0195136047.pdf

196 TIME-DEPENDENT CIRCUIT ANALYSIS

3.5.10A high-pass filter circuit is shown in Figure
P3.5.10. Using a PSpice program and PROBE,
obtain the Bode magnitude plot for the transfer
functionH(f) ̄ =V ̄out/V ̄infor frequency ranging
from 10 Hz to 100 kHz. Determine the rate (in
dB/decade) at which the magnitude falls off at low
frequencies, and also the half-power frequency.

3.5.11A bandpass filter circuit is shown in Figure
P3.5.11. Develop a PSpice program and use
PROBE to obtain a Bode magnitude plot for the
transfer functionH(f) ̄ =V ̄out/V ̄infor frequency
ranging from 1 Hz to 1 MHz. At what rate (in
dB/decade) does the magnitude fall off at low and
high frequencies? Also determine the half-power
frequencies.
3.6.1A periodic sequence of exponential wave forms
forms a pulse train whose first cycle is repre-
sented by
v(t)=[u(t)−u(t−T 0 )]vAe−t/TC
Use MATLAB to findVrmsof the pulse train for
vA=10 V,TC=2 ms, andT 0 = 5 TC.
3.6.2Use MATLAB to obtain the Laplace transform of
the waveform
f(t)=[200te−^25 t+ 10 e−^50 tsin( 25 t)]u(t)
which consists of a damped ramp and a damped
sine. Also show the pole–zero plot of the transform
F(s).
3.6.3With the use of MATLAB, find the expression for
the waveformf(t)corresponding to a transform

F(s)with a zero ats=−400, a simple zero at

s=−1000, a double pole ats=j400, a double

pole ats =−j400, and a value ats =0of

F( 0 )= 2 × 10 −^4. Plotf(t).

3.6.4Consider the circuit shown in Figure P3.6.4 in the

time domain as well as in thes-domain. Its transfer

functionV 2 (s)/V 1 (s)can be shown to be

T(s)=

s/RC

s^2 +s/RC+ 1 /LC

=

Ls/R

LCs^2 +(Ls/R)+ 1

which is a second-order bandpass transfer function

with a center frequency atω 0 = 1 /

√

LC. Using

MATLAB, evaluate the straight-line and actual

gain response of theRLCcircuit for the given

values.

*3.6.5Using MATLAB, plot the gain and phase response

of the transfer function

T(s)=

5000 (s+ 100 )

s^2 + 400 s+( 500 )^2

3.6.6The dual situations of Figure E3.6.3 is shown in

Figure P3.6.6, in which a high-pass and a low-

pass filter are connected in parallel to produce a

bandstopfilter.

With√ ωCLP = 10 << ωCHP = 50 ,ω 0 =

10 × 50 = 22 .4 rad/s, and

TLP(s)=

1

(s/ 10 )^2 +

√

2 (s/ 10 )+ 1

THP(s)=

(s/ 50 )^2

(s/ 50 )^2 +

√

2 (s/ 50 )+ 1

200 Ω

R 2

200 Ω

+

+

−

−

R 1

Vin 1 μF

__

Vout

__

C 1 C 2 1 μF

1 23

O

Figure P3.5.9

+ 0.1 μF

+

−

−

C 1

0.1 μF

C 2

Vin R 1

__

Vout

__

2 kΩ R 2 2 kΩ

1 23

O

Figure P3.5.10