HW6.pdf - 14.2 a Find the cutoff frequency(in hertz of the...

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Unformatted text preview: 14.2 a) Find the cutoff frequency (in hertz) of the low- pass filter shown in Fig. P14.2. b) Calculate H ( jw) at we, 0.1wc, and 10wc. c) If v,- = 25 cos cot mV, write the steady-state expression for '00 when a) = we, 0.1wc , and 10wc. Figure P14.2 160 Q + | + vi I 5 [LF ”0 14.3 A resistor, denoted as R,, is added in series with the inductor in the circuit in Fig. 14.4(a). The new low- pass filter circuit is shown in Fig. P143. a) Derive the expression for H (s) where H (S) = Vo/Vi- b) At what frequency will the magnitude of H ( jw) be maximum? c) What is the maximum value of the magnitude of H ( jw)? d) At what frequency will the magnitude of H ( jw) equal its maximum value divided by V2? 6) Assume a resistance of 300 Q is added in series with the 50 mH inductor in the circuit in Fig. P14.1. Find we, H(jO), H(jwc), H(j0.2wc), and H ( ijc). Figure P14.3 14.8 Use a 10 mH inductor to design a low-pass passive filter with a cutoff frequency of 1600 rad/s. a) Specify the cutoff frequency in hertz. b) Specify the value of the filter resistor. c) Assume the cutoff frequency cannot decrease by more than 10%. What is the smallest value of load resistance that can be connected across the output terminals of the filter? d) If the resistor found in (c) is connected across the output terminals, what is the magnitude of H ( jw) when w = 0? 14.12 A resistor, denoted as RC, is connected in series with the capacitor in the circuit in Fig. 14.11(a). The new high-pass filter circuit is shown in Fig. P14.12. a) Derive the expression for H (s) where H<s> = Vo/w. b) At what frequency will the magnitude of H ( jw) be maximum? c) What is the maximum value of the magnitude of H ( jw)? d) At what frequency will the magnitude of H ( jw) equal its maximum value divided by W? e) Assume a resistance of 5 Q is connected in series with the 80 ”F capacitor in the circuit in Fig. P14.11. Calculate we, H (jwc), H ( j0.125wc), and H ( j8wc). Figure P14.12 14.19 Calculate the center frequency, the bandwidth, and the quality factor of a bandpass filter that has an upper cutoff frequency of 121 krad/s and a lower cutoff frequency of 100 krad/s. 14.21 Design a series RLC bandpass filter (see Fig. 14.19[a]) with a quality of 8 and a center frequency of 50 krad/s, using a 0.01 ,u.F capacitor. a) Draw your circuit, labeling the component val- ues and output voltage. b) For the filter in part (a), calculate the bandwidth and the values of the two cutoff frequencies. L C + v, R 120 (a) L C + v, R 120 (b) L C + v, R 120 Figure 14.19 A (a) A series RLC bandpass filter; (b) the equivalent circuit for a) = 0; and (c) the equivalent circuit for w = 00. 14.31 Consider the circuit shown in Fig. P14.31. PSPICE MULTISIM a) Find wo. b) Find B. c) Find Q. (1) Find the steady-state expression for '00 when vi = 250 cos wot mV. e) Show that if RL is expressed in kilohms the Q of the circuit in Fig. P1431 is 20 Q = 1 + 100/1?L f) Plot Q versus RL for 20 k9 S RL S 2 M9. Figure P14.31 100 k!) 14.35 For the bandreject filter in Fig. P1435, calculate (a) mo; (b) f0; (C) Q; (d) B in hertZ;(e) wc1;(f)fc1; (g) wc2; and (h) fc2 - Figure P14.35 1875 Q + + 156.25 mH ’1)" ’00 14.36 For the bandreject filter in Fig. P1435, a) Find H020) at (00, (ad, (062, 0.1000, and 10mg. b) If v,- = 80 cos wt V, write the steady-state expres- sion for v0 when a) = (no, a) = wcl, w = (062, w = 0.1mm andw = 10(00. 14.49 Consider the series RLC circuit shown in Fig. P14.49. When the output is the voltage across the resistor, we know this circuit is a bandpass filter. When the output is the voltage across the series combination of the inductor and capacitor, we know this circuit is a ban- dreject filter. This problem investigates the behavior of this circuit when the output is across the inductor. a) Find the transfer function, H (s) = V0(s)/V,-(s) when Vo(s) is the voltage across the inductor. b) Find the magnitude of the transfer function in part (a) for very low frequencies. c) Find the magnitude of the transfer function in part (a) for very high frequencies. d) Based on your answers in parts (b) and (c), what type of filter is this? 6) Suppose R = 600 (l, L = 400 mH, C = 2.5 uF. Calculate the cutoff frequency of this filter, that is, the frequency at which the magnitude of the transfer function is 1/ Vi. Figure P14.49 ...
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