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Determine the lowest order of Chebyshev filter that meets the following specifications: (i) 1 dB ripple in the passband 0|ω|0.3π

Determine the lowest order of Chebyshev filter that meets the following specifications:

(i) 1 dB ripple in the passband 0|ω|0.3π

(ii) Atleast 60 dB attenuation in the stopband 0.35π|ω|π Use the bilinear transformation.

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Solution:

Step 1 Bilinear transformation is to be used.

Step 2 Attenuation constant

ε=[1A211]12=[1(0.891)21]12=0.509

Step 3 Ratio of analog edge frequencies

Ω2Ω1=2Ttanω222Ttanω12=tan0.35π2tan0.3π2=1.2

Step 4 Order of the filter

$$ \begin{aligned} & N \geq \frac{\cosh ^{-1}\left[\frac{1}{\varepsilon}\left(\frac{1}{A_2^2}-1\right)^{\frac{1}{2}}\right]}{\cosh ^{-1}\left(\frac{\Omega_2}{\Omega_1}\right)} \geq \frac{\cosh …

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