Handbook for Sound Engineers

Filters and Equalizers 791

23.2.3.5 Bandpass

The impedance characteristics of the series and parallel
resonant elements can be used to form a bandpass filter
as in Fig. 23-11. The frequencies f 1 and f 2 are the cutoff
frequencies of the pass band. The design equations for
the component values are

(23-29)

(23-30)

(23-31)

(23-32)

where,
f 1 is the lower cutoff frequency,
f 2 is the upper cutoff frequency,
Z 0 is the line impedance.

23.2.3.6 Band Reject

The configuration for a band reject filter using series
and parallel resonant elements is shown in Fig. 23-12.
The configuration is the reverse of the bandpass
T-network filter. In this case the frequencies f 1 and f 2 are
at the edge of the reject band. The design equation for
the component values are

(23-33)

(23-34)

(23-35)

(23-36)

23.2.3.7 Ladder Networks

Passive filters of arbitrary length may be constructed by

adding RC, RL, or LC L-type sections into a network of

arbitrary length called a Cauer network. The interaction

between the various stages in this topography starts to

become important as the impedance of one section loads

the next.

23.2.4 Filter Design

As the number of components in a filter increases, the

number of possible transfer functions also increases.

Increasing the order of a filter by adding more of the

same sections will not necessarily produce the optimum

results. Consider chaining two low-pass filters with a

cutoff frequency of fc. The attenuation at the cutoff is

3 dB, so with two sections in series, the attenuation at fc

Figure 23-11. T network bandpass filter.

L 1

Z 0

2 S f 2 – f 1

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

L 2

f 2 – f 1 Z 0

2 Sf 1 f 2

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

C 1

f 2 – f 1

2 Sf 1 f 2 Z 0

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

C 2 1

2 S f 2 – f 1 Z 0

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

A. Configuration.

B. Transmission characteristics.

L 1

C 2 L 2

C 1

Pass

Reject

f 1 f 2

f 1 d fm f 2 d

C 1

Reject

L 1

L 1

f 2 – f 1 Z 0

2 Sf 2 f 1

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

Figure 23-12. T network band-reject filter.

C 1 1

2 S f 2 – f 1 Z 0

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

L 2

Z 0

2 S f 2 – f 1

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

C 2

f 2 – f 1

2 Sf 1 f 2 Z 0

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

A. Configuration

B. Transmission characteristics

.

.

Zl Zl

L 1 L 1

2L 2

2C 2

C 1 C 1

± ±

Pass Pass

Reject

f 1 f 2

f 1 d f 2 d

fm