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Unformatted text preview: onse, iC ( t) Solutions 65 M. J. Roberts  8/16/04 R = 1 kΩ
+
iC(t)
C = 1 µF vi (t)
 In this case the transfer function is the reciprocal of the input impedance.
(c) Excitation, v i ( t)  Response, v R ( t) + vR(t)  R = 1 kΩ
+
vi (t) C = 1 µF L = 1 mH (d) Excitation, ii ( t)  Response, v R ( t) + ii (t)
R = 100 Ω vR(t) L = 1 mH
C = 1 µF Divide the excitation current between the two branches and multiply the
current in the right branch by R to get the response voltage. Then solve for
the ratio of the response voltage to the excitation current.
10. Classify each of these transfer functions as having a lowpass, highpass, bandpass or
bandstop frequency response.
1
1 + jf (a) H( f ) = (c) H( jω ) = − (b) j10ω
100 − ω 2 + j10ω Solutions 66 H( f ) = jf
1 + jf M. J. Roberts  8/16/04 (d) H( F ) = sin( 3πF )
sin(πF ) This case is not as “pure” as the previous ones. It is generally lowpass because the
transfer function magnitude at lower frequencies is generally greater than at high
frequencies. But there are nulls in the transfer function that make it look somewhat
like a bandstop filter or a multiple bandstop filter.
(e) H( jΩ) = j[sin(Ω) + sin(2Ω)] This case is also not perfectly clear. The response at zero frequency is zero and the
response at Ω = π is also zero. These criteria fit a bandpass filter. But the response
2π
is also zero at Ω =
. So it might again look like a bandstop in some ways.
3
11. Plot the magnitude frequency responses, both on a linearmagnitude and on a logmagnitude scale, of the systems with these transfer functions, over the frequency range
specified.
20
(a)
H( f ) =
, −100 < f < 100
22
20 − 4π f + j 42πf
(b) 2 × 10 5
H( jω ) =
, −500 < ω < 500
(100 + jω )(1700 − ω 2 + j 20ω ) 12. Draw asymptotic and exact magnitude and phase Bode diagrams for the frequency
responses of the following circuits and systems.
(a) An RC lowpass filter with R = 1 MΩ and C = 0.1 µF .
1
1
1
1
jωC
H( jω ) =
=
=
=
6
−7
1
+ R jωRC + 1 jω10 10 + 1 j 0.1ω + 1
jωC Solutions 67 M. J....
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This note was uploaded on 06/19/2013 for the course ENSC 380 taught by Professor Atousa during the Spring '09 term at Simon Fraser.
 Spring '09
 ATOUSA

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