Magnitude and Phase angle of the coefficients in the network function

Let the network function be written as :

N(s) = P(s) / Q(s)

Above equation consist of factors of the general form where pr and pn are complex frequencies. Their difference is also a complex frequency which  can be written as:

Where Mnr is the magnitude of the phasor and Φnr is the phase angle of the same phasor


All Ms and phase angles can be calculated using the pole-zero plot on s-plane

Procedure for calculation of M and Φ

    1. Plot the pole-zero of the network function
    2. Measure the distance of M1r, M2r … of a given pole from each zero
    3. Measure the distance of Mar, Mbr … of a given pole from each other finite pole
    4. Measure the angle Φ1r, Φ2r … from each of the finite zero
    5. Measure the angle Φar, Φbr … from each of the finite pole
    6. Substitute and find the values of Kr

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