Handbook for Sound Engineers

880 Chapter 25

A true gyrator is a four-terminal device that trans-
mutes any reactance or impedance presented at one port
into a mirror image form at the other port, Fig. 25-60A.

A capacitor on the input (with its falling reactance
versus frequency) creates inductance (with a rising reac-
tance versus frequency) at the output port. The scale of
inductive reactance generated may be easily and contin-
uously varied by altering the internal gain-balance
structure of the gyrator in Fig. 25-60B by changing the
transconductance of the back-to-back amplifiers,
creating a continuously variable inductor.

Real inductors have a justifiably bad name for audio
design, sharing transformers’ less pretty attributes. They
are big and heavy and they saturate easily. Their core
hysteresis causes distortion, and they are prone to
pickup of nearby electromagnetic fields (principally
power line ac hum and RF unless well screened, which
makes them even bigger and heavier). The windings
and terminations are prone to break. And they are
expensive.

It is quite easy to see why it is popular to avoid using
real inductors. Naturally, the simulated inductive reac-
tance is only as good as the quality of the capacitative
reactance it is modeled upon and the loading effect of
the gyrator circuit itself. Degradation of the inductance
takes the general form of effective series lossy resis-

tance, the Q of the inductors suffering (Q = X/R).

Leakage resistance across or through the image capac-

itor is partially to blame here. Fortunately, for the

purposes of normal equalizers, very large Qs are neither

necessary nor desirable, so selecting capacitor types to

this particular end is hardly necessary.

An obvious extension of the continuously variable

inductor is the continuously variable bandpass filter

formed by adding a capacitor either in series or parallel

with the gyrated inductor, forming series- and

parallel-tuned circuits to make notch and peak filters,

respectively. Although ideal for fixed-frequency filters

with the Q of the network or sharpness defined by a

resistor in series with the gyrator resonator, the idea

falls down when the resonance frequency is moved.

If the frequency is moved higher by altering either the

L or C, the reactances of the element at resonance

become lower; consequently, the ratio of the reactances

to the fixed-series resistor (this is the ratio that deter-

mines the Q) becomes smaller, and the bandwidth of the

filter becomes broader in response. In order to maintain

the same Q over the projected frequency variation, the

series resistor has to be ganged with the frequency

control, which is not easy. Should it be necessary to

make the Q a variable parameter also, as in a para-

metric-type EQ section, it would mean devising quite a

complex set of interactive variable controls. For this

reason parametric-type EQ sections are ordinarily

constructed around second-order, active-filter net-works,

not individual tuned circuits whether real or gyrated.

25.11.9 Gyrator Types

Let us not write off gyration for functionally variable

filters immediately. As we’ll see, they form in one way

or another the second reactance in many active filters.

True gyrators of the back-to-back transconductance

amplifier variety are difficult to make, set up, and use.

Fortunately, there are simpler ways of simulating vari-

able reactances—if not pure reactances at least a

predictable effect of a reactive/resistive network.

25.11.10 The Totem Pole

Fig. 25-61 performs the magic transformation of the

single capacitor C1 into a simulated inductance between

the terminals. Although emulating quite a pure induc-

tance when set up properly, it is precisely that setting up

that is not altogether straightforward. In fact, it is high

on a list of circuits most likely to do undesired things.

Figure 25-60. Gyrators.

A. Black box.

B. Using opposed transconductance amplifiers.