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1 1 _ 492 Subject Index I I Reflection: coefficient, 66, 94. Ill, 235 generalized. 46, 174, 235, 243 zeros, 48. J95 Register: arithmetic, 81 packing, 74, 71. 84. 234 primary/secondary pairing, 77, 89, 233 Relaxation search. 127, 129 Repeated linear interpolation, 14, 15 Residual. 223 Residues, 64 Resistance: direct·coupled filter input, 296 mapping of negative, 237 source, 279 Resistance excursion. 220. 224 Resistance function; from impedance functions, 60 input function: Butterworth. 68 Chebyshev. 67 rational. S9 Resonance, repeated, 299 Resonators: helical, 298 model, 276 number required, 306, 309. 311 slope equivalent, 297 stub, 298 Responses. network: band limited. 98, 100 impedance. 91 impu[se,98 inpuI,91 lossless source, 96 phase jumps in, 97 power. 91 time from frequency, 97 transfer, 91 Restart policy, 136, 145 Right-half plane. 235 Romberg example, 17 Romberg integration, 13, 153, 215 Root finder, 125 Roots: conjugate pairs, 38 multiple, 41, 65 quad,45 Rosenbrock banana function, 145 Saddle point, 116, 123 Samples, 23, 27, 100.223,224 Scaling: frequency, 208 impedance, 208 polynomial: examples. 42. 43 by root factor, 42 by root shifting, 42 variables, 149 SeaHering parameters:: definition, 93 port normalizing impedance, 93 power waves, 93 renormalized. 259 Search: direct, 167 heuristic algorithms, 167 steps, 37 stopping criteria, 145 trajectory, 149 Selectivity: commensurate network, 283 direct-coupled prototype network, 279, 280 doubly terminated minimum Joss filter, 315 equal-stub-admittance filter, 341 estimate for direct-coupled filters, 285 periodic, 336 singly terminated minimum loss filter. 318 Sensitivity: approximate, 103 complex, 102 defmition, 101 direct~coupled fitter, 324 LC resonance, 325, 466 load parameter, 331, 465 unit-source, 107, 108, 112 Series: Fourier. 24 power, 20 Taylor. 123. 124, 138 Series-parallel conversion. 176 Short-circuit parameters: ABeD parameter relationship, 55 bridged-T equalizer, 86 for paralleling two-port networks, 86 three-pole invulnerable filter, 380 Signal path. 57 Simpson's integration. 18.98, 100 Slope: directional. 37, 137, 138 trap susceptance. 367 Smith chart: generalized, 46, 235. 236 mapping. 181 transmission line matching, 184, 186 Source. current, 203 Stability: bilateral, 257 boundaries, 260 in cascaded amplifiers. 260 circles, 261 factor, 249, 251. 374 overall, 255 unconditional, 259 I
-------- - - - Stack, RPN calculator. 7 Stack XYZT registers, 7 Standing~wave ratio (SWR): bounds on input. 374 bounds when matching, 177 circle, 235 definition. 95 maximum for invulnerable bridged·T. 379 measurement of maximum, 376 passband ripple. 197 Steepest descent search. 129, 145, 148 Stripline, 342 Stubs: capacitive loading, 299 short circuited, 337 transmission line. 82. 85 Subroutine: argument list. 72 element type. 73 integrand. 17 Subspace, 119 SUMT algorithm, 1M Surface: corved val1eys in. 131 nonquadralic. 127 Symmetric elliptic filter, 350, 358 Synchronous fiher: definition, 207 resonator reactance, 289 tuning method. 325 tuning rule. 288 Synthesis: examples, 48 finding LC element values. S4 inpul impedance example, 59 input impedance from real part, 57 number of elements, 56 polynomials. 48 pseudobandpass network. 216 terminating resistances. 57, 67 Synthetic division: linear factors. 37. 43 quadratic factors, 38 System transfer function. 62 Taylor series: examples. 167-169 finite. 16 Tellegen's theorem: adjoint network. 105 definition. 104 example. 105, 106 excitation patterns. 107, 108 inner product (orm of. 105 for gradients. 153 Termination resistance. 57. 67, 95 Terminations: for bilateral gain, 263 Subject Index 493 complex. 257 Test problems, optimization, 145 Thevenin equivalent source, 173 Time delay: definition, 96 degrees per MHz. 96 equalizer. 86. 88 by frequency perturbation. 97 units. 97 T networks; configuration. 173 Norton equivalent. 209 reactance equations, 174 Topology code. ladder network: branch number, 13 bridged·T subnetwork, 89 combline filter. 301 component number, 73 component type, 72 degenerate branches, 77 dummy elements. 77 examples, 72, 75. 76. 84, 89, 90 levels. 72-74 menu. 72 null prior branch. 73. 76 pointer. 72. 85. 88 paired data for. 72 transmission line, 83 Total differential. 102 Trajectory of successive minima. 164 Transducer function, 50. 67, 94. 245, 253 Transducer functions: commensurate filter. 336 equal-stub-admittance filter. 341 lossless reciprocal symmetric network. 338 Transformation; bilinear (linear fractional), 231, 235 frequency. 213 inversion. 241 Le. exact. 363 linear. 241 lowpass-to-bandpass. 205. 206 node-type. 364 nonlinear. of variables. 158 rotation. 243 of scattering normalization. 258 Transformer: coupling coefficient. 302 ideal. 209. 351 reactance, 302 rf. 334 Translation. linear, 21 Transmission line: ABeD parameters. 82 in cascade. 83 input impedance. 183 input reflection coefficienl, 183 characteristic impedance. 82. 84, 300
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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
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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 504 and 505: 490 Subject Index equivalent: bandp
Page 508 and 509: 494 Subject Index length. electrica
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