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Prove phase shift is similar at pole and zero frequencies

The steady state transfer function of the certain electrode amplifier interface model demonstrated below is specified as:

1564_steady state transfer function.png

Here ωp = ωz /α and α is the attenuation factor at dc.  Prove here such the phase shift experienced through a signal at the amplifier input is similar at the pole as well as zero frequencies, ωp and ωz correspondingly.

 We suggest a useful hint to use the trigonometric identity for tan(AB).

2036_trigonometric identity.png

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