0195136047.pdf

PROBLEMS 187

4 pF

i(t)^1000 Ω 100 pF 100 i 1 500 Ω

i 1

v(t)

+

−

Figure P3.3.10

3.3.11For the networks shown in Figure P3.3.11, deter-

mine the transfer functionG(s)=Vo(s)/Vi(s).

3.3.12The responsev(t) of a linear system to a unit-step

excitationi(t) is given byv(t)=( 5 − 3 e−t+

2 e−^2 t) u(t). Determine the transfer function

H(s)=V (s)/I (s).

3.3.13The responsey(t) of a linear system to a unit-step
excitation isy(t)=( 4 − 10 e−t+ 8 e−^2 t) u(t).
(a) Find the system function.
(b) Find the frequency at which the forced re-
sponse is zero.
3.3.14The unit impulse responseh(t) of a linear system
ish(t)= 5 e−tcos( 2 t−30°). DetermineH(s).
3.3.15The responsey(t) of a linear system to an excitation
x(t)=e−^2 tu(t)isy(t)=(t+ 2 )e−tu(t). Find
the transfer function.
3.3.16A filter is a network employed to select one range
of frequencies while rejecting all other frequen-
cies. A basic building block often used in inte-
grated-circuit filters is shown in Figure P3.3.16.
Determine the following for the circuit:
(a) Transfer functionVo(s)/Vi(s).
(b) Responsevo(t) forvi(t)=u(t).
(c) Driving-point impedanceVi(s)/Ii(s).
3.4.1For the circuits shown in Figure P3.4.1, sketch
the frequency response (magnitude and phase) of
V ̄out/V ̄in.
3.4.2Design the low-pass filter shown in Figure P3.4.2
(by determiningL) to have a half-power frequency
of 10 kHz.
3.4.3Design the high-pass filter shown in Figure P3.4.3
(by determiningC) to have a half-power frequency
of 1 MHz.
3.4.4DetermineLandCof the bandpass filter circuit
of Figure P3.4.4 to have a center frequency of 1
MHz and a bandwidth of 10 kHz. Also find theQ
of the filter.
3.4.5DetermineLandCof the band reject filter circuit
of Figure P3.4.5 to have a center frequency of 100

kHz and a bandwidth of 5 kHz. Also find theQof

the filter.

3.4.6Determine the voltage transfer function of the low-

pass filter circuit shown in Figure P3.4.6, and find

the expression forω 0.

*3.4.7Determine the voltage transfer function of the

high-pass filter circuit shown in Figure P3.4.7, and

find the expression forω 0.

3.4.8Let a square-wave voltage source having an am-

plitude of 5 V, a frequency of 1 kHz, a pulse width

of 0.5 ms, and an internal source resistance of

50 be applied to a resistive load of 100.A

filter (inductanceL) is inserted between source

and load in order to reduce all the high-frequency

components above 5 kHz. Determine (a)Lof the

low-pass filter, (b) amplitude spectra ofVLandVS,

and (c)vL(t).

3.4.9Sketch the asymptotic Bode diagrams for the fol-

lowing functions:

(a)H 1 (s)=

200

( 1 +s)

(

1 +

s

10

)

(b)H 2 (s)=

200 s

( 1 +s)

(

1 +

s

10

)

(c)H 3 (s)=

200

(

1 +

s

10

)

( 1 +s)

(

1 +

s

20

)

(d)H 4 (s)=

0. 5

(

1 +

s

10

)

( 1 +s)^2

(

1 +

s

40

)

(e)H 5 (s)=

0. 5 ( 1 +s)^2

s

(

1 +

s

10

)(

1 +

s

50

)

(f) H 6 (s)=

20

(

1 +

s

8

)

( 1 +s)

(

1 +

s

10

) 2 (

1 +

s

40

)