7/27/2019 ECD4 Freq Response
1/63
3/29/2012
FrequencyRespons
e
Chapter4
BJT & FET Frequency
Response
Spring 2012
4
th
Semest
er
Mechatr
onicsSZABIST, Karachi
1229
CH 4
Frequency2
Response
CourseSupport
Office:100 Campus
(404) Official:
1
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]7/27/2019 ECD4 Freq Response
2/63
3/29/2012
ZABdesk
Subsidiary:
https://sites.google.com/site/zabistmechatronics/home/spring-2012/ecd
ebooks:
https://sites.google.com/site/zabistmechatronics/home/ebooks
1229
CH 4
2
7/27/2019 ECD4 Freq Response
3/63
FrequencyResp
onse
ChapterContents3
BJT & JFET FrequencyResponse Introduction
Logarithms and Decibels
GeneralFrequencyConsiderations
Bode plot Low Frequency Analysis
Low FrequencyResponse BJT Amplifier
Low FrequencyResponse FET Amplifier
High FrequencyResponse BJT Amplifier
High FrequencyResponse FET Amplifier
MultistageFrequencyEffects*
12
29
CH 4
Frequency4
Response
Introduction
7/27/2019 ECD4 Freq Response
4/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
5/63
FrequencyResp
onse
Introduction5
Frequency Response:
Phase and amplitude plots and equations of an amplifier
Frequency Response Prerequisites:
1. Logarithms
2. Semi-log plots
3. Decibels
4. Normalization
12
29
CH 4
Frequency6
Response
Logarithms
7/27/2019 ECD4 Freq Response
6/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
7/63
FrequencyResp
onse
Logarithms7
Logarithms:
The logarithm of a number is the exponent by which another
fixed value, the base, has to be raised to produce that number.a ::: : ::: og
10
a
Commonlogarithms:
Natural
logarithms:
::: og10
a
y ::: oge
a
Relationship of CL
and NL:
Benefits:
ogea ::: 2 . og
10a
Plotting of a variable between wide limits
Compression of large data
12
29
CH 4
Frequ
encyResponse
Logarithms8
Logarithms:
Broccoli,
which grows
in a
logarithmic
spiral
A low pressure
area over
Iceland shows
an
approximately
logarithmic
7/27/2019 ECD4 Freq Response
8/63
s piralpattern
The
whirlpool
Galaxy
A nautilusdisplaying a
logarithmic
spiral
12
29
CH 4
7/27/2019 ECD4 Freq Response
9/63
FrequencyResp
onse
Logarithms9
Example 9-1:
Using the calculator, determine the logarithm of the following
numbers to the base indicated:
a. log10
106
b. logee3
c. log10
102
d. logee1
Example 9-2:
Using the calculator, determine the logarithm of the following numbers:
a. log10
64 b.
loge64
c. log10
1600
d. log10
8000
12
29
CH 4
FrequencyResponse
1Logarithms0
og101 ::: 0
10 10 10
oga
::: og a og
1og10
::: og10
Example 9-3:
7/27/2019 ECD4 Freq Response
10/63
og10a ::: og
10a og
10
Using calculator, determine the antilogarithm of the following expressions:
a. 1.6 = log10
a b. 0.04
= logea
Example 9-4:
Using calculator, determine the logarithm of the following numbers:
a. log10
0.5
b. log10
(4000/250)
c. log10
(0.6 x 30)
12
29
CH 4
7/27/2019 ECD4 Freq Response
11/63
Frequency11
Response
Semilog
Plots
12
29
CH 4
FrequencyResponse
SemiloggraphpaperSemilog Plots
12
2
Linear
1
30% lo g102=0.3010
7/27/2019 ECD4 Freq Response
12/63
48%l
o
g1
0
9
=
0.9543
log108 =
0.9031
log10
7 =0.8451
12
29
Log103 = 0.4771
log104 =
0.6021
(60%)
log106
=
0.7781
log105 =
0.6999
CH 4
7/27/2019 ECD4 Freq Response
13/63
FrequencyResp
onse
Semilog Plots13
Identifying the numerical values ofthe tic marks on a log scale
12
29
CH 4
FrequencyResponse
Semilog Plots14
Va ue ::: 10 x 10d1jd2
d1
d2
1010 +1
Example 9-5:
Determine the value of the point appearing on the logarithmic
plot in Fig. 9-4 using the measures made by a ruler (linear).
7/27/2019 ECD4 Freq Response
14/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
15/63
Frequency15
Response
Decibels
12
29
CH 4
FrequencyResponse
Decibels16
::: og
P2
10 P1
e )
:::10 og
P2dB10
P1
dB )
:::10 ogP2
dB 10 P1R Oh s)
dBrr)
vdB 10
::: 20 ogV2
V1
dB )
7/27/2019 ECD4 Freq Response
16/63
AvT
=Av1
Av2
Av3
Avn
dBT=
dB1+
dB2+ . . . . . +
dBn
12
29
CH 4
7/27/2019 ECD4 Freq Response
17/63
FrequencyResp
onse
Decibels17
Example 9-6:
Find the magnitude gain corresponding to a voltage gain of 100 dB.
Example 9-7:
The input power to a device is 10,000 W at a voltage of 1000 V. The output power is500 W and the output impedance is 20 .
Example 9-8:
An amplifier rated at 40 W output is connected to a 10 speaker. Calculate:
a) The input power required for full power output if the power gain is 25 dB
b) The input voltage for rated output if the amplifier voltage gain is 40 dB
12
29
CH 4
Frequency18
Response
General FrequencyConsiderations
7/27/2019 ECD4 Freq Response
18/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
19/63
FrequencyResp
onse
Freq. Considerations19
General Frequency Considerations:
'r The frequency response of an amplifier refers to the
frequency range in which the amplifier will operate with
negligible effects from capacitors and device internal
capacitance.
'rThis range of frequencies can be called the mid-range.
At frequencies above and below the midrange, capacitanceand any inductance will affect the gain of the amplifier.
At low frequencies the coupling and bypass capacitors lower the gain.
At high frequencies stray capacitances associated with the
active device lower the gain.
Also, cascading amplifiers limits the gain at high and low frequencies.
12
29
CH 4
FrequencyResponse
Freq. Considerations20
General Frequency Considerations:
A Bode plotindicates the
frequency response
of an Amplifier:
The horizontal
scale indicates the
frequency (in Hz)
and the vertical
19
7/27/2019 ECD4 Freq Response
20/63
scale indicates the
gain (in dB)
The mid-range
frequency range
of an amplifier
is called the
bandwidth of theamplifier
The bandwidth is
defined by the
lower and upper
cutoff frequencies
Cutoff anyfrequency at which
the gain has
dropped by dB
12
29
CH 4
20
7/27/2019 ECD4 Freq Response
21/63
FrequencyResp
onse
Freq. Considerations21
General Frequency Considerations:
12
29
CH 4
Frequency22
Response
Normalization
7/27/2019 ECD4 Freq Response
22/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
23/63
FrequencyResp
onse
Normalization23
Normalization Process:
'rIn communication, a decibel plot vs frequency is normally
provided rather than gain vs frequency
'rAprocess in which the vertical parameter is divided by a
specific level orquantity sensitive to a combination or
variables ofthe system
'rThe band frequencies define a level where the gain or
quantity of interest will be 70.7% or its maximum value
12
29
CH 4
FrequencyResponse
Normalization24
NormalizationProcess:
Normalizedgainversus frequency plot
7/27/2019 ECD4 Freq Response
24/63
Decibelsplots of the normalizedgainversus frequency plot
12
29
CH 4
7/27/2019 ECD4 Freq Response
25/63
FrequencyResp
onse
Normalization25
Example 9-9:
Given the frequency response:a) Find the cutoff frequency f
1and f
2using the
measurements provided b) Find the bandwidth ofthe responsec) Sketch the normalized response
12
29
CH 4
FrequencyResponse
Normalization26
Example 9-9:
7/27/2019 ECD4 Freq Response
26/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
27/63
FrequencyResp
onse
Normalization27
Av
/Avmid
Av
/Avmid
|dB
1 0
0.7 -
0 -
0. -
0. -
dB Plot:
Decibelplot of the normalizedgainversus frequency plot
12
29
CH 4
Frequency28
Response
Low Frequency
Analysis
7/27/2019 ECD4 Freq Response
28/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
29/63
FrequencyResp
onse
LF AnalysisBode Plot29
Low frequency response for the R-C circuit
LowFrequency RCCircuitAnalysis:
12
29
CH 4
FrequencyResponse
LF AnalysisBode Plot30
Low Frequency RC Circuit Analysis:
Av
::: 0 707Xc=R
1f1 :::
2rrRC1Av :::
f1
1f
Av dB)
::: 20
og10
1
2
1
f1
7/27/2019 ECD4 Freq Response
30/63
f
Av dB)
::: 20
og10
f1
ff
7/27/2019 ECD4 Freq Response
31/63
FrequencyResp
onse
LF AnalysisBode Plot31
Low Frequency RC Circuit Analysis:
f f1
/f Av(dB)
f 1 0 f 2 -6
f 4 -12
1/10f 10 -20
12 29 CH 4
FrequencyResponse LF AnalysisBode Plot 32
Low Frequency RC Circuit Analysis:
fA
v(dB)
f 1 0
f1
2 -
f1
4 -
1/10f1
1 -
12 29 CH 4
7/27/2019 ECD4 Freq Response
32/63
FrequencyResponse LF AnalysisBode Plot 33
Low Frequency RC Circuit Analysis: The piecewise linear plot of the asymptotes and associated breakpoints is called a
Bode plot of the magnitude versus frequency
A change in frequency by a factor of 2, equivalent to 1 octave, results in a6-dB change in the ratio as noted by the change in gain from f
1/2 to f
1.
29 For a 10:1 change in frequency, equivalent to one decade,
there is a 20-dB change in the ratio as noted by the change in
gain from f1/10 to f
1.
A :::
V+o::: 10
Av
v Vi
dB)/20() ::: tan-1
f1
f
12 CH 4
FrequencyResponse
LF AnalysisBode Plot 34
Low Frequency RC Circuit Analysis:
7/27/2019 ECD4 Freq Response
33/63
Phase response for the RC circuit Example 9-9
12
29
CH 4
7/27/2019 ECD4 Freq Response
34/63
FrequencyResp
onse
LF AnalysisBode Plot35
Example 9-10:For the network of fig. 9-20: (R = 5 k, C = 0.1 F)
a) Determine the break frequencyb) Sketch the asymptotes and locate the 3dB point c) Sketch the frequencyresponse curved) Find the gain at A
v(dB)
= 6 dB
12
29
CH 4
FrequencyResponse
LF AnalysisBode Plot36
Example 9-10:
7/27/2019 ECD4 Freq Response
35/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
36/63
FrequencyResponse
Example 9-10:
% bode plot of
Example 9-10 f =
10:10^4;
fo = 318.5;
A = 20*log(1./(1+(fo./f).^2).^(1/2));
semilogx(f,A), xlabel('f
(log scale)'),
ylabel('Av(dB)')grid
LF AnalysisBode Plot37
ComputerAnalysis
0
-10
-20
-30
Av(dB)
-
4
0
-
5
0
-
60
-70 1 2 3 410 10 10 10f (log scale)
12
29
CH 4
Frequency38
Response
7/27/2019 ECD4 Freq Response
37/63
Low FrequencyResponse
BJT amplifiers
12
29
CH 4
7/27/2019 ECD4 Freq Response
38/63
FrequencyResp
onse
LF Response BJT Amplifiers39
BJT Amplifiers:
.
12
29
CH 4
FrequencyResponse
LF Response BJT Amplifiers40
Effects of Cs on the LF response:
38
7/27/2019 ECD4 Freq Response
39/63
12
29
CH 4
39
7/27/2019 ECD4 Freq Response
40/63
FrequencyResp
onse
LF Response BJT Amplifiers41
Effects of CC
on the LF response:
12
29
CH 4
FrequencyResponse
LF Response BJT Amplifiers42
Effects of CE
on the LF response:
7/27/2019 ECD4 Freq Response
41/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
42/63
FrequencyResp
onse
LF Response BJT Amplifiers43
Effects of Cs and CE
on the LF response:
The cutoff frequency due toC
Scan be calculated by
where
fL s
=
1
2 (Rs+ R
i)C
s
Ri= R
1||R
2
||re
The cutoff frequency dueto C
Ccan be calculated
withfLC=
12 (R
o
+ RL
)Cc
whereR
o= R
C||r
o
12
29
CH 4
FrequencyResponse
LF Response BJT Amplifiers44
Example 9-11:
a) Determine the lower cutoff frequency for the network ofFig. 9.23 using the following parameters:
CS= 10 F, C
E= 20 F, C
C= 1 F,
RS
= 1 k, R1
= 40 k, R2
= 10 k, RE
= 2 k, RC
= 4 k, RL
= 2.2 k,
= 100, ro
= , VCC
= 20 V
a) Sketch the frequency response using
a Bode plot b) Verify the result using a
Simulator.
7/27/2019 ECD4 Freq Response
43/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
44/63
FrequencyResp
onse
LF Response BJT Amplifiers45
Example 9-11:
12
29
CH 4
Frequency46
Response
Low Frequency
Response
FET amplifiers
7/27/2019 ECD4 Freq Response
45/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
46/63
FrequencyResp
onse
LF Response FET Amplifiers47
FET Amplifiers:
12
29
CH 4
FrequencyResponse
LF Response FET Amplifiers48
FET Amplifiers:
The cutoff frequency due to
CGcan be calculated with
1
where
f
L G =2 (R
sig
+ Ri
)CG
Ri
= RG
The cutoff frequency due to
CCcan be calculated with
1
7/27/2019 ECD4 Freq Response
47/63
where
f
L C = 2 (Ro
+ RL
)CG
RO
= RD
|| rG
12
29
CH 4
7/27/2019 ECD4 Freq Response
48/63
FrequencyResp
onse
LF Response FET Amplifiers49
FET Amplifiers:
The cutoff frequency due to
CScan be calculated with
fLS=
1
2 Req
CS
Req
where
R
1e q= R
S||g
m rd
12
29
CH 4
FrequencyResponse
LF Response FET Amplifiers50
Example 9-12:
a) Determine the lower cutoff frequency for the network of Fig.
11.32 using the following parameters:
CG
= 0.01 F, CC= 0.5 F, C
S= 2 F
Rsig
= 10 k, RG
= 1 M, RD
= 4.7 k, RS
= 1 k, RL
= 2.2 k
IDSS
= 8mA, VP
= 4 V rd
= , VDD
= 20 V
b) Sketch the frequency response using a Bode plot.
7/27/2019 ECD4 Freq Response
49/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
50/63
FrequencyResp
onse
LF Response FET Amplifiers51
Example 9-12:
12
29
CH 4
Frequency52
Response
HighFrequency
Response
FET amplifiers
7/27/2019 ECD4 Freq Response
51/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
52/63
7/27/2019 ECD4 Freq Response
53/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
54/63
FrequencyResp
onse
HF Response FET Amplifiers55
FET Amplifiers:
Capacitances that affect the high-frequency response are
Junction capacitancesC
gs, C
gd, C
ds
Wiring capacitancesC
wi, C
wo
Coupling capacitors
CG, C
C
Bypass capacitor
CS
12
29
CH 4
FrequencyResponse
HF Response FET Amplifiers56
FET Amplifiers:
fHi=
12R
Thi
Ci
Ci=C
Wi+ C
gs
+ CMi
CMi= (1 A
v)
Cgd
R
T
hi
Figure 9-64 (a) & (b)
7/27/2019 ECD4 Freq Response
55/63
fHo
=
1
2RTho
Co
Co= C
Wo+C
ds+C
Mo
? 1 ?C = 1 C
Mo ?? gd?A
v ?
RTho
= RD
||RL
||rd
12
29
CH 4
7/27/2019 ECD4 Freq Response
56/63
FrequencyResp
onse
HF Response FET Amplifiers57
Example 9-14:
12
29
CH 4
Frequency58
Response
Square Wave
Testing
7/27/2019 ECD4 Freq Response
57/63
12
29
CH 4
7/27/2019 ECD4 Freq Response
58/63
FrequencyResp
onse
Square Wave Testing59
Square Wave Testing:
12
29
CH 4
FrequencyResponse
Square Wave Testing60
Square Wave Testing:
58
7/27/2019 ECD4 Freq Response
59/63
12
29
CH 4
59
7/27/2019 ECD4 Freq Response
60/63
FrequencyResp
onse
Square Wave Testing61
Example 9-15:
The application of a 1-mV, 5-kHz square wave to an amplifier
resulted in the output waveform of Fig. 9-72.
(a) Write the Fourier series expansion for the square wave
through the ninth harmonic.
(b) Determine the bandwidth of the amplifier
(c) Calculate the low cutoff frequency.
12
29
CH 4
FrequencyResponse
Home Task62
Reading:
1. Summary
2. Equations3. Computer analysis
Problems:
1. Sec 8.2: (odd)
2. Sec 8.3: 17,18
3. Sec 8.4: 19,21
4. Sec 8.5:23,25
5. Sec 8.6: 27,29
7/27/2019 ECD4 Freq Response
61/63
6. Sec 8.7: 31
7. Sec 8.8: 33,35,37
8. Sec 8.10: 39,41
9. Sec 8.11: 43
10. Sec 8.12: 45
11. Sec 8.14: 47
12. Sec 8.15: 49
12
29
CH 4
7/27/2019 ECD4 Freq Response
62/63
Frequency
Response
References63
7/27/2019 ECD4 Freq Response
63/63
FET
1. Bolestad
2. Paynter
CH 1
12 29