Polar plot of sinusoidal transfer function is a plot of:

SOLUTION

Polar plot:

• The polar plot of a transfer function G(jω) is the plot of the magnitude of G(jω) versus the phase angle of G(jω) as ω is varied from 0 to positive infinity.
• For all pole systems, type indicates the starting point of the polar plot and order indicates the ending point of the polar plot.

The sinusoidal transfer function G(jω) is a complex function and it is given by

G(jω) = Re [G(jω)] + j Im [G(jω)]

G(jω) = \(\left| {G\left( {jω } \right)} \right|∠ G\left( {jω } \right)\)

= M ∠ϕ Polar form

From the above equation,

G(jω) may be represented as a phasor of magnitude M and phase angle ϕ

The starting points (ω = 0) of a polar plot for different types of minimum phase systems is given below:

• As seen from the above figure, when a zero is added the type decreases, and the end of the polar plot shifts by +90°. 
• When a pole is added, the type of the system increases, and hence the end of the polar plot shifts by -90°. 

Therefore, the Polar plot of the sinusoidal transfer function is a plot of magnitude and phase angle.