Shortly after my feedforward design was published in Electronics World in April 1998, they published another amplifier with a claimed maximum slew rate of 300 V/µsec. If anyone is wondering how my own design compares in this respect I didn't even bother to measure the maximum slew rate, and can see little point in doing so. Many years ago Peter Baxandall published, in Wireless World, measurements of the slew rates of a range of high quality recorded music, from a range of sources, and found that a power amplifier need only be capable of producing its full output swing undistorted up to 2 kHz to ensure it could give the maximum slew rate required by the music signals. In a 100 watt amplifier this represents a slew rate of about 0.5 V/µsec. A slightly higher slew rate was needed because of dust and scratches on vinyl records exciting tip-mass resonances. Unfiltered pilot tones from fm stereo radio and other unwanted non-music high frequency breakthrough were also found to increase the requirement.
These measurements were carried out before the advent of CDs, so I decided to repeat the Baxandall test using an identical differentiator circuit consisting of a 1n capacitor feeding a 1k resistor load. The output of a Marantz CD273SE was used, this being an old machine, widely rated as a 'best buy' when first produced. The output peaked at 2.5V, and the output across the 1k resistor was both calculated and checked with a sine wave source, the result being that the peak slew rate of a full level sine wave would give a peak output of 125mV at 8kHz, 156mV at 10kHz etc. The slew rate maximum observed by Baxandall would give an output of 31mV.
Checking a range of music CDs for a few hours it became apparent that a few recordings have maximum slew rate far greater than the Baxandall measurements. Peaks of 120mV were found on some recordings, though most were much lower. The prize for greatest slew rate found goes to a single peak from 'Year 3000' by Busted, which hit 150mV, equivalent to the slew rate of a full level sine wave about 10kHz, i.e. five times greater than Baxandall's figure, and equivalent to a level of 2.5V/µsec for a 100W power level.
An amplifier capable of close to full output at 8kHz should rarely if ever reach slew rate limiting, though Busted fans should aim for 10kHz. Any moderately well designed modern amplifier should of course have no problem exceeding this level by a very wide margin. It is not possible to give a general specification of how far maximum amplifier slew rate needs to exceed the maximum music slew rate. Some amplifiers using heavy local feedback in the input stage still have low distortion at beyond 90% of their maximum slew rate, while others may be adding worse distortion at under 10% of their maximum slew rate. For these poorer circuits it may be easier in practice to improve input stage linearity rather than aim for an extremely high maximum slew rate. In either case the maximum slew rate alone tells us little if anything about how much an amplifier distorts music signals. A high specified value may in some cases just indicate a bad choice of design priorities.
I have since found slew rate measurements for the newer DVD-A and SACD formats published by Stereophile. The maximum slew rate found was equivalent to that of a full level 12kHz sine-wave, so it appears that the maximum slew rates found are not much greater. The sampling rate for CDs of 44kHz gives a theoretical upper limit of 22kHz for a full level sine-wave output. That this level is not found in my tests, and such levels are not found in tests with the newer formats, even with higher sampling rates, suggests that the upper limit is a property of the music rather than a limit imposed by the sampling rate.
If amplifiers are to be tested with square waves close to the clipping level then to keep the slew rate down to the maximum level found in my CD tests the square wave must be passed through a low pass first order filter with its -3dB frequency at 5kHz. This gives the same maximum slew rate as a sine wave of the same peak level with frequency 10kHz. I have seen tests proposed using square waves passed through a 100kHz filter, equivalent to the slew rate of a similar level 200kHz sine wave. Such tests may be to the advantage of designs with very high maximum slew rate, but have nothing to do with amplifying music from a good quality source. A surprising number of amplifier designers actually quote figures for this 100kHz test, and it even has a name, 'DIM-100'. For many years methods have been known for detecting distortion using music signals, so it seems perverse to evaluate amplifiers using signals with slew rate 20 times greater than normal music at the same level, and therefore requiring different design priorities.
It is no doubt possible to find faulty, or badly designed signal sources with interference pickup and other non-music high frequency components at a high level (though I have never personally encountered any), but amplifying such a signal and applying it to your expensive speakers should definitely be avoided. Most high frequency speaker drivers use small light voice coils to extend the frequency response, and rely on the low average levels of high frequency energy in music to keep dissipation down to safe levels. Any excessive high frequency components should ideally be filtered out ahead of the power amplifier. If slew rate limiting occured this could actually reduce high frequency energy and help protect the speakers, but damage could be done well before this occurs. (Amplitude limiting can increase high frequency energy and make matters worse.)
Another term, related to supposed slew rate problems, is 'transient intermodulation distortion', or t.i.d. which was a common concern at one time, and still inspires some designers to abandon overall negative feedback in the belief that doing so will protect against this particular affliction.
One of the early treatments of t.i.d. may be responsible for some of the misunderstandings. It was published as an appendix to an article by Daugherty and Greiner entitled 'Some Design Objectives for Audio Power Amplifiers' (March 1966, IEEE Transactions on Audio and Electroacoustics.) The main conclusion of the analysis was that the 'open-loop response' of an amplifier using overall negative feedback should be at least 20kHz if this is the bandwidth of the signal source. This refers to the frequency at which the open loop gain falls by 3dB. An example was worked out to show that if this were not the case, then a step function applied via a 20kHz low-pass filter would produce an error signal with an overshoot at the input of the amplifier. It was shown in one example that although the error signal settled down eventually to a steady state level of 100mV the overshoot reached 527mV. This was described as a '427% momentary overload'. This is clearly an incorrect description. An overshoot is not the same thing as an overload. If the input stage is capable of remaining linear with the 527mV input, then there is no overload in this stage. If required such a stage can easily be designed using local negative feedback, though in practice such high error voltages are unlikely to occur in any modern amplifier.
A worse error, however, is merely to compare the overshoot amplitude to the steady state amplitude to give a percentage overshoot, and then state that the requirement to keep this percentage low will then keep distortion low also. Compare the two curves b and c in Fig.1. showing the voltage at the input of an amplifier input stage.
Curve b has no overshoot, but curve c has 58% overshoot relative to its final level, and yet it is curve b which has the greater amplitude, and will lead to the greater distortion in an amplifier stage. It is the maximum amplitude we must pay attention to, not the percentage overshoot relative to the eventual steady state level. The distortion produced by curve b will, however, not be associated with the transient any more than with the steady state signal, so in a sense we can say that there is no t.i.d. simply because the steady state distortion is at the same level as the transient distortion. Aiming to reduce t.i.d. irrespective of how this is achieved may in fact have the effect of increasing the steady state distortion to the point where the transient induced distortion is no longer distinguishable.
To see the origins of the curves in Fig.1 look at the circuit in Fig.2:
This shows a unit step function applied to a feedback amplifier via a first order low-pass filter with a response -3 dB at w1. The amplifier has open loop gain A at low frequencies, falling at 6dB per octave above w0. The gain of the feedback network is B, and the resulting error voltage at the input stage of the amplifier is Ve. For the unit step input the error voltage is given by the equation:
This function is plotted for three combinations of A, B, f1 and f0 in Fig.1. The frequencies in kHz are specified rather than the angular frequencies used in the equations, as these are more familiar to most of us. In all cases 100% overall fedback is applied, so B=1. The same input filter is used in all cases with -3dB at 20kHz. All we are varying are the open loop gain and frequency response of the amplifier, and the three different cases are plotted as straight-line approximations in Fig.3:
Response b is the commonly recommended 20kHz bandwidth to give zero t.i.d. and the other two responses are both -3dB at 10kHz, which we are often assured will lead to t.i.d. The reason why two such responses are shown can be seen by looking at one final diagram. Fig.4:
This is a commonly used configuration for a power amplifier. A differential input stage feeds an inverting driver stage which in turn feeds an output stage. The driver stage has local feedback via C and R which determine the open loop frequency response of the amplifier, and hopefully stabilise the overall feedback loop. Having chosen the minimum possible value of C to maintain stability we can then choose R to determine the -3dB open loop frequency response. Choosing R to give 20kHz bandwidth then gives result b in Figs 1 and 3. To reduce the open loop bandwidth to 10kHz we have a choice. We can increase either C or R. Increasing R by a factor of 2 gives result c, which gives the same open loop response at high frequencies as b, and therefore does not affect the stability to a great extent, yet it gives a peak error signal voltage reduced by 10% and twice as much negative feedback over most of the frequency range. Both transient and steady state distortion will be reduced, even though we have reduced the open loop frequency response to only half the value supposedly needed.
It is only if we instead increase C by a factor of 2 to reduce the bandwidth giving the results shown as 'a' that we find a 58% overshoot relative to the 100mV steady state error voltage, and we can truly say that transient induced distortion has been increased. But now C is much larger than is required for stability, and there is no justification for the increase. It is only the increase in R which is beneficial, and in general this can be omitted altogether and the open loop frequency response allowed to fall to under 100Hz, as is often done with op-amps, with no detrimental effects.
To summarise: the open-loop frequency response is not the factor we need to worry about, any more than it is the percentage overshoot on the error voltage. What matters is to keep the maximum error voltage down to a level at which the input stage remains adequately linear.
Other objections have occasionally been raised against negative feedback, one being that low order harmonic distortion is reduced but higher order harmonics increase. The high order harmonics are added because lower order harmonics are fed back to the input through the feedback network, and these intermodulate with the input signal to generate the higher harmonics. This is treated in more detail in Part 1 of my 'Feedback Works' series.
A simple six transistor mosfet amplifier I recently built uses 66dB feedback loop gain at 20kHz, and I tested it driving a speaker load (a Mordaunt-Short MS20) using music signals a little above my normal listening level, extracting distortion by a nulling method. I found all forms of distortion to be far below the noise level, which itself was inaudible even with an ear held against the speaker. I included the 'Year 3000' track mentioned above for this test to be sure 'high' slew rates were present. Had I chosen to use a far higher sound level, a speaker with lower efficiency and with an impedance falling to under 2ohms somewhere in the mid-range, then distortion would have been higher of course.
The point is that operated under reasonable conditions even a very simple amplifier with high overall feedback can have an inaudible effect on sound quality.