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 .

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