 Frequency Dependence

Subject Physics Electricity and Magnetism

Question

1) The drawing below shows a sine-wave generator of frequency f and internal resistance R1 connected to a high-pass filter. If the generator shown in the dotted outlined box produces a voltage V0(t) = V0 cos(2π ft) with no load, derive an expression for the output voltage V1(t) = V1 cos(2π ft + φ) as a function of frequency f.

2) If R1 = 50Ω, R2 = 10 KΩ, and C = 0.01 μF, simplify your expression for question (1) above to obtain a simple formula for the real ratio V1/V0.

3) Make two plots of the real ratio V1/V0 obtained in question (2) above as a function of the frequency f, one plot with linear scales, and another with a linear vertical scale but with a log scale for the frequency axis. At what frequency has the ratio dropped to 71% of its maximum value? At what frequency has the ratio dropped to 50% of its maximum value?

4) Using the values given in question (2) above, make a plot of the phase shift φ between the measured voltage V1(t) and the generator voltage V0(t) using whichever scale (log or linear) you prefer.

5) Using only one L, R, and C respectively, design a circuit that will pass only a band of frequencies centered at f = 20 kHz. Use practical values for your components (i.e., don’t use C = 20 F). How wide in frequency will your passband be?

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