Handbook for Sound Engineers

Consoles 883

A minor failing with this simple circuit is that at high
frequencies a parallel impedance (consisting of the vari-
able resistor and capacitor chain) hangs directly from
the terminal to ground. Buffering the chain from the
terminal by a follower eliminates this, Fig. 25-63C.

Fig. 25-63A creates an analog of an inductor with
the losses shown in Fig. 25-63B. The series resistor is
the 150: bootstrap resistor; after all, a proper inductive
reactance tends to zero at low frequencies, not 150:.
The resistor is in series with the faked inductance
tending to make it seem somewhat lossy or have a lower
Q than a perfect inductor. If a fake inductor can be said
to have winding resistance, this is it! The R/C network
across the lot represents, again, the high-pass filter
impedance, which on the addition of the follower disap-
pears to be replaced in Fig. 25-63D by the much greater
input impedance of the follower, which is high enough
to be discounted.
As a short footnote to this gyrator epic, consider what
happens to either Fig. 25-63C or F if the high-pass resis-
tance-capacitance filter is replaced by a low-pass filter
by swapping R with C. It may seem a bit strange to use
circuitry to imitate a capacitor, but imitating a continu-
ously variable capacitor does make sense. Real variable
capacitors of the large values needed in EQs (yet easily
created by gyrators) simply don’t exist otherwise.

25.11.12 Constant-Amplitude Phase-Shift Network

A constant-amplitude phase-shift (CAPS) circuit of

previously little real worth (other than for very short

time delays) is shown in Fig. 25-63E. Bearing more

than a little resemblance to a differential amplifier, this

circuit can rotate the output phase through 180° with

respect to the input, around the frequency primarily

determined by the high-pass RC filter. Additionally the

input and output amplitude relationship remains

constant throughout.

How? This is dealt with in Figs. 25-63G and H where

the simplistic assumptions that a capacitor is open

circuit at low frequencies and a short at high frequencies

show that at low frequencies the circuit operates as a

straightforward unity-gain inverting amplifier (180°

phase shift), while at high frequencies it operates as a

unity-gain noninverting amplifier (0° shift). The mecha-

nism for the latter mode is interesting. The op-amp is

actually operating at gain-of-two noninverting; this is

compensated for by the input leg also passing through

the still operating unity inverting path, which naturally

subtracts to leave unity gain, noninverting.

25.11.13 Simulated Resonance

Detailed up to here are all the variables needed to create

single- and second-order filters. Higher-order networks

can be made with combinations of the two. Tracking

variable capacitors and inductors allows the design of

consistent Q bandpass filters irrespective of frequency.

This eventually leads to a dawning of understanding in

how the much-touted integrator-loop filters such as the

state variable actually operate. The clue lies with the

180° phase-shift circuit of Fig. 25-63E. Connecting two

such filters (with the variable resistor elements ganged)

in series produces a remarkably performing circuit. At

any frequency within the design swing, it is possible for

the circuit output voltage to be exactly out of phase with

the source 180° phase shift). By summing input and

output, direct cancellation at that frequency and at no

other is achieved. In short, a variable-frequency notch

filter with a consistent resonant characteristic results.

Alternatively, bootstrapping the input from the output

actually changes that input port into something that

behaves exactly like a series-tuned circuit to ground, Fig.

25-63J. The circuit is continuously variable in frequency

with a consistent Q by virtue of the simultaneously

tracking simulated inductor and capacitor maintaining

exactly the same elemental reactances at whatever the

selected operating resonant frequency. This creates the

same source resistance, same reactance, same Q.

25.11.14 Consistent Q and Constant Bandwidth

The same Q definitely does not imply the same filter

bandwidth. As the resonant frequency changes, the

bandwidth changes proportionally. Bandwidth is, after

all, the ratio of frequency to Q. Some active filters, such

as the multifeedback variety, exhibit a constant band-

width when the resonant frequency is changed: a 10:1

variation of center frequency, a 10:1 variation of Q.

This, of course, is rarely useful for real EQ; it is note-

worthy though in that the change in Q with frequency

happens in the opposite sense to that expected from a

normal variable tuned circuit. The Q sharpens with

increasing frequency. It is a perfect example of a

constant-bandwidth filter.

25.11.15 Q, EQ, and Music

The near insistence on resonant-type filters being

constant in Q when varied in frequency is not through

an industrywide collective lack of imagination or desire

to keep things tidy. It stems from psychoacoustics, from