Computer Methods for Circuit Analysis and Design |
Contents
Fundamental Concepts | 1 |
12 INDEPENDENT SOURCES | 4 |
13 CAPACITORS AND INDUCTORS IN THE LAPLACE TRANSFORM DOMAIN | 5 |
14 DEFINITION OF PORTS AND TERMINALS | 9 |
15 TRANSDUCERS DEPENDENT SOURCES | 10 |
16 ELEMENTARY TWOPORTS | 12 |
17 THEVENIN AND NORTON TRANSFORMATIONS | 16 |
18 NETWORK SCALING | 18 |
92 ORDER OF INTEGRATION AND TRUNCATION ERROR | 268 |
93 STABILITY OF INTEGRATION | 270 |
94 TIME DOMAIN SOLUTION OF LINEAR NETWORKS | 275 |
Numerical Laplace Transform Inversion | 282 |
101 DEVELOPMENT OF THE METHOD | 283 |
102 PROPERTIES OF THE METHOD | 291 |
103 APPLICATION | 293 |
104 STEPPING ALGORITHM FOR NETWORKS AND NETWORK FUNCTIONS | 299 |
19 NETWORK FUNCTIONS POLES AND ZEROS | 19 |
110 TIME DOMAIN RESPONSE | 22 |
Network Equations and Their Solution | 28 |
21 NODAL FORMULATION | 29 |
22 NODAL FORMULATION FOR NETWORKS WITH VCTs | 35 |
23 MESH FORMULATION | 38 |
24 LINEAR EQUATIONS AND GAUSSIAN ELIMINATION | 40 |
25 TRIANGULAR DECOMPOSITION | 43 |
26 PIVOTING | 52 |
27 SPARSE MATRIX PRINCIPLES | 53 |
28 SPARSE MATRIX IMPLEMENTATION | 60 |
Graph Theoretic Formulation of Network Equations | 74 |
31 KVL KCL AND ORIENTED GRAPHS | 75 |
32 INCIDENCE MATRIX | 76 |
33 CUTSET AND LOOPSET MATRICES | 79 |
34 ORTHOGONALITY RELATIONS FOR THE Q AND B MATRICES | 84 |
35 INDEPENDENT CURRENTS AND VOLTAGES | 85 |
36 INCORPORATING SOURCES INTO GRAPH CONSIDERATIONS | 87 |
37 TOPOLOGICAL FORMULATION OF NODAL EQUATIONS | 88 |
38 TOPOLOGICAL FORMULATION OF LOOP EQUATIONS | 91 |
39 STATE VARIABLE FORMULATION | 94 |
General Formulation Methods | 100 |
41 TABLEAU FORMULATION | 101 |
42 BLOCK ELIMINATION ON THE TABLEAU | 109 |
43 MODIFIED NODAL FORMULATION USING ONE GRAPH | 110 |
44 MODIFIED NODAL FORMULATION BY INSPECTION | 114 |
45 NODAL ANALYSIS OF ACTIVE NETWORKS | 119 |
46 SEPARATE CURRENT AND VOLTAGE GRAPHS | 123 |
47 REPRESENTATION OF THE GRAPHS ON THE COMPUTER | 131 |
48 MODIFIED NODAL FORMULATION USING I AND V GRAPHS | 132 |
49 SUMMARY OF THE FORMULATION METHODS | 140 |
410 EXAMPLE | 141 |
Sensitivities | 152 |
51 SENSITIVITY DEFINITIONS | 153 |
52 MULTIPARAMETER SENSITIVITY | 158 |
53 SENSITIVITIES TO PARASITICS AND OPERATIONAL AMPLIFIERS | 162 |
Computer Generation of Sensitivities | 171 |
61 SENSITIVITY OF LINEAR ALGEBRAIC SYSTEMS | 172 |
63 ADJOINT SYSTEM METHOD APPLIED TO NETWORKS | 177 |
64 SENSITIVITY TO OPAMPS AND PARASITICS | 179 |
65 APPLICATIONS OF THE ADJOINT SYSTEM METHOD | 183 |
67 EXAMPLES | 201 |
Network Functions in the Frequency Domain | 208 |
71 NETWORK FUNCTIONS POLES AND ZEROS | 209 |
72 COMPUTER GENERATION OF NETWORK FUNCTIONS | 210 |
73 UNIT CIRCLE POLYNOMIAL INTERPOLATION | 211 |
74 CONDITION NUMBERS FOR INTERPOLATIONS | 214 |
75 ALGORITHM FOR SYMBOLIC FUNCTION GENERATION | 217 |
76 ROOTS OF FUNCTIONS AND POLYNOMIALS | 221 |
77 ROOT REFINEMENT | 223 |
78 POLES AND ZEROS FROM SYSTEM EQUATIONS | 228 |
79 EXAMPLE | 229 |
Large Change Sensitivity and Related Topics | 235 |
81 LARGE CHANGE SENSITIVITY | 236 |
82 DIFFERENTIAL SENSITIVITY USING THE 3 MATRIX | 245 |
83 FAULT ANALYSIS | 249 |
84 ZERO PIVOTS IN SPARSE MATRIX FACTORIZATION | 251 |
85 SYMBOLIC ANALYSIS | 253 |
Introduction to Numerical Integration of Differential Equations | 262 |
Modeling | 308 |
111 DIODE MODELS | 309 |
112 FIELD EFFECT TRANSISTOR MODELS | 313 |
113 BIPOLAR TRANSISTOR MODELS | 317 |
114 MACROMODELS | 325 |
115 APPROXIMATE DEVICE MODELS | 329 |
DC Solution of Networks | 339 |
122 NODAL FORMULATION | 344 |
123 TABLEAU AND MODIFIED NODAL FORMULATION | 348 |
124 CONVERGENCE IN DIODETRANSISTOR NETWORKS | 350 |
125 DC SENSITIVITY | 351 |
126 PIECEWISE LINEARIZATION | 354 |
Numerical Integration of Differential and AlgebraicDifferential Equations | 364 |
131 DERIVATION OF LMS FORMULAE | 365 |
132 THEORY OF LMS FORMULAE | 373 |
133 PROPERTIES OF LMS FORMULAE | 378 |
134 SYSTEMS OF DIFFERENTIAL EQUATIONS | 382 |
135 BACKWARD DIFFERENTIATION WITH VARIABLE STEP AND ORDER | 385 |
136 TABLEAU AND MODIFIED NODAL FORMULATIONS OF NONLINEAR NETWORKS | 389 |
Digital and SwitchedCapacitor Networks | 395 |
141 DISCRETE SIGNALS | 396 |
142 zTRANSFORM | 402 |
143 FORMULATION OF DIGITAL NETWORK EQUATIONS | 404 |
144 SWITCHEDCAPACITOR NETWORKS | 408 |
145 FORMULATION OF MINIMALSIZE SC NETWORK EQUATIONS | 413 |
146 FREQUENCY REPRESENTATION OF PERIODIC AND SAMPLED SIGNALS | 416 |
147 ANALYSIS OF THE DIGITAL SYSTEM | 421 |
148 SPECTRAL ANALYSIS OF SWITCHEDCAPACITOR NETWORKS | 423 |
149 SINGLE OUTPUT AND ITS SENSITIVITY | 424 |
1410 SOLUTION OF THE DIGITAL SYSTEM BY BLOCK SUBSTITUTION | 427 |
1411 SAMPLEHOLD INPUT AND SYMBOLIC ANALYSIS | 429 |
Introduction to Optimization Theory | 436 |
151 BASIC DEFINITIONS | 437 |
152 CLASSICAL MINIMIZATION | 439 |
153 BASIC ITERATIVE ALGORITHM | 441 |
155 QUADRATIC FUNCTIONS IN SEVERAL VARIABLES | 447 |
156 DESCENT METHODS FOR MINIMIZATION | 452 |
157 CONSTRAINED MINIMIZATION | 457 |
Time Domain Sensitivities and Steady State | 464 |
161 SENSITIVITY NETWORKS | 465 |
162 SENSITIVITIES OF OJBECTIVE FUNCTIONS | 469 |
163 STEADY STATE USING SENSITIVITY NETWORKS | 472 |
164 STEADY STATE ON OBJECTIVE FUNCTION | 474 |
165 STEADY STATE BY EXTRAPOLATION | 476 |
Design by Minimization | 483 |
171 MEANSQUARE OBJECTIVE FUNCTIONS | 484 |
172 MATCHING OF COMPLEX VALUES | 487 |
173 MINIMAX SOLUTIONS | 491 |
174 MINIMIZATION OF SENSITIVITIES | 496 |
175 MONTE CARLO ANALYSIS | 500 |
Laplace Transforms | 505 |
Partial Fraction Decomposition of Rational Functions | 511 |
Special Complex Integration of a Rational Function | 516 |
Program for Network Analysis | 518 |
Sparse Matrix Solver | 558 |
Selected Mathematical Topics | 571 |
Bibliography | 579 |
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Computer Methods for Circuit Analysis and Design Kishore Singhal,Jiri Vlach No preview available - 2010 |
Common terms and phrases
adjoint system admittance algorithm analysis applied back substitution C₁ Calculate capacitor Chapter circuit coefficients column components Consider constitutive equations corrector current source decomposition defined denoted derivatives differential edges elements entries equivalent error Euler formula EXAMPLE factorization G₁ G₂ Gaussian elimination given graph IEEE inductor initial conditions input integration iteration Jacobian Laplace transform LU decomposition matrix equation method modified nodal formulation NEMT network function network in Fig network shown Newton-Raphson node nonlinear nonzero obtained OPAMP operational amplifier output parameter pivot poles and zeros polynomial predictor problem resistor respect response result right-hand side Section sensitivity shown in Fig solution solved sparse matrix step SUBROUTINE symbolic system matrix tableau tion transfer function transistor two-graph unit circle V-graph V₁ V₂ values variable vector voltage source Vout WRITE x₁ Xn+k ΚΩ