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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 steadystate
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 lowpass 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 highpass 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 steadystate 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 steadystate 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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 Fall '09
 Frequency, Hertz, Highpass filter, Bandpass filter, Lowpass filter, Cutoff frequency

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