Introduction to Electric Circuits

130 Resonance

Figure 6.12

I L

I

C

Jl I O

Vo

o

bandpass filter circuit is shown in Fig. 6.12. A bandpass filter is designed to

allow signals at the resonant frequency (f0) and those within a band of

frequencies above and below f0 to pass from the input terminals to the output

terminals. Signals at frequencies outside this band are passed at a very much

reduced level or not at all and are said to be rejected.

Bandwidth

For a signal to be 'passed' it has to have a voltage not less than 0.707 of the

voltage at the resonant frequency f0. The current (I), similarly, will be not less

than 70.7 per cent of the current at f0. The lowest frequency at which V0 has this

minimum value is called the lower cut-off frequency and the highest frequency

at which V0 has this minimum value is called the upper cut-off frequency. The

band of frequencies which are 'passed' are those between the lower cut-off

frequency and the upper cut-off frequency and this is called the pass-band.

These points are illustrated in Fig. 6.13.

o.7o7v I---~/

yi

0 f fo f2 rf

Figure 6.13

The pass-band is the band of frequencies lying between f~ and f2 and this is

also referred to as the bandwidth (B) of the circuit so that

B - (f2 - fl) (6.6)

The unit of bandwidth is the hertz or radians per second if angular frequency is

used.

Half-power frequencies

As we have seen, at resonance the current is a maximum so that the power in