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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
,epartment of Eletrial Engineering
Linkoping university
Linkoping ()!"
"
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$
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resentation date
()!(-)'-!(
u!lis"ing date #Electronic version$
Department and Division
Eletronis Systems
,epartment of Eletrial Engineering
%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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Implementation of an *-bit ,#3 5onverter
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.
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Implementation of an *-bit ,#3 5onverter
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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Implementation of an *-bit ,#3 5onverter
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.(!'-(!.
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3pproahes to Improve the ,ynami 5harateristis of 5urrent-Steering ,35s
!))
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8/12/2019 Fulltext03 Ok Esp
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.
!)!
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8/12/2019 Fulltext03 Ok Esp
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.
!)(
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8/12/2019 Fulltext03 Ok Esp
98/111
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8/12/2019 Fulltext03 Ok Esp
99/111
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8/12/2019 Fulltext03 Ok Esp
100/111
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8/12/2019 Fulltext03 Ok Esp
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*
!)'
-
8/12/2019 Fulltext03 Ok Esp
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*
!)&
-
8/12/2019 Fulltext03 Ok Esp
103/111
-
8/12/2019 Fulltext03 Ok Esp
104/111
-
8/12/2019 Fulltext03 Ok Esp
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
!!)
-
8/12/2019 Fulltext03 Ok Esp
106/111
Fole-ero analysis using 2olfram +athematia tool
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%
%%
-
8/12/2019 Fulltext03 Ok Esp
107/111
3ppendix
$7cl7c*cygds*gds7* :7cl*c7cygds*gds7* $4cl*c*cy*gds*gds7*
$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**
$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+ * :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*
$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 $
!!(
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Fole-ero analysis using 2olfram +athematia tool
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+
!!"
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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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