Chapter 7- Frequency Response
-
Upload
fakrul-hanif -
Category
Documents
-
view
269 -
download
1
Transcript of Chapter 7- Frequency Response
-
8/12/2019 Chapter 7- Frequency Response
1/47
Chapter 7
Frequency Response
-
8/12/2019 Chapter 7- Frequency Response
2/47
Amplifier Frequency Response
-
8/12/2019 Chapter 7- Frequency Response
3/47
1-3
Electronic Circuits
Amplifier Frequency Response
In linear amplifier analyses, coupling and bypasscapacitors act as short circuits to the signal voltagesand open circuits to dc voltages.Capacitors do not change instantaneously from a shortcircuit to an open circuit as the frequency approacheszero.Internal capacitances in BJT and FET affect thefrequency response.
All amplifier gain factors are functions of signalfrequency.Includes voltage, current, transconductance, andtransresistance
-
8/12/2019 Chapter 7- Frequency Response
4/47
1-4
Electronic Circuits
Amplifier gain versus frequency
(f < f L ) (f > f H )
Gain decreases as the frequencydecreases because of coupling and
bypass capacitor effects
-
8/12/2019 Chapter 7- Frequency Response
5/47
-
8/12/2019 Chapter 7- Frequency Response
6/47
1-6
Electronic Circuits
(f < f L ) (f > f H )
Coupling and bypass capacitors act asshort circuits, and stray and transistorcapacitances act as open circuits
Amplifier gain versus frequency
-
8/12/2019 Chapter 7- Frequency Response
7/47
1-7
Electronic Circuits
(f < f L ) (f > f H )
Gain at f = f L and at f = f H is 3dB
Bandwidth f BW = f H - f L
Amplifier gain versus frequency
Gain at f = f L and at f = f H is 3dB
Bandwidth f BW = f H - f L
-
8/12/2019 Chapter 7- Frequency Response
8/47
1-8
Electronic Circuits
System Transfer Functions
The frequency response of a circuit is usuallydetermined by using the complex frequency s (s = j =
j2 f ).Each capacitor is represented by its compleximpedance, 1/sC .Each inductor is represented by its compleximpedance, sL .
Name of function Expression
Voltage transfer function T(s) = V o(s) / V i(s)
Current transfer function I o(s) / I i(s)
Transresistance function V o(s) / I i(s)
Transconductance function I o(s) / V i(s)
-
8/12/2019 Chapter 7- Frequency Response
9/47
1-9
Electronic Circuits
s -Domain Analysis
A transfer function in the s -domain
K = constantz = zeroes
p = poles
s = z i , the transfer function is zeros = p i , the transfer function is infinite
n
m p s p s p s
z s z s z s K sT
21
21
-
8/12/2019 Chapter 7- Frequency Response
10/47
1-10
Electronic Circuits
s -Domain Analysis
Simple transfer functions
2
2
2
11
1
11
s
s K sT
s K sT
-
8/12/2019 Chapter 7- Frequency Response
11/47
1-11
Electronic Circuits
s -Domain Analysis
Series coupling capacitor circuit
+
-
R sCs
Vo
R pVi
s s
K C R R s
C R R s
R R
R
sV sV
C R R s
C sR
sV sV
sC R R
R
sV sV
s p s
s p s
p s
p
i
o
s p s
s p
i
o
s p s
p
i
o
11)()(
1)()(
1)()(
2
-
8/12/2019 Chapter 7- Frequency Response
12/47
1-12
Electronic Circuits
s -Domain Analysis
Parallel load capacitor circuit
+
-
R s
C p
Vo
R pVi
s K
C R R s R R
R
sV sV
C R R
R R s
R R
R
sV sV
sC V
RV
RV V
p p s p s
p
i
o
p p s
p s p s
p
i
o
p
o
p
o
s
io
11
11
)()(
1
1)()(
01
1
KCL at output node
-
8/12/2019 Chapter 7- Frequency Response
13/47
1-13
Electronic Circuits
Bode Plots
+
-
R sCs
Vo
R pVi
2
22
2
21
2)(
1)(
1)()()()(
11)()(
s
s
p s
p
s
s
p s
p
s s
p s p
io
s p s
s p s
p s
p
i
o
f
f R R
R jf T
R R
R jT
j j
R R R
jV jV jT sT
s s
K C R R s
C R R s
R R
R
sV sV
-
8/12/2019 Chapter 7- Frequency Response
14/47
1-14
Electronic Circuits
Bode Plots
+
-
R sCs
Vo
R pVi
2101010
210
21log202log20log20)(
21
2log20)(
s s p s
pdB
s
s
p s
p
dB
f f R R
R jf T
f
f
R R
R jf T
-
8/12/2019 Chapter 7- Frequency Response
15/47
1-15
Electronic Circuits
Bode Plots
2101010 21log202log20log20)( s s p s
pdB f f R R
R jf T
-
8/12/2019 Chapter 7- Frequency Response
16/47
1-16
Electronic Circuits
Bode Plots
p s
p
R R
R10log20
This term is a constant thus independent of frequency[R p /(R s+R p)] is less than unity thus dB value is less thanzero
-
8/12/2019 Chapter 7- Frequency Response
17/47
1-17
Electronic Circuits
Bode Plots
s f 2log20 10
When f = 1/2 s , 20log 10 (1) = 0
-
8/12/2019 Chapter 7- Frequency Response
18/47
1-18
Electronic Circuits
Bode Plots
The slopes in Bode plot magnitudes are described inunits of either dB/octave or dB/decade
An octave means that frequency is increased by afactor of two
A decade implies that the frequency is increased by afactor of 10The value of the function 20log 10 (2 f s ) increases by afactor of 6dB for every factor of 2 increases in
frequency, thus a slope is considered 6dB/octaveThe value of the function 20log 10 (2 f s ) increases by afactor of 20dB for every factor of 10 increases infrequency, thus a slope is considered 20dB/decade
-
8/12/2019 Chapter 7- Frequency Response
19/47
-
8/12/2019 Chapter 7- Frequency Response
20/47
1-20
Electronic Circuits
Bode Plots
For f >> 1/2 s , the 2 nd and 3 rd term cancel For f
-
8/12/2019 Chapter 7- Frequency Response
21/47
1-21
Electronic Circuits
Bode Plots
The series capacitor C s is a coupling capacitor between theinput and output signals At a high enough frequency, C s acts as a short circuit, andthe output voltage isV o = [R p /(R s+R p )]V i
For very low frequencies, the impedance of C s increasesand approaches as an open circuit, and the output voltageapproaches zeroThis circuit is called a high-pass network
The high-frequency signals are passed through to the output
+
-
R sCs
Vo
R pVi
-
8/12/2019 Chapter 7- Frequency Response
22/47
1-22
Electronic Circuits
Bode Plot of The Phase Function
j Ke jB A
K =
.
22 B A
)/(tan 1 A B
-
8/12/2019 Chapter 7- Frequency Response
23/47
1-23
Electronic Circuits
Bode Plot of The Phase Function
3213
2
1
3
2
1
3
21
3
21)(
21
2)(
212)(
1)()(
)(
j j
j j
j s
j s j
p s
p
s
s
p s
p
s
s
p s
p
i
o
e K
K K e K e K
e K jf T
e f j
e f je
R R
R jf T
f j f j
R R R jf T
j j
R R
R
jV jV
jT
-
8/12/2019 Chapter 7- Frequency Response
24/47
1-24
Electronic Circuits
Bode Plot of The Phase Function
3213
2
1
3
2
1
3
21
3
2
1)(
21
2)(
j
j
j j
j s
j s j
p s
p
e K
K K
e K
e K e K jf T
e f j
e f je
R R
R jf T
The first term is a positive real quantity, the phase is 1 = 0The second term is purely imaginary, the phase is 2 =
90 oThe third term is complex, the phase is 3 = tan -1 (2 f s ) The net phase is = 90- tan -1 (2 f s)
-
8/12/2019 Chapter 7- Frequency Response
25/47
1-25
Electronic Circuits
Bode Plot of The Phase Function
so f 2tan90 1
-
8/12/2019 Chapter 7- Frequency Response
26/47
1-26
Electronic Circuits
Bode Plots
2
22
1
21
1)(
1
1)(
11
)()(
)()(
11
11
)()(
p p s
p
p p s
p
p p s
p
io
p p s p s
p
i
o
f R R
R jf T
R R
R jT
j R R
R
jV jV
jT sT
s K
C R R s R R
R
sV sV
+
-
R s
C p
Vo
R pVi
-
8/12/2019 Chapter 7- Frequency Response
27/47
1-27
Electronic Circuits
Bode Plots
2101010
210
21log201log20log20)(
21
1log20)(
p p s
pdB
p p s
pdB
f R R
R jf T
f R R
R jf T
+
-
R s
C p
Vo
R pVi
-
8/12/2019 Chapter 7- Frequency Response
28/47
1-28
Electronic Circuits
Bode Plots
2101010 21log201log20log20)( p p s
pdB f R R
R jf T
-
8/12/2019 Chapter 7- Frequency Response
29/47
1-29
Electronic Circuits
Bode Plots
The parallel capacitor C p is a load or parasitic capacitance At low frequency, C p acts as an open circuit, and the outputvoltage is
V o = [R p /(R s+R p )]V i At high frequency, the impedance of C p decreases andapproaches as a short circuit, and the output voltage is zeroThis circuit is called a low-pass network
The low-frequency signals are passed through to the output
+
-
R s
C p
Vo
R pVi
-
8/12/2019 Chapter 7- Frequency Response
30/47
1-30
Electronic Circuits
Bode Plot of The Phase Function
321
3
2
1
3
2
1
3
21
3
21)(
21)(
211)(
11
)()(
)(
j j
j j
j p
j j
p s
p
p p s
p
p p s
p
i
o
e K
K K e K e K
e K jf T
e f j
ee
R R
R jf T
f j R R R jf T
j R R
R
jV jV
jT
-
8/12/2019 Chapter 7- Frequency Response
31/47
1-31
Electronic Circuits
Bode Plot of The Phase Function
3213
2
1
3
2
1
3
21
3
21)(
21)(
j j
j j
j p
j j
p s
p
e K
K K
e K
e K e K jf T
e f je
e R R
R jf T
The first term is a positive real quantity, the phase is 1 = 0The second term is a positive real quantity, the phase
is 2 = 0
The third term is complex, the phase is 3 = tan -1 (2 f p ) The net phase is = - tan -1 (2 f p)
-
8/12/2019 Chapter 7- Frequency Response
32/47
1-32
Electronic Circuits
Bode Plot of The Phase Function
s f 2tan 1
-
8/12/2019 Chapter 7- Frequency Response
33/47
1-33
Electronic Circuits
Short-Circuit and Open-CircuitTime Constant
Vo
+
-
R s
C pR pVi
Cs
p s s
p
p s
p p s
p
i
o
s sC
C
R R
R R R
R
sV sV
11
1)()(
Both C S and C P presentKCL at output node
-
8/12/2019 Chapter 7- Frequency Response
34/47
1-34
Electronic Circuits
Short-Circuit and Open-CircuitTime Constant
C s affects the low frequency response and C p affects thehigh frequency response At low frequencies, load capacitor is treated as an opencircuitEquivalent resistor seen by C s is found by setting all
independent sources equal to zero. Thus the effectiveresistance is (R s+R p )
The time constant associated with C s is s = (R s+R p )C sSince C p was made an open circuit, thus s is called anopen-circuit time constant
Vo
+
-
R s
C pR pVi
Cs
-
8/12/2019 Chapter 7- Frequency Response
35/47
1-35
Electronic Circuits
Short-Circuit and Open-CircuitTime Constant
At high frequencies, coupling capacitor is treated as ashort circuit
Effective resistance seen by C p is (R s ||R p ) The time constant associated with C p is p = (R s ||R p )C pSince C s was made a short circuit, thus p is called ashort-circuit time constant
Vo
+
-
R s
C pR pVi
Cs
-
8/12/2019 Chapter 7- Frequency Response
36/47
1-36
Electronic Circuits
Short-Circuit and Open-CircuitTime Constant
The lower corner or 3dB frequency is at the low end ofthe frequency scale, is a function of the open-circuittime constantf L = 1/2 s
The upper corner or 3dB frequency is at the high endof the frequency scale, is a function of the short-circuittime constantf H = 1/2 p
Midband range or bandwidthf BW = f H - f L
-
8/12/2019 Chapter 7- Frequency Response
37/47
1-37
Electronic Circuits
Short-Circuit and Open-CircuitTime Constant
-
8/12/2019 Chapter 7- Frequency Response
38/47
Frequency Response:Transistor Amplifiers withCircuit Capacitors
-
8/12/2019 Chapter 7- Frequency Response
39/47
1-39
Electronic Circuits
(a) Common-emitter circuit with coupling capacitor and(b) small-signal equivalent circuit
Coupling Capacitor Effects
Small signal outputresistance r o is infinite
r o >> R C, r o >> R E
This circuit is a high-pass network
At high frequencies, C C acts as a short circuitand the input signal iscoupled through thetransistor to the output
At low frequencies, theimpedance of C C becomes large and theoutput is zero
-
8/12/2019 Chapter 7- Frequency Response
40/47
1-40
Electronic Circuits
Current-Voltage Analysis
Coupling CapacitorEffects
r g
Rr I V
R
r I V
Rr I g I r I
RV g I r I V
m
E b
inib
b
E bmbb
E mbbin
1
-
8/12/2019 Chapter 7- Frequency Response
41/47
-
8/12/2019 Chapter 7- Frequency Response
42/47
-
8/12/2019 Chapter 7- Frequency Response
43/47
1-43
Electronic Circuits
Coupling CapacitorEffects
i
gs
gs
o
i
ov V
V
V V
V V
A
Set all independent source 0, thus V i=0, V gs =0, g mVgs =0.Resistance seen by C C is (R D+R L)Corner frequency f L=1/2 s
-
8/12/2019 Chapter 7- Frequency Response
44/47
1-44
Electronic Circuits
(a) Emitter-follower circuit with output coupling capacitor and(b) small-signal equivalent circuit
Coupling Capacitor Effects
CC1 is very large and acts as a short circuit to the input signal The equivalent resistance seen by C C2 is [R o+R L]
-
8/12/2019 Chapter 7- Frequency Response
45/47
1-45
Electronic Circuits
Coupling CapacitorEffects
-
8/12/2019 Chapter 7- Frequency Response
46/47
1-46
Electronic Circuits
Review: OutputImpedance
-
8/12/2019 Chapter 7- Frequency Response
47/47
1-47Problem-Solving Technique