Capacitor Distortion

From: "Saved by Internet Explorer 11" Subject: Capacitor Distortion Date: Wed, 27 Jan 2016 13:34:30 -0800 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01D15907.737EADA0" X-MimeOLE: Produced By Microsoft MimeOLE V6.1.7601.17609 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01D15907.737EADA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.renardson-audio.com/capdist.html =20 =20 Capacitor Distortion=20 =20

Capacitor=20 Distortion

Applying a sine wave voltage and measuring the distortion in the = current=20 through a capacitor can provide figures for harmonic distortion. At = zero dc=20 bias non-polarised types with symmetrical construction should have = mostly=20 third harmonic, expected from their symmetry, and higher order = harmonics are=20 generally found to be much smaller. Adding a dc bias increases the 2nd = harmonic, as expected for any device with a primarily cubic = non-linearity.=20 Some capacitor types, e.g. high-k ceramics, are found to have = unusually high=20 levels of distortion and should be avoided in some audio applications. = Most=20 other types have very low distortion levels compared to other parts of = the=20 audio chain. Even electrolytics can have low distortion provided we = take care=20 to avoid reverse bias and keep the signal voltage across the capacitor = small,=20 which can be ensured by using a sufficiently large value, and keeping = the=20 current low, which is easy in some applications, but not in the case = of a=20 speaker coupling capacitor. D.Self found that a 'standard' 6800uF = driving=20 40watts into 8ohms added no more than 0.0025% distortion down to = 20Hz.

Small levels of low order harmonic distortion should be of little = concern,=20 but are there other problems beyond this? Dielectric absorption is = often=20 mentioned as a cause of distortion, but the usual model of this effect = is=20 entirely linear:

This equivalent circuit for dielectric absorption in a = typical=20 capacitor includes a number of resistors and capacitors. ('Circuits, = Systems=20 & Standards' by Bob Pease, reprinted in Electronics World Oct.1992 = p832-835). The series resistors typically range from 200k to 1000M in = a 1uF=20 mylar capacitor, and the parallel capacitors from 0.0006uF to 0.006uF. = At any=20 single frequency this is equivalent to a single capacitor and series = resistor,=20 but this equivalent series resistance will be different at different=20 frequencies. Different types of capacitor will have different = equivalent=20 circuits, but the only effects of this in coupling capacitor = applications are=20 small amplitude and phase variations.

The phase differences between capacitors may be thought to be a = problem,=20 and in some applications careful selection is needed, but in the case = of a=20 coupling capacitor the low frequency phase shift from even an ideal = capacitor=20 is in principle undesirable. A typical non-ideal capacitor will merely = give a=20 slightly different undesirable phase shift. Both are wrong, but if we = compare=20 them this can lead to a surprising conclusion.

Keeping the capacitor fixed at 1uF and adding another 1uF in series = with=20 100k to simulate a rather extreme example of the DA effect we actually = find=20 that the amplitude errors are little different, but there is a clear = reduction=20 in phase error at low frequencies when the DA is added (shown below in = green).=20 It would be misleading to suggest that DA is therefore a good thing.=20 Increasing the coupling capacitor to 10uF will give a far greater = reduction of=20 amplitude and phase errors. (Actually, it is debatable whether the 1uF = with=20 added DA described here should be regarded as a 1uF or a 2uF = capacitor, it=20 depends on how we choose to define or measure capacitance.) Just = comparing the=20 two phase graphs the DA effect reduces the phase advance, easily = interpreted=20 as a relative phase delay if we mistakenly take the ideal capacitor to = be our=20 reference standard, which could lead to the conclusion that DA adds = time delay=20 when in this application it actually adds less phase advance.

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A more appropriate reference standard would be the direct coupled = response,=20 shown in blue, with no amplitude or phase errors. Direct coupling has = its own=20 problems, and generally the effects of phase shifts from input filters = must=20 be balanced against the increased noise, switch-on thumps from signal = sources,=20 danger of interference, offset voltages etc. My own choice for the = MJR7=20 amplifier is to use input filters with -1dB around 12Hz and 30kHz. = Without the=20 rest of the audio chain, particularly the speakers, having flat = response down=20 to dc there is little to be gained by using direct coupled amplifiers, = and=20 extending the -3dB frequency to something like a tenth that of the = speakers is=20 enough to keep the increase in phase errors relatively = insignificant.

The high frequency response needs far less extension beyond the = nominal=20 20kHz upper limit, most of the phase error from a typical low-pass = filter is=20 equivalent to a constant time delay, which will be inaudible and can = be=20 ignored. An article by Dr Leach, The=20 Differential Time-Delay Distortion and Phase-Shift Distortion as = Measures of=20 Phase Linearity, examined this and concluded that for a less than = 5deg=20 phase nonlinearity up to 20kHz a first-order low-pass filter needs to = be -3dB=20 at 35kHz or more, while a second-order Bessel filter can be -3dB as = low as=20 25kHz for the same error, though here the gain error may be considered = more=20 important. He suggested that higher order Bessel filters add even less = error.=20 My own MJR7 has a second order low-pass response, and the phase shift = is=20 almost perfectly linear from 1kHz to 20kHz, equivalent to a constant = time=20 delay of 3.3usec.

I have never personally heard any difference between different = capacitors,=20 which may be either a hearing deficiency on my part, or just a lack of = imagination. There are well documented listening tests with relevance = to=20 'capacitor sound'. One example is the famous Quad amplifier test in = which the=20 conventional class-B type 303 using an electrolytic output capacitor = was=20 compared with the direct coupled feedforward 'current dumping' 405 and = the=20 Quad II transformer coupled valve (tube) amplifier. ('Valves versus=20 transistors' by James Moir, Wireless World July 1978 p.55-58.) Using = top=20 quality master-tape recordings and two different experienced listening = panels=20 no statistically significant differences could be found, either for = the group=20 averages or for any individual member. Care had been taken to = accurately match=20 gains and avoid clipping to eliminate these common causes of audible=20 difference. The test was originally intended as a challenge to those = audio=20 reviewers who claimed to hear clear differences between what were = known to be=20 good amplifiers. Peter Walker said that Quad would stake their = reputation on=20 the outcome, predicting that no differences could be heard, even = though these=20 are radically different designs. In earlier tests ('Dynamic testing of = audio=20 amplifiers', Hi-Fi News, Nov.1970, p1655), the distortion of the 303 = including=20 output capacitor was extracted while using a music test signal, and = the=20 distortion alone without the masking effect of the music was found to = be=20 inaudible, and had to be increased many times before becoming audible. = If=20 output coupling electrolytic capacitor distortion can have so little = effect it=20 seems unlikely that we need to worry too much about coupling = capacitors in=20 other parts of an amplifier which handle much smaller signal currents, = though=20 it may do no harm to choose types reputed to have lower distortion = than=20 others, apart from possibly higher cost and also increased = interference pickup=20 from physically larger sizes.

In my MJR6 and MJR7 amplifier designs the speaker coupling = capacitor was=20 included in the overall feedback loop, primarily to improve the low = frequency=20 damping factor, but this will also minimise distortion, and the low = measured=20 distortion figures included the effect of this and all the other = capacitors.=20 Only the input filtering capacitors are expected to add significant = distortion=20 if badly chosen, these being outside the feedback loop. Looking at = published=20 distortion measurements by Bateman and others there seems general = agreement=20 that at 470pF good types are polypropylene, polystyrene and NPO/COG = ceramic.=20 The 2.2uF input coupling capacitor is more of a problem, = polypropylene at=20 this value are both large and expensive. My tests revealed that a = large=20 physical size for this component can lead to a large increase in = interference=20 pickup, particularly if the signal source impedance is high.

My measured distortion was with a polyester input capacitor. I used = a very=20 small 2.2uF 100V polyester, Epcos type B32560 from Farnell. Tests = published by=20 C.Bateman included Epcos polyester types, and found third harmonic at = -90db at=20 1kHz at 4V capacitor voltage. The distortion is relative to the = voltage across=20 the capacitor, which in my amplifier will be more than 400 times lower = at=20 1kHz, and third harmonic can be expected to be proportional to the = square of=20 the signal level, so capacitor distortion relative to total input = voltage at=20 1kHz could be something like -234dB. At 20Hz the figure will be = higher, about=20 -142dB. Worrying about this sort of distortion level in capacitors = seems=20 pointless when in most audio amplifiers far higher distortion is = produced by=20 the nonlinear semiconductor junction capacitances.

Transients

I did a simple simulation to see how the DA effect changes pulse = response.

=20

The pulse is a single 1V positive pulse starting from zero and = returning to=20 zero after 5 msec. This pulse is applied to a capacitor which drives a = 1k=20 load. The green trace is the output across the resistor for an ideal = 8uF=20 capacitor and the red trace is for the same capacitor with a series = 1uF plus=20 10k connected in parallel to simulate a DA effect, similar to the = circuit used=20 earlier to investigate phase shifts. For clarity the plots start 1msec = before=20 the start of the input pulse.

=20

It can be seen that the two results are very similar, both have = significant=20 negative output voltage for some time after the input pulse has ended = at=20 6msec. The capacitor plus DA has slightly less of this continuing = output and=20 so if we wanted to minimise this 'error' we again find that DA could = actually=20 be a benefit. Again however a far greater improvement can be achieved = just by=20 increasing the capacitor value.

The pulse test can be made more sensitive by subtracting the = different=20 outputs with and without the DA effect added, and the result is shown=20 next.

=20

The difference is more obvious now, but do real capacitors give the = same=20 sort of result? It appears that they do. An article in 'The Audio = amateur', A=20 Real-Time Signal Test for Capacitor Quality (1985) shows the = difference=20 signal extracted for several pairs of capacitors, and apart from a = short spike=20 at the pulse edge the results have a more or less similar shape to my=20 simulation result.
Unfortunately, just looking at this result we = can no=20 longer see which of the two outputs is more accurate, and we could = easily=20 assume the capacitor with DA is adding this difference signal compared = to the=20 output of the 'ideal' capacitor, when it is the capacitor with DA = which gives=20 a slightly more accurate output.

So is there a better approach? If we want to get some idea of how = the=20 actual sounds differ it may be more instructive to look at the = individual=20 error voltages, which are just the difference between the input = voltage and=20 the output voltage. Ideally the input and output will be identical, so = the=20 differences would be zero, but the two results are as shown=20 next:

=20

The capacitor with DA has the error voltage shown in green, and = this has a=20 lower magnitude peak value, but becomes slightly greater at around = 40msec. It=20 is difficult to imagine why one of these error voltages would cause = the=20 'smeared transients' and other audible effects supposedly caused by DA = but the=20 other would not.

I could find no examples of testing real capacitors by extracting = the=20 difference between input and output, so I tried a few tests myself, Capacitor=20 Distortion Part 2, using a 'musical' test signal. The results were = not=20 particularly revealing, but given the simulation results on this page = that is=20 not too surprising.

Real capacitors are more complex, but extracting and amplifying the = small=20 difference between two capacitors seems unhelpful as a method of = choosing=20 audio frequency coupling capacitors, where linear effects such as DA = generally=20 do no harm. Using a higher value coupling capacitor can be expected to = reduce=20 errors, while choosing one with low DA is not necessarily of any = benefit, and=20 may even increase errors slightly. There may be real causes of audible = differences, one I have observed is the increased pickup of = interference by a=20 capacitor with large physical size, which is why I recommend small = polyester=20 input capacitors for my amplifier designs rather than big = polypropylene=20 types.

There is some evidence that capacitor types with high dielectric = absorption=20 also tend to have relatively high distortion, possibly because both = effects=20 can be worse with materials having polar molecules. The distortion is = usually=20 nothing much worse than low levels of third harmonic, and is only at a = serious=20 level in a few types, such as high-k ceramics, which should certainly = be=20 avoided in some applications. The distortion levels are greatest when = there is=20 significant signal voltage across the capacitor, so is less of a = problem for=20 signal coupling where the idea is to avoid signal loss across the = capacitor by=20 choosing a sufficiently high value.

HOME=20

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