The Design of Active Crossovers by Douglas Self

Author:Douglas Self [Self, Douglas]
Language: eng
Format: epub
ISBN: 9781138733022
Publisher: Taylor and Francis
Published: 2018-03-27T23:00:00+00:00

Figure 13.11: The group delay response of the 1st-order 80 usec allpass filter. The delay is down by 10% at 2.5 kHz and 50% at 9.3 kHz.

Figure 13.12: The 1 V step input is Trace 1; putting it through a 4th-order Bessel-Thomson filter gives Trace 2, and the 80 usec 1st-order allpass filter delays it to give Trace 3.

The circuit in Figure 13.7a must be non-inverting at low frequencies, because when C1 is effectively an open circuit, we get a non-inverting stage because of the direct connection to the non-inverting input. Likewise, in Figure 13.7b, when C1 is effectively open circuit, the configuration is clearly a unity-gain inverter.

The input impedance of the RC version in Figure 13.8 is 2.7 kΩ at 10 Hz, falling to 646 Ω at 1 kHz, whereafter it remains flat (it happens to be 666 Ω at 100 Hz, but I don’t think you should try to read too much into that). The equivalent CR version (with all component values the same) has an input impedance that is flat at 1 kΩ from 10 Hz to 1 kHz. Above that the impedance rises slowly until it levels off at 1.8 kΩ around 30 kHz. It is pretty clear that the CR version will be an easier load for the preceding stage, especially at high audio frequencies, and this will have its effect on the distortion performance of that stage. There is more on that in the later section on the performance of 3rd-order allpass filters.

Figure 13.11 shows an elegantly sinuous curve, quite unlike the tidy straight-line approximation roll-offs we are used to when we look at filter amplitude responses. These latter of course are plotted logarithmically with dB on the vertical axis, whereas here we have group delay time as a linear vertical axis. This is how it is normally done; dB are useful for measuring amplitude, not least because they follow the logarithmic nature of how we perceive loudness, but there is no perceptual analogue for how we experience small time delays. Still, I thought it might be interesting to plot group delay with the log-of-time as the vertical axis, and the result is seen in Figure 13.13. I don’t recall seeing this done before.

Figure 13.13: The group delay response of the 1st-order 80 usec allpass filter plotted on a log time axis. The delay is down by 10% at 2.5 kHz.

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