Node list tolerance analysis enhacing SPICE capabilities with mathcad

Developed at UC Berkeley more than two decades ago, SPICE software is the tool of choice for performing nominal analysis for electronic circuits. However, attempts to use SPICE for worst-case analysis (WCA) reveal several shortcomings, including: a 400-sample limit for Monte Carlo Analysis (MCA); lack of Rot-Sum-Square (RSS) analysis, asymmetric component tolerances, Fast MCA, or AC sensitivity capability; no single-run method of tolerancing inputs; and no predefined beta (skewed) or bimodal (gapped) distributions for MCA. While several commercial versions of SPICE may have corrected some of these limitations, they still remain rather expensive.

Based on extensive experience in WCA, Node List Tolerance Analysis: Enhancing SPICE Capabilities with Mathcad presents software methods that overcome the many limitations of SPICE WCA using less expensive tools. The author demonstrates correct and incorrect methods of extreme value analysis, demonstrates the necessity of tolerancing multiple inputs, and provides output histograms for unusual inputs. He also shows how to detect non-monotonic components, which cause severe errors in all WCA methods except MCA. The book also includes demonstrations of tolerance analysis of three-phase AC circuits.

Node List Tolerance Analysis: Enhancing SPICE Capabilities with Mathcad requires no circuit analysis mathematics, supplying original methods of nominal circuit analysis using node lists. It is ideal for performing effective analyses while adhering to a budget.

Part I Nominal Analysis
Chapter 1 Introduction	p. 3
1.1 Nominal Analysis	p. 3
1.1.1 Introduction	p. 3
1.1.2 The NDS Method of Nominal Circuit Analysis	p. 4
1.1.3 General Guidelines	p. 5
1.2 Introduction to Node List Circuit Analysis	p. 6
1.2.1 Rules and Definitions	p. 6
Chapter 2 Passive Circuits	p. 9
2.1 Introduction to Node List Circuit Analysis (Part One)	p. 9
2.2 Introduction to Node List Circuit Analysis (Part Two)	p. 16
2.3 All-Capacitive Circuit	p. 21
2.4 All-Inductive Circuit	p. 23
2.5 Twin-T RC Network	p. 24
2.6 Broadband Pulse Transformer Model	p. 27
2.7 All-Capacitive Loops (ACL)	p. 30
2.8 All-Inductive Cutsets (ICS)	p. 31
2.9 All-Capacitive Loop Example	p. 32
References	p. 34
Chapter 3 Controlled Sources	p. 35
3.1 Controlled (Dependent) Sources	p. 35
3.1.1 Voltage-Controlled Current Source (VCCS)	p. 35
3.1.2 Current-Controlled Current Source (CCCS)	p. 35
3.1.3 Voltage-Controlled Voltage Source (VCVS)	p. 35
3.1.4 Current-Controlled Voltage Source (CCVS)	p. 36
3.1.5 CCVS to VCVS	p. 36
3.1.6 CCCS to VCCS	p. 36
3.1.7 Four Rules that Must be Observed	p. 37
3.2 Floating VCVS	p. 38
3.3 Circuits with M > 1	p. 41
3.4 First-Order MOSFET Model	p. 44
3.5 VCVS and CCCS Example	p. 46
3.6 Two Inputs, Three Outputs	p. 50
3.7 Third-Order Opamp Model	p. 54
3.8 A Subcircuit Scheme	p. 56
3.9 Subcircuit Opamp Model	p. 58
3.10 Fifth-Order Active Filter	p. 59
3.11 State Variable Filter	p. 60
3.12 Seventh-Order Elliptical Low-Pass Filter	p. 63
3.12.1 Stepping One Resistor Value	p. 68
3.12.2 Stepping All Seven Capacitor Values	p. 71
3.13 Square Root of Frequency (+10 dB/decade) Circuit	p. 74
3.14 HV (200 V) Shunt MOSFET Regulator	p. 76
3.15 LTC 1562 Band-Pass Filter IC in a Quad IC	p. 78
3.16 LTC 1562 Quad Band Filter IC	p. 79
3.17 BJT Constant Current Source - A Simple Linear Model Using the NDS Method	p. 87
3.18 uA733 Video Amplifier	p. 89
References	p. 95
Chapter 4 Leverrier's Algorithm	p. 97
4.1 Numerical Transfer Function [1]	p. 97
4.2 Transfer Function Using Leverrier's Algorithm for Twin-T RC Network	p. 100
References	p. 101
Chapter 5 Stability Analysis	p. 103
5.1 Unity Gain Differential Amplifiers	p. 103
5.2 Stability of LM158 Opamp Model	p. 106
5.3 High-Voltage Shunt Regulator - Stability Analysis	p. 109
Chapter 6 Transient Analysis	p. 115
6.1 Introduction	p. 115
6.2 Switched Transient Analysis	p. 118
6.3 N = 2 Switched Circuit Transient Response	p. 120
6.4 Comparator 100-Hz Oscillator	p. 123
6.5 Transient Analysis of Pulse Transformer	p. 127
6.6 Passive RCL Circuit Transient Analysis	p. 131
6.7 Mathcad's Differential Equation Solvers	p. 133
6.8 A Mathematical Pulse Width Modulator (PWM)	p. 135
6.9 Switching Power Supply Output Stage - Buck Regulator	p. 137
6.10 State Space Averaging	p. 140
6.11 Simple Triangular Waveform Generator	p. 143
6.12 Quadrature Oscillator	p. 145
6.13 Wein Bridge Oscillator	p. 148
References	p. 149
Chapter 7 DC Circuit Analysis	p. 151
7.1 Resistance Temperature Detector (RTD) Circuit	p. 151
7.2 An Undergraduate EE Textbook Problem	p. 152
7.2.1 Matrix Solution To Demonstrate the Utility of the NDS Method	p. 153
7.3 DC Test Circuit	p. 154
7.4 Stacking VCVS's and Paralleling VCCS's	p. 158
7.5 DC Voltage Sweep (RTD Circuit)	p. 159
7.6 RTD Circuit - Step Resistor Value	p. 161
7.7 Floating 5-V Input Source	p. 164
Chapter 8 Three-Phase Circuits	p. 167
8.1 Convert [Delta] Floating Voltage Inputs to Single-Ended Y Inputs	p. 167
8.2 Three-Phase NDS Solution	p. 170
8.2.1 Unbalanced Delta Load - Single-Ended Inputs on A and B	p. 170
8.2.2 Unbalanced Delta Load - Single-Ended Inputs on A and C	p. 172
8.3 Three-Phase Y - Unbalanced Load	p. 174
8.4 Three-Phase Y-Connected Unbalanced Load - Floating Delta Input	p. 177
8.5 Balanced Y- Load	p. 181
References	p. 186
Appendix I	p. 187
Background Theory of NDS Method	p. 187
A-I.1 Theory of NDS Method	p. 196
A-I.1.1 An AC Floating VCVS	p. 199
A-I.1.2 VCVS and CCCS	p. 203
Part II Tolerance Analysis
Chapter 9 Introduction	p. 211
9.1 Introduction	p. 211
9.1.1 Tolerance Analysis of Circuits with Discrete Components	p. 211
9.1.2 Analysis Methods	p. 212
9.2 Some Facts about Tolerance Analysis	p. 212
9.2.1 DC Analysis	p. 212
9.2.1.1 Monte Carlo Analysis	p. 213
9.2.2 AC Analysis	p. 213
9.2.3 Transient Analysis	p. 217
9.2.4 Asymmetric Tolerances	p. 217
References	p. 217
Chapter 10 DC Circuits	p. 219
10.1 Resistance Temperature Detector (RTD) Circuit	p. 219
10.2 A Note on Asymmetric Tolerances	p. 221
10.3 Centered Difference Approximation - Sensitivities	p. 222
10.4 RTD Circuit Monte Carlo Analysis (MCA)	p. 224
10.5 RTD MCA with R4 Tolerance = 10%	p. 226
10.6 RTD Circuit Fast Monte Carlo Analysis (FMCA)	p. 227
10.7 A CASE FMCA Greater than EVA	p. 228
10.8 Tolerancing Inputs	p. 231
10.9 Beta Distributions [4-6]	p. 232
10.10 RTD MCA - Beta (Skewed) Distribution	p. 234
10.11 MCA of RTD Circuit using Bimodal (Gapped) Distribution Inputs	p. 236
References	p. 239
Chapter 11 AC Circuits	p. 241
11.1 Circuit Output vs. Component Value	p. 241
11.2 Exact Values of C1 Sensitivity	p. 247
11.3 Multiple-Output EVA	p. 248
11.4 Butterworth Low-Pass Filter Circuit	p. 250
11.5 Butterworth Low-Pass Filter MCA	p. 251
11.6 Butterworth Low-Pass Filter EVA	p. 253
11.7 Butterworth Low-Pass Filter FMCA	p. 254
11.8 Multiple-Feedback Band-Pass Filter (BPF) Circuit	p. 255
11.9 Multiple-Feedback BPF MCA	p. 256
11.10 Multiple-Feedback BPF EVA	p. 257
11.11 Multiple-Feedback BPF FMCA	p. 259
11.12 Switching Power Supply Compensation Circuit	p. 260
11.13 Switching Power Supply Compensation MCA	p. 261
11.14 Switching Power Supply Compensation EVA	p. 262
11.15 Switching Power Supply Compensation FMCA	p. 264
11.16 Sallen and Key Band-Pass Filter (BPF) Circuit	p. 265
11.17 Sallen and Key BPF MCA	p. 266
11.17.1 Sallen and Key BPF - MCA with both Common and Precision Tolerances	p. 267
11.18 Sallen and Key BPF EVA	p. 268
11.19 Sallen and Key BPF FMCA	p. 270
11.20 State Variable Filter Circuit	p. 271
11.21 State Variable Filter MCA	p. 272
11.22 State Variable Filter EVA	p. 273
11.23 State Variable Filter FMCA and MCA Combined	p. 275
11.24 High-Q Hum Notch Filter Circuit	p. 276
11.25 High-Q Hum Notch Filter MCA	p. 278
11.26 High-Q Hum Notch Filter EVA	p. 279
11.27 High-Q Hum Notch Filter FMCA	p. 280
11.28 LTC 1562 MCA	p. 281
11.29 LTC 1562 EVA	p. 282
References	p. 284
Chapter 12 Transient Tolerance Analysis	p. 285
12.1 Transient MCA - Twin-T RC Network	p. 285
12.2 Transient MCA - Multiple Feedback BPF	p. 286
12.3 AC and Transient MCA - Bessel HPF	p. 288
12.4 Transient MCA - State Variable Filter	p. 291
Chapter 13 Three-Phase Circuits	p. 295
13.1 Three-Phase Y-Connected Unbalanced Load MCA	p. 295
13.2 Three-Phase Y-Connected Unbalanced Load EVA	p. 297
13.3 Three-Phase Y-Connected Unbalanced Load FMCA	p. 300
Chapter 14 Miscellaneous Topics	p. 303
14.1 Components Nominally Zero	p. 303
14.2 Tolerance Analysis of Opamp Offsets	p. 305
14.3 Best-Fit Resistor Ratios	p. 309
14.4 Truncated Gaussian Distribution	p. 311
14.5 LTC1060 Switched Capacitor Filter	p. 313
14.5.1 Design Procedure from the Data Sheet	p. 313
Appendix II	p. 319
Summary of Tolerance Analysis Methods	p. 319
DC	p. 319
AC	p. 319
Transient	p. 319
Table of Subprograms	p. 320
Part I Nominal Analysis Subprograms	p. 320
Part II Tolerance Analysis Subprograms (Used with Part I Subprograms)	p. 320
In Case of Difficulty	p. 320
Abbreviations	p. 321
Index	p. 323

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