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486 Subject Index second kind, 32. 314, 341 Chebyshev response, 67, 458 Circles: bilateral gain, 264 concentric, 264 eccentric, 253 unilateral gain, 269 Circutator. three·pan, 78 Coefficients: bilinear, 232, 241, 261 complex. 11. 35 Levy's, 27 mapping, 242, 245, 249 normalization, 10 pivot. 10 power series. 20, 22 real linear equations, 8 reflection, generalized, 46 scaling, 21 weighting. 22 Combline fiher, 301 Commensurate filters, 336 Complex four functions, 7, 386 Comptex linear update, 73, &0, 92 Complex variables: polar format, 7 polar.to-reclangular conversion. 82 rectangular format, 7t Computer program features. 2. 46 Computing. an of. 1 Conditioning:, numerical. 21, 26, 64. 232 Conic. 121 Conjugate gradient: algorithm. 134 directions. 450 Conjugate match, 173 Conjugate pairs. 38. 45, 64 Conjugate terminations, 252 Conjugate vectors. 134, 135 Constraints: active, 157 binding, 157 equality, 157 feasible, 165 implicit, 157 inequality. 157 linear. 162 mixed, 165 satisfied~when-exceeded. 157, 165 transformations for variables, 161 upper and lower bounds, 157. 159 Continued fraction expansion', examples, 52 Hurwitz test using, 54 input resistance, 296 (owpass and highpass. 52 of reactance functions, 51 shorthand notation for, 52 Convergence, 136. 145 Conversion, three~port to two-port, 238 Convolution integral. 97 Coupling: between bars, 343 coefficient. 285, 302 edge, 336 end, 302 mutual magnetic, 284 selectivity effects. 303 Cramer's rule. 233 Current division, 87 Currents in shunt branches, 70 Curve fitting. complex, 26 Damping. terminating conductance, 255 Data: discrete, 25 noisy, 25, 234 transistor, 252, 255, 265. 270, 272 triple~, 27, 232 DATA statement, JI Decrement, 74, 88, 112. 193, 198. 201, 378. 380 Derivative: by Cauchy-Riemann principle, 35 directional, 137, 138. 168 exact panial, 104, 11 L 112 by finite differences, 103, ilL 112, 144 normalized partial, 102 by numerical differentiation, 97 of objective function, 116 operator notation. 101, 105 partial. 26, 33, 36, 65, 103 programming of, 126 scaling. 101 second, 124 Design steps, I 13 Determinant, 233 Direct~coup\ed filters: equivalent network at tune frequency, 296 design example. 327 design flowchart, 321 design limitations, 323 equal-stub realiLation, 337 equations. 457 origins, 273 overview. 5 prototype network, 273. 276, 278, 337 selectivity, 275 sensitivities, 324 shunt-L adjustments, 323 transfer function, 279 tuning rule, 288 Direct filter design overview. 6 Dissipation effect on: input resistance. 295 inverters. 297
------------_.- - - - - - -- - - - ------------------- Subject Index 487 L·sections. 302 resonators, 295, 297 stopband selectivity, 297 Divide by zero. 8. 74 Droop parameter; definition. 310 maximum, 310, 313 Dummy: branch elements. 77 load, 24, 57 Edge~collpJed filters, 343 Efficiency; circle, 264 definition, 92 of direct-coupled filters, 295 loci of constant, 253 maximum, 250, 264, 374, 377 resonator, 295 from scattering parameters, 263 Eigenvalue; definition, 122 example, 132, 168 Eigenvector: in ellipsoid, J22 in orthogonal matrix. 132 Electromagnetic modes. extraneous, 336 Element: commensurate, 336 negative, 284. 351, 361 subroutines, 73 type numbers, 72 units, 73 unsealed value of, 78 Ellipse: rotation, 120 translation, J20 Elliptic filter: input impedance relationships, 353 permutation algorithm. 354. 357 precision teslS. 360 selectivity family, 345 selectivity function, 346 types, 350 Elliptic integral, 348 Equalization. time delay. 152,219 Equal~stub admittance filters. 336 Equations: comp1e:\ linear. 11 matrix. 9,11. 27, 31 nonlinear simultaneous, 26 real linear, 9. 59 Equipment costs, 1 Error: integral' function, 150 least pth. 114 minimum. 27 overflow. 159 round-off. 348 Simpson's rule, 18 surface, 36, 115 trapezoidal rule, 15 Evaluation: of partial derivatives, 39. 40 of polynomials with complex coefficients, 39. 40. 43 Extrapolation: linear, 15 Richardson, 16, 153, 165 Romberg, 16 slope, 139, 141 Feedback, transistor, 78, 241 Feldkeller energy equation, 47 Filter, invulnerable: bridged-To 377 definition, 377 three-pole, 380 Finite differences, 223 Flag, 73, 82, 155 Fletcher-Powell search, 134 Fletcher-Reeves search, 134, 136,450 Fourier integral; fast transform, lOt graphic interpretation, 99 for real causal functions, 98 frequency, fractional. 287 Function: analytic. 35 barrier. 163, 169 bilinear, 232, 242 Butterworth, 308 characteristic. 48, 50, 55 Chebyshev. 305 composite bilinear, 240 compound, for constraints. 165 cross terms in, 121, 131. 133 cubic, in extrapolation, 140 curved valley, 146 discontinuous, 144. 152 error, 26. 36 even. 23, 24. 26, 47. 48, 51 Fano. 310 fitting, 140, 152 global minimum. 135 impulse, 62 inflection point. JJ9 input impedance. 58. 82 mapping. 133 maximum, 115 minimum. 119, 120 bounded, 140 minimum phase, 222 objective. 116, 145. lSI odd, 23, 26, 47, 48, 51 piecewise linear. 219, 226
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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
Page 450 and 451: Flowchart for Ladder Analysis Progr
Page 452 and 453: 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 502 and 503: 488 Subject Index proper, 62 quadra
Page 504 and 505: 490 Subject Index equivalent: bandp
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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