Polar Plot

What is Polar Plot? Polar plot(also called Nyquist Plot)

Sinusoidal TF G(j) is a complex function & is given by

G(j)=Re[G(.)]+j Im[G(.)] or G(j)

G(.) can be represented as a phasor of magnitude M & phase As the I/P freq. varied (0 to ) , M & vary/change & hence the tip of the phasor G() traces a locus in complex s-plane. This locus obtained is called polar plot.Adv: It depicts freq. res ch of a syst over entire fre range in a single plot

Frequency response of the typical elementsFrequency response of the typical elementsFrequency response of the typical elementsFrequency response of the typical elements

Integrating element

Transfer function:ssR

sCsG 1)(

)()( ========Frequency response:

jjG

1)( =

Polar plot

Re

Im

0

Delay element

Transfer function: sesRsC

sG ======== )()()(

===

)()()()( jG

jGejG j

ImR=1

Polar plot

Re

ImR=1

Polar Plots of some simple Functions