The Sorensen Audio Experiment, design description version 0.5
Copyright (c) 2002 Johan Sörensen.
This document is a historical description of an obsolete audio amplifier design.
This is one of the first working pulse-width modulated amplifiers I ever built (back in the end of 1995). The idea came from a project I did during my Master-of-Science education, where I built and studied a very simple one-bit A/D converter. The theory I studied explains how you can construct a digital one-bit signal, that when filtered, resembles a desired analog signal with very good fidelity. This technology is used in commercial Sigma-Delta A/D converters. The quality “only” depends on the oversampling-factor (how much higher the 1-bit sampling frequency is, compared to the Nyquist-frequency), and the order of an integrating loop-filter (which in effect “shapes” the noise, to push noise energy away from the audible frequency band.)
“My” own invention was to control two power transistors directly with the A/D-converted signal, thereby creating what I later learned is a “class D” amplifier. I also removed the fixed sampling frequency from the A/D-converter, thereby creating a self-oscillating class D circuit, which is discrete in its output levels (positive or negative), but continuous in the time-domain (there is no fixed switching frequency determining when the output change levels).
The operating theory of this design is better explained elsewhere on http://listen.to/audioexperiment. See e.g. the Design Description for the amplifier version 2.1.
The main purpose with this file is to document the early history of the “Sorensen Audio Experiment”, and to provide other Do-It-Yourself’ers with a very simple example that is quick and easy to build on a breadboard for evaluation purposes. It is only suitable to drive with low supply voltages, in the range from ±5 V to ±12 V.
The descriptions in this chapter refer to the schematics diagram.
The present design described in this document creates the pulse-width modulated output signal through self-oscillation. Oscillation is something that is normally avoided at all cost in amplifiers in general, but this case is very different.
In this design, the comparator and the “power output stage”, together make a very high gain amplifier, which is (only) optimized to swing to the positive or negative supply voltage alternatively. A feedback loop is then applied around this composite amplifier, and an integrating error amplifier controls the input to the aforementioned composite amplifier. This in effect creates a very fast on-off regulation, which in real life oscillates at around 1 MHz. This pulse-width modulation frequency is significantly higher than the highest audible frequency to any human.
Another way of understanding the operation of this circuit is that the error amplifier compares the integrated momentary value of the output stage with the desired value defined by the input signal, and then drives the output to the positive or negative supply respectively depending on the outcome of the comparison. Of course, driving the output to the positive supply for a while invariably and quickly leads to a integrated output value that is slightly “too high”, thus forcing the output to the negative supply instead, and so on… The point is that this process is so quick and accurate compared to the fluctuations in the input signal, that the latter is followed quite closely by the filtered output signal.
The remaining sections in this chapter contain some notes and explanations of the different sub-circuits of the complete design.
The LF356 (U18) serves as an integrating error amplifier. (The integration is a critical part, in that it performs the noise shaping.)
The value of C8 determines the integration constant. The suggested value of C8 has been determined empirically – you may try to tweak this up or down slightly, and observe the effect on the overall amplifier operation (in particular, the audible result in terms of distortion).
The comparator used is the LM311 (U20). This component unfortunately only has an open collector output, which means that it’s output can only pull to the negative supply, and there has to be a pull-up resistor to the positive supply. This is not critical for a simple test circuit, but there is a more elaborate buffer stage in the 2.1 version of the amplifier design.
The output transistors Q10-Q11 aren’t really “power transistors”, but thanks to the high efficiency of the class D design, you’ll be surprised how much power they can deliver to real speakers (exceeding one Watt), given the moderate supply voltage recommended above.
When working with higher output power levels, there is a definite need to apply output filtering to avoid having the amplifier disturb every radio/TV set within your home. But at the very moderate levels supported by this simplistic design, you may try it without any filters at all…