Audio Engineering

226 Chapter 7

network attenuation, whereas the active system gain block will typically have a gain of
unity in the fi at response mode, with a consequently lower distortion level.

As a fi nal point, it should be remembered that any treble lift circuit will cause an increase
in harmonic distortion, simply because it increases the gain at the frequencies associated
with harmonics, in comparison with that at the frequency of the fundamental.

The verdict of the amplifi er designers appears to be substantially in favor of the Baxandall
system in that this is the layout employed most commonly.

Both of these tone control systems—indeed this is true of all such circuitry—rely for their
operation on the fact that the AC impedance of a capacitor will depend on the applied
frequency, as defi ned by the equation:

Z

c f



1

() 2

,

π c

or, more accurately,

Z

c jf



1

() 2

,

πc

where j is the square root of  1.

Commonly, in circuit calculations, the 2 πf group of terms is lumped together and
represented by the Greek symbolω.

The purpose of the j term, which appears as a “ quadrature ” element in the algebraic
manipulations, is to permit the circuit calculations to take account of the 90° phase shift
introduced by the capacitative element. (The same is also true of inductors within such a
circuit, except that the phase shift will be in the opposite sense.) This is important in most
circuits of this type.

The effect of the change in impedance of the capacitor on the output signal voltage from
a simple RC network, of the kind shown in Figures 7.59(a) and 7.60(a) , is shown in
Figures 7.59(b) and 7.60(b). If a further resistor, R 2 , is added to the networks, the result is
modifi ed in the manner shown in Figures 7.61 and 7.62. This type of structure, elaborated
by the use of variable resistors to control the amount of lift or fall of output as a function
of frequency, is the basis of the passive tone control circuitry of Figure 7.57.