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Institutionen fr systemteknik

Examensarbete

A Study of Output Impedance Effects in Current-

Steering Digital-to-Analog Converters

Examensarbete utfrt i Elektroniksystem

vid Tekniska hgskolan vid Linkpings universitet

av

Alaja Kumari Sadda

Niraja Madavaneri

LiTH-ISY-E-!"#$%&'-SE

Linkping()!"

Linkpings tekniska hgskola

Institutionen fr systemteknik

SE-%*! *" Linkping


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(


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A Study of Output Impedance Effects in Current-Steering Digital-to-Analog Converters

+aster thesis performed in

,ivision of Eletronis Systems

by

Alaja Kumari Sadda

Niraja Madavaneri

LiTH-ISY-E-!"#$%&'-SE

Supervisor +. /e0a Sadeghifar

,epartment of Eletrial Engineering

Linkoping university

Examiner 1. 1aob 2ikner


Linkoping university

Linkoping ()!"

"


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$


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resentation date

()!(-)'-!(

u!lis"ing date #Electronic version$

Department and Division

Eletronis Systems


%anguage &eport category IS'N

-

IS&N LiTH-ISY-EX--13/4576--SE

(itle of series

Series num!er)ISSN

*&%+ Electronic version

"ttp,)).es.isy.liu.se

"ttp,)).es.isy.liu.se

(itle 3 Study of 4utput Impedane Effets in 5urrent-Steering ,igital-to-3nalog

5onverters

Aut"or#s$ 6ira7a +adavaneri8 3la7a 9umari Sadda

Abstract

In this thesis8 :e have explained the different types of ,35 ;,igital-to-3nalog< arhitetures and

their advantages and disadvantages. 2e have mainly foused on urrent-steering digital-to-analog

design for ahieving high speed and high performane. The urrent-steering ,35 is designed

using binary :eighted arhiteture. The benefits of this arhiteture is that it oupies less area8

onsumes less po:er and the number of ontrol signals re=uired are very less.

The re=uirements for high speed and high performane ,35 are disussed in detail. The iruit is

implemented in a state-of-the-art '% nm proess8 :ith a supply voltage of !.( > and at a sampling

speed of ( ?H0. The resolution of the ,35 is *-bits. The design of *-bit urrent-steering ,35onverts * most signifiant bits ;+S@s< into their binary :eighted e=uivalent8 :hih ontrols (%'

unit urrent soures.

The performane of the ,35 is measured using the stati and dynami parameters. In

ommuniation appliations the stati performane measures suh as I6L and ,6L are not of

utmost importane. In this :ork8 :e have mainly onentrated on the dynami performane

harateristis like S6/ ;Signal to 6oise /atio< and SA,/ ;Spurious Aree ,ynami /ange< . Aor

measuring the dynami parameters8 fre=ueny domain analysis is a better hoie.

%

English4ther ;speify belo:ideo Enoder Dsed to onvert proessed digital video signals and produe analog video

output signals.

3udio 3mplifier ,35s are typially used in an audio amplifier to provide a ,5 gain to the

output of digital filters used in the audio signal proessing units.

Soft:are /adio ,ata 3=uisition Systems

,ata 3=uisition

Systems

3 ,35 is typially used in the analog feedbak loop of a data a=uisition

system.

((

Aigure ! @asi ,35 blok diagram.

Digital input

Analog

reference

input

VREF

VDD

VSS Ground

may be internally

connectedto Vss

DAC


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,#3 5onversion 3ppliations

Application DAC 1unction Summary

+otor 5ontrol 3 typial modern motor ontrol system is ontrolled by a miro ontroller

:hose output is digital8 hene a ,35 is used to onvert them to their

orresponding analog voltages.5alibration In a typial measurement system8 a ,35 is used in the feedbak loop for

alibration and dynami error orretion.

Table ! Typial ,35 appliations M%N.

/.2 erformance Metrics

Aor system performane8 digital-to-analog or analog-to-digital onverters are very important. The

main attributes of the ,35s are stati and dynami performane parameters like resolution8

sampling rate8 dynami range et.8 :hih are explained in detail in set !.$8set. !.%and set. !.'.

/.3 &esolution+ Sampling rate and Dynamic range

The resolution of a ,35 is defined by the number of input bits8 N 8 and the number of levels at the

output is (N . There are many different versions of ,35s8 not only in terms of arhiteture8 but also

in terms of resolution. 5ompared :ith other versions an *-bit ,35 :ould be heaper than a !(-bit

,35. Ho:ever8 higher-resolution ,35s are more popular due to their balane bet:een auray

and ost. The sampling rate is the rate at :hih the ,35 is onverting the digital input to its

orresponding analog output value. The dynami range is the ratio bet:een the smallest and the

largest signals :hih an be onverted.

/.4 Static erformance Errors

The stati performane depends on =uanti0ation noise or trunation noise8 gain errors8 offset errors8

monotoni behaviour8 non-uniform =uanti0ation8 integral non-linearities and differential non-

linearities. Stati errors our due to mismath of the omponents at lo: speed and are measured

using I6L ;Integral 6on-Linearity< and ,6L ;,ifferential 6on-Linearity< M*N.

@y using I6L8 ,6L8 the ,5 transfer harateristis an be alulated and also the bits that ontains

largest error an be identified. The set. !.%.!.8set. !.%.(.and set. !.%.".gives more information

on stati performane errors.

/.4./. 5uanti6ation Noise or (runcation Error

The =uanti0ation ;trunation< noise is the differene bet:een the ideal :anted ,35 output and the

orresponding atual analog signal. The =uanti0ation plot :ith digital input and analog output is

sho:n in Aigure (M*N.

("


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Introdution

The magnified plot of error due to =uanti0ation noise is sho:n in Aigure "M*N. The error due to

=uanti0ation noise is ! /( LS@ ;Least Signifiant @it


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Stati Ferformane Errors

/.4.2. Integral Non %inearity #IN%$ and Differential Non %inearity #DN%$

Integral and differential non-linearities are used to define the errors bet:een ideal and real ,5

transfer funtion of a ,35.

(%

Aigure $ ?ain errors :ith digital input and analog output.

))) !)) !)! !!) !!!)

$

%

'

&

Analog outputLS

!deal ma" output #alue

Digital input

Actual ma"$

output #alue

!deal

Gain error

!! / $LS

Aigure % Integral non linearity plot.

!NL

!NL


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Introdution

The integral non linearity is defined as the deviation of analog output from ideal linear line passing

through the end points M(8 *N. 3n example plot for integral non linearity is sho:n in Error

/eferene soure not foundM*N.

The differential non linearity is defined as the analog output differene bet:een t:o ad7aent odesfrom the ideal step si0eM*N. 3n example plot for differential non linearity is sho:n in Aigure 'M*N.

/.8 Dynamic erformance Errors

These are more important for evaluating high speed ,35s beause they operate at inreased

fre=ueny and sampling rate. The errors observed are settling time8 glithes8 lok feed-through

errors M$N.

/.8./. Settling (ime of D)A Conversion

Settling time is one of the important parameters for ,35s. The time taken by ,35 to reah %)O of

lo:er signifiant bit of its ne: voltage or the final value based on the input ode is alled the

settling time. It an be attributed to the sle: time and delay time M'N.

3n example plot of settling time is sho:n in Aigure &M&N.

('

Aigure ' 3n example plot for differential non linearity.

DNL=!LS@%onotonic


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,ynami Ferformane Errors

/.8.0. 7litc"es in D)A Conversion

?lith energy is the time domain performane of ,35 and it is one of the ommon speifiations

for high fre=ueny ,35s. The unontrolled movement of ,35 output from one value to a ne:

value during the transition is alled as glith.

?lithes our due to the apaitive#indutive relation in the output of ,35 M!"N. ,uring a short

time period8 false ode :ill our8 for example if the ode transition is )!!!...! then the output :ill

be !)))...). This is ho: glithes our M(N. 3n example plot of ,35 glith energy :ith positive and

(&

Aigure * ?lith energy in ,35 :ith positive and negative glithes.

Rising edgeglitc& energy

Falling edgeglitc& energy

%a'or carriertransition

[one LS s(ing]

)ositi#e glitc&es

Negati#e glitc&es

)ositi#e glitc&es

Negati#e glitc&es

Aigure & Settling time harateristi plot.

tsettle

!

/(

LS

! /(LSE"pected


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4utline

In hapter "8 :e have explained about binary :eighted *-bit urrent-steering ,358 its building

bloks like the unit element8 s:ithing sheme8 biasing sheme8 synhroni0ation bloks and

different types of urrent mirrors. Their advantages and disadvantages are also disussed. The

theoretial alulation of SA,/8 S6/ and simulation results using sinusoidal and ramp signals are

disussed. Are=ueny response of input and output using +3TL3@ is also disussed in detail.

In hapter $8 :e have explained briefly about unit element performane :ith the help of different

tehni=ues and have sho:n ho: it relates to output impedane. 2hih tehni=ue gives good output

impedane and the limitations of unit element are also disussed.

:e have disussed ho: the pole#0ero analysis an be used to arrive at the dynami performane

metris of unit element of the ,35 at higher fre=uenies. ,ifferent methods have been disussed

here to sho: the effets of poles and 0eroes on the output impedane of the unit element at higher

fre=uenies8 like by hand alulation8 using +athematia and by using adene.

In hapter %8:e have disussed different tehni=ues for enhanement of output impedane at higherfre=uenies :ith the help of pole#0ero modifiation and implemented the onept at iruit level M(N.

The simulation results for sho:ing the differenes bet:een the SA,/ and output impedane using

the normal and omplimentary urrent solution tehni=ue is elaborated in detail.

In hapter '8presents onlusion of the :hole pro7et :ork and :e have explained about future

:ork of the urrent-steering ,35. Ho: it improves the performane of output impedane by

hanging the iruits are explained.

(


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Introdution

&eferences

M!N 9. 4. 3nderson8 BStudies on performane limitations in 5+4S ,35sC.Linkping Linkpings

universitet8 ())(.

M(N S. E. ite8 B,esign of a unit urrent ell for a !(-bit urrent-steering digital-to-analog

onverterC8 +S thesis8 Eindhoven Dniversity of tehnology8 Eindhoven8 ())'.

M"N 1. 1. 2ikner8 BStudies on 5+4S digital-to-analog onvertersC.Linkping Linkpings

universitet8 ())!.

M$N C5onvertersC8 3nalog ,evies ()). 3nalog ,ialogue. M4nlineN. 3vailable

http##:::.analog.om#library#analogdialogue#arhives#$"-)#E,5hO()'O()5onverter.pdf

M%N @. +5ulley8 B@ridging the ,ivide ;Fart "


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,igital-to-3nalog 5onverters

0 Digital-to-Analog

ConvertersThe main purpose of the ,35 ;,igital-to-3nalog 5onverter< is to onvert a digital input signal to

its analog e=uivalent i.e.8 binary input to its orresponding voltage8 urrent or eletri harge output.

0./ ("e Structure of a Digital-to-Analog Converter

The ideal ,35 struture :ith filter is sho:n in Aigure M(N. ,35 onverts digital input to analog

output and that analog output is given to lo: pass filter8 it filters the images in the signal.

Airstly8 the input signal +n is band limited to a fre=ueny fu and it is sampled at a fre=uenyfN;6y=uist fre=ueny< suh that fN(fu)/( . @y doing so it an be guaranteed that no aliasing:ill our. The output of ,35 :ill be a pulse amplitude modulated and this is given to a LFA ;Lo:

Fass Ailter< :hose ut-off fre=ueny is fN.

This LFA is alled image re7etion filter8 sine it attenuates all the image fre=ueny omponents at

multiples of (fu)/( . The blok diagram of ,35 :ith image re7etion filter is sho:n in Aigure M(N.

"!

Aigure @lok diagram of the ,35 :ith image re7etion filter.

DAC L)

) t

f,

fN

+n


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,igital-to-3nalog 5onverters

0.0 Different (ypes of Digital-to-Analog Arc"itectures

,35 arhitetures are lassified into different ategories.

3bout these arhitetures briefly explained in set. (.(.!.8set. (.(.(.and set. (.(."..

0.0./. 'inary-:eig"ted D)A Conversion Arc"itecture

This type of ,35 arhiteture utili0es a number of urrent soures8 resistors or apaitors. These

elements are al:ays binary :eighted. The ,35 output in stati ase an be :ritten at the time

instant n-is

A(n-)=Aos+A)m=!

N

((m!)bm(n-)

;' MA(%A' and Cadence Co-simulation

The main purpose of o-simulation is to redue the simulation time for generating the input8 output

signal and also for alulating the dynami parameters like S6/ and SA,/ respetively.

The proedure for o-simulation is sho:n in Aigure (. Airstly8 using +3TL3@ generated

sinusoidal input signal is generated8 after that design is set up using variables and reated model file

and stored it in result folder.

5reated file reader in shemati level8 file reader reads digital data using file and sripts and given it

to input of ,35 in adene. Dsing transient output8 data is simulated and taken output at file :riter

to :rite bak the output ,35 to text file using net-list and this text file is given bak to +3TL3@

and performane post proessing done to alulate S6/ and SA,/.

2.// Simulation &esults

The simulation results for test-benh of unit-element for output impedane and SA,/ are sho:n in

Aigure ")in set. ".!!.!.and input and output response of *-bit urrent-steering ,35 shemati

using sine :ave results are sho:n in Aigure "! and Aigure "(and using ramp signal sho:n in

Aigure ""andAigure "%.

2.//./. Simulation &esults for *nit Element

Aigure ")Sho:s the results for unit element8 red olour is orresponds to SA,/ and green olour is

orresponds to output impedane. Dnit-element performane is tested in 5adene '.!% version :ith

the voltage of !.( >8 rload=!)) 8 iRef=& A 8 Vs(ing=())mA and :ith the follo:ing transistorsi0es sho:n in Table ".

%%

Aigure ( +3TL3@ and adene o-simulation.

Generate input

Setup design

aria!"es

#$de" %i"e

resu"t %$"der

&i"e reader

Transient

si'u"ati$n

&i"e (riter

)et-"ist

*er%$r'ane p$st

*r$essing

*"$ts


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Implementation of an *-bit ,#3 5onverter

arameters Names s:ing ; >oltage s:ing< ()) mV

fJb: ; @and:idth< fs(

Table " ,esign parameters and the 2#L ratios of various transistors used in unit element sho:n in

Aigure !andAigure ().

2e obtain SFDR='% d and 7out=!)*d at ! ?H0 fre=ueny range the simulation result issho:n in Aigure ").

%'

Aigure ") 4utput impedane and SA,/.


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Simulation /esults

2.//.0. Simulation &esults for =-!it current-steering DAC

Aor testing the funtionality of the ,358 a sinusoidal signal is given as input signal is sho:n in

Aigure "!.Airstly8 :e generated an input oherent sinusoidal signal using +3TL3@. The sinusoidal

signal is tested :ith band:idth of %)) +H08 input signal fre=ueny of &.*! +H0 and samplingfre=ueny of ( ?H0 to ompare result :ith theoretial result. The fre=ueny domain input plot

using sine signal is sho:n in Aigure "!.

The output response of *-bit urrent-steering ,35 is sho:n in Aigure "(.The sinusoidal output

signal is obtained :ith the band:idth of %)) +H08 input sine signal fre=ueny of &.*! +H0 and

sampling fre=ueny of ( ?H0.

%&

Aigure "! Input sine :ave to the ,35.


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The *-bit urrent-steering ,35 design is also tested :ith ramp signal is sho:n in Aigure "". The

orresponding fre=uenies are band:idth of %)) +H08 signal fre=ueny of &.*! +H0 and sampling

fre=ueny of ( ?H0.

The orresponding ramp output signal for Aigure ""is sho:n in Aigure "%.

%*

Aigure "" Input of *-bit urrent-steering ,35 using /3+F.

Aigure "( 4utput of the ,35 orresponding to a sinusoidal

input.


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Simulation /esults

The 0oomed plot for ramp output signal is sho:n in Aigure "%.

%

Aigure "$ 4utput of *-bit urrent-steering ,35 using /3+F.

Aigure "% oomed in ramp signal.


57/111


The fre=ueny spetrum of input is sho:n in Aigure "'.

The output fre=ueny spetrum plot is sho:n in Aigure "&.

')

Aigure "& 4utput fre=ueny spetrum.

Aigure "' Input fre=ueny spetrum.


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Simulation /esults

Arom Aigure "'and Aigure "&8 in the input fre=ueny spetrum8 input is at * +H0 and at output

fre=ueny spetrum the input is also at * +H0. @ased on this8 one an onlude that the ,35 is

:orking fine.

The Input and output results of dynami performane8 for an *-bit ,35 using +3TL3@-adeneo-simulation is

Input results

These are the values of S6/ and SA,/ at input of ,35 from Aigure "'.

S6/ R '' d@.

SA,/ R '%.'%" d@.

3s ompared to theoretial value of S6/ ;&! d@< pratial values are =uite good beause S6/

pratial result is '' d@.

Output results

These are the values of S6/ and SA,/ at output of ,35 from Aigure "&.

S6/ R $) d@.

SA,/ R %! d@.

The output result are =uite lo: due to more noise present at output result and in our implementation

:e does not added any filter at the output of ,35. If filter is added at output of ,358 the result

:ill be good ompared :ith this result. @ut :e are mainly onentrated on unit element to alulate

the performane of output impedane at higher fre=uenies. So :e are explained ho: output

impedane effet at higher fre=uenies in hapter$and hapter %.

2./0 Conclusion

In this hapter8 :e have implemented *-bit urrent-steering ,358 also explained and implements

various sub-bloks. The sub-bloks are asode urrent soure and :ide-s:ing urrent mirror.

5asode urrent soure is used to ahieve high output impedane8 :ide-s:ing urrent mirror isimplemented to improve the performane and output impedane of ,35 and it :orks at lo:er bias

voltage. The *-bit urrent-steering ,35 is implemented using adene and +3TL3@ o-simulation

to test the performane metris. The estimated values of ,35 are sho:n in Table $.

'!


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arameters

/esolution *-bits

4utput s:ing $)) mVppDi ff

@and:idth FCL2

(

Load resistane !))

3rea ).% mm(

Froess '% nm

Spurious Aree dynami range !))d@

Signal to 6oise /atio *)d@

Table $ Expeted parameters and speifiations for the ,35 to be designed in this :ork.

Fratial results for ,35 is sho:n in Table %.

arameters


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/eferenes

&eferences

M!N T. @ellamine8 B*-bit urrent-steering ,35 3 pro7et for E5E %$& >LSI ,esignC8 ,ept. of

Eletrial and 5omputer Engineering8 Dniversity of +aine8 ())&. M(N @. /a0avi8 B,esign of analog 5+4S integrated iruitsC8 Frofessor of Eletrial Engineering

Dniversity of 5alifornia8 Los 3ngles8 ())*.

M"N F. E. 3llen8 Q5urrent +irrors and simple referenesQ8 5urrent mirrors and simple referenes8

()!).

M$N 9. 4. 3nderson8 BStudies on performane limitations in 5+4S ,35sC8 ,epartment of

Eletrial Engineering8 Linkpings universitet8 6ovember ())(.

M%N F. /eal8 ?rove land ,avid H8 /obes-ton8 Somerville8 B5asode urrent mirrorC8 Dnited state

patent8!*$.

M'N L 6alpantidis!8 > 9alenteridis!8 S Siskos!8 5 3 ,imitriadis(8 3 3 Hat0opoulos"8 3ristotle

Dniversity of Thessaloniki8 B3 study of different types of urrent mirrors using polysilion TATs I

Fappas!8C ,epartment of Eletrial and 5omputer Engineering8 %$!($8 ?reee.

M&N B,-lath flip-flopsC8 ELT!$* ,igital ,evies II8 @enhmark ompanies.

M*N Ho:e and Sodini8 B+ultistage amplifiers ;II


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,ynami Ferformane of Dnit Element

3 Dynamic erformance

of *nit ElementIn a urrent-steering ,358 based on the digital inputs urrent soures are s:ithed to their analog

outputs. The dynami performane of urrent-steering ,35 mainly depends on the follo:ing

limitations M!N

3./ Dynamic %imitations

The different dynami limitations of a unit element are explained in set. $.!.!.8 set. $.!.(. and

$.!.".

3././.


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,ynami Ferformane of Dnit Element

V= nCgd:

(CL+Cdtot:)VG: ;"'. @osh8 +. Steyaert and 2. Sansen8 BSA,/ band:idth limitation for high speed high

resolution urrent-steering 5+4S digital-to-analog onvertersC8 IEEE I5E5S8 !8 pp. !!"-

!!'.

M(N 1. @atos8 3.+. +ar=ues 8+.S.1. Steyaert and 2. Sansen8 B3 !(-bit intrinsi auray high-speed

5+4S ,358C IEEE 1. Solid-State 5iruits vol. ""8 no. !(8 pp. !%-!'8 !*.

M"N 1. 1. 2ikner8 BStudies on 5+4S digital-to-analog onvertersC.Linkping Linkpings

universitet8 ())!.

M$N http##en.:ikipedia.org#:iki#+athematia8aptured8 8 3ugust8 !"8 ()!(

M%N http##:::.:olfram.om#solutions#eduation#higher-eduation#8aptured8 3ugust8 ()8 ()!(

M'N TSEI") 36TI9 5ase Study8 ES8 ISY8 Linkpings universitet.

*"
http://en.wikipedia.org/wiki/Mathematicahttp://www.wolfram.com/solutions/education/higher-education/http://www.wolfram.com/solutions/education/higher-education/http://en.wikipedia.org/wiki/Mathematicahttp://www.wolfram.com/solutions/education/higher-education/


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3pproahes to Improve the ,ynami 5harateristis of 5urrent-Steering ,35s

4 Approac"es to Improve t"e

Dynamic C"aracteristics ofCurrent-Steering DACs

In previous hapter8 :e have explained the various methods of finding output impedane. 2e have

alulated the output-impedane and SA,/ at higher fre=ueny range bet:een ! +H0 to !) ?H0.

Ho:ever8 the output impedanes obtained using the previous methods :ere not promising enough

for '%nm tehnology. In order to improve the output impedane at higher fre=uenies8 various

tehni=ues are introdued in set. %.!8 %.(8 %."and %.$.

4./ C"arge-&emoval-&eplacement (ec"niue

The asoded s:ith tehnology has been disussed in set. $.$.!..It is possible to get better output

and digital signal feed through isolations by using t:o asode transistors. 4n the other hand using

this tehnology8 the dynami performane is dereased due to the asymmetry in rising-falling

transitions and long settling time8 :hih is partiularly disadvantageous in ase of high speed and

high resolution appliations M!N

To improve the performane8 a ne: tehni=ue alled the harge-removal-replaement ;5// (.%-m2 transient-improved urrent-

steering ,35 using harge-removal-replaement tehni=ue8C IEEE 3F553S8 ())'8 pp.!*"-!*'.

M(N L. Aang-1ie8 Y. Yong-Sheng8 L. Shang-Guan8 ?. +ing-Lun8 B5urrent s:ith driver and urrent

soure designs for high-speed urrent-steering ,358C International 5onferene on 3SI,8 ())*8 pp.

"'$-"'&.

M"N T. eng and ,. 5hen8 B4utput Impedane lineari0ation tehni=ue for urrent- steering ,35s8C

IEEE IS53S8 ()))8 pp. ""%&-""').

M$N . Li8 G. 2ei and H. Yang8 B5ode-independent output impedane 3 ne: approah to inreasing

the linearity of urrent- steering ,35s8C IEEE I5ES58 ()!!8 pp.(!'-(!.


95/111

3pproahes to Improve the ,ynami 5harateristis of 5urrent-Steering ,35s

!))


96/111

5onlusions

8 Conclusions

&'% Conclusion

This thesis :ork explains the design of a urrent-steering ,35 using binary :eighted

arhiteture for ahieving high speed and performane at high fre=uenies. This arhiteture has a

lot of advantages over other tehni=ues suh as lo: ost8 po:er effiieny8 beause there are no op-

amps in this design and all the po:er is direted to the output.

The proposed arhiteture ontains several sub bloks suh as unit-elements8 , flip-flops8 s:ithing

sheme8 biasing sheme and all these bloks are designed in adene version '.!.% environment.

The asoded urrent soure is implemented for ahieving the high-output impedane. 2ide s:ing

urrent mirror is hosen for biasing purpose beause it is good in lo: voltage appliations and also

:here high output impedane is re=uired.

The operating fre=ueny is ( ?H08 signal band:idth is %)) +H0 :ith resolution of *-bits. Some

models are designed using +3TL3@8 so the simulation time is redued for generating the input

signal and alulation of dynami performane matries like S6/ and SA,/. This design ;urrent-

steering ,35< is useful in many appliations8 suh as high speed8 high performane and most of the

teleommuniation and mixed signal appliations.

This thesis mainly fouses on optimi0ing a unit-element8 for ahieving the high-output impedane.

Fole-0ero analyses :as done by using different methods suh as8 :ith the help of +athematia tool8numerial alulation ;@ode-plot< and in adene. 2ith the help of pole and 0ero modifiation and

manipulation8 output impedane :as improved at higher fre=uenies. @ased on this8 the parameters

that affet the output impedane and the dominant pole :ere found.

,ifferent tehni=ues are studied for enhanement of output impedane at higher fre=uenies :ith

the help of pole and 0ero modifiation and manipulation. 5omplimentary urrent solution tehni=ue

:as implemented in adene for improving the output impedane. The ob7etive of this arhiteture

is to inrease the output impedane at higher fre=uenies. This arhiteture has given best results at

high fre=uenies8 in the giga-hert0 range.

!)!


97/111

5onlusions

&'( Future work

The :ork done in this thesis an be taken for:ard using some of the ideas mentioned belo:.

3dvaned urrent mirroring tehni=ues an be used to implement the bias iruitry8 sine :ide

s:ing urrent mirror used in this :ork :ill not aurately opy the urrent due to drain- soure

voltage variations.

4ther tehni=ues like8 harge removal replaement tehni=ue8 urrent s:ith driver and urrent

soure design tehni=ue8 output impedane lineari0ation tehni=ue8 et.8 an also be tried and

analysed to improve the output impedane at higher fre=uenies8 :ith the help of pole and 0ero

modifiation#manipulation8 sine the omplimentary urrent solution tehni=ue improves SA,/

only !) d@ at higher fre=uenies.

To improve the dynami performanes of the ,358 a filter an introdued after the ,35. It :ill

help to redue noise.

To improve output impedane8 :e used a simple differential s:ith in our ase. @etter s:ithing

tehni=ues like dummy transistors8 bootstrapping tehni=ue8 et.8 an be tried.

The next level is to do the layout. Layout simulations an be performed and those layout results an

be ompared :ith transistor level results and see the differene bet:een transistor level result and

layout level result.

!)(


98/111


99/111


100/111


101/111

3ppendix

gds1* gds7 $ 4 cl7 c* cy gds1 gds* gds7 $ 4 cl7 c cy* gds1 gds* gds7 : 1* cl*

c* cy* gds1 gds* gds7 $ 4 cl* c cy7 gds1 gds* gds7 : 4 cl7 c7 gds** gds7 : 7

cl7 c* cy gds** gds7 $ 7 cl* c7 cy gds** gds7 $ 7 cl7 c cy* gds** gds7 $ 4

cl* c* cy* gds** gds7 $7 cl* c cy7 gds** gds7 $ 7 cl7 c* cy gds1 gds7* $ 4

cl* c* cy* gds1 gds7* $ 7 cl c* cy7 gds1 gds7* : 4 cl7 c7 gds* gds7* $ 7

cl7 c* cy gds* gds7* : 7 cl* c7 cy gds* gds7* $ 4 cl* c* cy* gds* gds7* $ 7

cl c7 cy* gds* gds7* $ 7 cl c* cy7 gds* gds7* : * cl7 c7 gds77 : 4 cl* c7

cy gds77 : 4 cl c7 cy* gds77 : * c7 cy7 gds77 $ 4 cl7 cy7 gds1* gm* $ 7 cl7

c cy* gds1 gds* gm* $ 1* cl7 cy7 gds1 gds* gm* $ 4 cl7 c* cy gds** gm* $ 1*

cl7 c cy* gds** gm* $ 4 cl7 cy7 gds** gm* :4 cl7 c cy* gds1 gds7 gm* :4

cl* c cy7 gds1 gds7 gm* $ 7 cl7 c* cy gds* gds7 gm* : 4 cl7 c cy* gds*

gds7 gm* : 4 cl* c* cy* gds* gds7 gm* : 4 cl* c cy7 gds* gds7 gm* : 7 cl7

c* cy gds7* gm* : 4 cl* c* cy* gds7* gm* : 7 cl c* cy7 gds7* gm* : 4 cl7

cy7 gds1 gm** : 4 cl7 c cy* gds* gm** : 4 cl7 cy7 gds* gm** $ 7 cl7 c cy*

gds7 gm** $ 7 cl* c cy7 gds7 gm** $ * cl7 cy7 gm*7 : 7 cl7 c cy* gds1* gm7: 4 cl7 c* cy gds1 gds* gm7 : 4 cl7 c cy* gds1 gds* gm7 $ 4 cl7 c7 gds**

gm7 $ 7 cl7 c* cy gds** gm7 : 7 cl7 c cy* gds** gm7 : 4 cl7 c* cy gds1

gds7 gm7 : 4 cl* c* cy* gds1 gds7 gm7 $ 1* cl7 c7 gds* gds7 gm7 : 4 cl7 c*

cy gds* gds7 gm7 $ cl* c7 cy gds* gds7 gm7 : 4 cl* c* cy* gds* gds7 gm7 $ 4

cl7 c7 gds7* gm7 $ 1* cl* c7 cy gds7* gm7 $ 4 cl c7 cy* gds7* gm7 $ 4 cl7

c cy* gds1 gm* gm7 : 7 cl7 c* cy gds* gm* gm7 $ 4 cl7 c cy* gds* gm* gm7

$ 4 cl7 c* cy gds7 gm* gm7 $ 4 cl* c* cy* gds7 gm* gm7 :7 cl7 c cy* gm**

gm7 $ 7 cl7 c* cy gds1 gm7* : 4 cl7 c7 gds* gm7* $ 7 cl7 c* cy gds* gm7* :

4 cl7 c7 gds7 gm7* : 4 cl* c7 cy gds7 gm7* : 7 cl7 c* cy gm* gm7* $ *

cl7 c7 gm77 ; ) ) )* cl7 cy7 gds17 $ 7 cl7 c cy* gds1* gds* : 4 cl7 cy7 gds1*

gds* $ 7 cl7 c* cy gds1 gds** : 7 cl7 c cy* gds1 gds** : 4 cl7 cy7 gds1 gds**

: * cl7 c7 gds*7 : 4 cl7 c* cy gds*7 : 4 cl7 c cy* gds*7 : * cl7 cy7 gds*7 $

7 cl7 c cy* gds1* gds7 $ 7 cl* c cy7 gds1* gds7 $ 4 cl7 c* cy gds1 gds*

gds7 $ 4 cl7 c cy* gds1 gds* gds7 : 1* cl* c* cy* gds1 gds* gds7 $ 4 cl* c

cy7 gds1 gds* gds7 : 4 cl7 c7 gds** gds7 : 7 cl7 c* cy gds** gds7 $ 7 cl*

c7 cy gds** gds7 $ 7 cl7 c cy* gds** gds7 $ 4 cl* c* cy* gds** gds7 $ 7 cl*

c cy7 gds** gds7 $ 7 cl7 c* cy gds1 gds7* $ 4 cl* c* cy* gds1 gds7* $ 7 cl

c* cy7 gds1 gds7* : 4 cl7 c7 gds* gds7* $ 7 cl7 c* cy gds* gds7* : 7 cl*

c7 cy gds* gds7* $ 4 cl* c* cy* gds* gds7* $ 7 cl c7 cy* gds* gds7* $ 7 cl

c* cy7 gds* gds7* : * cl7 c7 gds77 : 4 cl* c7 cy gds77 : 4 cl c7 cy*

gds77 : * c7 cy7 gds77 $ 4 cl7 cy7 gds1* gm* $ 7 cl7 c cy* gds1 gds* gm* $ 1*cl7 cy7 gds1 gds* gm* $ 4 cl7 c* cy gds** gm* $ 1* cl7 c cy* gds** gm* $ 4

cl7 cy7 gds** gm* : 4 cl7 c cy* gds1 gds7 gm* : 4 cl* c cy7 gds1 gds7 gm* $

7 cl7 c* cy gds* gds7 gm* : 4 cl7 c cy* gds* gds7 gm* :4 cl* c* cy* gds*

gds7 gm* : 4 cl* c cy7 gds* gds7 gm* : 7 cl7 c* cy gds7* gm* : 4 cl* c*

cy* gds7* gm* : 7 cl c* cy7 gds7* gm* : 4 cl7 cy7 gds1 gm** : 4 cl7 c cy*

gds* gm** : 4 cl7 cy7 gds* gm** $ 7 cl7 c cy* gds7 gm** $ 7 cl* c cy7 gds7

gm** $ * cl7 cy7 gm*7 : 7 cl7 c cy* gds1* gm7 : 4 cl7 c* cy gds1 gds* gm7 :

4 cl7 c cy* gds1 gds* gm7 $ 4 cl7 c7 gds** gm7 $ 7 cl7 c* cy gds** gm7 : 7

cl7 c cy* gds** gm7 : 4 cl7 c* cy gds1 gds7 gm7 : 4 cl* c* cy* gds1 gds7

gm7 $ 1* cl7 c7 gds* gds7 gm7 : 4 cl7 c* cy gds* gds7 gm7 $ 7 cl* c7 cy

gds* gds7 gm7 : 4 cl* c* cy* gds* gds7 gm7 $ 4 cl7 c7 gds7* gm7 $ 1* cl*

!)'


102/111

Fole-ero analysis using 2olfram +athematia tool

c7 cy gds7* gm7 $ 4 cl c7 cy* gds7* gm7 $ 4 cl7 c cy* gds1 gm* gm7 : 7

cl7 c* cy gds* gm* gm7 $ 4 cl7 c cy* gds* gm* gm7 $ 4 cl7 c* cy gds7 gm*

gm7 $ 4 cl* c* cy* gds7 gm* gm7 : 7 cl7 c cy* gm** gm7 $ 7 cl7 c* cy

gds1 gm7* : 4 cl7 c7 gds* gm7* $ 7 cl7 c* cy gds* gm7* : 4 cl7 c7 gds7

gm7* : 4 cl* c7 cy gds7 gm7* : 7 cl7 c* cy gm* gm7* $ * cl7 c7 gm77+ * : 5

)$ )$cl cy gds1 $ cl c gds* $ cl cy gds* $ cl c gds7 $ c cy gds7 : cl cy gm* : cl c

gm7+ * $ 7 cl c cy )$cl gds1 gds* $ cl gds1 gds7 $ cy gds1 gds7 $ cl gds* gds7 $ c

gds* gds7 $ cy gds* gds7 : cl gds7 gm* : cy gds7 gm* : cl gds1 gm7 : cl gds* gm7 $ cl

gm* gm7+ + 7+ + 0.2+ 0.77 + $ )1/7* )0.77+ ccycl+ )* cl7 cy7 gds17 $ 7 cl7 c cy*

gds1* gds* : 4 cl7 cy7 gds1* gds* $ 7 cl7 c* cy gds1 gds** : 7 cl7 c cy*

gds1 gds** : 4 cl7 cy7 gds1 gds** : * cl7 c7 gds*7 : 4 cl7 c* cy gds*7 : 4

cl7 c cy* gds*7 : * cl7 cy7 gds*7 $ 7 cl7 c cy* gds1* gds7 $ 7 cl* c cy7

gds1* gds7 $ 4 cl7 c* cy gds1 gds* gds7 $ 4 cl7 c cy* gds1 gds* gds7 : 1* cl*

c* cy* gds1 gds* gds7 $ 4 cl* c cy7 gds1 gds* gds7 : 4 cl7 c7 gds** gds7 : 7

cl7 c* cy gds** gds7 $ 7 cl* c7 cy gds** gds7 $ 7 cl7 c cy* gds** gds7 $ 4cl* c* cy* gds** gds7 $ 7 cl* c cy7 gds** gds7 $ 7 cl7 c* cy gds1 gds7* $ 4

cl* c* cy* gds1 gds7* $ 7 cl c* cy7 gds1 gds7* : 4 cl7 c7 gds* gds7* $ 7

cl7 c* cy gds* gds7* : 7 cl* c7 cy gds* gds7* $ 4 cl* c* cy* gds* gds7* $ 7

cl c7 cy* gds* gds7* $ 7 cl c* cy7 gds* gds7* : * cl7 c7 gds77 : 4 cl* c7

cy gds77 : 4 cl c7 cy* gds77 : * c7 cy7 gds77 $ 4 cl7 cy7 gds1* gm* $ 7 cl7

c cy* gds1 gds* gm* $ 1* cl7 cy7 gds1 gds* gm* $ 4 cl7 c* cy gds** gm* $ 1*

cl7 c cy* gds** gm* $ 4 cl7 cy7 gds** gm* : 4 cl7 c cy* gds1 gds7 gm* : 4

cl* c cy7 gds1 gds7 gm* $ 7 cl7 c* cy gds* gds7 gm* : 4 cl7 c cy* gds*

gds7 gm* : 4 cl* c* cy* gds* gds7 gm* : 4 cl* c cy7 gds* gds7 gm* : 7 cl7

c* cy gds7* gm* : 4 cl* c* cy* gds7* gm* : 7 cl c* cy7 gds7* gm* : 4 cl7

cy7 gds1 gm** : 4 cl7 c cy* gds* gm** : 4 cl7 cy7 gds* gm** $ 7 cl7 c cy*

gds7 gm** $ 7 cl* c cy7 gds7 gm** $ * cl7 cy7 gm*7 : 7 cl7 c cy* gds1* gm7

: 4 cl7 c* cy gds1 gds* gm7 : 4 cl7 c cy* gds1 gds* gm7 $ 4 cl7 c7 gds**

gm7 $ 7 cl7 c* cy gds** gm7 : 7 cl7 c cy* gds** gm7 : 4 cl7 c* cy gds1

gds7 gm7 : 4 cl* c* cy* gds1 gds7 gm7 $ 1* cl7 c7 gds* gds7 gm7 : 4 cl7 c*

cy gds* gds7 gm7 $ 7 cl* c7 cy gds* gds7 gm7 : 4 cl* c* cy* gds* gds7 gm7 $

4 cl7 c7 gds7* gm7 $ 1* cl* c7 cy gds7* gm7 $ 4 cl c7 cy* gds7* gm7 $ 4 cl7

c cy* gds1 gm* gm7 : 7 cl7 c* cy gds* gm* gm7 $ 4 cl7 c cy* gds* gm* gm7

$ 4 cl7 c* cy gds7 gm* gm7 $ 4 cl* c* cy* gds7 gm* gm7 : 7 cl7 c cy*

gm** gm7 $ 7 cl7 c* cy gds1 gm7* : 4 cl7 c7 gds* gm7* $ 7 cl7 c* cy gds*

gm7* : 4 cl7 c7 gds7 gm7* : 4 cl* c7 cy gds7 gm7* : 7 cl7 c* cy gm* gm7*$ * cl7 c7 gm77 : ) ) )* cl7 cy7 gds17 $ 7 cl7 c cy* gds1* gds* : 4 cl7 cy7

gds1* gds* $ 7 cl7 c* cy gds1 gds** : 7 cl7 c cy* gds1 gds** : 4 cl7 cy7

gds1 gds** : * cl7 c7 gds*7 : 4 cl7 c* cy gds*7 : 4 cl7 c cy* gds*7 : * cl7

cy7 gds*7 $ 7 cl7 c cy* gds1* gds7 $ 7 cl* c cy7 gds1* gds7 $ 4 cl7 c* cy

gds1 gds* gds7 $ 4 cl7 c cy* gds1 gds* gds7 : 1* cl* c* cy* gds1 gds* gds7 $ 4

cl* c cy7 gds1 gds* gds7 : 4 cl7 c7 gds** gds7 : 7 cl7 c* cy gds** gds7 $ 7

cl* c7 cy gds** gds7 $ 7 cl7 c cy* gds** gds7 $ 4 cl* c* cy* gds** gds7 $ 7

cl* c cy7 gds** gds7 $ 7 cl7 c* cy gds1 gds7* $ 4 cl* c* cy* gds1 gds7* $ 7

cl c* cy7 gds1 gds7* : 4 cl7 c7 gds* gds7* $ 7 cl7 c* cy gds* gds7* : 7 cl*

c7 cy gds* gds7* $ 4 cl* c* cy* gds* gds7* $ 7 cl c7 cy* gds* gds7* $ 7 cl

c* cy7 gds* gds7* : * cl7 c7 gds77 : 4 cl* c7 cy gds77 : 4 cl c7 cy*

!)&


103/111


104/111


105/111

3ppendix

$4cl*c*cy*gds**gds7 $7cl*ccy7gds**gds7 $ 7cl7c*cygds1gds7*

$4cl*c*cy*gds1gds7* $7clc*cy7gds1gds7* :4cl7c7gds*gds7*

$7cl7c*cygds*gds7* :7cl*c7cygds*gds7* $4cl*c*cy*gds*gds7*

$7clc7cy*gds*gds7* $ 7clc*cy7gds*gds7* : *cl7c7gds77

:4cl*c7cygds77 : 4clc7cy*gds77 : *c7cy7gds77$ 4 cl7 cy7 gds1* gm*

$7cl7ccy*gds1gds*gm* $ 1*cl7cy7 gds1 gds*gm* $4cl7c*cygds**gm*

$1*cl7ccy*gds**gm* $ 4cl7cy7gds**gm* : 4cl7ccy*gds1gds7gm*

:4cl*ccy7gds1gds7gm* $7cl7c*cy gds*gds7gm* :4cl7ccy*gds*gds7gm*

:4cl*c*cy*gds*gds7gm* : 4cl*ccy7gds*gds7gm* :7cl7c*cygds7*gm*

:4cl*c*cy*gds7* gm* :7clc*cy7gds7*gm* : 4cl7cy7gds1gm** :

4cl7ccy*gds*gm** : 4cl7cy7gds*gm** $7cl7ccy*gds7gm**

$7cl*ccy7gds7gm** $ *cl7cy7gm*7 :7cl7ccy*gds1*gm7

:4cl7c*cygds1gds*gm7 :4cl7ccy*gds1gds*gm7 $4cl7c7gds**gm7 $

7cl7c*cygds**gm7 :7cl7ccy*gds**gm7 : 4cl7c*cygds1gds7gm7

:4cl*c*cy* gds1gds7gm7 $1*cl7c7gds*gds7gm7 :4cl7c*cygds*gds7gm7$7cl*c7cygds*gds7gm7 :4cl*c*cy*gds*gds7gm7 $4cl7c7gds7*gm7 $

1*cl*c7cygds7*gm7 $4clc7cy*gds7*gm7 $4cl7ccy*gds1gm*gm7

:7cl7c*cygds*gm*gm7 $4cl7ccy*gds*gm*gm7 $4cl7c*cygds7gm*gm7 $

4cl*c*cy*gds7gm*gm7 :7cl7ccy*gm**gm7 $7cl7c*cygds1gm7* :

4cl7c7gds*gm7* $7cl7c*cygds*gm7* : 4cl7c7gds7gm7*

:4cl*c7cygds7gm7* : 7cl7c*cygm*gm7* $*cl7c7gm77 :

) ) )*cl7cy7gds17 $7 cl7 c cy* gds1* gds* :4cl7cy7gds1*gds*

$7cl7c*cygds1gds** :7cl7ccy*gds1gds** :4cl7cy7gds1gds** :

*cl7c7gds*7 :4 cl7 c* cy gds*7 : 4 cl7 c cy* gds*7 :* cl7 cy7 gds*7 $ 7

cl7 c cy* gds1* gds7 $7cl* c cy7 gds1* gds7 $ 4 cl7 c* cy gds1 gds* gds7

$4 cl7 c cy* gds1 gds* gds7 :1* cl* c* cy* gds1 gds* gds7 $4 cl* c cy7

gds1 gds* gds7 :4 cl7 c7 gds** gds7 :7 cl7 c* cy gds** gds7 $7 cl* c7 cy

gds** gds7 $7 cl7 c cy* gds** gds7 $ 4 cl* c* cy* gds** gds7 $ 7 cl* c cy7

gds** gds7 $ 7 cl7 c* cy gds1 gds7* $4 cl* c* cy* gds1 gds7* $7 cl c* cy7

gds1 gds7* :4 cl7 c7 gds* gds7* $7 cl7 c* cy gds* gds7* :7 cl* c7 cy gds*

gds7* $4 cl* c* cy* gds* gds7* $7 cl c7 cy* gds* gds7* $7 cl c* cy7 gds*

gds7* : * cl7 c7 gds77 :4 cl* c7cygds77 : 4 cl c7 cy* gds77 :* c7 cy7

gds77 $ 4 cl7 cy7 gds1* gm* $7 cl7 c cy* gds1 gds* gm* $ 1* cl7 cy7 gds1 gds*

gm* $4 cl7 c*cy gds** gm* $1* cl7 c cy* gds** gm* $4 cl7 cy7 gds** gm* : 4

cl7 c cy* gds1 gds7 gm* :4 cl* c cy7 gds1 gds7 gm* $7 cl7 c* cy gds* gds7

gm* :4 cl7 c cy* gds* gds7 gm* : 4 cl* c* cy* gds* gds7 gm* :4 cl* c cy7gds* gds7 gm* :7 cl7 c* cy gds7* gm* :4 cl* c* cy* gds7* gm* :7 cl c*

cy7 gds7* gm* :4 cl7 cy7 gds1 gm** : 4 cl7 c cy* gds* gm**

:4cl7cy7gds*gm** $7cl7ccy*gds7gm** $7cl*ccy7gds7gm** $ * cl7 cy7

gm*7 :7 cl7 c cy* gds1* gm7 : 4 cl7 c* cy gds1 gds* gm7 :4 cl7 c cy*

gds1 gds* gm7 $4 cl7 c7 gds** gm7 $7cl7c*cygds**gm7 :

7cl7ccy*gds**gm7 :4cl7c*cygds1gds7gm7 :4cl*c*cy*gds1gds7gm7

$1*cl7 c7 gds* gds7 gm7 : 4 cl7 c* cy gds* gds7 gm7 $7 cl* c7 cy gds* gds7

gm7 : 4 cl* c* cy* gds* gds7 gm7 $ 4cl7c7 gds7* gm7 $1* cl* c7 cy gds7*

gm7 $4 cl c7 cy* gds7* gm7 $4 cl7 c cy* gds1 gm* gm7 :7 cl7 c* cy gds*

gm* gm7 $4 cl7 c cy* gds* gm* gm7 $4 cl7 c* cy gds7 gm* gm7 $4 cl* c*

cy* gds7 gm* gm7 :7 cl7 c cy* gm** gm7 $ 7 cl7 c* cy gds1 gm7* :4 cl7

!!)


106/111


c7 gds* gm7* $ 7 cl7 c* cy gds* gm7* :4cl7c7gds7gm7* :

4cl*c7cygds7gm7* : 7cl7c*cygm*gm7* $ *cl7c7gm77+ * :5 )$ )$clcygds1

$ clcgds* $ clcygds* $clcgds7 $ ccygds7 : clcygm* :clc gm7+ * $7clccy )$

clgds1gds* $ clgds1gds7 $cygds1gds7 $ clgds*gds7 $ cgds*gds7 $ cygds*gds7 :

clgds7gm* : cygds7gm* :clgds1gm7 : clgds*gm7 $clgm*gm7+ + 7+ 0.2+ )1/7+ + + + + 3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%

%%


107/111

3ppendix


$7clc7cy*gds*gds7* $7clc*cy7gds*gds7* : *cl7c7gds77 :

4cl*c7cygds77 :4clc7cy*gds77 : *c7cy7gds77 $4cl7cy7gds1*gm*

$7cl7ccy*gds1gds*gm* $1*cl7cy7gds1gds*gm* $ 4cl7c*cygds**gm*

$1*cl7ccy*gds**gm* $4cl7cy7gds**gm* :4cl7ccy*gds1gds7gm*

:4cl*ccy7gds1gds7gm* $7cl7c*cygds*gds7gm* : 4cl7ccy*gds*gds7gm*

:4cl*c*cy*gds*gds7gm* :4cl*ccy7gds*gds7gm* :7cl7c*cy gds7*gm* :

4cl*c*cy*gds7*gm* :7clc*cy7gds7*gm* :4cl7cy7gds1gm** :

4cl7ccy*gds*gm** :4cl7cy7gds*gm** $7cl7ccy*gds7gm**



7cl7c*cygds**gm7 : 7cl7ccy*gds**gm7 : 4cl7c*cygds1gds7gm7 :

4cl*c*cy*gds1gds7gm7 $1*cl7c7gds*gds7gm7 : 4cl7c*cygds*gds7gm7 $

7cl*c7cygds*gds7gm7 :4cl*c*cy*gds*gds7gm7 $4cl7c7gds7*gm7$

1*cl*c7cygds7*gm7 $4clc7cy*gds7*gm7 $4cl7ccy*gds1gm*gm7:7cl7c*cygds*gm*gm7 $ 4cl7ccy*gds*gm*gm7 $4cl7c*cygds7gm*gm7

$4cl*c*cy*gds7gm*gm7 :7cl7ccy*gm**gm7 $ 7cl7c*cygds1gm7* :

4cl7c7gds*gm7* $ 7cl7c*cygds*gm7* :4cl7c7gds7gm7* :

4cl*c7cygds7gm7* :7cl7c*cygm*gm7* $ *cl7c7gm77+ * :5 )$ )$clcygds1 $

clcgds* $ clcygds* $clcgds7 $ ccygds7 : clcygm* :clcgm7+ * $7clccy )$

clgds1gds* $ clgds1gds7 $cygds1gds7 $ clgds*gds7 $cgds*gds7 $ cygds*gds7 :

clgds7gm* :cygds7gm* : clgds1gm7 : clgds*gm7 $clgm*gm7+ + 7+ 0.2+ )1/7+ + : )1/

)4* )1/7+ clccy+ + )imag )1 : i )7+ 0.2+ )*cl7cy7gds17 $7cl7ccy*gds1*gds*

:4cl7cy7gds1*gds* $7cl7c*cygds1gds** :7cl7ccy*gds1gds**

:4cl7cy7gds1gds** : *cl7c7gds*7 :4cl7c*cygds*7 : 4cl7ccy*gds*7

:*cl7cy7gds*7 $ 7cl7ccy*gds1*gds7 $7cl*ccy7gds1*gds7

$4cl7c*cygds1gds*gds7 $4cl7ccy*gds1gds*gds7 :

1*cl*c*cy*gds1gds*gds7 $4cl*ccy7gds1gds*gds7 :4cl7c7gds**gds7

:7cl7c*cygds**gds7 $7cl*c7cygds**gds7 $7cl7ccy*gds**gds7

$4cl*c*cy*gds**gds7 $7cl*ccy7gds**gds7 $ 7cl7c*cygds1gds7*

$4cl*c*cy*gds1gds7* $7clc*cy7gds1gds7* :4cl7c7gds*gds7*


$7clc7cy*gds*gds7* $ 7clc*cy7gds*gds7* : *cl7c7gds77

:4cl*c7cygds77 : 4clc7cy*gds77 : *c7cy7gds77$ 4 cl7 cy7 gds1* gm*

$7cl7ccy*gds1gds*gm* $ 1*cl7cy7 gds1 gds*gm* $4cl7c*cygds**gm*

$1*cl7ccy*gds**gm* $ 4cl7cy7gds**gm* : 4cl7ccy*gds1gds7gm*:4cl*ccy7gds1gds7gm* $7cl7c*cy gds*gds7gm* :4cl7ccy*gds*gds7gm*

:4cl*c*cy*gds*gds7gm* : 4cl*ccy7gds*gds7gm* :7cl7c*cygds7*gm*

:4cl*c*cy*gds7* gm* :7clc*cy7gds7*gm* : 4cl7cy7gds1gm** :

4cl7ccy*gds*gm** : 4cl7cy7gds*gm** $7cl7ccy*gds7gm**



7cl7c*cygds**gm7 :7cl7ccy*gds**gm7 : 4cl7c*cygds1gds7gm7

:4cl*c*cy* gds1gds7gm7 $1*cl7c7gds*gds7gm7 :4cl7c*cygds*gds7gm7

$7cl*c7cygds*gds7gm7 :4cl*c*cy*gds*gds7gm7 $4cl7c7gds7*gm7 $

1*cl*c7cygds7*gm7 $4clc7cy*gds7*gm7 $4cl7ccy*gds1gm*gm7

:7cl7c*cygds*gm*gm7 $4cl7ccy*gds*gm*gm7 $4cl7c*cygds7gm*gm7 $

!!(


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4cl*c*cy*gds7gm*gm7 :7cl7ccy*gm**gm7 $7cl7c*cygds1gm7* :

4cl7c7gds*gm7* $7cl7c*cygds*gm7* : 4cl7c7gds7gm7*

:4cl*c7cygds7gm7* : 7cl7c*cygm*gm7* $*cl7c7gm77 :

) ) )*cl7cy7gds17 $7 cl7 c cy* gds1* gds* :4cl7cy7gds1*gds*

$7cl7c*cygds1gds** :7cl7ccy*gds1gds** :4cl7cy7gds1gds** :

*cl7c7gds*7 :4 cl7 c* cy gds*7 : 4 cl7 c cy* gds*7 :* cl7 cy7 gds*7 $ 7

cl7 c cy* gds1* gds7 $7cl* c cy7 gds1* gds7 $ 4 cl7 c* cy gds1 gds* gds7

$4 cl7 c cy* gds1 gds* gds7 :1* cl* c* cy* gds1 gds* gds7 $4 cl* c cy7

gds1 gds* gds7 :4 cl7 c7 gds** gds7 :7 cl7 c* cy gds** gds7 $7 cl* c7 cy

gds** gds7 $7 cl7 c cy* gds** gds7 $ 4 cl* c* cy* gds** gds7 $ 7 cl* c cy7

gds** gds7 $ 7 cl7 c* cy gds1 gds7* $4 cl* c* cy* gds1 gds7* $7 cl c* cy7

gds1 gds7* :4 cl7 c7 gds* gds7* $7 cl7 c* cy gds* gds7* :7 cl* c7 cy gds*

gds7* $4 cl* c* cy* gds* gds7* $7 cl c7 cy* gds* gds7* $7 cl c* cy7 gds*

gds7* : * cl7 c7 gds77 :4 cl* c7cygds77 : 4 cl c7 cy* gds77 :* c7 cy7

gds77 $ 4 cl7 cy7 gds1* gm* $7 cl7 c cy* gds1 gds* gm* $ 1* cl7 cy7 gds1 gds*gm* $4 cl7 c*cy gds** gm* $1* cl7 c cy* gds** gm* $4 cl7 cy7 gds** gm* : 4

cl7 c cy* gds1 gds7 gm* :4 cl* c cy7 gds1 gds7 gm* $7 cl7 c* cy gds* gds7

gm* :4 cl7 c cy* gds* gds7 gm* : 4 cl* c* cy* gds* gds7 gm* :4 cl* c cy7

gds* gds7 gm* :7 cl7 c* cy gds7* gm* :4 cl* c* cy* gds7* gm* :7 cl c*

cy7 gds7* gm* :4 cl7 cy7 gds1 gm** : 4 cl7 c cy* gds* gm**

:4cl7cy7gds*gm** $7cl7ccy*gds7gm** $7cl*ccy7gds7gm** $ * cl7 cy7

gm*7 :7 cl7 c cy* gds1* gm7 : 4 cl7 c* cy gds1 gds* gm7 :4 cl7 c cy*

gds1 gds* gm7 $4 cl7 c7 gds** gm7 $7cl7c*cygds**gm7 :

7cl7ccy*gds**gm7 :4cl7c*cygds1gds7gm7 :4cl*c*cy*gds1gds7gm7

$1*cl7 c7 gds* gds7 gm7 : 4 cl7 c* cy gds* gds7 gm7 $7 cl* c7 cy gds* gds7

gm7 : 4 cl* c* cy* gds* gds7 gm7 $ 4cl7c7 gds7* gm7 $1* cl* c7 cy gds7*

gm7 $4 cl c7 cy* gds7* gm7 $4 cl7 c cy* gds1 gm* gm7 :7 cl7 c* cy gds*

gm* gm7 $4 cl7 c cy* gds* gm* gm7 $4 cl7 c* cy gds7 gm* gm7 $4 cl* c*

cy* gds7 gm* gm7 :7 cl7 c cy* gm** gm7 $ 7 cl7 c* cy gds1 gm7* :4 cl7

c7 gds* gm7* $ 7 cl7 c* cy gds* gm7* :4cl7c7gds7gm7* :

4cl*c7cygds7gm7* : 7cl7c*cygm*gm7* $ *cl7c7gm77+ * :5 )$ )$clcygds1

$ clcgds* $ clcygds* $clcgds7 $ ccygds7 : clcygm* :clc gm7+ * $7clccy )$

clgds1gds* $ clgds1gds7 $cygds1gds7 $ clgds*gds7 $ cgds*gds7 $ cygds*gds7 :

clgds7gm* : cygds7gm* :clgds1gm7 : clgds*gm7 $clgm*gm7+ + 7+ 0.2+ )1/7+ + + + + 3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hold on

f logs"ace )0,10,10*5+ 3

s 1i*"if3

9 ) )s$91+ . )s$9*+ + ./ ) )s$"1+ . )s$"*+ . )s$"7+ + 3

figure )*+

9oom on3

grid on3

if )!** l*1+

col>#>3

elseif )!*1 l*7+

!!"


109/111

3ppendix

col>r>3

elseif )!** l*7+

col>g>3

elseif )!*7 l*1+

col>y>3

else

col>b>3

end

semilog )f,d?*0 )9+ ,col+

label )>@reuency )B9+ >+ 3

ylabel )>Magnitude )d?+ >+ 3

title )>Cut"ut Im"edance from Mathematica by &arying length>+ 3

hold off

end

end

)'- .umerical Calculation for ole0ero Location

The numerator and denominator of the transfer funtion :ere alulated by hand alulation

and the values :ere used to alulate the poles and 0eroes in +3TL3@ using bode plot.

%% Dumerical calculation of "oles and 9eroes using bode "lot

numE155.06*10$70 7.02710$18 1.F4*210$5G3

den E$1.67110$57 $7.*8410$77 $*.726810$1F 2.*0410$10G3mytftf )num,den+ 3

tf*ss )num,den+ 3 % Hon&ert this to tate "ace form

E9,",#Gtf*9" )num,den+ % Hon&ert to 9ero$"ole$gain form

< bodeo"tions3 % et "hase &isibility to off and freuency units to B9 in o"tions

3

B9>3 % Hreate "lot !ith the o"tions s"ecified by ariation in 5adene

% ! 0.4

adlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/!idth 0.4.cs&>+ 3

1 a ),1+ 3

y1 a ),*+ 3

semilog )1, y1,>b>+

hold on

% ! 1.*

bdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/!idth 1.*.cs&>+ 3

*b ),1+ 3

y*b ),*+ 3

semilog )*, y*, >r>+

% ! 1.8

% bdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/!idth 1.8.cs&> + 3

% *b ),1+ 3

% y*b ),*+ 3% semilog )*, y*, >#>+

% ! *.5

cdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/!idth *.5.cs&>+ 3

7c ),1+ 3

y7c ),*+ 3

semilog )7, y7, >g>+

figure )1+ 3

% 9oom on3

% grid on3

label )>@reuency )B9+ >+ 3

ylabel )>Magnitude )d?+ >+ 3

title )>Cut"ut Im"edance from cadence>+ 3

hold off

%% Hhanging s!itch length to reach high im"edance at 1LB9

% ( 0.4

adlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/length 0.7.cs&>+ 3

1 a ),1+ 3

y1 a ),*+ 3

semilog )1, y1,>b>+

hold on

% ( 1.*bdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/length 0.4.cs&>+ 3

*b ),1+ 3

y*b ),*+ 3

semilog )*, y*, >r>+

% (1.8

% bdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/!idth 1.8.cs&> + 3

% *b ),1+ 3

% y*b ),*+ 3

% semilog )*, y*, >#>+

% ( *.5

cdlmread )>/site/edu/es/KNC??/digOf/digOfPac@ir/sim/length 0.F.cs&>+ 3

!!%


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fulltext03 ok esp

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