1. Zaichen Chen, M. Raginsky & E. Rosenbaum
Year One Report (part 2 of 2): Models to Enable System-level Electrostatic Discharge Analysis (1A6)
Zaichen Chen, M. Raginsky & E. Rosenbaum
Objective: IC behavioral model for transient simulation of ESD
RNN structure and equations:
Ensure model stability:
A sufficient condition for model stability is
Matrix be negative definite
Our approach: Regularize cost function to penalize positive eigenvalues of T
Convert learned RNN to Verilog-A model:
RNN equation can be approximated by differential eq.:
In Verilog-A model:
Hidden states x are node
voltages
i[1:n] = LHS – RHS of diff.
equation above
RNN Models for Transient Circuit Simulation
5-input 5-output system
Need to formulate KCL at all terminals except ground reference: VDD, two inputs, two outputs
Reduced complexity model:
2-input 2-output RNN; Verilog-A model is VCVS
Underlying assumptions:
VDD constant
Open load
Verilog-A RNN Model Evaluation
Differential-mode and common-mode output signals extracted from the same transient simulation
Modeling Example 2: Continuous-Time Linear Equalizer
RNN
Circuit
Verilog-A RNN Model
Training
Recurrent layer
Output
layer
Modeling Example 1: Active Rail Clamp
Verilog-A RNN model is validated by simulating circuit’s response to stimuli not included in training set
Root-mean-square error less than 2% of peak-to-peak amplitude for both V and I waveforms
Used Spectre simulator
Remaining Challenges
Data collection for multi-port circuits
Naïve way to generate training data: select S different stimuli (waveforms) for each of the N terminals, excluding the reference terminal
Total number of training waveforms needed: SN-1
Not feasible even for S=10 and N=6
Need: Smarter, adaptive method of selecting training samples
RNN poorly predicts behavior of certain circuits
Need: Identify cause and adjust data generation process or modify RNN structure accordingly