase noise model or digital

FIR filter

5 The LO s-function block can be used in SIMULINK simulations for communication

systems

61

BIBLIOGRAPHY

1 Behzad Razavi A study of phase noise in cmos oscillators IEEE JSSC 31(3)331~ 343 1996

2 DB Leeson A simple model of feedback oscillator noise spectrum Proceedings of IEEE 54(2) 329~330 1966

3 Asad A Abidi Analog Circuit Design Rf Analog-To-Digital Converters Sensor and Actuator Interfaces Low-Noise Oscillators Plls and Synthesizers Chapter 4 How Phase Noise Appears in Oscillators Kluwer Academic Publications 1997

4 Wang HongMo A Hajimiri and T H Lee Design issues in cmos differential Ie oscillators IEEE JSSC 35(2)286~287 2000

5 Ali Hajimiri and Thomas H Lee A general theory of phase noise in electrical oscillators IEEE JSSC 33(2)179~194 1998

6 S Limotyrakis Ali Hajimiri and Thomas H Lee Jitter and phase noise in ring oscillators IEEE JSSC 34(6)790~804 1999

7 Ali Hajimiri Jitter and phase noise in electrical oscillators Special University Oral Examination April 8 1998

8 Ali Hajimiri and Thomas H Lee Corrections to a general theory of phase noise in electrical oscillators IEEE JSSC 33(6)928 1998

9 Theodore S Rappaport Wireless Communications Principles and Practice Prenshytice Hall 1995

10 Couch II Leon W Digital and Analog Communication Systems Prentice Hall 1995

11 John G Proakis and Dimitris G Manolakis Digital Signal Processing Principles Algorithms and Applications Prentice Hall 1995

12 Behzad Razavi RF Microelectronics Prentice Hall 1997

13 Behzad Razavi Design of Analog CMOS Integrated Circuits McGraw Hill College Division 2000

14 Thomas H Lee The Design of CMOS Radio-Frequency Integrated Circuits Camshybridge University Press 1998

15 David A Johns and Ken Martin Analog Integrated Circuit Design John Wiley amp Sons 1996

16 BP Lathi Modern Digital and Analog Communication Systems Oxford University Press 1998

62

17 Adel S Sedra and Kenneth C Smith Microelectronic Circuits Oxford University Press 1998

18 Bernard Sklar Digital Communications Fundamentals and Applications Prentice Hall 1988

19 Thomas H Lee and Ali Hajimiri Oscillator phase noise A tutorial IEEE JSSC 35(3)326-336 2000

20 Ali Hajimiri and Thomas H Lee Phase noise in cmos differential Ie oscillators Symposium on VLSI Circuits June 11-13 1998 Honolulu Hawaii

21 Ali Hajimiri S Limotyrakis and Thomas H Lee Phase noise in multi-gigahertz cmos ring oscillators Custom Integrated Circuits Conference May 11-14 1998 Santa Clara California

22 Ali Hajimiri and Thomas H Lee Design issues in cmos differential Ie oscillators IEEE JSSC 3(5)717-724 1999

copyCopyright by Devavrata Godbole

October 3 2000

All rights reserved


by

Devavrata Godbole

A THESIS

submitted to



degree of

Master of Science



APPROVED









ACKNOWLEDGMENT










I

TABLE OF CONTENTS

Page

1 INTRODUCTION 1








22 Explanation 10












Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








by

Devavrata Godbole

A THESIS

submitted to



degree of

Master of Science



APPROVED









ACKNOWLEDGMENT










I

TABLE OF CONTENTS

Page

1 INTRODUCTION 1








22 Explanation 10












Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








APPROVED









ACKNOWLEDGMENT










I

TABLE OF CONTENTS

Page

1 INTRODUCTION 1








22 Explanation 10












Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







ACKNOWLEDGMENT










I

TABLE OF CONTENTS

Page

1 INTRODUCTION 1








22 Explanation 10












Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







TABLE OF CONTENTS

Page

1 INTRODUCTION 1








22 Explanation 10












Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








Page












5 CONCLUSIONS 60

BIBLIOGRAPHy 61

LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







LIST OF FIGURES

Figure Page




14 Jitter 3

15 PLL system 4


17 Ideal case 6



110 LC oscillator 9













Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








Figure






















Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








Figure Page









1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62








1 INTRODUCTION









by





Frequency


2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







2

Frequency














3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







3

dB

1Hz Frequency


113 What lS Jitter











Reference I Edg



is here

FIGURE 14 Jitter

4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







4























5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







5

Low Noise Amplifier

Duplexer Filter

Band-Pass Filter


Power Amplifier

Band-Pass Filter



















6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







6

t Signal Band (J)

LO

(J)

t Downconverted (J)

Band
















7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







7




















8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







8

Actual Case


t 1--



9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







9


C

~ c 0Q)


Co (f)

-40 ~ I0 (L

-60

-80 01 02 03 04 05 4

Frequency



C

YOU


10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







10


21 Salient Features







are






22 Explanation










11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







11

i(t) ltp(t)


o o t

i(t) A(t

A(t)

~

o o t



time-variant system







(21)








12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







12

(a)


Phase7H-- shift i

05 r

v 1 r

-05

j

I middot 1

L-~~_~~_~~~_~~------J o 02 0_ 011 2

L ---- 2 ~ I 2 -----~ 1- 1808 -150 O~ 04------cO6--08-~-- 4 ~6 ~=----bull o~

(b) (c)







(22)







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







--

13


qmax

X t

f ltp (t)


-00



00





(23)













14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







14

Ideal integration

t

f CI Cos(~t +ell

t

f bull


Phase modulation




(24)








15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







15

[(01)

I I I I I I I I

~O1 ~O1 I-- I

I I I I

0

Co

S(o1) ) 010

I I I I I I I

~O1 I

--I I I I I

2x01o

C

CJ

I I I I I I I I I

~O1 I

--I I I I I

3x01o

o ~o1 (J)









cent(t) = Incn

~ sm(~wt)2qmax w

(26)

16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







16

in 2(W) Jj

I iNoise

Thennal Noi se

lo lo lOlo - - ~

loo 2xWo 3xWo w












(2 7) x qmax X W





17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







17















(28)L(~w) =




(29)L(~w) =

18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







18



1f 6w ~ I I I I

w

Co

S~(w)

o 6w w

PM

Sv(w)


19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







19





(210)





[5]

1 1 ( Co )2 (211)bw j3 = bwy x J2 f rms




1 127rCo = - f(x)dx (212)21f 0









20


02

I O~

I -02 C l ~ ggt -04

-06

10 15 20 25 30 35 40 45 50 points

















21

Symmetrical ISF

08

06

04

C 3 02~c

I

o~ ~ iiE -02

~ -04

-06

-08

-1 0 5 10 15 20 25 30 35 40 45 50

Sample Points










08 x C tpHL = K TT

n X VDD


08 x C tpLH = K V

P X DD

22

Voo

Voo ---------~------

(a) (b)


I

F E Voo


AD ~________~____~~______~

o Voo V Voo Vo

(c)





23









is given by


Where








given by

(215)

00


24


00



(218)

Giving



2 x qmax X tlw






25











31784 MHz 31523 MHz 31756 MHz









using (220)






SpectreS HSPICE

9mN 9mP 9mN 9mP

1588e-3 2056e-3 1560e-3 212e-3






are as shown



-1511 -1512004



27















-100

-110

-1 20

~ -130 pound

-g 1sect -140 ggt

-1 50

-160

-170 -

_180 L-_--____ --__-----_-L_--__L_--__L_-- o 4 6 7 8 9

Frequency


28



-100

-110

-120

u lD

~ -130 Q) 0 J

lsect -140 ggt

-150

-160

-170

J _____ -1 __-180 o 2 3 4 5 6 7 8 9 10

Frequency 6 X 10




(221 )


Vi~ (f) = 4kTY~ = (29681e-9)2 (222)9m



Y = (29681e-9)2 x Ikr = 0633 (223)


Hajimiri model

29

V~lV ~ VdC=2 5V f

25V


V out






500397 MHz 495689 MHz 500001 MHz




-13053 -13061





154087 MHz 152419 MHz 15384 MHz

30





-13519 -13526

middot70 I-----------

-80 -

-90

g g -120 g ~

-130

-140

-150

-160 --------------shyo 2



3 4 5 6 7 8 9 10 Frequency

X 10


31



7 - ~--~-----

-60

-70 -

-80 - ltl III 0 -90shy~

middot5Q)

-100 Z I Q)

~ -110 c a

-120

-130

-140

-150

-160 L __-----_L_----__---

o 2 3 4 5 6 7 8 9 10 Frequency in Hz 6

X 10








32




lesser than 6V


lesser than lOOOpm


lesser than lOOOpm


lesser than 100pm


lesser than lOOpm










33


HSP(CE program

HSPICE

3


frequency and (SF











and amptsP and gdsN

MATLABGUI



2

Generate the HSPICE


34









for this netlist




















SC2 ator erw

35


Node 1 Vee Vee Vee

Vout



















36


100 100

I I


10 ~r-----------------------~~


















37


Enter Vee (odd)




Enter c 10 (PF)





38







by




















39






M M



(227)





M M



transforms to








40






(230)

















41

















below


Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 999932

999502

236427

237702

Oscillation

cycles

Mean

(Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -07 -05 16433 16559

42





Oscillation

cycles

Sampling

Frequency


aged over

Max FFT

value (Orig-

inalFast)

Min FFT

value (Orig-

inalFast)

105 10 104 103 973064

965318

208774

209542

Oscillation

cycles

Mean

( Original)

Mean

(Fast)

Variance

(Original)

Variance

(Fast)

104 -04679 -03013 17128 17204

43

Symmetrical ISF

08

06

I OAL

0 3 02middot2 Ol co

0aJ ~ mE -02 ~

-004

-06

-08

-1 0 5 10 25 30 35 40 45 50

Sample Points




40

30

20

i-0 10 13

ro

-10

-20

-30

-40 0 2000 4000 6000 8000 10000 12000

TIme in sec


44



-10~

-20

-30 ID 0


-60

-70

~-----~----60 o 05 15 2 25




02

0


-06

-08

-1

0 5 10 15 20 25 30 35 40 45 50 points


45



30

20

10

Ql0 3

0 OJ

-10

1-

-20

-30

-40 0 2000 4000 6000

TIme in sec 8000 10000 12000





-20

-30 co 0 5 ~ -40

dege ggt -50

-60

-70

-80 o 05 15 2 25



46



















47



current iteration

Feedback values





48




















oscillators phase



49


dB


1Hz Frequency











Therefore


(34)

50






(35)

(36)






(38)












(39)



51



dB dB

o o

dB

o















52












- ----

53

r- ------ - -~- --------------------------~~~--- ---_=_1





-~ 2 ~~ ~o 9 ~- tf- I ic-~t - 62 l

3 5 -60 I 4 ----- rTn l 5 - 2 -4 0

6 3 -

-50

7 05 - 15

0

9 --

0

10 ~

-



5 g -15 _

c f -20 - Ii


54





Fig 41






Fig 42






Source block


I Channel I






55

Real-lmag to LO





cos(cent (t ))






is shown in Fig 4 7

56


Hajimiri Model




Entor In (um)

10 Entor lp 10

(um)

Entor C (pFJ



57

Digital Filter


Tri~~~~~~trlc


- -

58

~- -~



Enable 1

Enable2





59




60

5 CONCLUSIONS








FIR filter


systems

61

BIBLIOGRAPHY

















62







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