Passive Components for Active Crossovers  447

Table 15.15: Relative cost of polyester and polypropylene capacitors, relative to 100 nF polyester.

slowly than proportionally. Therefore, making up a capacitance with two equal values, as in our example of 440 nF = 2 × 220 nF, is going to cost more than using a single 470 nF capacitor. The table also demonstrates that polypropylene capacitors cost a lot more than polyester, so the cost difference is much greater. In making your design decisions you will of course be working with prices from your intended supplier.

Polypropylene capacitors are much more expensive than polyester, but their great advantage is that they do not generate distortion (see later). In many filter types only one of the capacitors needs to be polypropylene for capacitor distortion to be eliminated, and this can save some serious money. This intriguing state of affairs is described in detail in Chapter 11.

Capacitor Shortcomings

Capacitors fall short of being an ideal circuit element in several ways, notably leakage, equivalent series resistance (ESR), equivalent series inductance (ESL), dielectric absorption, and non-linearity:

Capacitor leakage is equivalent to a high value resistance across the capacitor terminals, which allows a trickle of current to flow when a DC voltage is applied. Leakage is usually negligible for nonelectrolytics, but is much greater for electrolytics. It is not normally a problem in audio design.

Equivalent series resistance (ESR) is a measure of how much the component deviates from a mathematically pure capacitance. The series resistance is partly due to the physical resistance of leads and foils and partly due to losses in the dielectric. It can also be expressed as tan-δ (tan-delta), which is the tangent of the phase angle between the voltage across and the current flowing through the capacitor. Once again it is rarely a problem in the audio field, the values being small fractions of an ohm and very low compared with normal circuit resistances.

Equivalent series inductance (ESL) is always present. Even a straight piece of wire has inductance, and any capacitor has lead-out wires and internal connections. The values are normally measured in nanohenries and have no effect in normal audio circuitry.

Dielectric absorption is a well-known effect; take a large electrolytic, charge it up, and then fully discharge it. Over a few minutes the charge will partially reappear. This “memory effect” also occurs in non-electrolytics to a lesser degree; it is a property of the dielectric and is minimised by using polystyrene, polypropylene, NP0 ceramic, or PTFE dielectrics. Dielectric absorption is invariably

modelled by adding extra resistors and capacitances to an ideal main capacitor, such as Figure15.9 for a 1

448  Passive Components for Active Crossovers

Figure 15.9:  A model of dielectric absorption in a 1 uF polystyrene capacitor. All components are linear.

uF polystyrene capacitor, which does not hint at any source of non-linearity. [12] However, the dielectric absorption mechanism does seem to have some connection with capacitor distortion, since the dielectrics that show the least dielectric absorption also show the lowest non-linearity. Dielectric absorption is

a major consideration in sample-and-hold circuits but of no account in itself for normal linear audio circuitry; you can see from Figure15.9 that the additional components are relatively small capacitors with very large resistances in series, and the effect these could have on the response of a filter is microscopic, and far smaller than the effects of component tolerances. Note that the model is just an approximation and is not meant to imply that each extra component directly represents some part of a physical process.

Capacitor non-linearity is the least known but by far the most troublesome of capacitor shortcomings.

An RC lowpass filter to demonstrate the effect can be made with a series resistor and a shunt polyester capacitor, as in Figure 15.10, and if you examine the output with a distortion analyser, you will find to your consternation that the circuit is not linear. If the capacitor is a non-electrolytic type with a dielectric such as polyester, then the distortion is relatively pure third harmonic, showing that the effect is symmetrical. For a 10 Vrms input, the THD level may be 0.001% or more. This may not sound like much, but it is substantially greater than the midband distortion of a good opamp. The definitive work on capacitor distortion is a magnificent series of articles by Cyril Bateman in Electronics World. [13] The authority of this is underpinned by Cyril’s background in capacitor manufacture.

Capacitors are used in audio circuitry for four main functions, where their possible non-linearity has varying consequences:

1.Coupling or DC-blocking capacitors. These are usually electrolytics, and if properly sized have a negligible signal voltage across them at the lowest frequencies of interest. The non-linear properties of the capacitor are then unimportant unless current levels are high; power amplifier

output capacitors can generate considerable midband distortion. [14] This makes you wonder what sort of non-linearity is happening in those big non-polarised electrolytics in passive crossovers.

A great deal of futile nonsense has been talked about the mysterious properties of coupling capacitors, but it is all total twaddle. How could a component with negligible voltage across it put its imprint on a signal passing through it? For small-signal use, as long as the signal voltage across the coupling capacitor is kept low, non-linearity is not detectable by the best THD methods. The capacitance value is non-critical, as it has to be, given the wide tolerances of electrolytics.

2.Supply filtering or decoupling capacitors. Electrolytics are used for filtering out supply rail ripple, etc, and non-electrolytics, usually around 100 nF, are used to keep the supply impedance low at high frequencies and thus keep opamps stable. The capacitance value is again non-critical.

Passive Components for Active Crossovers  451

Figure 15.12: Reducing capacitor distortion by series-parallel connection.

Table 15.16: The reduction of polyester capacitor distortion by series-parallel connection.

The series-parallel arrangement has obvious limitations in terms of cost and PCB area occupied but might be useful in some cases. It has the advantage that, as described earlier in the chapter, using multiple components improves the average accuracy of the total value.

An unexpected complication in these tests was that every time a polyester sample was remeasured, the distortion was lower than before. I found a steady reduction in distortion over time; if a test signal was applied continuously, 9 Vrms at 1 kHz would roughly halve the THD over 11 hours. This change consists of both temporary and permanent components. When the signal is removed, over days the distortion increases again but never rises to its original value. When the signal is reapplied, the distortion slowly falls again. This self-improvement effect is therefore of little practical use, but if nothing else it demonstrates that polyester capacitors are more complicated than you might think. I do not believe this has anything to do with dim-witted audio commentators claiming that circuitry has to be left switched on for months or years before it attains its optimum sound; for one thing, nothing happens unless you also continuously apply a signal of much higher amplitude than normal, which would be hard to arrange and has never been touted as a good way to run-in equipment. For fuller details of this strange self-improvement business, see my Linear Audio article. [16]

Clearly polyester capacitors can generate significant distortion, despite their extensive use in audio circuitry of all kinds. The next dielectric we will try is polystyrene. Capacitors with a polystyrene dielectric are extremely useful for some filtering and RIAAequalisation applications because they can be obtained at a 1% tolerance at up to 10 nF at a reasonable price. They can be obtained in larger sizes but at much higher prices.

452  Passive Components for Active Crossovers

Figure 15.13: The THD plot with three samples of 4n7 2.5% polystyrene capacitors, at 10 Vrms input level. The reading is entirely noise.

The distortion test results are shown in Figure 15.13 for three samples of a 4n7 2.5% capacitor; the series resistor R1 has been increased to 4.7 kΩ to keep the −3 dB point inside the audio band, and it is now at 7200 Hz. Note that the THD scale has been extended down to a subterranean 0.0001%, because if it was plotted on the same scale as Figure 15.11 it would be bumping along the bottom of the graph. Figure 15.13 in fact shows no distortion at all, just the measurement noise floor, and the apparent rise at the HF end is simply due to the fact that the output level is decreasing because of the lowpass action, and so the noise floor is relatively increasing. This is at an input level of 10 Vrms, which is about as high as might be expected to occur in normal opamp circuitry. The test was repeated at 20 Vrms, which might be encountered in discrete circuitry, and the results were the same, yielding no measurable distortion.

The tests were done with four samples of 10 nF 1% polystyrene from LCR at 10 Vrms and 20 Vrms, with the same results for each sample. This shows that polystyrene capacitors can be used with confidence; this finding is in complete agreement with Cyril Bateman’s results. [17]

Having resolved the problem of capacitor distortion below 10 nF, we need now to tackle it for larger capacitor values. Polyester having proven unsatisfactory, the next most common capacitor type is polypropylene, and I am glad to report that these are effectively distortion free in values up to 220 nF. Figure 15.14 shows the results for four samples of a 220 nF 250 V 5% polypropylene capacitor from RIFA. The plot shows no distortion at all, just the noise floor, with the apparent rise at the HF end being increasing relative noise due to the lowpass roll-off, as in Figure 15.13. This is also in agreement with Cyril Bateman’s findings. [18] Rerunning the tests at 20 Vrms gave the same result—

no distortion. This is very pleasing, but there is a downside. Polypropylene capacitors of this value and voltage rating are much larger physically than the commonly used 63 or 100 V polyester capacitor, and more expensive.

Passive Components for Active Crossovers  453

Figure 15.14: The THD plot with four samples of 220 nF 250 V 5% polypropylene capacitors, at 10 Vrms input level. The reading is again entirely noise.

It was therefore important to find out if the good distortion performance was a result of the 250 V rating, and so I tested a series of polypropylene capacitors with lower voltage ratings from different manufacturers.Axial 47 nF 160 V 5% polypropylene capacitors from Vishay proved to be THD-free at both 10 Vrms and 20 Vrms. Likewise, microbox polypropylene capacitors from 10 nF to 47 nF with ratings of 63 V and 160 V from Vishay and Wima proved to generate no measurable distortion, so the voltage rating appears not to be an issue. This finding is particularly important, because the Vishay range has a 1% tolerance, making them very suitable for precision filters and equalisation networks. The 1% tolerance is naturally reflected in the price.

The higher values of polypropylene capacitors (above 100 nF) appear to be currently only available with 250 V or 400 V ratings, and that means a physically big component. For example, the EPCOS 330 nF 400 V 5% part has a footprint of 26 mm by 6.5 mm, with a height of 15 mm, and capacitors like that take up a lot of PCB area. One way of dealing with this is to use a smaller capacitor in a capacitance multiplication configuration, so a 100 nF 1% component could be made to emulate 330 nF. It has to be said that this is only straightforward if one end of the capacitor is connected to ground; see

Chapter 14 for an example of this concept applied to a biquad equaliser.

When I first started looking at capacitor distortion, I thought that the distortion would probably be lowest for the capacitors with the highest voltage rating. I therefore tested some RF-suppression X2 capacitors, rated at 275 Vrms, equivalent to a peak or DC rating of 389 V. The dielectric material is unknown.An immediate snag is that the tolerance is 10 or 20%, not exactly ideal for precision filtering or equalisation. A more serious problem, however, is that they are far from distortion free. Four samples of a 470 nF X2 capacitor showed THD between 0.002% and 0.003% at 10 Vrms.Ahighvoltage rating alone does not mean low distortion.

For more information on how capacitor non-linearity affects filters see Chapter 11.