Footnote added Oct 2008. Why high feedback?
Footnote added July 2009. Input stage distortion.
Footnote added Oct 2010. Shunt compensation.
Audio power amplifiers are, in principle, very simple. There is an input voltage and an output voltage, and at any instant of time these are both just numbers (with units of volts). If the input voltage is 1 volt at a certain instant of time and the output voltage is then 20 volts, then the amplifier has a gain of 20. In an ideal amplifier this number, 20, would be a complete description of the performance, and the output voltage would always be simply 20 times the input voltage. In a real amplifier with an input voltage varying with time the output voltage has a maximum level, and a maximum rate of change, and the gain falls at high frequencies, but within these limits it is still possible to approach the ideal behaviour.
There is a very simple way to find out how close to the ideal a given amplifier comes. If the gain is supposed to be 20, then all we need to do is divide the output voltage by 20 using an accurate resistive divider, and for an ideal amplifier the result will be identical to the input voltage. The most informative way to observe any differences is to subtract the input voltage from the attenuated output signal and display the result on an oscilloscope. For useful results careful balancing of amplitudes and phase shifts is needed so that the nonlinear distortion alone can be extracted and investigated. The earliest example of the method I have found appeared in Wireless World in 1953 (E.R.Wigan, "Diagnosis of Distortion" June 1953 pp261-266), and it was the subject of my own M.Sc. dissertation in 1978, which is included on this site.
Some forms of distortion are of greater importance than others. For example, crossover distortion in class-B amplifiers can increase in percentage as signal level falls. Music often has a low average level and only short duration peaks, and then much of our listening is done at low levels, so reducing crossover distortion needs to be a high priority. Examples here show the distortion at 20kHz of underbiased class-B, correctly biased class-B (difficult to maintain in practice because of thermal effects), and overbiased class-B. Avoiding the problem completely with class-A, or allowing crossover nonlinearity, but only at higher signal levels, with class-AB, generates a lot of heat and requires large efficient heatsinks.
Designs presented on this site illustrate two alternative methods, both capable of reducing crossover effects to around the noise level. One method using feedforward error correction in the output stage was my own original idea, published in Electronics World, April 1998. This and a later improved version are capable of excellent results.
For the benefit of less experienced constructors I added a more conventional design (the MJR-6) using only 6 transistors and a high level of overall negative feedback, intended as a simple and reliable mosfet power amplifier. I had not expected this design to be anything special, and yet the performance was as good as the feedforward designs, but with more easily predictable stability and no need for accurately matched component values.
Adding one more transistor to reduce distortion even further this became the MJR-7, which is by far the best amplifier I ever made, with all measured harmonic and intermodulation products within the audio frequency range well below -100dB (0.001%). My interest was in reducing crossover distortion, and so my measurements were at 100mA quiescent current with 6V output into a 7R5 load to ensure each mosfet switches off over part of the signal cycle to reveal any crossover effects and confirm how effectively these have been reduced. There are certainly other designs with similar or lower distortion levels, but all those I have seen so far are either far more complex, or operate at a higher quiescent current with distortion specified at a signal level where operation remains in class-A.
Harmonic distortion figures are widely believed to be an inadequate measure of amplifier performance, so to check that there are no overlooked effects only apparent when listening to music with a speaker load I also carried out tests using the direct comparison method mentioned above. Using a Mordaunt-Short MS20 speaker, with music output a little above my normal listening level, recording the extracted and amplified 'error' signal of the MJR-6 and later listening to this alone the amplifier noise became clearly audible, together with some low level uncancelled music, but distortion is less easily identified. An example of the recorded error signal is shown here. Here also is a ten second extract as a wav file (1.69MB). Although amplified considerably this is still at a very low level.
If you think you can identify a distortion component with the volume turned up high, then try reducing the level to the point where the noise component becomes only just audible with an ear close to the speaker, then listen at a typical listening distance, say 3 metres, then imagine how audible the distortion component would now be with loud music being played at the same time. This gives some idea how far below audibility any non-linear distortion from this amplifier really is in normal operation.
This approach is only useful if we wish to design amplifiers to be accurate. Conventional listening tests may lead to entirely different conclusions, and amplifiers which change the signal in some audible way may be preferred by some listeners. In some cases distortion from an amplifier may be cancelling distortion from the speaker, and the overall effect may turn out to be greater accuracy, but generally, apart from fortuitous cancellation effects, amplifiers can only make the signal worse, not better. It seems fair to assume that when someone talks about 'a good sounding amplifier' it is either one which damages the signal less than some other amplifiers, or one which adds pleasant sounding errors.
There is sufficient information given for anyone who wants to build either mosfet amplifier, including pcb layouts designed to be easily made using an etch resist pen. It can be difficult to obtain the lateral mosfets at a reasonable price in some parts of the world, though here in the UK they can be bought for as little as £4.50 each. I have been asked a few times if cheaper vertical mosfets could be substituted, but these have different temperature coefficients and higher internal capacitances, also higher bias voltages are needed, preventing direct substitution.
Many published designs are incomplete, requiring the addition of further circuitry to provide speaker protection in the event of an amplifier fault. Without such protection a direct coupled design could apply the full supply voltage to the speaker, causing serious damage. I previously used speaker protection relays, but found these to be too unreliable. (One failed after 20 years, but another only lasted a few weeks.) My present designs include speaker protection in the form of capacitor coupling. This normally adds some distortion, and reduces speaker damping at low frequencies, but by including the capacitors inside the feedback loop these problems are avoided, and the damping factor, measured as 1500 at 20Hz, is better than for many direct coupled designs. All my distortion testing, both sinewave and music, includes the effect of the output capacitor, and nothing unexpected is found.
Footnote 1. Why High Feedback?
My mosfet amplifiers use relatively high levels of overall (global) negative feedback (around 80dB up to 5kHz). Some 'high-end' amplifier designers promote the idea that high negative feedback in general and high global feedback in particular cause serious sonic deficiencies.
I have included a series of articles, some of which aim to counteract widespread claims about feedback 'problems', but no matter how far the arguments against feedback can be discredited one argument remaining is 'we can hear a difference, so there must be something wrong'. For example, one writer described his impressions of high feedback designs, which included 'mid-range glare' and 'false tonal color' and so on.
Listening to the extracted distortion of the MJR-6 at the above link, there is simply nothing there remotely like the claimed effects. There is a remote possibility that sounds which are inaudible alone can become audible when heard as part of a music signal. The only evidence I have heard of relates to low frequency sub-threshold binaural beats, G.Oster 'Auditory Beats in the Brain'. ( Maybe I should also include the somewhat controversial evidence of ultrasonic 'audibility' published by Tsutomu Oohashi, which is perhaps not strictly speaking 'sub threshold', and appears not to have been replicated in subsequent attempts by others, and is anyway concerned with perception rather than audibility). To be more certain we could go a step further by inverting the extracted distortion and adding it back to the music signal at its original level to give distortion cancellation, then any feedback related problems will disappear, or at least be reduced another 40dB or more. Try it yourself, or just take my word for it, nothing miraculous happens. Whatever some people think they can hear from well designed feedback amplifiers, I can see no reason to believe it has anything to do with errors in the amplifier output signal.
What could be the source of that 'mid-range glare' if it is not present as a change to the output voltage? It is easy to suggest that it is just imagination, and there are endless examples of blind listening tests where 'obvious audible effects' no longer seem obvious when the identity of the equipment being compared is unknown. There may however be other explanations, for example that zero or low feedback amplifiers often have relatively high output impedance, and many speakers have a mid-range dip in their impedance, which will then cause a dip in the frequency response. If we have become accustomed to this dip and then switch to a high feedback amplifier with lower output impedance there will be far less mid-range dip, but the result can be perceived as colouration, and possibly glare, even though an error has been reduced. This sort of misleading effect is perhaps not always taken into account.
Another possible explanation is that 'well designed feedback amplifiers' are not as common as we might hope, and distortion and instability are often real audible problems. On the MJR-6 page I mentioned a French site with simulation tests involving about 30 published DIY and commercial designs, and from these results it was found that 12 had serious stability problems with high value capacitor loads, and 10 had distortion more than 100 times greater than my own design. The situation may be even worse, because stability problems are not always revealed by the traditional 'square wave into a 2uF capacitor load' test. For example some amplifiers are perfectly stable with one type of speaker cable, but oscillate with another. A number of highly regarded amplifiers were found to have problems when high capacitance cables became popular, and recently my own MJR-7 had to be modified when someone using higher capacitance cables found a problem, although I had tested with what I had believed was a sufficiently wide range of capacitors. The problem was only for loads around 2nF, and in this case the explanation involves resonance with the output inductor near to the unity gain frequency. This sort of problem is not always easy to spot, and just testing with a wide range of capacitances, as I found, may not be enough. The widespread belief that cables affect the sound quality may seem ridiculous to some of us, but amplifier design errors can make cable effects very real and possibly audible. Changing the cable or the amplifier may then have equally audible effects.
Footnote 2. Input stage distortion.
TID, PIM and other similar distortions are often ascribed to input stage nonlinearity. My own emphasis has been almost entirely on output stages and methods including feedforward and global feedback which can reduce the distortion to low levels. The input stage is generally a small-signal class-A amplifier, so why the big problem making it adequately linear?
There are at least two ways to reduce input stage distortion, one is to linearise the stage, the other is to reduce the signal it needs to handle. To improve linearity we can use local feedback, which is commonly done with emitter degeneration resistors, also using complementary feedback pairs instead of single transistors. There are other approaches, e.g. using matched complementary jfets in such a way that their nonlinearities partly cancel.
The input stage signal level is easy to calculate for a given amplifier output level, it is the output signal divided by the open-loop gain of the amplifier. My mosfet designs can have open-loop gain as much as 200000 up to 5kHz, and so for a 20V output the input stage has an input of only 100uV. At this level achieving good linearity is relatively easy.
Transient analysis leads to the same conclusions as sinewave analysis, if we consider the peak amplitude of the input stage signal. A frequent error, which appears to originate in an article from 1966, is to look instead at the percentage overshoot and confuse this with overshoot amplitude, which is not the same thing. A high percentage overshoot compared to the steady state level often indicates only that the steady state level is very low, not that the overshoot is high. For example, 'The Theory of Transient Intermodulation Distortion' by Otala and Lienonen from 1977 includes a graph, their Fig. 6, showing the ratio of overshoot amplitude to steady state amplitude, clearly marked as such on the vertical axis of the graph, yet the description below describes it as 'The maximum value Vmax of the overshoot', which it is certainly not. The text then says that feedback over 40dB inevitably leads to rather large overshoots within the amplifier. My own mosfet amplifiers have about 80dB feedback at low to medium frequencies, but the overshoot from an input step function is well under 1mV at the input base.
Footnote 3. Shunt Compensation.
I have seen a quote, usually attributed to Peter Baxandall, concerning shunt compensation, which is achieved by adding a capacitor from the voltage amplification stage (VAS) output to ground as in my MJR7 designs. The quote is that 'The technique is in all respects sub-optimum'. Looking at the original Baxandall article, 'Audio power amplifier design-4'. Wireless World July 1978 p76, he was actually writing about compensation at the input stage collector not at the VAS output, and the only problem mentioned is that the fall in open-loop gain caused by the shunt capacitor continues even at very high frequencies, giving lower loop gain at high frequencies than is necessary for stability. The solution given is the one I also chose, to include a resistor in series with the shunt capacitance so that additional phase lags in the circuit at higher frequencies maintain the phase lag rather than add more to it. The more common Miller compensated VAS can have additional problems because of feedforward through the compensation capacitor adding a zero to the response and causing even more high frequency phase lag. Baxandall mentions this in Part 3 of his Wireless World series, and compares the Miller compensation with the RC shunt circuit, shown as his Fig.6. Again one solution is to add a series resistor, which can eliminate the zero. (It replaces it with a pole, but generally at a sufficiently high frequency to not matter).
A different objection to shunt compensation is mentioned by Douglas Self on page 281 of 'Self on Audio' Second Edition, where he gives one example in which he determined that a VAS shunt capacitance of 43.6nF was needed, which then requires a peak current from the VAS of 155mA. This may be a real problem for some circuits, but my latest MJR7-Mk5 need only 100p shunt capacitance, and even this is not essential, it could be reduced several times provided the 1R5 input stage resistor is increased in the same proportion.