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Chapter 12 Filters and Tuned Amplifiers
• 12.1 Filter transmission, types and specification• 12.2 The filter trasnfer function• 12.3 Butterworth and Chebyshev filters• 12.4 First-order and second-order filter functions• 12.11 Tuned amplifiers
12.1 Filter transmission , types and specification .12.1.1 Filter Transmission.
Fig. 12.1 A general two-port network .
Fig. 12.1.2 Filter Types . Fig. 12.2 Ideal transmission characteristics of the four major filter types : (a)
low pass (LP), (b) high pass (HP), (c ) bandpass (BP) and (d) bandstop (BS) .
12.1.3 Filter Specification . Fig. 12.3 Specification of the transmission characteristics of a low pass filter .
Fig. 12.4 Transmission specifications for a bandpass filter . The filter has a monotonically decreasing transmission in the passband on both
sides of the peak frequency .
12.2 The filter transfer function
12.2 The filter Transfer Function . Fig. 12.5 Pole-zero pattern for the low pass filter whose transmission is sketched in Fig. 12.3 . This is a fifth-
order filter (N=5)
Fig. 12.6 Pole- zero pattern for the bandpass filter whose transmission function is shown in Fig. 12.4 . This is a sixth –order filter (N=6) .
12.3 The Butterworth Filters
12.3 Butterworth and Chebyshev Filters .12.3.1 The Butterworth filter
Fig. 12.8 The magnitude response of a Butterworth filter .
The Procedure for finding H(s) for a Given N
• 1. Find roots of the polynomial 1+(-1)Ns2N
• 2. Align the left half plane roots to H(s) and the right half plane roots to H(-s) .
• 3. Combine terms in the denominator of H(s) to form first and second order factors .
Fig. 12.9 Magnitude response for Butterworth filters of various order with ε=1
Fig. 12.10 Graphical construction for determining the poles of a Butterworth filter of order N .(a) the general case, (b) N=2, (c ) N=3 and (d) N=4 .
To Find a Butterworth transfer function that meets transmission specifications of the form in Fig. 12.3
ε= passband deviation parameter
Fig. 12.11 Poles of the ninth –order Butterworth filter of Example 12.1
12. 3.2 The Chebyshev Filter . Fig. 12.12 Sketches of the transmission characteristics of representative (a) even-order and (b) odd-order Chebyshev
filters .
Example 12-2
12.11 Tuned Amplifiers .12.11.1 The basic principle
Fig. 12.38 Frequency response of a tuned amplifier .
2
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