Neural-based Transient Behavioral Modeling of IC Buffers for High-speed Interconnect Design

Abstract

Artiflcial neural networks (ANN) have gained attention as fast and ∞exible vehicles to microwave modeling and design. This paper reviews a recent advance of neural network modeling, i.e., state-space dynamic neural network (SSDNN) for transient behavioral modeling of high-speed nonlinear circuits. The SSDNN model can be directly trained from the input and output waveforms without relying on the circuit internal details. A training algorithm exploiting adjoint sensitivities is summarized for training the model in an e-cient manner. An example of the SSDNN technique for IC bufier modeling and its use with transmission line elements in high-speed interconnect design are included. DOI: 10.2529/PIERS060907175229 With the continuous increase of signal speed and frequency, signal integrity (SI) in VLSI pack- ages becomes more and more prominent. Fast and accurate representations of the nonlinear analog behaviors of driver/receiver bufiers are the key to the success of SI-based design of high-speed inter- connects with nonlinear terminations (1,2). As such, developing e-cient bufier models for transient applications has become an important topic (3{5). To ensure model reliability in circuit simula- tions, the model stability remains one of the most critical aspects of nonlinear transient modeling. In the neural network community, global asymptotical stability and global exponential stability have been studied for some special classes of dynamic networks, e.g., Hopfleld neural networks (6), recurrent neural networks (7), and discrete-time state-space neural networks (8). Recently stability for ANN-based analog microwave modeling has also been addressed (9). This paper summarizes a state-space dynamic neural network (SSDNN) technique for modeling nonlinear transient behaviors of IC drivers and receivers (5). We describe the detailed structure of SSDNN and how to train the model based on the transient waveforms from the original circuits. An example is provided to demonstrate the application of the SSDNN model in coupled transmission line environments. Let u 2 < M be transient input signals of a nonlinear circuit, e.g., input voltages and currents, and y 2 < K be transient output signals of a nonlinear circuit, e.g., output voltages and currents where M and K are the numbers of circuit inputs and outputs respectively. Based on combining state-space concept and continuous recurrent neural network method (10), the SSDNN nonlinear model is formulated as (5) ( _ x(t) = ix(t) + ?g ANN (u(t);x(t);w)