ESE 498 Senior Design

An Analysis of Pulse Width Modulation

David Morin and Tim Thannum

Department of Electrical and System Engineering, Washington University

Abstract

This experiment is meant to allow for and increased understanding and simulation of the use of Pulse Width Modulation within the application of amplifier design. A carrier wave is used to sample the input signal, by comparing the signals’ amplitudes and outputs a true or false value at each sample point. This project aims to better define the effects of carrier frequency and jitter, addition of dead time, and the sampling rate. 



Introduction

Pulse Width Modulation of PWM is a method of creating a simplified representation of a signal that can more easily be used in power and amplification techniques.  This is accomplished by quantizing the signal.  The modulation of the signal is accomplished by taking the input signal and comparing it with a carrier frequency of at least twice the maximum frequency of the input signal.  For optimal results it is best to use a signal of at least ten times the maximum frequency present in the input signal.

  The goal of our project was to simulate a basic PWM system and ten investigate the effects of various issues involved in the implementation of a PWM based amplifier. Some of the possible sources of non-ideal behavior include the necessity of creating dead time within the modulated signal to ensure efficiency and efficacy of the power MOSFETs. It is also necessary to be able to account for the distortion induced by the addition of jitter in the clock or carrier frequency.  




Methods





 Results



Discussion

  This simulation provides results inline with our expectations.  The results from the different frequencies show that the carrier frequency does have an effect, however theoretically the SNR constantly increases with carrier frequency though it is subject to diminishing returns.  This projects results differ from this and demonstrate the effect of a reduced oversampling ratio. From these results it was determined that 96kHz should be used for the rest of the project.

  The result of this was an increase in the noise floor, from -100dB to -80db with the addition of 0.02 variance in the Gaussian noise. However this had little effect on the system since the total increase in noise was negligible in comparison to the harmonic peaks.

Next steps:

The modification of the simulation or movement of the simulation to a more powerful computing source to allow for better precision since there were some issues with its current implementation.
Add a means for simulating non linear components in the creation of an analog circuit
Use this simulation to identify the optimal design for a PWM amplifier, since this simulation is meant to take into an amplifier

References and Acknowledgements

[1] Floros, A.; Mourjopoulos, J.; Tsoukalas, D. “Jither: The Effects of Jitter and Dither for 1-bit Audio PWM Signals," 106th Audio Engineering Society Convention, 1999. pp.1-13, 26 Apr. 2013

 

[2] Midya, P.; Miller, M. “Integral Noise Shaping for quantization of Pulse Width Modulation,“ 109th Audio Engineering Society Convention, 2000. pp.1-23, 26 Apr. 2013


We would like to thank the Bob Morley, and Ed Richter for all their help with this project.