1. No category

ACTIVE RC・s挙NT嚇事Is OF SINGLE AND MULTIVARIABLE
-NETWORK FUNCTIONS USING OPERATIONAL AMPLIFIERS
M. T. AHMED
A DISSERTATiON SUBMITTED FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN ELECTRICAL ENGINEERING
OF THE
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
Nove加aber, :ioア唾
(i')
CER 質FICA']E
Certified that t加 t加sis entitled, 'tAc 七ive RC
s伽the離s of Sing 加 and Multivariable Network F叫ctions
・
、響地 o胆rational Amplifiers 、、」 which is bei鵬 submitted
切し町．い M.T. Ahmed f 叩 the degree of Doctor of Philosophy
In Electrical E鵬me e ? i鵬 of the Indian Institute,of
,
恥 C 血ol略 y, Delhi, is a record of the s tude nts own work
cai'ried out by him un肥r my supervision and guidance.
The matter embodied in this ti治 sis has no七 keri submitted
fGr the award of any other degree.
19孤
Da te d:Nov . i 974
乙 C 司一魯り
S.C 。 DUTTA R叫 ）
費 ofe ss s or .De par 七men七 of Elec 切leaよ E昭g.,
Indian Institute;of 喪 Chaal 喝y,
New Delhi-110029 。
AC畑叫LEDGE皿NT
Tle au七hor wishes to express his profound gratitu肥
to his 叫胆ry i s or，即of. S.0 . Du t 七a Roy, for his valuable
guidance and co鵬 tant 癌hc ourage 肥 nt duri 鵬 the entire
course Of，七 his dissertation 。 丑嶋 auth叩 is also grateful
to Pr叫・＆Yr ・Mi tra, 叱 the 血iversity of Calif 叩nj, Davis,
f or 雄s鵬ゆnerous help and also for providi旭 s t irnula t i鵬
advice and. discussiots, es 胆 C i, a i i y 胆 rtaini鵬 to
active multivariable s翼1七 hes is.
Thanks are also due 七 o 即of 。 Ja la lud di' ・jof AUg町h
Muslim Ikiiversity,for his encourage 肥 nt,and 七。 七he authoー
rities of エ．I T.,Del吐， f 叩 providing research facili 七ie s.
Appreciation is exten的d. to 七he Mi吐stry of E 如ca 七i on,
Governmen七 of India for the 鋤ard of a scholarship under
r '-i 肥・
Q.I.P. Sと .2.
Affoc tionate apprecia 七i。鵬 are also due to the auth加も
wife yasmin,for her patience and understandi鵬 dur i聴 the
course 'of 七his reAearch, tohis sis七er Nikha 七， for her
help in the preparation of the manuscript and to his parents,
for t加 ir good wishes.
M 。T. AHIVED
(iv)
A E6 FLAC T
The t加sis is concerned with the s皿t加sis of si昭le
and rnultivariable network functions usi鳩 operational amplifiers
(OA 's)and RC networks,in a f 叩m suitable for hybrid integrated
C ircuit （エ C)fabrication. An at 切mpt is also ma的 to evolve ・
generalized and unified active s皿七hesis sche 肥s for multivariable network functio鵬， which, as a s 胆cial case,can be
adapted for si鵬le -variable functi叩s as well 。 丑肥 MV 切chniques are suitable for active lumped-distributed syntbesis.
Active simulation of groun肥 d inductance is consi 加re d
in 肥 tail. A technique for groundi鳩 t加 C 0fl的nsers of an
OA:RC network, with low active 叫d passive components,has
been given, and its applica七 ion is demonstrated by derivi昭
gr oem 加 d con的nser circuits for inductance simula七 ors （工 S's)
and fil七ers 。
A computer aided 肥 thod, based on t 加 dominant
po le 七e C hni 叫e (DPT) is proposed f 叩 t地 frequency limi 加ti on
study of general second-order OA;RC networks. It has been
applied to study t加 h蛇h frequency performance of some
important IS's .
Floati昭 inductance (FI)si niulat i叩， which is relatively
more difficuユ七 than 七he groun臨 d in如ctance simula 七ion, is
cri 七 ically irrves七 igated. Ac 七 ive non-ideal F1's むe considered,
which enjoy a number of advantages over t1 ideal ones.
豊肥
F 工，s discussed in this thesis have a low coriponent count,
uni 七 y capaci 七 or spread and 上叩 sensitivity; they むe easy to
(v)
design and. adjust and do not require critical component
matching. Moreover, the use of OA's in uni 七 y.gaifl connection
gives highly stable Q胆 ra七 ion 』
The disadvantage is that t加y
realize a finite maximum Q, furt加r, t麗 highes 七 usable fre ー
quency is limited to a small fraction of t1- gain-ban曲id七I-i
pr o如et of t旭 OA 's.
(1A c 加on&c，い o－切 v町iant band-pass filter usi昭 a si鳩 le
OA in i叫 gain (unity 叩 two)connection is examined in 肥 tails,
Its gro叫ded capacitor version is obtained withou七 inoreasi昭
I
the number of O編 used. Inves tigati 叩s based on sens itjv ity
and frequency limi 七ation s 加町 indicate 七1ュa 七 tho filter with
gain K=2, is far superior wi七 h regard 七 o ao 七 ive Q-sensitivity,
gain-sens i 七 ivi 七 y produc 七 and the highes七 usable frequency over
the one usi昭 K = i 。
However，血七he unity-gain case, the
passive sensi七 ivities are very low （く i）。
The filters are
suitable for IC implementation
A generalized syn七 hesis approach for active RC networ鵬
is develo卵d usi鵬 non-ideal simulated-L.
丑迫 method genera加s
a biquaむatje filter section, and a basic bloc1 is shown to
realize all 七he important filter sections 。
OEe s 七 rue ture
has 1叫 c onponen七 c oun 七 and very low sensi七 iv i 七 ie s.
Generalized ac 七 ive RC:CR,RC:LC and LC:RC transf 叩mati. ons
are develo胆 d for multivariable (Mv)ne七w or ks .
豊肥 correspondi集
well known 七 rans f orma 七 ions of single-v町 jable ne 七 work fune 七 i ons
fo11dras a 。胆 dial case of tue general theory.
A oom叫ter msed 5皿tmsis teohnlque 15 glven for t加
reallza七iQn of two-varlable(w),n七h-order，むivi鵬 polnt
immi 七七ance func 七 lons into ladder networks 。 亜e applioation
of Routh,5 ：沿七 hod to tm oontinued fraotion expansion(CFE)
15 extended to 七m MV case.
皿旧 5 皿七hesls tecmlque 15
based Qn 七 he algori七hm,which tests the TV funC 七 ion for
realizabili七 y and slmul 七aneously realizes it into One 町
more of tm 切len七 y Woposed RC lad肥 rs.
Finally,ageneraユ lzed smthesis teomlque 細 9如en for tl
realiza 七lon of MV 切叫sfer funo 七 lons and grounded and f1Oati理
admlttance polynomlalS. Tm smtmsls Scmm e!nploys a ne曹
aotive device － 七he mul七ivariable generalized immitt如ce
51 eapacltlve elements and
oonverter,obtalned from OA 、
resistances. The smtmsls somme 15 oapable of reallzi昭
a very large class Of MV ne 加ork func 七 ions and 15 also
suitable for IC implementatlon. Antonlou,5 method for
51肥 le－・larlable functions 15 sh叫n to form a smclal oase
of tm Woposed tecmique.
TA瓦E OF CONTEN昭
ABS '11AC T.,
CHAP 正R
im皿のtJOTION......................,i ・
i .iElectromechanical Inductorless
Ne tworkcs 。． . . . . . . . . . . . . . . . . . . . . . . .i
i 。2Active Inぬctorless Networks .......う・
i う
Active RC Ne 七 w or 鵬：Single-Variable6
1 。う。i Review and Preliminary Considera七 ions 6
i，う。2 Direct-Form Realization 。。』． .－。． ,．。．8
二．う。う Cascade-Form Realiza 七 i on, .'.．。． . . . .io
i 。う。4 Se 鵬 J-七 ivi 七 y Study and Frequency
Liml 七a 七 ions . . . . . . . . . . . . . . . . . . .，。． .li
i 。午
Ac 七 jre RC Ne 七 w叩ks! Multivariable ．。i う
i 。』」 ,i Rev 士ew
iう
i,>1.2 S皿thesis of ActLre RC MV Ne 加or 鵬．14
i.5Score of the Dissertation 。．。．．。。．。．14
2 。」Review 。． . . . . . . . . . . . . . . . . . . .,. . . . .
2.2Grcinding of Condensers...........
All grounded Capaci 七 or Inductance
2．う
Sま mulator 。． .,. . . . . . . . . . .,. . . . . . . . . .
2.4GC-High Q. Induc 七ance Simula 七 or . -．・・
2.5Seコsi 七 ivi 七 y,......................,
2 。5,1 Sensi 七 ivity of GO-In如c tance
Si 廿ュ la t or s . . . . . .,. . . . . . . . . . . . . . . . .
2.5,2 Sensi 七 ivi 七 jes of GC-Hi言 hQ
Inductance Si置u la 七 or 。。． . . . . . . . .'.
2.6Fre叫ency Limi 七ati ons 。． ...........
2.6.1 Dominant Pole Technique(DPT). .....
2.7 Freqaency Limitations of Grounded
.
In duc 七 .nce Si出ulators . . . . . . . . . . . ，。．
6 7 心
1 5 8う1う5う 7 う4 4
か 92
4 5
2
2
銀 OIDED INDUCTA瓦CE SIM皿ATION 。．。。．
CHAP四R2
(v 士 fr)
乃
拓
スノ
スノ
よ 1〈」
ノ
0
スノ
乃乃
弱
78
スノ
スノ
つ
五「
ー
ノ
ス ろノ
3 ノ
ノ
I Lf
8688叩 10 10
FL叫 TBJG INDUCTANCE SIMULATION . . .,．。
Introduc tion . . . . . . . . . . . . . . . . . . . . . . . .
Schemes for FI Simulation. .'.'... .. .
Simulation of Ac 七ive Lossy Floati昭
In duc 七 ors 。。． . . . . . . . . . . . . . . . . . . . . . .;.
s wi 七h Unitrう o 。i Lossy Floati昭 Induc 七叩
Gain Amplifiers 。．. . . . . . . . . . . . .. . . . ..
… 2.2 Effect of Component Mismatch．、． .，。。，
Design,
Sensitivity .
Frequency Limi 七a 七 ions . . . . . . . . . . . . . . .
Ex加rimental Re 融I.tS．・・・・・・・・……
う．o
Conclusion:. . . . . . . . . . . . . .'. . . . .. . . .
う．Y
う
59676771
CHAP呪R
卵
2 。7 。1 Exis七 i昭 Inductance Simulators .．。。。．
2 。7.2 GC-Induotance Simulat 加s .. . . . . . . .,.
2.7.2.1 Experimen七al Resul 七s. . . . . .. . . . . . .,．・
2.7 。う GC-High Q. Inductance Simula 七叩．. . . .
2 。 BConclusion 。． ........................
ACTI\電 ' IL正RS . . . . .. . . . . . . . . . . . . .．。 i 09
Band-pass Fil七er Usi肥 叫ノs in Low- 110
4 。i
Gain Connection. .,. . . . . . . . . . . . . . . . 1 .
Sensi七 iv i 七 y Considera 七 ions めr BP
4 。2
F i i ter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11う
-t 。う Design Equa 七 ions . . ..，・…，・・・・．・・… 114
i Case A：血ity-Gain Configura 七 ion 。．。 114
＞
4．う．
115
-' う．2 Case B: General K Configuration
CHAP密R J-
。
・
404FreO.鵬ncy Limita七 ions.,..........．・
4.4.i Usi昭 &.dak and Petrela Me 七hod 。．，。
、。・― ,2 Results Usi鵬 Dominant Pole
脱C bni que
-,．カ。う Exper imen七 al Resul七s 。． . . . . . . . . .．…
Ac 七 ive Fil 七ers Using Non-Ideal
と片
S imu la七ed Induc 七ances 。． . . . . . .,. . . . .
ii8
i18
i 22
124
i 27
(ix
. . . . . - . . . '
Sensi七 ivity Studies．。
4.7
4 、7 i Case A: Using 肋e s ta o t七／s Circu土七。
>1 7 2 Case B: Using Bernd七－Du 七七a Roys
C ir C U I t. . . . . . . . . . . . . . . . . . . . . . . . . ．
. 。
. . 、． . . . . . . . . . .
Conclusion 。． . . . . . . . . . . . . . . . . . . . . .．。
GENERAL I ZE D 皿ANSFORト仏町 ONS FOR
ACTI\厄 NUL T IVAR 孤瓦.LE NE 叩OR 瑠。。．
CHA PTER ら
只）
［ノ
ro
1 1
スノ
スノ
ア
ノ
ブノ スノ
11 1
JwelJIJ Jll
41 一
4.6 Realization of Various 町pes of
Filter Sections《。． . . . . .
140
一 1 「 we Jtl
・
一 Il ro 0
ノ
五 I L4. 九ー
一
5
0 0 1
一らノ 「つ
140
.
Introduc tion 。． . . . . . . . . . . . . . . . . . . ．。
i 41
N o ta 七 i ons . . . . . .'. . . . . . .'. . . . . . . . . .
Si昭le -Vむ jable Ne 七 w or k 町ansf ormati ons. . . .,. . . . . . . . . . . . . . ..．。． . . . . .
翻o-Variable RC:CR 町ans f or臣 ation 。．
5.2
5 。2. Ac 七 jre RC:CR 町ans f 叩mati on
Active 血 o-Variable RC :LC 卿ans5．う
;ormation 。． . . . . . . . . . . . . . . . . . . . . . . . .
Idtive Multivariable 正ansf orma 七i叫s
ョxample s . .. . . . . . . . . . . .,. . . . .:. . . . . .
引
56
郭
61
しr
・
0
り
「 ノh ー
つ
al 「
「
つ
C 吐氾 lus ion
. . . . . . ■ ■ ．. . . . . . . ■ 、 ． . . . . . .
j,O
JI
JI
ニマ ／ C
. . . . . . . . . . ' . .
411 1-
Outi加e of 七he Pr鴨ram
Exampユ es of いdder S皿七he sis. . .. .
SConclu旨 ion 。
／ー ープ
－。フ
一 11
62
Generati叫 of Forms 6 to 20,.. . ..
An A ユgoritbm for Compu七er 肋ogram
「 に一 ノ
0 つ L
J- h
ノ
ワー 「ー 」
R ロリ
Q
20 。。． ..
Use of 印．sic Su加ou 七mnes in the
68
O O
i Realiz,tion of Forms i
。2 Realiz4ti叫 of Foniis 6
十〕 十〕
血七rQguetion.
卿o-V 雛！jable RC Ladders
血碑あ
62
s VN 質狙 S IS 卯 卿0一 rAR lAB工E RC LADDER
NE 嘱銀粥．
C 孤 P正R6
(x)
C 弘 P四R?
7 。o
7 。i
'7 。2
り Fune tions .:
4 。 i Re a i i z atj on
7,4 2 Realizati叩
一
一よ ・ ロ よ
P ・
0 0・
0-
7 。う．
7 。lt
Introdue tion . . . . . . . . ... . . .. . .. . . ..19う
Multivariable Generalized Irumittance
C onv e r te r:A New Ac 七 ive E1ern6ri 七。． ..i 94
Decomposition of MV 卿如s fer
Runo tions .,. . . . . . . . . . . . . . .,. . . . .. . .i 97
Synthesis of Multivariable 14e加叫k
Fune tions 。． . . . . . . . . . . . . . . . . . . . . . . . .202
Nota 七 i叩s Used......．。． .... ... ...．。2 飽
Realization
伽o -Variable かans fe r
・・
7 。う
SYNTIE8IS OF MULT五TARIA瓦E ACT玉電
RC NEEWOR 鵬．'：。． ...............．。．19う
－
・
・
■
・
1
サ
h ワー
7- つ一1
l
フ」
2
」2
へ
ど1
ハ
ど 2
22
ど
rD
じ、
「
ど‘
22
山
f
Q O
山
P
Yh(s-1,s一｝ anci. Y 一 tS4,sへ） .
i
-.I
7.7 Example s 。． . . . . . . . . . . . . . . . . . . . . .
'7 。8 Generalization 七 o Nul七 ivaria ble
S皿thesis 。，。． . . . . . . . . . . . . . . . . . .
7 。Q Conclusion．。． . . . . . . . . . . . . . . .'. .
ー
J
a li z a七 ion of A面 J-七 t如ce Po ly nomials 。。． . .
7 。5.i Realiza七 ion
YA(51,52）・． . . . . . . .
7 。52 Realizati叫
YB(51,52)and
Yc
（「
,52)
．・・…
7.6 Realiza七 ion of Fica七 J-昭－A 面 J-七 t如ce
Pol 皿α-niais 。 ．. . . 1 . . . . . . . . ．。．
. . . ．。
.
Realization of Floating Adrni 七七ano e
7,tu
郵「 i2)
．・・・・・・・・……
7・＆2 聾aliza七1叩 of＿男oa tl叫 Admi ttances
75
208
ニノ
e
NnV R
ぬbne 加叩k 弘・・。・。
Subne 加orks NB and
20う
206
2う2
2う2
と．
ろノ
Main Iesu1is of 血is 吸呪 s is. . .. .．。．
Scope f叩 Further W叩k. .......... ..
DERIVA 虹ON OF ANTONIOUノS SYN丑犯SIS
sCI狙ト正 AS A S1ECIAL CASE 価1 贋E MV
四CHN IQUE.
1
REFERENCE S
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妬 タ
APPENDIX II
杉
mANSF ORMA 虹ON OF，即、:010(s)
皿伽ORK TO RC:GIC（ず）皿側観K.....
22 2
APPENDIX I
ノ
R ノ
Q
ス ノ スノ
8。i
8.2
CONCLUSI ONS . .
2 2 2
CHAP正R 8