The Sorensen Audio Experiment, design description version 0.5
3.2. Error
Amplifier / Integrator
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…