Transmission Waveform Simulation on Printed Circuit Boards Using MATLAB and ChatGPT

This article introduces a method for designing high-performance printed circuit board (PCB) traces by using ChatGPT to generate MATLAB code for numerical analysis—without relying on expensive EM-field simulators or high-speed oscilloscopes.

By predicting waveform degradation caused by transmission-line loss with good accuracy, this practical evaluation technique allows you to estimate transmission quality and the bit error rate (BER) before fabricating a prototype PCB.

We reinterpret the high-speed square-wave-like signals output by modern semiconductor devices—such as microcontrollers, digital ICs, and PWM drivers—not as mere time-domain waveforms, but as a superposition of frequency components in the frequency domain.

Frequency components in the multi-GHz range are attenuated by line loss as they propagate along PCB traces. In practice, trace loss is described by a complex frequency response that includes both amplitude and phase. To simplify the discussion, we assume a constant group delay (i.e., a linear phase response versus frequency). Specifically, we take the frequency-dependent loss characteristic (S21) obtained from PCB physical parameters or measurements and apply an inverse fast Fourier transform (IFFT) to obtain a finite impulse response (FIR) filter that models the transmission line. We then input a test digital waveform such as a pseudo-random binary sequence (PRBS) into this FIR model and evaluate waveform rounding and amplitude reduction after the signal passes through the line.

We present two waveform estimation approaches: one using Excel and one using MATLAB.

First, to help you understand the algorithm, we use Excel to explain the workflow from transmission-line modeling to waveform reconstruction. Because Excel is not well suited to computationally intensive interpolation, computation can be relatively slow. Therefore, we start from a pre-prepared 4,096-point loss-versus-frequency dataset, perform an IFFT to obtain FIR coefficients that emulate the transmission line, and then input measured waveform data to calculate the waveform after transmission through the line.

For practical use, the MATLAB-based approach is more suitable because MATLAB is optimized for large-scale numerical computation. From five characteristic points sampled from the transmission line’s loss-versus-frequency characteristic, we generate 16,384 points by interpolation, apply an IFFT to obtain an FIR model of the line, and then drive it with a naturally shaped pulse synthesized from rise and fall times. Finally, we demonstrate the effectiveness of this method by comparing the simulated waveform with measured results.

For full details, including the step-by-step workflow and MATLAB code, please download the document.