Application of artificial neural networks for eye-height/width prediction from s-parameters

Signal speeds of high speed serial data links double almost every generation and with increasing speeds, simulation and modeling challenges are getting more complex. The present popular and widely accepted metric for simulating a high speed link from signal integrity (SI) perspective is Bit Error Rate (BER) testing. SI engineers look at eye-height and eye-width to determine the quality of an interface for a given set of design parameters. In order to perform BER simulations, time domain simulations need to be performed over billions of bits for serial links using statistical approaches and these simulations are time, processing power and memory intensive. Design of Experiments (DoE) is typically used to decrease the number of time-domain simulations needed to cover the design space, however it is sometimes in-accurate as compared to full-factorial design sweeps. End to end channel simulation in frequency domain is much faster and less resource intensive. In this paper, a DoE based set of channel parameters are simulated in both time-domain and frequency-domain to train a multi-layer perceptron (MLP) type of artificial neural network (ANN) to predict eye-height from frequency domain metrics like return loss (RL) and insertion loss (IL). This results in a significant speed-up towards a more accurate all corner study as compared to DoE based analysis.

I. Introduction

With increasing signal speeds for high speed interfaces on blade and rack servers, signal integrity (SI) evaluation based on eye height (EH), eye width (EW) and bit error rate (BER) testing becomes intensive in compute power, memory and time. For a selected channel topology, there are several variables impacting the signal quality. These variables include controllable variables like trace length, impedance, termination and uncontrollable variables such as process and manufacturing tolerances. Design rules are needed to ensure signal quality is good. In order to come up with design rules, several Time Domain (TD) simulations are needed to cover the design space. State of art existing methods involve statistical or optimization techniques to span over the design space, covering all possible corners. Design of experiments (DoE) is a technique based on generating orthogonal vectors in a multi-dimensional design space to generate a design set that would cover the entire design space. Response surface method (RSM) is used to fit the DoE based designs to predict EH and EW and to perform Monte-Carlo analysis based on RSM analysis [1]. A Multi-Layer Perceptron (MLP) based Artificial Neural Network (ANN) method to predict EH and EW from channel topology variables, using a DoE to train the network and capture the non-linear dependence of the EH and EW on the variables is presented in [2]. However, from [3], it is also evident that a DoE based approach can sometimes provide an in-accurate sensitivity analysis of EH and EW to certain variables when compared to a full-factorial sweep across all possible design and process variations. Performing TD simulations for full-factorial sweep will take excessive time. However, Frequency Domain (FD) simulations take much less time and can be used to perform full-factorial design sweeps.