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Unilateral Scattering Gain 269 The maximum value of Ixl when IS,,1 of merit u: u lSI "IS"IIS"S"I (7.125) II-lSIII'III-IS"\'1 . Therefore, the ratio of true to maximum unilateral transducer gain is bounded as follows: I GT of true to approximate transducer gain is bounded between 0.83 and 1.23. Clearly, u must be much less than 0.1 for the unilateral scattering analysis to produce valid results. 7.5.3. Unilateral Gain Circles. A block diagram interpretation of unilateral gain (7.118)-(7.121) is useful. This is shown in Figure 7.£2. The active device's 50-ohm maximum transducer gain (!!o) is the middle block. Once the device and its bias conditions are established, the middle block is invariant. The left-hand block corresponds to the g, term in (7.118) and (7.119); it is the mismatch between the device's SII and the source reflection coefficient rI' The load block denotes a similar interpretation. Corresponding to developments leading to maximum unilateral transducer gain (7.121), conjugate matches at the device interfaces maximize power transfer, i.e., when r t =Srl and [2 = S~2' Both the g, and gL blocks in Figure 7.22 may provide gain, even though they represent passive matching components. This is true because a mismatch (reflection) loss exists between rI and SI I; tbe matching network makes up some of this loss, and is a relative gain in this sense. The output network functions similarly. Families of constant-gain circles may be obtained by setting g, and gL to fixed values and solving for r I and r, in (7.119) and (7.120), respectively. For input gain circles, the centers are located by I-ISIII'(I-g,) , (7.127) Figure 7.22. Unilateral gain block diagram according to (7.121),
270 Linear Amplifier Design Tools with radius Pul= h (1-ISIlI') I-ISIII'(I-g,)' (7.128) where g,=g,/g,ma>' Locations of output gain circles have similar forms and involve normalized gL and S22' When lSI II > 1, plot [(SIl)-I), on a Smith chart, using dotted lines for the locus versus frequency. The values may be interpreted as explained in Section 7.1.2. The locations and radii of constant-gain circles are given by (7.127) and (7.128), except that - 00
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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
Page 234 and 235: ----- -- Carlin's Broodband-Matchin
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Page 238 and 239: Car/in's Broadband.Matching Method
Page 240 and 241: Carlin's Broadband-Matching Methad
Page 242 and 243: Prohle"" 227 Third, an objective fu
Page 244 and 245: Problems 229 6.16. Program Equation
Page 246 and 247: Bilinear Tronsfonnatl'ons 231 I, ~-
Page 248 and 249: Bi/inear Transjormations 233 (w" w"
Page 250 and 251: Bilinear Transfonnations 235 accomp
Page 252 and 253: Bilinear Transfonnations 237 circle
Page 254 and 255: Impedance Mapping 239 1 3 al~ ~a3 [
Page 256 and 257: Impedance Mapping 241 r-- Z, s" I,
Page 258 and 259: ---------- Impedan£e Mapping 243 T
Page 260 and 261: Impedance Mapping 245 in Figure 7.7
Page 262 and 263: Two-Port Impedance and Power Models
Page 264 and 265: ---------------- This may be put in
Page 266 and 267: ----~-------~--- - - --------------
Page 268 and 269: -------- -- - -------------- and th
Page 270 and 271: Two-Port Impedance and Power Models
Page 272 and 273: Billlteral Scattering Stability and
Page 274 and 275: Bilateral Scattering Stability and
Page 280 and 281: --- -------- Bilateral Scattering S
Page 282 and 283: Unilateral Scattering Gain 267 the
Page 286 and 287: Prohle"" 271 _merit is u=0.08; by (
Page 288 and 289: Chapter Eight Direct-Coupled Filter
Page 290 and 291: - -- ~-------~- -------------- Dire
Page 292 and 293: Prototype Network 277 and Wo is the
Page 294 and 295: Prototype Network 279 element value
Page 296 and 297: Prototype Network 281 8./.4. Protot
Page 298 and 299: Designing with Lande Inverters 283
Page 300 and 301: Designing with L and C Inverters 28
Page 302 and 303: Designilrg with Lande Inverters Sup
Page 304 and 305: Designing with L and C Inverters 28
Page 306 and 307: General Inverters, Resonators, and
Page 310 and 311: Genera/Inverters, Resonators, and E
Page 312 and 313: conductance of the Kth resonator is
Page 316 and 317: Table 8.2. General Inverters, Reson
Page 318 and 319: General Inveners, Resonators, and E
Page 320 and 321: Four Importunt Pussband Shapes 305
Page 322 and 323: Four Important Passband Shapes 307
Page 324 and 325: FOIl' Important Possband Shopes 309
Page 332 and 333: 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
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Flowchart for Matching Program B6-1
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Program B6-3. Levy Matching to Resi
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---------- -- Program 86-5. Hilbert
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--~-- - ---------- Program B9-1. El
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---------- - -_.-------------------
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3260 TO~(TO+W)/(l-TO'N) 3270 B(l,=B
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Appendix D Linear Search Flowchart*
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Appendix E Defined Complex Constan
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Appendix F _ Doubly Terminated Mini
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Appendix G _ Direct-Coupled Filter
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461 (G.22) (G.23) (G.24) A,= (G.25)
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G.4.2. Resonator Asymptote Slopes D
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Appendix G 465 except for overcoupl
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----------_._-_.- ---- - - -_.. - A
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Appendix H _ Zverev's Tables ofEqui
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------ 6(0) 6(b) L _ (L,C,- L,C,)'
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L, L, c. " 12(a) C\=W C 2 =X L\=Y L
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Appendix H 475 Simplified Notations
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References 477 Box, M. J., D. Davie
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--------- Johnson, L. W" References
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References 481 Van Valkenburg, M. E
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_ 484 Author Index Noble, B.. 120.
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486 Subject Index second kind, 32.
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488 Subject Index proper, 62 quadra
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490 Subject Index equivalent: bandp
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1 1 _ 492 Subject Index I I Reflect
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494 Subject Index length. electrica
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