Distortion in Tow-Thomas Filters: 2nd-Order Highpass

Lowpass and Highpass Filter Performance  327

Figure 11.32: THD plot from Tow-Thomas 2nd-order highpass filter; input level 10 Vrms. Upper trace is THD with polyester capacitor at C2; lower trace, with both capacitors polypropylene.

gives much more, ten times as much as in the lowpass version; see Figure 11.32. The same capacitor was used in each case, with precautions taken to minimise self-improvement (see Chapter 15). Once more this seems to be completely explained by the differing signal voltages across the capacitors.

The situation is slightly more complicated in Figure 10.14 (highpass) than in Figure 10.11 (lowpass) because of the presence of R3 in series with C2, but again there is no doubt that if you can afford only one polyprop capacitor, you should make it C2.

This chapter has not been able to give a completely worked-out account of distortion in active filters; some questions remain. Nonetheless I think it is the most comprehensive study ever published.

Noise in Active Filters

In active filters distortion may come from the amplifiers and the capacitors. Noise, on the other hand, will come from the amplifiers and the resistors. Each amplifier generates its own voltage noise and current noise, while each resistor generates Johnson noise, which can be treated as a voltage or a current as convenient. Low-impedance design can be applied just as in other circuitry; it does not affect voltage noise but reduces the effect of current noise, because that is flowing through lower impedances and so produces less additional voltage noise. Reducing resistor values reduces their

Johnson noise, but only slowly, as the noise voltage is proportional to the square root of the resistance.

328  Lowpass and Highpass Filter Performance

The capacitors will be proportionally larger to obtain the same filter response, but a capacitor is a very close approximation to a pure reactance and so does not generate detectable Johnson noise.

Low-impedance design and the selection of appropriate amplifiers, such as the 5532 or LM4562, make it straightforward to design low-noise active filters. The limits of the low-impedance design approach are the need for amplifiers to drive the impedances chosen without excess distortion, and the need to keep the size of expensive precision capacitors within bounds.

All the noise measurements in the rest of this chapter were taken with the filter completely screened by metal plates to exclude hum from electric fields.All the noise results given here are for a bandwidth of 22 Hz–22 kHz, rms sensing. In each case the noise level for 22 Hz–22 kHz bandwidth was compared with that for 400 Hz–22 kHz bandwidth to ensure the hum component was negligible. Noise is of its very nature variable, and to deal with this each noise level given is the average of six readings. Where appropriate the noise of the testgear has been subtracted RMS fashion to give more accurate readings.

Noise and Bandwidth

In assessing the noise performance of a system using filters, a difficulty is that the frequency response is of course very much not flat, and that must be allowed for. This is done by using the equivalent noise bandwidth (EQNBW)of the filter, this defined as the bandwidth of an infinitely sharp filter with infinite passband attenuation that will give the same results as our real filter when it filters white noise, including its own internally generated noise. In crossover work the greatest modification to the noise readings is usually made by the lowpass filters, as white noise has equal power in equal absolute bandwidth, not equal bandwidth ratios, and there is more absolute bandwidth in the upper half of

the audio spectrum. The equivalent noise bandwidths for some common lowpass filters are given in Tables 11.8 to 11.10. For the Butterworth and Bessel filters, the cutoff frequency is as usual the −3 dB point, and for the Chebyshev as usual even-order versions have peaks above the 0 dB line and

a response going through 0 dB at cutoff, while odd-order versions have dips below it and instead pass through the ripple value (e.g. −1 dB) at cutoff.

Table 11.8: The equivalent noise bandwidth of

Butterworth lowpass filters.

Lowpass and Highpass Filter Performance  329

Table 11.9: The equivalent noise bandwidth of Bessel lowpass filters.

Table 11.10: The equivalent noise bandwidth of Chebyshev lowpass filters for various ripple amplitudes.

For the higher-order Butterworth filters the EQNBW gets very close to unity. This is not the case for the Bessel filters in Table 11.9, because of their slower roll-off.

When assessing the noise performance of non-standard filters, it is not usually a good idea to plod through heavy mathematics to determine the EQNBW. Usually it is much quicker to simply build the circuit and measure it.

Noise in Sallen & Key Filters: 2nd-Order Lowpass

It is difficult to give a comprehensive summary of the noise performance of even one type of filter in a reasonable space. There are a large number of variables, even if we restrict ourselves to the Sallen & Key configuration. There is the cutoff frequency, the Q, the impedance level at which it operates, whether it is highpass or lowpass, and whether it is 2nd-order or higher.

If we start with the 2nd-order 510 Hz lowpass filter in Figure 11.6a, it can be built with 1 kΩ resistors and 220 nF capacitors (using two for C1), as shown, in which case the noise output (corrected by subtracting the internal noise of the measuring system, as are all noise data in this section) is −117.8 dBu, which is pretty low. The measurement bandwidth was 22 Hz–22 kHz as usual. If we rebuild our