By Kendall L. Su (auth.)

ISBN-10: 1461358515

ISBN-13: 9781461358510

ISBN-10: 1461520517

ISBN-13: 9781461520511

Analog filters are widely used in components reminiscent of electronics, communications, controls and sign processing. it truly is fascinating for engineers and scholars in those parts to have a valid realizing of simple clear out concept. This e-book is meant to be an intermediate point treatise of this topic. it may be used both as a textbook in a path at both the undergraduate or graduate point, or as a reference for engineers who locate it worthy to have an introductory knowlege or a common evaluate of analog filters. It introduces the speculation in the back of clear out improvement and the layout options ordinary in perform, together with the applying of ordinary software program applications. wide use is made from MATLAB for examples and challenge units, permitting readers to obtain familiarity with the tools for designing filters with a contemporary software program tool.

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Further, any Chebyshev polynomial may be expressed in terms of the two polynomials of degrees immediately lower than itself. 1: Chebyshev polynomials of order 0 to 10 n Cn{w) 0 1 1 w 2 2w 2 -1 3 4w 3 4 8w 4 5 6 7 8 9 10 - 3w +1 16w 5 - 20w 3 + 5w 32w 6 - 48w 4 + 18w 2 - 1 64w 7 - 112w 5 + 56w 3 - 7w 128w 8 - 256w 6 + 160w4 - 32w 2 + 1 256w 9 - 576w 7 + 432w 5 - 120w3 + 9w 512w 10 - 1280w8 + 1120w6 - 400w 4 + 50w 2 - 8w 2 C1(w) = cos(cos- 1 w) = 1 W we can write successively etc. 1. The Chebyshev polynomials are really the trigonometric identities that express cos ne as a function of cos e = w.

5? What is the value of w at which the attenuation is exactly 30 dB? 2 What is the exact value of a p ? 3 2 Cg(w) What are the maximum and minimum gains in the pass band (0 < w < I)? What is the attenuation at w = 2 compared with the maximum gain? 5 dB as = 45 dB it is necessary that n = 6. What is the necessary n if a Butterworth filter is used? What if a Chebyshev filter is used? 17 Show that the inverse Chebyshev lowpass characteristic of Fig. 8 for which is maximally flat at w = o. 29). 9, N = 1, and use the RN(W) of and IH(jw)1 will vary as in the plot shown below.

2: Zeros of Q(s)Q( -s) for (a) n plane (b) =6 and (b) n = 9. Since Q(s) is the denominator of H(s), it must be Hurwitz. Hence we must include only left-halfplane zeros of B( _s2) to form Q(s). Polynomials formed to have left-halfplane zeros are known as Butterworth polynomials. Of course, zeros of Q(s) are poles of H(s). 3. Obtain the network function of the normalized Butterworth fourth-order lowpass filter. SOLUTION The poles of H(8) are shown in Fig. 3 . // / . "*_, ,, / ~.... I I '- .... ), 7.

### Analog Filters by Kendall L. Su (auth.)

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