6.776 high speed communication circuits and systems lecture 9 … · 2020-01-04 · -now the...

6.776High Speed Communication Circuits and Systems

Lecture 9Enhancement Techniques for Broadband Amplifiers,

Narrowband Amplifiers

Massachusetts Institute of TechnologyMarch 3, 2005

Copyright © 2005 by Hae-Seung Lee and Michael H. Perrott

H.-S. Lee & M.H. Perrott MIT OCW

Shunt-Series Peaking

Series inductors isolate load capacitance from M1: delays charging of load capacitanceTrades delay for bandwidthL1, L2, L3 can be implemented by 2 coupled inductors with coupling coefficient of k


T-Coil Bandwidth Enhancement

M1

RL

vout

M2

Cfixed

Id

Vbias

vin

Vdd

L1

L2L3

M1

vout

M2

CfixedVbias

vin

L2

L1

CB

k

RL

Vdd

Uses coupled inductors to realize T inductor network- Works best if capacitance at drain of M1 is much less than

the capacitance being driven at the output loadCB provides parallel resonance to improve bandwidth further See Chap. 9 (Ch. 8, 1st ed.) of Tom Lee’s book pp 279-282 (187-191)


T-Coil Continued

The self inductance L (with the other winding open-circuited) must be

The bridging capacitance

Coupling coefficientk=1/3 for Butterworth responsek=1/2 for maximally flat delay (linear phase)

Bandwidth extension: approximately 2.8 (Butterworth)

- See S. Galal, B. Ravazi, “10 Gb/s Limiting Amplifier and Laser/Modulator Driver in 0.18u CMOS”, ISSCC 2003, pp 188-189 and “Broadband ESD Protection …”, pp. 182-183

- Also see "Circuit Techniques for a 40 Gb/s Transmitter in 0.13um CMOS", J. Kim, et. al. ISSCC 2005, Paper 8.1


Bandwidth Enhancement With ft Doublers

A MOS transistor has ft calculated as

ft doubler amplifiers attempt to increase the ratio of transconductance to capacitance

M1 M2

2Ibias

I1 I2

Vbias

vin

We can make the argument that differential amplifiers are ft doublers- Capacitance seen by Vin for single-ended input:- Difference in current:

Transconductance to Cap ratio is doubled:


Creating a Single-Ended Output

M1 M2

2Ibias

I1 I2

Vbias

vinM1

M2

Ibias

Io

Vbias

vin

Ibias

Input voltage is again dropped across two transistors- Ratio given by voltage divider in capacitance

Ideally is ½ of input voltage on Cgs of each deviceInput voltage source sees the series combination of the capacitances of each device- Ideally sees ½ of the Cgs of M1

Currents of each device add to ideally yield ratio:


Creating the Bias for M2

M1 M2

2Ibias

I1 I2

Vbias

vinM1

M2

Ibias

Io

Vbias

vin

Ibias

M1

M2

Io

Vbias

vin

IbiasM3

Use current mirror for bias (Battjes ft doubler)- Inspired by bipolar circuits (see Tom Lee’s book, pp288-

290 (197-199))Need to set Vbias such that current through M1 has the desired current of Ibias- The current through M2 will ideally match that of M1


Problems of ft Doubler in Modern CMOS RF Circuits

Problems: - Works if Cgs dominates capacitance , but in modern

CMOS, this is not the case (for example, Cgd=0.45Cgs in 0.18 µ CMOS)

- achievable bias voltage across M1 (and M2) is severely reducedby 2x!) (thereby reducing effective ft of device)

- Input capacitance degrades due to Cgs, Cdb of M3: at most 1.5x improvement in transconductance/capacitance ratio

Assuming zero Cdb:


Increasing Gain-Bandwidth Product Through Cascading

Amp Amp

Cfixed

Amp

Cfixed

A1 + s/wo

A1 + s/wo

A1 + s/wo

vin vout

vin vout

We can significantly increase the gain of an amplifier by cascading n stages

- Issue – bandwidth degrades, but by how much?


Analytical Derivation of Overall Bandwidth

The overall 3-db bandwidth of the amplifier is where

- w1 is the overall bandwidth- A and wo are the gain and bandwidth of each section

- Bandwidth decreases much slower than gain increasesOverall gain bandwidth product of amp can be increased


Transfer Function for Cascaded Sections

1/100 1/10 1 10 100-80

-70

-60

-50

-40

-30

-20

-10

0

Nor

mal

ized

Gai

n (d

B)

Normalized Frequency (Hz)

Normalized Transfer Function for Cascaded Sections

n=1

n=2

n=3

n=4

-3


Choosing the Optimal Number of Stages

To first order, there is a constant gain-bandwidth product for each stage

- Increasing the bandwidth of each stage requires that we lower its gain

- Can make up for lost gain by cascading more stagesWe found that the overall bandwidth is calculated as

Assume that we want to achieve gain G with n stages

From this, optimum gain/stage ≈ sqrt(e) = 1.65- See Tom Lee’s book, pp 299-302 (207-211,1st ed.)


Achievable Bandwidth Versus G and n

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

Achievable Bandwidth (Normalized to f )t Versus Gain (G) and Number of Stages (n)

n

w1/

wt

0.3

A=1.65

A=3

G=10

G=100

G=1000

Optimum gain per stage is about 1.65- Note than gain

per stage derived from plot as

- Maximum is fairly soft, though

Can dramatically lower power (and improve noise) by using larger gain per stage

ω1ωu

ωu


Motivation for Distributed Amplifiers

M1 M2 M3

vout

vin

Rs=Z0

RL=Z0

Cin CinCin

Cout Cout Cout

We achieve higher gain for a given load resistance by increasing the device size (i.e., increase gm)- Increased capacitance lowers bandwidth

We therefore get a relatively constant gain-bandwidth productWe know that transmission lines have (ideally) infinite bandwidth, but can be modeled as LC networks- Can we lump device capacitances into transmission line?


Distributing the Input Capacitance

M1 M2 M3

Zo Zo Zo Zo

vout

RL=Z0

delay

vin

Rs=Z0

RL=Z0

Cout Cout Cout

Lump input capacitance into LC network corresponding to a transmission line- Signal ideally sees Zo=RL rather than an RC lowpass- Often implemented as lumped networks such as T-coils- We can now trade delay (rather than bandwidth) for gain

Issue: outputs are delayed from each other


Distributing the Output Capacitance

M1

Zo Zo Zo Zo

M2 M3

Zo Zo Zo Zo

RL=Z0

vout

RL=Z0

delay

delay

vin

Rs=Z0

RL=Z0

Delay the outputs same amount as the inputs- Now the signals match up- We have also distributed the output capacitance

Benefit – high bandwidthNegatives – high power, poorer noise performance, expensive in terms of chip area- Each transistor gain is adding rather than multiplying!


Narrowband Amplifiers

VLC1 RL

L1Delay = xCharacteristic Impedance = Zo

Transmission Line

Z1

VinC2

dieConnector

Controlled ImpedancePCB trace

package

On-ChipDrivingSource

AmpVout

MatchingNetwork

MatchingNetwork

For wireless systems, we are interested in conditioning and amplifying the signal over a narrow frequency range centered at a high frequency- Allows us to apply narrowband transformers to create

matching networksCan we take advantage of this fact when designing the amplifier?


Tuned Amplifiers

M1

vout

CL

Vbias

vinRs

Vdd

LT RL

Put inductor in parallel across RL to create bandpassfilter- It will turn out that the gain-bandwidth product is

roughly conserved regardless of the center frequencyTo see this and other design issues, we must look closer at the parallel resonant circuit


Tuned Amp Transfer Function About Resonance

Evaluate at s = jω

Look at frequencies about resonance:

RpLpCp

iin=gmvinZtank

vout

Amplifier transfer function

Note that conductancesadd in parallel


Tuned Amp Transfer Function About Resonance (Cont.)

From previous slide

Simplifies to RC circuit for bandwidth calculation

=0

RpLpCp

iin=gmvinZtank

vout

voutvin

w

slope =-20 dB/dec

gmRp

Rp2Cp

1

wo

Rp2Cp

1

RpCp

1


Comparison between Low-Pass and Band-Pass

low-passamplifier

band-pass(tuned)

amplifier


Comparison between Low-Pass and Band-Pass

Tuned amplifier characteristic is a frequency translated version of the low-pass amplifierThe band-pass bandwidth is equal to the low-pass bandwidth (the band-pass shape is 2x narrower but upper and lower sidebands give the same bandwidth as LP)We are tuning out the effect of capacitor (parallel LC looks like an open circuit at resonance, so C doesn’t load the amplifier)This is often called low-pass to band-pass transform in filter design:- Replace C with parallel LC tank- Replace L with series LC tank


Gain-Bandwidth Product for Tuned Amplifiers

RpLpCp

iin=gmvinZtank

vout

voutvin

w

slope =-20 dB/dec

gmRp

Rp2Cp

1

wo

Rp2Cp

1

RpCp

1

The gain-bandwidth product:

The above expression is just like the low-pass and independent of center frequency!- In practice, we need to operate at a frequency less than

the ft of the device


The Issue of Q

RpLpCp

iin=gmvinZtank

vout

voutvin

w

slope =-20 dB/dec

gmRp

Rp2Cp

1

wo

Rp2Cp

1

RpCp

1

By definition

For parallel tank

Comparing to above:


Design of Tuned Amplifiers

RpLpCp

iin=gmvinZtank

vout

voutvin

w

slope =-20 dB/dec

gmRp

Rp2Cp

1

wo

Rp2Cp

1

RpCp

1

Three key parameters- Gain = gmRp- Center frequency = ωo- Q = ωo/BW

Impact of high Q - Benefit: allows achievement of high gain with low power- Problem: makes circuit sensitive to process/temp

variations


Issue: Cgd Can Cause Undesired Oscillation

At frequencies below resonance, tank looks inductive

M1

vout

CL

Vbias

vin

CgdZin

Rs

Cgs

Vdd

LT RL

NegativeResistance!


Use Cascode Device to Remove Impact of Cgd

M1

vout

CL

Vbias

vin

CgdZin

Rs

Cgs

Vbias2M2

Vdd

LT RL

At frequencies above and below resonance

PurelyCapacitive!


Neutralization in Tuned Amplifier

Recall the neutralization for broadband amplifier

For narrowband amplifier, the inverting signal can be generated by a tapped transformer

M1

RL

vout

CL

Id

Vbias

vin

CgdZin

Rs

Cgs

-1CN


Neutralization with Tapped Transformer

Problems: Area and quality of on chip transformerThe neutralization cap CN must be matched to Cgd


Differential Neutralization for Narrow Band Amplifier

Same principle as differential neutralization in broadband ampOnly issue left is matching CN to Cgd- Often use lateral metal caps for CN (or CMOS transistor)


Superregenerative Amplifier

quench

Vin is sampled at the rate fc (in actual implementation fc may be input level dependent)

The sampled output voltage

Can be used for both broadband and narrowband – we’ll do a simple analysis for broadband amp.


Superregenerative Amplifier

Nyquist theorem

Gain calculation

Trades bandwidth only logarithmically with gain!


Superregenerative Amplifier Example (Narrowband)

RB: DC bias resistorLC, C1: Tuning LCC2 : positive feedbackLE: RF choke (large inductance)

•When the RF amplitude becomes large, it is rectified at the emitter of Q1•This raises the DC potential at the emitter Q1 eventually turning it off•The RF oscillation dies (quenched), and the DC potential at emitter of Q1 returns•Amplitude of oscillation grows again due to positive feedback


Active Real Impedance Generator

Input admittance:

Zin

Av(s)VoutVin

Av(s) = -Aoe-jΦ

Cf

Resistive component!


This Principle Can Be Applied To Impedance Matching

M1

Vbias

vinRs

Ls

ZinIout

We will see that it’s advantageous to make Zin real without using resistors- For the above circuit (ignoring Cgd)

Ls

vgs gmvgsCgsItest Vtest

Looks like series resonant circuit!


Use A Series Inductor to Tune Resonant Frequency

M1

Vbias

vinRs

Ls

ZinIout

M1

Vbias

vinRs

Ls

ZinIout

Lg

Calculate input impedance with added inductor (in order to choose resonance freq. and input resistance separately)

Often want purely resistive component at frequency ωo- Choose Lg such that resonant frequency = ωo


Narrowband Alternative to LC

On-chip inductors take up considerable die area and have relatively poor Q. Is there any other alternatives?

- Use quarter-wavelength transmission line (waveguide) resonator?- In Lecture 5 we found the λ/4 waveguide with shorted load behave much like

a parallel LC circuit, while with open load it behaves like a series LC- The problem is the dimension. For 900MHz mobile phone frequency, λ/4 in

free space is 3.25 inches!- With high permittivity dielectric material (ceramic), the size can be reduced to a reasonable dimensions. With εr=10, the length of waveguide is only about inch.- Different configurations of filters can be built by combining sections of series and parallel LC equivalents - More appropriate at frequencies over GHz

SAW (Surface Acoustic Wave) filters are another popular alternative


SAW Filters

SAW filters use piezoelectric substrate to generate surface acoustic wave

electrodes

input output

piezoelectric substrate

λ Adapted from Japan Radio Co.


SAW Filters

Piezoelectric substrate- LiTaO3- LiNbO3- QuartzFilter Structures- Longitudinal Filter- Transversal Filter- Ladder Filter

Saw filters have high selectivity and low insertion loss (down to a fraction of % fractional bandwidth, ~2dB insertion loss

Wide range of enter frequency (few 100 kHz-GHz)

At 1-2 GHz, the dimensions of SAW filters are 1-2mmFor more information on SAW filters look over www.njr.com


SAW Filters in Mobile Phones

ANT

RX

RF Amp

Ant. SW

IF Amp

Buff Amp

IF Detection

OSC(1)

OSC(2)

Buff Amp

Buff Amp Power Amp

TX

BPF

BPFBPF

BPF Mixer

Mixer

Figure by MIT OCW.

Adapted from Japan Radio Co.


SAW Filter Example

JRC NSVS754 2.4 GHz RF SAW Filter Charactersitic

Inse

rtion

Los

s [d

B]

Frequency [MHz]24502200 2700

5045

4035

302520

1510

50

109

87

654

3210

Figure by MIT OCW.

Adapted from Japan Radio Co.

6.776 high speed communication circuits and systems lecture 9 … · 2020-01-04 · -now the...

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