| Preface |
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ix | |
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Introduction to Circuit Simulation |
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1 | (26) |
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Traditional Circuit Simulation |
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1 | (1) |
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Linear, Time-Invariant Circuits |
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2 | (2) |
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4 | (2) |
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Nodal Admittance Equation Stamps |
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6 | (5) |
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Nonlinear (dc) Circuit Analysis |
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11 | (6) |
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Small Signal (ac) Analysis |
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17 | (1) |
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Linear Transient Analysis |
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18 | (6) |
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Nonlinear Transient Analysis |
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24 | (1) |
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24 | (2) |
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26 | (1) |
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27 | (20) |
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Voltage-Controlled Current Sources |
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27 | (4) |
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Independent Voltage Sources |
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31 | (3) |
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(Conventional) Nodal Analysis |
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34 | (2) |
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Controlled Sources in General |
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36 | (4) |
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40 | (2) |
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When Do Nodal Equations Fail? |
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42 | (1) |
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DC Solution of Circuits with Energy Storage: C-cutsets and L-loops |
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43 | (1) |
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44 | (1) |
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45 | (2) |
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Solution of Linear Equations |
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47 | (28) |
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47 | (3) |
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50 | (4) |
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How LU Factorization Works |
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54 | (4) |
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58 | (6) |
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64 | (3) |
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67 | (7) |
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74 | (1) |
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74 | (1) |
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Linear Transient Analysis I |
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75 | (40) |
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The One-Step Integration Approximations |
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75 | (5) |
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Forward Euler Approximation |
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80 | (1) |
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Backward Euler Approximation |
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81 | (1) |
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Trapezoidal Approximation |
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82 | (1) |
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Companion Models for Inductors |
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82 | (4) |
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Preliminary Comments on Accuracy |
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86 | (1) |
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The Exact Solution of a Simple Series RC Circuit |
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87 | (8) |
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Comparison of One-Step Integration Approximations with the Exact Solution |
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95 | (5) |
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Accuracy of One-Step Approximations |
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100 | (5) |
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Stability of One-Step Integration Approximation |
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105 | (4) |
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LTE Estimation via Divided Difference Approximations |
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109 | (4) |
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113 | (1) |
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113 | (1) |
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113 | (2) |
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Linear Transient Analysis II |
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115 | (26) |
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Multiple Energy Storage Elements |
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115 | (10) |
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125 | (3) |
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One-Step Integration Approximations |
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128 | (6) |
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134 | (5) |
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Limitations of One-Step Integration Models |
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139 | (1) |
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140 | (1) |
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Frequency Domain Analysis and Moment-Matching Methods |
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141 | (48) |
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141 | (4) |
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145 | (2) |
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Laplace Transform of the State Equations |
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147 | (2) |
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Moments of the Impulse Response and Linear Delay Estimation |
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149 | (3) |
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The Elmore Delay and RC Trees |
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152 | (1) |
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Moments of the Impulse Response |
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153 | (3) |
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Efficiently Computing Moments for RC Trees |
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156 | (2) |
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Dominant Pole Approximations |
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158 | (3) |
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Dominant Poles via Moment Matching |
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161 | (4) |
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Computing Moments for Generalized Circuits |
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165 | (4) |
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Generalized Moment Matching |
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169 | (6) |
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Practical (Numerical) Considerations |
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175 | (7) |
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182 | (4) |
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186 | (1) |
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186 | (3) |
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Sparse Matrices and Some of Their Implications |
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189 | (28) |
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189 | (1) |
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Sparse Nodal Admittance Matrices |
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190 | (4) |
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Ordering of Sparse Matrices |
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194 | (2) |
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196 | (2) |
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Numerical Conditioning and Partial Pivoting |
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198 | (2) |
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200 | (4) |
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Qualitative Attributes of the Sparse Tableau |
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204 | (2) |
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Relation of the Sparse Tableau to Other Solution Schemes |
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206 | (2) |
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The Original Sparse Tableau Approach |
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208 | (2) |
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Some Sparse Tableau Modeling Considerations |
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210 | (4) |
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214 | (3) |
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Circuit Partitioning and Large Change Sensitivity |
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217 | (22) |
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Adding a Resistance Between Two Nodes |
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218 | (9) |
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227 | (4) |
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Multiple Voltage Source Additions |
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231 | (6) |
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237 | (2) |
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239 | (46) |
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Direct Circuit Sensitivities |
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240 | (4) |
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Matrix Interpretation of Direct Sensitivity |
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244 | (2) |
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Controlled Sources and Nonlinear Elements |
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246 | (3) |
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Adjoint Sensitivity Analysis |
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249 | (2) |
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The Adjoint Sensitivity Relation |
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251 | (1) |
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Simple Reciprocal (R, G, V, I) Linear dc Circuits |
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252 | (7) |
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Sensitivities with Respect to Dependent Source Values |
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259 | (5) |
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Adjoint Circuit Representation of Some Other Multi-Terminal Circuit Elements |
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264 | (3) |
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The Sparse Tableau Interpretation of Adjoint Sensitivity |
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267 | (7) |
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Some Possible Applications of Adjoint Sensitivity |
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274 | (3) |
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Time and Frequency Domain Sensitivity Analysis |
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277 | (6) |
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283 | (2) |
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Simulation of Nonlinear Circuits |
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285 | (30) |
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285 | (2) |
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287 | (1) |
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288 | (3) |
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Damped Newton-Raphson Iteration |
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291 | (4) |
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Multi-Dimensional Newton-Raphson Iteration |
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295 | (2) |
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297 | (9) |
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Nonlinear Transient Analysis |
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306 | (2) |
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Nonlinear Energy Storage Elements |
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308 | (5) |
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313 | (1) |
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314 | (1) |
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315 | (46) |
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The Quest for Other Methods of Simulation |
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315 | (1) |
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Static vs. Dynamic Simulation |
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316 | (1) |
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317 | (5) |
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Motivation for Timing Simulation |
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322 | (3) |
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The MOS Timing Simulator (MOTIS) |
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325 | (3) |
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328 | (4) |
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Piecewise Approximate Timing Simulation |
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332 | (17) |
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Relaxation Methods in Circuit Simulation |
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349 | (7) |
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356 | (1) |
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356 | (5) |
| Appendix A Tree/Link Analysis |
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361 | (24) |
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361 | (2) |
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A.2 Fundamental Loops and Cutsets |
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363 | (3) |
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366 | (2) |
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A.4 Sparse Tableau and Reduced Tableau Analysis |
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368 | (1) |
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A.5 Loop and Cutset Matrices |
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369 | (2) |
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A.6 Circuit Equations in Terms of Loops and Cutsets |
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371 | (5) |
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A.7 Tree Selection Procedure |
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376 | (7) |
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383 | (2) |
| Index |
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385 | |
