What is the transfer function? Take the output as the voltage across the resisto

Question

What is the transfer function? Take the output as the voltage across the resistor. If the input voltage, V, is u(t)-u(t-tf/2), where u(t) is the usual step function, and is the period at the resonance frequency, what is the output? Do this analytically using the inverse Fourier transform. Hint: Remember, V out(omega)=T(omega)Vin(omega) Do this in Matlab. Use the FFT function. To recover the time domain, use the 1FFT function. Don't change the length of the vector. FFT will work just fine. Think about the sampling frequency. You have to specify it Also, use Matlab to get the current, I. Verify your answer using 5SPICE.

Explanation / Answer

LET   VO = IS OUTPUT VOLTAGE ACROSS RESISTPOR

       VO =IR

    I   = VO/R..............(1)

NOW XC =REACTANCE OF CAPACITOR = -J/WC

          XL =RACTANCE OF INDUCTOR = JWL

NOW    V = I(R +XC +XL )

PUT THE VALUE OF I FROM (1)

WE GET:       V   = VO(R +XC +XL )/R

           TRANSFER FUNCTION   = VO/V

                                              =   R/(R +XC +XL )

                                              = R/(R+ JWL -J/WC)

AT RESONANCE FREQUENCY JWL -J/WC =0

HENCE TRANSFER FUNCTION = R/R =1

       VO/V = 1

    VO = V

HENCE THE AT RESONANCE FREQUENCY, INPUT VOLTAGE = OUTPUT VOLTAGE

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