Numerical 1

Derive an expression to calculate the order of Inverse Chebyshev low pass filter. Using the formula to estimate the order of Inverse Chebyshev low pass filter having following specifications.

αp = 0.9 rad/sec αp = αmax = 0.5db

αs = 1 rad/sec αs = αmin = 22db

The order is given by

\[
n = \frac{
\cosh^{-1}\!\left(\sqrt{\dfrac{10^{\tfrac{\alpha_{\min}}{10}} - 1}{10^{\tfrac{\alpha_{\max}}{10}} - 1}}\right)
}{
\cosh^{-1}\!\left(\tfrac{1}{\omega_p}\right)
}
\]

Substituting values:

\[
n = \frac{
\cosh^{-1}\!\left(\sqrt{\dfrac{10^{\tfrac{22}{10}} - 1}{10^{\tfrac{0.5}{10}} - 1}}\right)
}{
\cosh^{-1}\!\left(\tfrac{1}{0.9}\right)
}
\]

\[
n = \frac{\cosh^{-1}(4.469)}{\cosh^{-1}(1.111)} = 9.15 \;\;\approx 10
\]