Table Of ContentBroadband
Direct-Coupled
and
Matching RF Networks
Thomas R. Cuthbert, Jr., Ph.D.
Cuthbert This practical guide is for engineers and
technicians who design RF networks that
filter and match impedances over wide
bands or match at a just one frequency.
The networks may consist of L’s, C's,
open- and short-circuited stubs and cas-
cade transmission lines, and transform-
ers. New techniques are described
clearly and at a level between seminars
and graduate-level instruction.
Direct-coupled filters consist of parallel
(or all series) resonators coupled by re-
active subnetworks and are found in
many forms in all frequency bands.
aB Simple couplings are combinations of L’s
nr and/or Cs to provide all-pole or elliptic
do response shapes over any band width.
a Until now, direct-coupled filters were lim-
M
d ited to narrow passband widths. Now
About the Author ab broadband design is easy in terms of the
T homas R . Cuthbert, J r., Ph.D., PE, is ta loaded Q,s of resonators. A wide range
c
a consultant and teacher. He was the n of positive element values is always avail-
h
D irector of Advanced Technology at d able, with automatic adjustment of de-
i
R ockwell I nternational a nd Manager of n sign parameters to useful criteria simpli-
D
M icrowave Technology at Texas Instru- g fied by spreadsheet optimizers.
i
mT eecnhts, . anH de S s.Mtu.dUie. d Hi sa t twMo .I .Tot.h, er Geboorogkias Rre The grid approach to broadband imped-
were originally published by John Wiley: Fc ance matching (GRABIM) maximizes or
shapes poer transfer between source
C ircuit Design Using Personal Comput- Nt- and load described only by discrete-fre-
ers (1983) and Optimization Using Per- C
e quency impedance data. It reliably lo-
sonal Computers (1987).
to cates the neighborhood of the likely glo-
w
u
bal solution by an efficient grid search
op based on knowing each benign reflection
rl function versus element parameters.
ke
Then, a minimax-constrained gradient
sd
optimization precisely locates the solu-
tion while pruning any unnecessary ele-
ments from candidate networks.
GRABIM replaces sophisticated polyno-
mial mathematics by optimization with
assured outcome.
Many equations, illustrations, algorithms
and 100 references support programming
and further study. What little software is
required is available. The most important
feature is the concise explanation of
these useful techniques.
J.F.
Seiders
Broadband
Direct-Coupled and Matching
RF Networks
\
Broadband
DBrectEBCoupied and Match~ng
RF Networks
Tlhi.omas R. CMthll»errtt, Jrr.
lP'irofessnl{])lillal lEIDlgD.lill<e<ell." alilld JP'iillct
~15 Mairyim.cn11; IDrD.v<e
<GreieIDlwco<dl Arlk&lill.sas 12g35
9
1I'lhom.as R. C1!llttllllben:, Jfll".
Copyright© 1999 by Thomas R. Cuthbert, Jr.
All Rights Reserved.
This book reports original research and development and provides
references to highly regarded sources. Reasonable efforts have been
made to publish reliable ·data and information, but the author and
publisher cannot assume responsibility for the validity of all materials or
for the consequences of their use.
Reproduction, transmission, or translation of this book or any part in any
form or by any means, including photocopying, microfilming, recording,
or by information storage and retrieval system, without permission of the
copyright owner is unlawful.
Direct all inquiries to:
Thomas R. Cuthbert, Jr.,
975 Marymont Drive,
Greenwood, AR 72936.
ISBN 0-9669220-0-X
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
To my brother,
Dr. Jerry W. Cuthbert,
who is always there to help Buddy
with all his projects,
including this one
Curving Line
In a crevice, in a corner
Of the parametric space,
Live conception's few exceptions
To the unimodal case.
0 my darlin' 0 my darlin:
0 my darlin' Curving Line,
You're not always unimodal;
Dreadful sorry, Curving Line!
J. W. Cuthbert
This book is for engineers and technicians who want to use new
and useful techniques to design RF networks that filter and match
impedances over a wide band and those that match only at one frequency.
Direct-coupled filters provide a bandpass frequency response by
using reactive structures to couple cascaded resonators from one to
another and to source and load impedances. The resonators can be all
series LC or all parallel LC pairs and the coupling can be any
combination of L's or C's or parallel LC traps for stop band enhancement.
Direct-coupled networks can be terminated by resistances at one or both
ends to function as singly- or doubly-terminated filters, respectively.
Direct-coupled filters occur in a many physical forms for use in frequency
bands from VLF to K-band; their common design basis is the LC model.
When load and/or source impedances are described by data
measured at a set of discrete frequencies over a band, then the broadband
matching problem is to find a network that minimizes the power loss over
all those frequencies. Since 1977, the highly mathematical real
frequency technique has been employed to solve that problem. This book
describes the grid approach to broadband matching, GRABIM, a much
superior method that is simple, reliable, and very likely optimal.
My two previous books treat direct-coupled filters, broadband
impedance matching, and optimization in considerable detail. For the
past four years I have been able to devote most of my time to researching,
teaching, and consulting on these and related subjects. My more
important discoveries have been new and useful methods for design of
broadband direct-coupled and matching RF networks.
These new techniques are presented at a level between the
valuable one-to-one contact in my seminars and the practical but
graduate-level treatment in my two prior books. Much more detail is
included here than is possible to present in my seminars, and more than
100 very specific references are cited.
In addition to direct-coupled and matching networks, there is
considerable material included on comprehensive equal-ripple filters and
special optimization topics. The former motivates the latter: the most
straightforward and reliable way to obtain optimal impedance-matching
results is by a grid search followed by minimax-constrained optimization.
The articles by Herbert Carlin, John Orchard, Virginia Torczon,
and Mike Powell that inspired GRABIM are acknowledged. I also greatly
appreciate the reviews of this manuscript and many valuable suggestions
by Stephen Sussman-Fort, Bruce Murdock, and Jerry Cuthbert.
Thomas R. Cuthbert, Jr.
Greenwood, Arkansas
January 1999
vii
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1.2O vell."view 2
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1.3R elate§do ftwall."e . . . 5
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Jl..41R evision.s . ;. .........7. ..............
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2.f l!JNJIOAMENTAIL� . . .. . . 8
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2.1 JP>ower1' ran.sfer 8
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2.1.Clo mpleSxo urcteo C ompleLxo ad. ............................8. .....
. . . . .... . .
2.1.G2e neraliRzeeflde ctiCoone fficie.n. �t .. .......................... ..... ......9.
2.1.C3ir clteo C irclMaep pin.g. ...........................................1..2.
. . . . . . . . ..
2.1.D4o ubly-TerminNaettewdo r.ks. .................. ... ..13
... . . . . . . .. . . .... ... ... .
2.1.S5i ngly-TermiNneattweodr k.s. .................................1.5.
.. . .. . . . . . . . .
2.2M ajoll."R espons§e hapes . 17
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2.2.L1o wpastso B andpasTsr ansformati.o.n. .........................1...7
. . . .
2.2.I2n sertiLoons sB ehavi.or. .............................................1 .9
. ... . . . .. .
2.2.R3e flectiCoone fficinetB ehavi.o.r.. ..........................2.0. .
.. . .. . ... ... . .
2.2.F4l aLto s.s. ..............................................................2.1. .
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2.2.S5t opbanRdi ppl.e. ......................................................2..2. .
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2.2.E6ff ectosf C omponnetD issipat.i.o.n.. ........................2...3 ..
... . . . . ..
2.3S ignificancoefL oadledlQ .. . 241
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2.3.S1e ries-ParCaolnlveelr si.o.n. .....................................2.4. .
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2.3.R2e sonatVoA/Wr ..................................... ... 25
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2.3.R3e sonatEoffirc ienc.y. ...........................................2.6
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2.41L adderN etworkT opologi.e.s.. .............................2..7. ............... .....
2.4.L1o wpasPsr ototyNpeet work..s. ..................................27
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2.4.C2l assicBaaln dpasPsr ototyNpeet work..s. .................2.8. ....
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2.4.D3i rect-CouPprloetdo tyBpaen dpasNse tworks. ..............3..1.
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2.4.T4r ansformatiionnBs a ndpasNse twork.s. ....................3..2 .
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2.4.D5u alit.y. .....................................................3..4.. ........ ..........
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x
2.5N etworkC omponentV alues . . . . . .35
..... .......... .... ..... ....... . ................ .
2.5.E1q ual-ElemeLnotw pasPs rototy..p.e. ........................3 .5. ........
. . .
2.5.P2r ogramA LLCHEBY.EXE. ......................................36
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2.5.E3l liptFiuncc tioLno wpasPsr ototy.p..e. ...........................3.8
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2.5.S4c alnig. .....................................................................3.9.
. . . . . . . . . . . . . .
2.6N etworkA nalysis. . . . . 40
.... ....... ........... ........... .......... .... ...... .......... .......
2.6.A1B CD Two-PorPta ramete.r.s.. ...........................40
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2.6.C2a scadinTgw o-PorStu bnetwor.k.s.. ..............:... ... ......4.1. .......
. .
2.6.S3c atteriPnagra mete.r.s. ..............................................42
. . . . . .. . ...
2.6.S4p eciaRlel atiofonrs AB CD Paramete.r.s. .......................4. 3. .
. . .
2.6.H5i lberTtr ansfo.r.m. ..................................................4. 3. .
. . . . . . . . . . ..
2.7 Summary ofF undamental.s. .....................4.5. ................................
3.D IRECT-COUPLEFDI LTERS. . . .4 7
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3.1P riorT echnology 47
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3.1.C1l assicFaill te.r.s.. .........................................................4.8.
. . . . . . . .
3.1.C2o upleRde sonatCoorn cept. ........................................4..8. ..
.. . . . .
3.2P roperties 49
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3.2.T1o poloegs. i.................................................................4. 9
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3.2.R2e sonato.r..s. ..............................................................5..0..
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3.2.I3n verte..r.s... .........................................................5.1. ......
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3.2.N4a rrowbanCdh oiceisnP arallReels istanScpea ce. ........5..3 . ..
. .
3.3R esponseC haracteristic.s . 55
..... ..................... .................... .......... ..
3.3l. S tobpa ndS electi.v.i.t..y... .............................................5 .5
. . . . . . . . . .
3.3.P2a ssbnad Width. ......................................................5 .7.
.. . . .. . . . . . . ..
3.3.M3i smatcheTde rminati.o.n.s. ................................6..0.. . .......
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3.3.E4ff ectosf D issipat.i.o.n.. .........................................6..1 . .......
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3.3.P5a ssbnad Distort.i.o..n. .................................................6.2.
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3.4E liminatinPga ssbandD istortion 65
...... ................ .............. ........ ..
3.4.S1t aggre-Tunngi Two Resnoator.s. ...............................65
. .. . . .. . . . . .
3.4.S2t aggeru-nTingT hreeR esonato.r..s. ...........................6..7
.. . . . . . . .
3.4.E3x actR eplacemeonftR esonato.r..s... ..........................68
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3.4.Al4l PossiblAlel -Poel Topolog.i.e.s. ................................7..1. .
. .. . . .
3.4.W5i debanCdh oiceisnP arallReels istanScpea c.e.. ............7..2 .
. .
3.5T he Methodo fC hoice.s. ........................7.5. .....................................
3.5.A1 S preadshefoert F ourR esontaor.s. ...........................7 .6
. . .. . . . . . .
3.5.A2 Spreadshefoert F iveR esonato.r.s. .......................8.0
.. . .. . .. . . . . ..
3.5.A3 Spreadshefoert a FourR esonatEolrl iptFiicl t.e.r. .........8 .2
. .
x:i
3.6T uning 84
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3.6.A1l ternatOipnegn -andS hort-CirMceutihto .d. .......8.4. .............
3.6.R2e actiIvnep uRte flectiFounn cti.o.n. ......................8.5. ..........
. ..
3.6.N3a rrow-BaRnedfl ectiPoonl easn dZ ero.s. ..............8..6.. . ........
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3.6.W4i debanNde tworkHsa vinEgx acRte spons.e.s. ......8.7. ............
3.7 Summary ofD irect-CoupJFlieldt ers . . 87
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t!-.C OM�Rli:fti�N$BVIEIE QUAIL.cll�l6'»1?1LIE!F ITLIE RS .... .. .9 0
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4.1P urpos.e. .................................90. ........................................................
4.2R esponsCeo ntinuu.m. ........................90. .........................................
4.2.T1r ansducaenrd C haracteriFsutnicct io.n.s. .........9.0. ................
4.2.T2r ansmissZieorno. s. .....................................9. 2.
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4.2.P3a ssbanSde lecti.v.i.t..y. .........................................9..4.. .....
... . . . . .
4.2.S4t obpa ndS electi.v.i.t.y. ................................9.5. .....................
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4.3C hallengoefsP olynomiaSly nthesis .96
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4.3.U1n derlyiCnogn cep.t.s. ..................................9....6 .. ...............
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4.3.M2a thematiOcpaelr atioannsdS ensitiv.i.t..i.e.s. ......9. 6. ..........
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4.3.T3h eA pproximatPiroonb le.m. ................................9...7.... .. .....
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4.3.R4e alizatoifEo lne menVta lue.s. ...............................9..8.. ..... .
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4.3.R5o adM ap forT opolog.i.e.s. ........................................9..8. ......
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4A ElementR esponseast D iscretJFer equencies . .99
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4.4.F1i lte.r.s. ..................................................................1.0.0. ....
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4.4.S2i ngle-MaBtrcoha dbanNde twork..s.. ....................1..0.2. .
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4.4.D3o uble-MaBtrcoha dbanNde twork.s. ........................1.0.4. ....
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4.4.L4e ssonLse arne.d. ...............................................1..0 .5. ..........
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4.5S ynthesbiys IterateAdn alysis . 105
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4.5.Z1e roasn dP oleosf t heC haracteriFsutnicct i.o.n. .........1..0..6. .
.
4.5.C2h aracteriZsetrioocsf L addeFri lte.r.s. ................1..0..6.. .......
.
4.5.B3a lanciVnagr iablaensd C onstrai.n.t..s.. ..............1..0..7.. .... ..
. ..
4.5.E4ffi cienNte tworAkn alys.i.s. ..............................1.0.8. ............
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4.5.E5ffi cienOtp timizat.i.o..n.. .....................................1..0.9. ...
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4.6S ummary ofC omprehensivEeq ual-RippJFliel ters. .1 10
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5.M ATCftiBNGN IETWOIRKS. ..........................1.1.2. ........................................
5.1S ingle-FrequeMnactyc hing . 113
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5.1.Z1e roR eflectan.c..e. ................................................1 .1.3. ......
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5.1.E2l S ectioMnast chinRge sistan.c.e.s.. .................1..1..4 . .........
.. . .
5.1.E3l S ectioMnast chinIgm pedanc.e.s. ............................1..1 .5.
. . . . .
