Transcript ELECTRIC CIRCUIT THEORY - DIT School of Electronics and

ELECTRIC CIRCUIT
THEORY
WAED 2
Paul Tobin
DIT
7/17/2015
Paul Tobin Dublin Institute of
Technology
Transfer functions
 A potential divider circuit
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Paul Tobin Dublin Institute of
Technology
Transfer functions
 The Voltage function for this potential
divider circuit is:
E2
R2

E1 R1  R 2
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Paul Tobin Dublin Institute of
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Low-pass CR filter
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Paul Tobin Dublin Institute of
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1
The voltage transfer function is
the output voltage divided by the
input voltage
1
1
TF 

1  jCR 1  j 2fCR
3
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Paul Tobin Dublin Institute of
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Brief visit to the complex
numbers world
 Z =A+ jB.
The magnitude of this vector is:
B
Z  ( A  B ) tan ( )
A
2
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2
1
Paul Tobin Dublin Institute of
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The magnitude of the TF is:
Vo
1
1
T .F 


 0.707
2 2 2
Vin
2
1  C R
 The frequency for which the transfer
function has a value of 0.5, is called
the cut-off frequency
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Paul Tobin Dublin Institute of
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The cut-off frequency is:
1

 c
CR
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Paul Tobin Dublin Institute of
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Bode
plotting estimates the amplitude
and phase response two-port networks using
straight-line segments.
 The asymptotic straight lines may
represent the actual response for a
two-port network
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Paul Tobin Dublin Institute of
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Bode plotting terms
A constant term K which does not
change with frequency,
A (1+j) n term, and
A j term.
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Paul Tobin Dublin Institute of
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The transfer function expressed in magnitude form:
TF 
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1
[1   /  c  ]

2 12
  tan( /  c )
Paul Tobin Dublin Institute of
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Decibels
Vout
dB  20log10
Vin
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Expressing the numerator and denominator in dB
TF dB
 2 1/ 2
 20log(1)  20log[1  ( ) ]
c
TF dB
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 2
 0  10 log[1  ( ) ]
c
Paul Tobin Dublin Institute of
Technology
Evaluate the transfer function by
plotting each part of the TF
separately. Consider the value of
the TF at two frequencies: a
decade below the cut-off
frequency, c and a decade above
c
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Paul Tobin Dublin Institute of
Technology
Asymptotic plotting
Substituting for  
c
10
into the transfer function
c
TF
1
2
10
) ]  10 log[1  (
)]
dB =  10 log[1  (
c
100
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Paul Tobin Dublin Institute of
Technology
0 dB
Asymptotic plotting
Substituting for  = 10c
TF dB =  10 log[1  (
10 c
c

TF dB =  10 log[1  100]
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)2 ]
- 20 dB/decade
Paul Tobin Dublin Institute of
Technology
The actual and asymptotic
response
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Part (a): A decade below fc
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Complete asymptotic response
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Paul Tobin Dublin Institute of
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Paul Tobin Dublin Institute of
Technology