6.38 What is the frequency response, Vout ()/Ns(@), for the circuit of Figure P6.38? Sketch the frequency response of the circuit (magnitude and phase) if Rs = R1 = 5,000 2, L= 10 µH, and C = 0.1 µF. Rs ww R, Source Filter Load ele

It says the resonate frequency is not the arithmetic mean of the high and low cutoff frequencies and that 6.5 is wrong? Any insight?

Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough Vịn C Vout Figure Q6: LCR filter then the frequency transfer function (in terms of the circular frequency w) of this filter can be approximated, 1 H(w) 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 kQ. (a) Calculate the expected resonant frequency, vo, of this filter (in kHz). (b) Find the –3 dB points (in power) for this filter and hence determine its bandwidth. (c) Determine the value of the quality factor Q for this filter. (d) Using the properties of Fourier transforms and the tabulated selected transforms, determine the impulse response function corresponding to this transfer function. (e) Sketch the form of the real part of the impulse response function. (f) A bandpass filter, such as the one described above, is usually inserted after a chopper or rectifier modulator: explain why and identify the requirements on the resonant frequency and the bandwidth of such a bandpass filter.

6.1 a. Determine the frequency response Vout (ja)/Vin (jw) for the circuit of Figure P6.1. b. Plot the magnitude and phase of the circuit for frequencies between 1 and 100 rad/s on graph paper, with a linear scale for frequency. c. Repeat part b, using semilog paper. (Place the frequency on the logarithmic axis.) d. Plot the magnitude response on semilog paper with magnitude in dB. + Vin(1) 0.1 H 000 100 ΚΩ Figure P6.1 www + Vout(1)

QUESTION 4 Q4.1 Show how can a series RLC can be used as a crude band-reject filter? Q4.2 How would you determine the centre frequency for this filter? Q4.3 Show how a graph of H(jo) versus oo for this filter will look like. Q4.4 In the graph, show the possible locations of the centre frequency, and the two cutoff frequencies. Justify why you chose these locations in the graph.