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490 Subject Index equivalent: bandpass. 365, 366 LC.467 node·type. 364 lossless, 47, 52, 57 lowpass, 51 mi.nimum phase. 57, 58 singly terminated, S7, 96 synthesis realization. 56 terminated, S9 Network analysis overview. 4 Network synthesis aids overview, 3 Neutralization, 241 Newton's method, 35, 125. J26, 133, 167. 169. 196.201 . Nodal analysis. 69, 86 Node bridging, nonadjacent: current interpolation, 89 example. 90. llO, III using bridged-T chain parameters, 86 Noise, numerical. 144 Noise figure calculations. 79 Nonlinear programming overview. 4 Norm, 37 Norton source, 247 Norton transformation, 172,209,210,290, 365. 369 Numerical analysis tools. 3 Numerical instability, 13 Numerical integration. 13 Numerical noise. 14 Numerical overflow, 41 Objective function: gradient of, 153 minimax. 152 prh difference, 151 satisfied-when-exceeded, 15 J squared-error, 223 Open-circuit parameters: ABeD parameters relationship, 55 of bridged~T invulnerable network, 378 Optimization: blind man analogy, 116, 124 constrained, 158 flowchart. 115 linear search, 127 network. flowchart, 154 overview, 4 Oscillator frequency stability, 96 Overshoot, 313 Paraboloid. output power, 247 Paralleled reactances, 178, 277 Parallel resistance, 276 Parameter. two-port: conversion, 78 normalization, 80 open-circuit, 209 scattering, 92 Partial fraction expansion: algorithm, 63 definition, 62 Passband, recurring, 299 Passband shapes: Butterworth (maximally flat). 308 Chebyshev (overcoupled), 305 comparison, 313 Fano (undercoupled), 310 minimum loss. 314 Pessimization, L62 Phase compensation, 86 Piecewise linear function, 19, 21 Pi network: configuration, 173 mapping, 245 reactance equations, 174 Pole at origin. 60 Polynomial: ABCD.50 addition and subtraction of parts, 49, 50 complex, 34 creation from zeros, 44 for doubly termirH\\ed minimum loss filters, 316 evaluation, 31 even and odd. 60 fundamental synthesis relationship. 48 Hurwitz test. 54 Legendre, 68 multiplication. 45 network synthesis, 41 rational, 52, 59 for singly terminated minimum loss filters, 318 Polynomial approximation: example of piecewise linear. 23 minimax, 19 piecewise linear functions, 19 rational, 24 Power: available at two·port output, 247, 272 bounds on transfer, 372 efficiency, 92 input, 92 load. 46 maximum added. 254, 272 max.imum available, 46. 173, 203 reactive, 277 real incident, 93 transfer, 46. 94, 235 transmitter harmonic, 373 waves, 93 Power series, 20, 32
Subjeer Index 491 Prediction. first-order. 102 Prinled circuit: edge coupling. 336 filters, 342 microstrip, 342 stripline. 342 Product form. 35. 37. 38 Programming techniques. 233 Programs: desktop computer: B2-1 Gauss-Jordan solution of real equations, 10,59.226.417 92·2 Gauss-Jordan solution of complex equations. 12,419 B2~3 Romberg integration. 17. 215.421 B2-4 Polynomial appro,ximation of piecewise linear functions. 22, 422 82-5 Levy's matrix coefficients. 27. 425 83-1 Moore's root finder. 40. 426 83-2 Polynomials from complex zeros, 44, 429 B3·3 Polynomial multiplication. 45. 430 B3-4 Polynomial addition and subtraction of even. odd. or all parts. 49. 431 B3-5 Continued fraction expansion. 52, 432 83-6 Long division, 62. 432 83-7 Panial fraction expansion. 64. 433 84-j Level -0 ladder network analysis. '13, 74, 155, 221, 245, 289, 356, 434 84·2 Discrete Fourier transform and convolution, 98. 436 95-1 The Fletcher·Reeves optimizer. 141-143, 153, 159,224,437 B5-2 L-seclion optimization, 153, 155. 439 86-1 L. T. and pi matching. 175. 177. 440 86-2 Fano, Newton·Raphson solution, 197,442 96-3 Levy matching to resistive source with g, prototype values, 201, 203. 207, 208, 443 86-4 Romberg integration of two Fano gain·bandwidth inugrals, 2J5. 244 86-5 Hilbert minimum reactance calculaled from piecewise linear resistance, 221, 224. 445 86-.6 Carlin resistance excursion oplimization wilh independent source resistance, 224, 225, 446 B9·1 EIliptic filter pole/zero and loss calculations. 348, 350, 352. 447 B9-2 Symmetric elliptic filters, 358, 448 B9-3 Antirnetric elliptic filters, 360. 449 hand-held computer: A2-1 Polar complex four functions. 7, 233, 386 A5-1 Swain's surface. J)6, 123. 127. 387 AS-2 Central quadratic function. 120, 121, 128, 136, 168,388 A5-3 Calculate quadratic-form level curves. 121. 389 A5-4 Linear search, inner products, and conjugate forms. 128, 168. 390 A6-1 1+Q2 series-parallel and parallel reactances. 288, 29 L 391 A6-2 Transmission line matching, 185. 198, 291, 392 A6-3 Min SWRm.~ and lowpass-tobandpass transformation, 193. 198. 394 A6·4 Norton transformations. 21 I, 395 A 7-1 Bilinear coefficients from arbitrary triples. 233. 396 A7·2 Three·port to two-port conversion. 239,241,399 A7-3 Impedance mapping for a scaHering two-pon network. 243, 402 A7-4 MaximaIly efficient gain design. 255, 267, 405 AS·l Bode breakpoint selectivity estimate, 285-287, 408 A8~2 Doubly terminafed minimum loss filters. 318, 411 A8-3 Singly terminated minimum loss filters. 319, 413 A9· 1 Equal-admictance·swb filters. 341, 415 Proper rational functions. 62 Prototype network: bandpass, 364 direct coupled. 273. 278 Q parameter: bandwidth. 193 in decrement, 74 loaded. 277 in resistance matching. 177 resonator loaded, 277 sensitivity, 112 singly terminated, 277 unloaded. 295 Quadratic: form. 121 function. 118, 131 termination. 135 Quadratic factor, 38, 45, 66 Quadrature. 13 Quasi-Newton search, 135 READ commands, 11 Reciprocity, 51. 87 Recursion, ladder network analysis, 71, 89 Reference phase. 95
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Wile,.· Interactenee ..A. .. 1 18
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Circuit Design U sing Personal Comp
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To my late parents, Tommy and Brown
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viii Preface computer. Excessive th
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Contents l. Introduction 1 2. Some
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Contetlts xiii 4.3.4. Transmission
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~----- ---- Contents xv 6.6. Pseudo
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-------------------------- Contents
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-- ------- 2 Introduction viewpoint
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4 Introduction Chapters Four and Fi
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6 Introduction the selectivity effe
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8 Some Fundamenurl Numerical Method
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10 Some Fundamental Numerical Metho
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--------------------- Romberg Integ
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and it is convenient to rearrange (
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Romberg Integranon 17 Truncation Er
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---~-- - - -- ----- - -------------
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Polynomial Minimox Approximation of
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Polynomial Minimax Approximation of
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Rational Polynomial LSE Approximati
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---~~--_._--- ------ ID(w)£(w)1 2
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Rational Polynomial LSE Approximati
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Problems 31 2.6. If a,Z+a2 w = -a'-
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sense by the sum of first-kind Cheb
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Complex Zeros of Complex Polynomial
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Complex Zeros ofComplex Polynomials
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which are equal to the polynomial C
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Complex Zeros of Complex Polynomial
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Table 3.3. Complex Zeros of Complex
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Polynomials From Complex Zeros and
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Polynomials From Complex Zeros and
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Polynomial Addition and Subtraction
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Continued Fraction Expansion 51 Not
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Case 1 (row ~t (al N" 3 -1 '" 25 +
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---- ------------------------- Cont
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----~------- Input ImpedafJce $ytrt
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Input Impedance Synthesis From Its
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------- - ------------- ---- Input
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Long Division and Partial Fraction
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Problems 6S magnitude. The program
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- Problems 67 3.12. Given the resis
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.Chapter Four Ladder Network Analys
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- -- - -------- Recun;"" ludder Met
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Recursive Ladder Method 73 This alw
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--------------- Example a: 3,325,20
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Recursive Ladder Method 77 This las
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- - - -------------- Embedded T>vo-
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- - - - - --- - - - ---- Unifonn Tr
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--- - .._----- Unifonn T/'Qnsmissio
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--------------- Uniform Transmissio
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------- --- -----------_. - ------
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Table 4.4. 6.d L1 6.dc, 6.d L2 6.d
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------- - _. - - Input and Transfer
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Input and Transfer Network Response
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Input and Transfer Network Response
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----------------------------- Time
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----- - - h(-rJ h(2.6.Tl o I II ---
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-------- Sensitivities 101 the corr
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formula: Sensitivities 103 dZ""A,Z
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Sensitivities 105 obeying at least
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and its derivative with respect to
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Problems 109 branch immittance; the
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Problems 111 Solve by using (4.40)
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Chapter Five Gradient Optimization
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Gradient Optimization 115 Figure 5.
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-- ------------------ Quadratic Fon
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Quadratic Fonns and Ellipsoids 119
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Quadratic Forms and EUipsoids 121 F
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Quadratic Fonm and Ellipsoids 123 x
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Quadratic Forms and Ellipsoids 115
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Conjugate Gradient Search 127 choic
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-_.. ---------- Conjugate Gradient
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Conjugate Gradient Search 131 x, Fi
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-- -~--- Conjugate Gradient Search
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Conjugate Gradient Search 135 Hxl =
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Linear Search 137 the variable metr
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Then, the minimum function value in
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- ------- Linear Search 141 subtrac
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The F/etcher- Reeves Optimizer 143
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The netcher- Reeves Optimizer 145 c
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Table 5.4. Typical Output for the R
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The Fletcher- Reeves Optimizer 149
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Network Objective Functions 151 and
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-------- - - Network Objecti"" Func
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Network Objective Functions 155 Tab
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-- ------------ Constraints 157 tra
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- - - - - -------------- Constraint
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Table 5.7. Objective Subroutine lor
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-70. Constrainis 163 315-325). For
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Constraints 165 In fact, one applic
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--------~ - - ---------------------
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(b) Problems 169 Find the diagonal
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Impedance Matching 171 I, z, ---+__
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Narrow·Band L, T, and Pi Networks
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- - - --------------- + '" R, . " N
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NalTO...Band L, T, and Pi Networks
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Narrow-Bond L, T, and Pi Networks ]
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Narrow-BaruJ L, T, aruJ Pi Networks
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Loss/ess Unifonn Transmission Lines
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------- - -------------------------
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----------- and (6.34) can be writt
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Fano's Broodband-Matching Limitatio
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Fano's Broadband-Matching Limitatio
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----------------- Fano's Broadband-
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Fono's Broadband·Matching Limitati
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Green's recursive element formula i
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f 9, Figure 6.24. 92
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Bandpass Network Transformations 20
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Bandpass Network Trans/onnotions 20
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50 II 2.6548 16.594 Bandpass Networ
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BaruJpass Network TransJof1lUltions
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Pseudobandpass Matching Networks 21
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I InlPJ =In Pseudobandpass Matching
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Pseudobandpass Matching Networks 21
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----- -- Carlin's Broodband-Matchin
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---- -------------------- expressio
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Car/in's Broadband.Matching Method
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Carlin's Broadband-Matching Methad
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Prohle"" 227 Third, an objective fu
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Problems 229 6.16. Program Equation
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Bilinear Tronsfonnatl'ons 231 I, ~-
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Bi/inear Transjormations 233 (w" w"
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Bilinear Transfonnations 235 accomp
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Bilinear Transfonnations 237 circle
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Impedance Mapping 239 1 3 al~ ~a3 [
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Impedance Mapping 241 r-- Z, s" I,
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---------- Impedan£e Mapping 243 T
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Impedance Mapping 245 in Figure 7.7
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Two-Port Impedance and Power Models
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---------------- This may be put in
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----~-------~--- - - --------------
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-------- -- - -------------- and th
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Two-Port Impedance and Power Models
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Billlteral Scattering Stability and
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Bilateral Scattering Stability and
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--- -------- Bilateral Scattering S
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Unilateral Scattering Gain 267 the
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Unilateral Scattering Gain 269 The
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Prohle"" 271 _merit is u=0.08; by (
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Chapter Eight Direct-Coupled Filter
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- -- ~-------~- -------------- Dire
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Prototype Network 277 and Wo is the
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Prototype Network 279 element value
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Prototype Network 281 8./.4. Protot
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Designing with Lande Inverters 283
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Designing with L and C Inverters 28
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Designilrg with Lande Inverters Sup
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Designing with L and C Inverters 28
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General Inverters, Resonators, and
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Genera/Inverters, Resonators, and E
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conductance of the Kth resonator is
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Table 8.2. General Inverters, Reson
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General Inveners, Resonators, and E
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Four Importunt Pussband Shapes 305
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Four Important Passband Shapes 307
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FOIl' Important Possband Shopes 309
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Fou, Important Passband Shapes 317
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Four lmporlunt Pussband Shupes 319
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Comments on a Design Procedure 321
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-----~------------ A Complete Desig
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A Complete Design Example 329 DB3 =
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A Complete Design Example 331 R,,(l
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------- Problems 333 For Z=O+jX, fi
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------------- Chapter Nine Other Di
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, I II r L;.. I I . C, ~ ~ Wo ell :
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• e/2 e/2 Figure 9.3. A typical e
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Another trigonometric identity can
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o---iS~-----, I '--------;::==-----
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Introduction to Cauer Elliptic Filt
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Introduction to Cauer Elliptic Filt
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40 20 140 12 11 130 10 120 110 9 10
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00 Introduction to Cauer Elliptic F
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Doubly Termi/lllted Elliptic Filter
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Doubly TermillQted Elliptic Filters
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Doubly Terminated Elliptic Filters
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Doubly Terminated Elliptic FilteN 3
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Doubly TerrnilUlted Elliptic Filten
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Some Lumped.Element Transformations
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-lin '" 1 +jOn : c, 3L, L, I ) r So
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1 1CT (T Some Lumped.Element Tronsj
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Load Effects on Passive Networks 36
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Invulnerable Filters 377 9.6. Invul
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Invulnerable Filters 379 20 t lmin
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Invulnerable Filters 381 40 t L mil
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Problems. 383' corresponding number
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Problems 385 9.11. A passive networ
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Program AS-I. Swain's Snrface See E
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------- -------- - _. _. - Program
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----- _. - ------------- - Program
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- - - _._------------------ &61 TAN
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Program A6-4. Norton Transformation
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861 862 863 86' 865 866 B6? 868 869
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Program A7·2. Three-Port to Two·P
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15B .LBU Cue & 5to 3x3 Elements J5J
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e61 STOB 32 degrees 115 RCL9 a3 deg
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Program A7-4. Maximally Efficient G
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169 CHS Register Assignments: 17e e
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84e 841 842 843 844 845 846 847 848
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Program A8-2. Doubly Termiuated Min
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----- - - - _. - _.--------- - -- _
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-------_._--- ------- Program A9-1.
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Appendix B PET BASIC Programs Progr
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Program B2-2A. Gauss-Jordan Solutio
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- - -------------------------------
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Program B2-4B. Polynomial Minimax A
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Program B2-5. Levy's Matrix Coeffic
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----------- _. - - - Flowchart for
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Program B3-2. Polynomials From Comp
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--------- - - Program 83-4. Polynom
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Program 83-7. Partial Fraction Expa
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Flowchart for Ladder Analysis Progr
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Program B5-1. The Fletcher-Reeves O
Page 454 and 455: Program B5-2. L-Seetion Optimizatio
Page 456 and 457: Flowchart for Matching Program B6-1
Page 458 and 459: Program B6-3. Levy Matching to Resi
Page 460 and 461: ---------- -- Program 86-5. Hilbert
Page 462 and 463: --~-- - ---------- Program B9-1. El
Page 464 and 465: ---------- - -_.-------------------
Page 466 and 467: 3260 TO~(TO+W)/(l-TO'N) 3270 B(l,=B
Page 468 and 469: Appendix D Linear Search Flowchart*
Page 470 and 471: Appendix E Defined Complex Constan
Page 472 and 473: Appendix F _ Doubly Terminated Mini
Page 474 and 475: Appendix G _ Direct-Coupled Filter
Page 476 and 477: 461 (G.22) (G.23) (G.24) A,= (G.25)
Page 478 and 479: G.4.2. Resonator Asymptote Slopes D
Page 480 and 481: Appendix G 465 except for overcoupl
Page 482 and 483: ----------_._-_.- ---- - - -_.. - A
Page 484 and 485: Appendix H _ Zverev's Tables ofEqui
Page 486 and 487: ------ 6(0) 6(b) L _ (L,C,- L,C,)'
Page 488 and 489: L, L, c. " 12(a) C\=W C 2 =X L\=Y L
Page 490 and 491: Appendix H 475 Simplified Notations
Page 492 and 493: References 477 Box, M. J., D. Davie
Page 494 and 495: --------- Johnson, L. W" References
Page 496 and 497: References 481 Van Valkenburg, M. E
Page 498 and 499: _ 484 Author Index Noble, B.. 120.
Page 500 and 501: 486 Subject Index second kind, 32.
Page 502 and 503: 488 Subject Index proper, 62 quadra
Page 506 and 507: 1 1 _ 492 Subject Index I I Reflect
Page 508 and 509: 494 Subject Index length. electrica
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