E1C06 09/14/2010
11:55:6 Page 240
elements in the filter design. Passive analog filter circuits consist of combinations of resistors,
capacitors, and inductors. Active filters incorporate operational amplifiers into the circuit, as well.
The sharp cutoff of the ideal filter cannot be realized in a practical filter. As an example, a plot of
the magnitude ratio for a real low-pass filter is shown in Figure 6.28. All filter response curves
contain a transition band over which the magnitude ratio decreases relative to the frequency from the
f
f c
1
0
(a) Low-pass filter
M(f)
f
f c
1
0
Stopband
Passband
(b) High-pass filter
M(f)
Stopband
Passband
f
f c2
f c2
f c1
f c1
1
0
(c) Bandpass filter
M(f)
f
1
0
Stopband
Passband
Passband
(d) Notch filter
M(f)
Stopband
Stopband
Passband
Figure 6.27 Ideal filter characteristics.
0.1
Passband
Transition band
Stopband
Roll-off
slope
100
10
1
f / f c
M(f)
0.01
0.1
1
2
Figure 6.28 Magnitude ratio for a lowpass Butterworth filter.
240 Chapter 6 Analog Electrical Devices and Measurements