In a series RLC circuit, if we have VR(peak to peak) across resitor and Vin(peak

Question

In a series RLC circuit, if we have VR(peak to peak) across resitor and Vin(peak to peak) across source and delta T(difference in phase shift in seconds) at a frequency. How can we find magnitude of transfer function at that frequency?

Example: if R=100ohm,L=220microH,C=1microF. At f=5.4KHz, Vin=0.728V(peak to peak), VR=0.624V(peak to peak), delta T=1microsec. These were measured values and i know theoretical how to find it. how can i find magnitude of transfer function in this case

Notice that: VR and Vin are not in phasor notations(complex) but are sinusoidals

Explanation / Answer

Since you are asked for the magnitude of the transfer function, you only need to take the ratio of the rms values of Vr to Vin (I assume that the transfer function Vout/Vin = Vr/Vin). Since both measured values are in peak-to-peak format and you"ll have to perform the same operation on both to get the rms values, you only have to take the ratio of the peak-to-peak values: |Tf|=0.624/0.728=0.857 If you need to find the phase angle then you use the delta T of 1 microsecond and the frequency of 5.4 kHz. The period of the 5.4kHz signal is 1/5.4x10^3=185.2 microseconds. That represents a phase angle of 360 degrees. Taking the ratio of delta T to the period and multiplying by 360 should give you the phase difference in degrees: 1/185.2x360=1.94 degrees. You'll have to decide the + or - depending which waveform leads the other. The calculated transfer function gives: 0.977/_+12.4degrees. The difference comes from the actual values of the components, the added resistance that the inductor introduces and measurement error.

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