Handbook for Sound Engineers

800 Chapter 23

(23-61)

This gives us the expression for the Z transform:

(23-62)

The biquad has two poles in the denominator and
two zeros in the numerator. It may be expressed in the
factored form as:

(23-63)

where,
G is the gain,
r 0 denotes the real part of the zero location,
q 0 denotes the imaginary part of the zero location,
rp denotes the real part of the pole location,
qp denotes the imaginary part of the pole location.

Table 23-3 lists the equations for the individual coef-
ficients for a purely real implementation of a biquad
filter, given the locations of the poles and zeros.

23.6 Equalizers

Equalizers are devices or components that are designed
to compensate for undesirable characteristics in the
magnitude or phase response of another part of the
system and thus make the response equal again. Equal-
izers consist of filters implemented in such away as to
provide control over the frequency response in terms of
how the operator thinks of the response curve that they
are trying to recreate. Equalizers give control over one
or more of the parameters that affect the response over
the audio range, usually 20 Hz to 20 kHz, and ideally do
so such that the parameters do not interact. Controls are
arranged in terms of center frequencies, bandwidths, and
gains rather than actual circuit values that control these
things. This means that often the controls are

dual-ganged so that the ratio of two resistor values may

be kept constant while their absolute values are changed.

23.6.1 Tone Control

The simplest form of equalizer is the tone control as

used on portable radios. The control only acts to atten-

uate the high frequency. Another version of this type of

equalizer that is becoming more prevalent than the tone

control is the bass boost, which as its name suggests

acts as the exact opposite to add a controlled gain to the

low frequencies.

The tone control circuit shown in Fig. 23-27 includes

transistor-based buffer amplifiers around the passive

filter section in the middle. This allows the operation of

the equalizer to be independent of source and load

impedances.

23.6.2 Graphic Equalizers

A graphic equalizer is used to shape the overall spec-

trum of program material. The term graphic refers to

the way that the controls are set out on the front panel

such that the positions of the slider controls draw the

desired frequency response. Graphic equalizers typi-

cally use -octave band filters but may be constructed

with any spacing. The -octave refers to the spacing

between adjacent filters and not necessarily the width of

the filter.

A graphic equalizer is constructed using a series of

filters with fixed frequency and width. The centers of

the filters are typically on the ISO preferred frequencies

rather than the mathematically correct -octave

spacing. This means that in order to cover the spectrum

completely, some of the filters must have different

widths. The output of each filter is added to the original

signal to a degree controlled by a slider control. The

levels add together and are prone to producing a ripple

in the response between the centers. In Fig. 23-28, the

Table 23-3. Relation of Biquad Coefficients to Pole
and Zero Location

Zeros Poles

a 0 = 1

a 1 =  2 rocos(qo) b 1 = -2rpcos(qp)

a 2 = ro^2 b 2 = rp^2

z–n=ejZn't

Hz hn>@z–n

n –=f

f

= ¦

Hz

Gz r 01 e

• jq 01


• zr 02 e


• jq 02


• 
  

zrp 0 e

• jqp 0


• zrp 1 e


• jqp 1


• 
  

=------------------------------------------------------------------------

Figure 23-27. Simple low-pass tone control

Tone control

Input Output

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