1.1 Modelling for Circuit Simulation
1.2 Physical Modelling and Table Modelling
1.3 Artificial Neural Networks for Circuit Simulation
1.4 Potential Advantages of Neural Modelling
1.5 Overview of the Thesis
2 Dynamic Neural Networks
2.1 Introduction to Dynamic Feedforward Neural Networks
2.1.1 Electrical Behaviour and Dynamic Feedforward Neural Networks
2.1.2 Device and Subcircuit Models with Embedded Neural Networks
2.2 Dynamic Feedforward Neural Network Equations
2.2.1 Notational Conventions
2.2.2 Neural Network Differential Equations and Output Scaling
2.2.3 Motivation for Neural Network Differential Equations
2.2.4 Specific Choices for the Neuron Nonlinearity
2.3 Analysis of Neural Network Differential Equations
2.3.1 Solutions and Eigenvalues
2.3.2 Stability of Dynamic Feedforward Neural Networks
2.3.3 Examples of Neuron Soma Response to Net Input sik(t)
2.4 Representations by Dynamic Neural Networks
2.4.1 Representation of Quasistatic Behaviour
2.4.2 Representation of Linear Dynamic Systems
2.4.2.1 Poles of H(s)
2.4.2.2 Zeros of H(s)
2.4.2.3 Constructing H(s) from H(s)
2.4.3 Representations by Neural Networks with Feedback
2.4.3.1 Representation of Linear Dynamic Systems
2.4.3.2 Representation of General Nonlinear Dynamic Systems
2.5 Mapping Neural Networks to Circuit Simulators
2.5.1 Relations with Basic Semiconductor Device Models
2.5.1.1 SPICE Equivalent Electrical Circuit for
2
2.5.1.2 SPICE Equivalent Electrical Circuit for Logistic Function
2.5.2 Pstar Equivalent Electrical Circuit for Neuron Soma
2.6 Some Known and Anticipated Modelling Limitations
3 Dynamic Neural Network Learning
3.1 Time Domain Learning
3.1.1 Transient Analysis and Transient & DC Sensitivity
3.1.1.1 Time Integration and Time Differentiation
3.1.1.2 Neural Network Transient & DC Sensitivity
3.1.2 Notes on Error Estimation
3.1.3 Time Domain Neural Network Learning
3.2 Frequency Domain Learning
3.2.1 AC Analysis & AC Sensitivity
3.2.1.1 Neural Network AC Analysis
3.2.1.2 Neural Network AC Sensitivity
3.2.2 Frequency Domain Neural Network Learning
3.2.3 Example of AC Response of a Single-Neuron Neural Network
3.2.4 On the Modelling of Bias-Dependent Cut-Off Frequencies
3.2.5 On the Generality of AC/DC Characterization
3.3 Optional Guarantees for DC Monotonicity
4 Results
4.1 Experimental Software
4.1.1 On the Use of Scaling Techniques
4.1.2 Nonlinear Constraints on Dynamic Behaviour
4.1.2.1 Scheme for τ1,ik,τ2,ik > 0 and bounded τ1,ik
4.1.2.2 Alternative scheme for τ1,ik,τ2,ik ≥ 0
4.1.3 Software Self-Test Mode
4.1.4 Graphical Output in Learning Mode
4.2 Preliminary Results and Examples
4.2.1 Multiple Neural Behavioural Model Generators
4.2.2 A Single-Neuron Neural Network Example
4.2.2.1 Illustration of Time Domain Learning
4.2.2.2 Frequency Domain Learning and Model Generation
4.2.3 MOSFET DC Current Modelling
4.2.4 Example of AC Circuit Macromodelling
4.2.5 Bipolar Transistor AC/DC Modelling
4.2.6 Video Circuit AC & Transient Macromodelling
5 Conclusions
5.1 Summary
5.2 Recommendations for Further Research
A Gradient Based Optimization Methods
A.1 Alternatives for Steepest Descent
A.2 Heuristic Optimization Method
B Input Format for Training Data
B.1 File Header
B.1.1 Optional Pstar Model Generation
B.2 DC and Transient Data Block
B.3 AC Data Block
B.4 Example of Combination of Data Blocks
C Examples of Generated Models
C.1 Pstar Example
C.2 Standard SPICE Input Deck Example
C.3 C Code Example
C.4 FORTRAN Code Example
C.5 Mathematica Code Example
D Time Domain Extensions
D.1 Generalized Expressions for Time Integration
D.2 Generalized Expressions for Transient Sensitivity
D.3 Trapezoidal versus Backward Euler Integration
Bibliography
Summary
Samenvatting
Curriculum Vitae