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Electricity, Electronics, and Communications 299

significant attenuation of signalð whose frequencieð are outside
this range.

Constant-k bandpass filter

Let f be the lower cutoff frequency (in hertz) for a constant-k
1
bandpass LC filter as shown in Fig. 4.12. Let f be the upper
2
cutoff frequency (in hertz)˜ Let R be the load resistance (in
ohm0. Then the optimum inductanceð (in henry0 are given by:

L R/( (f f ))
2
1
1
L (f f )R/(4 ff )
2
1
1 2
2
The optimum capacitanceð (in farad0 for the filter shown in Fig.
4.12 are given by:
C (f f )/(4 ffR)
1
1 2
2
1
C 1/( R(f f ))
2 2 1
Series m-derived bandpass filter
Let frequencieð f , f , f , and f be expressed in hertz and defined
1
4
3
2
as shown in Fig. 4.13. Let R be the load resistance (in ohm0.
Define the quantitieð x, m (the filter constan'x y, and z as fol-
lows:
2
2
2
2
x ((1 f /f )(1 f /f )) 1/2
4
3
3
2
2
m x/(1 ff /f )
4
23

Figure 4.12 Constant-k band-
pass filter.