A phase shift circuit is shown below with an inductor of 20 mH. Here R is a vari

Question

A phase shift circuit is shown below with an inductor of 20 mH. Here R is a variable resistor; by varying R the phase shift between the input voltage Vin and the outputVout can be made to vary. Here Vin has a peak voltage of 3 V at ?=600 rad/s.

a) Write out the complex impedance of the series combination of the inductor and the resistor as a function of a resistance R.

b) Let R0 be the resistance where R0=?L. What is the phase shift between Vout and Vin at R< R0?

c) What is the phase shift between Vout and Vin for R >> R0

Explanation / Answer

L = 20 mH = 0.02 H

W = 600 rad/s

1) Z = impedance   = R +JWL = R + J*600*0.02 = R + 12 J

2)    Given R = Ro    , where R0 = WL = 12

                 then   

        then Z = 12 + 2 J

   Vout = Vin * R/Z

                = 3 * 12/(12+12J)

                = 3/(1+J)

                = 3(1-J)/( 2)

                = 1.5(1-J)

               = 1.5* 2^0.5 <(-45)

               =2.12 <(-45)

phase shift = -45 degree

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