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TRANSISTORTRANSISTORTRANSISTORTRANSISTORTRANSISTOREQUIVALENTEQUIVALENTEQUIVALENTEQUIVALENTEQUIVALENTCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDCIRCUITS ANDMODELSMODELSMODELSMODELSMODELS
Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives General DC Equivalent Circuit AC Equivalent Circuit Equivalent Circuit of a
CB Amplifier Effect of Source Resistance
Rs on Voltage Gain Equivalent Circuit of a
CE Amplifier Equivalent Circuit of a
CC Amplifier Small-signal Low-frequency
Model or Representation T-Model Formulas for T-Equivalent of
a CC Circuit What are h-parameters ? Input Impedance of a Two
Port Network Voltage Gain of a Two Port
Network The h-parameters of an
Ideal CB Transistor The h-parameters of an
ideal CE Transistor Approximate Hybrid
Equivalent Circuits Transistor Amplifier
Formulae Usingh-parameters
Typical Values of Transistorh-parameters
Approximate HybridFormulas
Common Emitterh- parameter Analysis
Common Collectorh-parameter Analysis
Conversion ofh-parameters
2238 Electrical Technology
Fig. 59.2
Fig. 59.1
59.1. General59.1. General59.1. General59.1. General59.1. General
±
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"
#β$
"
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&
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%'
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(
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59.2. DC Equivalent Circuit59.2. DC Equivalent Circuit59.2. DC Equivalent Circuit59.2. DC Equivalent Circuit59.2. DC Equivalent Circuit
%"α)
)
!
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"
%
"
"
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.
#.,-/$+,-#$"
+
,-0
2239Transistor Equivalent Circuits and Models 2239
+,-/
1
.,-/%"
!!
59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit59.3. AC Equivalent Circuit
% "
."
+,-2
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)0,5
6.
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7 0,5
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+,-,
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∆ )∆
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0,5
6
Fig. 59.3
Fig. 59.4
Fig. 59.5
.!
2240 Electrical Technology
0,5 0,5"
9
70,5"
!"
)#4β$7≅ β
6.:02
β
" )β
59.4. Equivalent Circuit of a CB Amplifier59.4. Equivalent Circuit of a CB Amplifier59.4. Equivalent Circuit of a CB Amplifier59.4. Equivalent Circuit of a CB Amplifier59.4. Equivalent Circuit of a CB Amplifier%+,-:#$ ."
;
4
υ
Fig. 59.7
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7
< 0,5
.
."
7=+,->#$?.!
C1C2
R C
+VCC +VCC-VEE-VEE
R E
RL
RERC
VCBIC
IE
Vin VoutVs
(( ba ))
NPNA B
Fig. 59.6
2241Transistor Equivalent Circuits and Models 2241
.+,-:#$"
7
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+'
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"
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7
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∴
≅ ) 7
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∴ )
@@
%
%#%""
)
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&
%
'(#&
%
B" )
)#4β$
) )β
Fig. 59.8
Fig. 59.9
C *"5υ
%"
#.,-,$
2242 Electrical Technology
∴ # $
!β9#4β$"7
)#*&
)
")
"+,--
+,)- !" #!$% &'()*+,$,
,
,υ
-%!#!$ !! !$#!$
(&#.#! #!α/)'0#. /$0
Fig. 59.10
1# #+"
:
>8.,D
7 0,5 0,
2. >8
) 7
@@)2Ω@@,D≅ 'ΩΩΩΩΩ
)
)'2
+,-#$
)α)3-4
7
2
2
1
45
)
)->E0>8)0>
)
0>
)')$
F)E
∴
)E
)0>8E,)20-5)3'-(
+,)-#!$ % &'((*+,$
!
!
!
))2
1# #)#0;:$9/D)82.( 7
)0,982)/-Ω
) 7 @@
)/-Ω@@/D≅ /-Ω
)@@
)/D@@,D)32
2243Transistor Equivalent Circuits and Models 2243
+,-
)
@@
+"
B" 8
2/-
.
Fig. 59.11
)
)2.(
)
)2ED)25
7 7
D
/-
)3
B" 0, 8 25
3'(
59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance R59.5. Effect of Source Resistance Rs s s s s on Voltage Gainon Voltage Gainon Voltage Gainon Voltage Gainon Voltage Gain
3
3
3
3
+,-0
3
+
,-/#$*"3#7@@A$
3
F"
7@@3GH5
+"
C1RSC2
R C
+VCC-VEE
RE
RLin outVs V V
!"
)/D
#3$7*"/
D")
Fig. 59.12
2244 Electrical Technology
7
7
@@
@@
%"II
7"
7@@
≅
7
Fig. 59.13
∴7
7
7
.3
7"
39
7!
J""
34
799
≅
34
7 ∴
7# $
33
6
3II
7
J!3
7!
7
7
+,)-#!$ $ &'(4,$
! $# ! $##
5#!$
#. 0
1# #
7# $
3 3
)@@
)D@@0J
≅ D()0,90,D).
7)0,9)0,Ω
D
#D 08 $
3
Fig. 59.14
+20 V-25 V
RS
in out
Vs
2 mV(rms)
1K
25 K 10 K
2 MV V
2245Transistor Equivalent Circuits and Models 2245
B"
)99
7)0,D@@0,Ω≅ 0,Ω ∴
0,
3
1
400400400400400
'
.A#$")
2
" B"A#$"
Fig. 59.15
))E0)05 ∴ /0
2
)3µµµµµ(
.#+,-,$"
3
7#!
7@@
$
∴7
7
0,0
0,
)3µµµµµ(
59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier59.6. Equivalent Circuit of a CE Amplifier
K+,-8#$
Fig. 59.16
+".,-0%
+,-8#$
."
(
)β
(
≅
≅ β
iS
IB
IBIC
IC VCCVCC
RB
RL
RL
IE
RCRC
ib
C1
C2
in
out
Vs
E
(a) (b)
B
V
V
2246 Electrical Technology
L+,-:
..,-/"!
)β7%
#$
+,-:#$
Fig. 59.17
%3"
β7
.3β7
#)9
$
3
"
*"+,-:#$")
!
.+,-:"
)99β
7≅ β
7
IIβ
7
)
* +
)*+
"#$!)
@@
&
' (#
B" 7
∴ 7 7
6
IIβ
7
) #*&)
)
+,)-'$ $ &'(6*+,
/7),/()1,
/(8,
/(
8,/7#β/&),$
##,670--
1# # )09J) 0µ.(
)β
),E0.).
7)0,59.)0,Ω(
*+)β
7),E0)0,Ω
.+,-:#$"
# $
05
0,
5µµµµµ(
)β
),E8)43µµµµµ
)
99β
7)J@@0,Ω ≅ )3ΩΩΩΩΩ
)
@@
)J@@D≅ 32
2247Transistor Equivalent Circuits and Models 2247
7 7
D
0,
'33
)
),E2)0"(
)
0")'$
+,)-)#!$ $ &'(0#!9 #$ :,$'
;:β)<%%!!! $#9 #M
#8 /$0
1# #%
*"
*"
+,--
B"/
0J D
)µ.()β
)E.).
≅ )."
7)0,9))ΩΩΩΩΩ(
β7)E0,))33ΩΩΩΩΩ
.+,--
)
@@
7
)0J@@0,Ω≅ )33ΩΩΩΩΩ
)
@@
)D@@0D
)5592
7
88: D
0,59
)
)E08:)5933(
)
08":)''$
When Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is RemovedWhen Emitter Bypass Capacitor is Removed"B"
.β .,:02"
#4β$#74
$ ≅ β
#74
$
7
+
,-0#$
B"
+,-0#$
)
@@β
#4
$ ≅
@@β
%
7
Fig. 59.19
Fig. 59.18
Fig. 59.20
2248 Electrical Technology
Fig. 59.22
Fig. 59.21
7)0,Ω 6
∴ β #74
$≅ β
)ED)J
∴ )
@@β
)0J@@J
)0
J/
)55592 6
)5592 6
)
β#
74
$(
)
)β
∴ # 7 $ # 7 $
88: D
D3559 6
)
)E88:)559 6
%"
+,)-5 % &'7(, #*+
!
:β/7))1# #%
0,
/ :,5, 2,
A)5
0;5
&A≅ 5
0):,5
A):,9:,D).
7)0,59.)0,Ω
+,-00
" 2,D"
F "
,D$2,D
β 7
*+
K7
"
7,D
D
*+
) β7)0E0,))2
),59,D)µ.
#F"
$B" )β
)0E)0µ.)0.
)D@@,D)9/D)///D"
)
)0E///)3559(
88:5
, 5
7
///D//
0,
+,-00 %
*+
F"
),D@@2,D@@,D)/,2D
2249Transistor Equivalent Circuits and Models 2249
+,)-9#!$ $ &'7=,$
*+
;:β/&)
3/) $#. :60--
1# #
0
,.2
7)0,9,),Ω
β7),E,)0,Ω
)D@@0,Ω )333ΩΩΩΩΩ
)0D@@0D)32
7
,
1
33
)
)0E,)"
))'3$
)E
)0E0)'3,(,
3 "
+,)-4 !" #!$ "
$ &'74, $ 5# ! $
;:β/())
>/&)#?
#. & :0--
1# # 0,
0 05(, 2,
0 0
0.
7),90)0,Ω(
β7)0,E)0,D
)
@@
7@@β
7)2,@@,@@0,)52
),D@@,D)0,D
0,D
0,
33
)
)E)3333
)
"
)'3$
%#
=
+,)--5#!$@$5&'0 9 "
= &'74#
1# #%"
)
(@@
7@@β#
74
$)2,D@@,D@@#0,4D$
≅ 2,D@@,D@@D))2
)0,D6
7
0,D
D# $
)
#H$
$)E0,))3 )0,)'$
Fig. 59.23
Fig. 59.24
20V
C1RS
C2
C3
VoutVs
20 K
20 K
2mV(rms)
40 K10 K
20 V
R1
RL
RC
RE
C1
R2
C2
C3
2
Vs
45 K 5 K
5 K
5 K1 K
+
_
2250 Electrical Technology
59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance R59.7. Effect of Source Resistance Rsssss
N
"
)
;
3
KKA+,-0,
+,-08
.+,-08""3
@@β
7*"
3
%3
@@β
7"
≅
7
%""
"
"
"
+,)-3#!"
$ $ &'72,$# "
!! %3())Ω=1;:/&)
1# #
+,-0/3
.A->"7),Ω"
β7)0,Ω
∴ @@β
7 )D@@00,Ω )0Ω
;!1<33ΩΩΩΩΩ
% "05
Ω0Ω1Ω
0Ω*"
)
)05
)0
∴
)E
)0E0)'33,(,
;!1<2
%"@@β
7)0D
7
7
@@ 00 >5
/ 0# @@ $
∴
)0E>)53,(
F"3"
59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier59.8. Equivalent Circuit of a CC Amplifier
+,-0>#$
#$
!,=##*
Fig. 59.25
Fig. 59.26
Fig. 59.27
RS
RL
RC
VCC
RE
RBC
Vs
2251Transistor Equivalent Circuits and Models 2251
%%
+,-0>#$
9
%+,-0-
!
3
*+B"
*+
!
%#4β$
#74
$≅ β
β
∴
* +
)O&@@
*+
)@@β#
74
$ ≅ β#
74
$
6
≅ β
67PP
) β
6)
"#$!>)
@@
%
#!$
& # $
' (#&
)
)
β#
74
$ '
))β
7 7
# $
67PP
%,
, $
) #*& )
)E#4β$)#4β$≅ β
)
&
%
,$%
*"
%
#$
?
.!
*"
J"
Fig. 59.28
Fig. 59.29
2252 Electrical Technology
Fig. 59.32
+,)-#$!!%% &'=),$
* +
;:β),
#0
1# #)090).
7)0,9)0,Ω
)
@@
)0@@,)2D
*+
)β#74
$≅ β
),E2)0D
∴ #70,Ω
2D$
* +
)
@@
*+
)2D@@0D
)2
)0D@@,D)'2
≅
7
%"
)
βE)β),(
)
,)9$
+,)-"!A#$!!% $ &'=(,$
*+ * + !β)
#@##7/7#0
1# #0
0 0
0 ,5
2
0 ,
.,
7)0,9)0,Ω
),@@,)0,D
*+)β#74$
)#0,40,$))32
*+
)(@@
7@@
*+
)/D@@D@@0,D≅ >D
),D@@,D))2
)
≅ Eβ)100 (
)
)3$
+,)- $ &'=7,$
* +
!
β)0
1# #)090). 7)0,9)0,Ω
)0D@@,Ω),Ω
*+
) β#74
$)0#0,4,$),D(
* +
)@@
*+
)D@@,D)2
7
"
,7 0, ,
3559
Fig. 59.31
Fig. 59.30
RL
RBRE
-20
+20
rinVoutVs 5 K20 K
400 K
20V
R1
V2R2
VCC
RLREVout
Vs
30 K
10 K5 K5 K
+
_
2253Transistor Equivalent Circuits and Models 2253
)
)88:E0)
59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation59.9. Small-signal Low-frequency Model or Representation."
; ""
!
59.10. T-Model59.10. T-Model59.10. T-Model59.10. T-Model59.10. T-Model !
%+,-// ;
% ; .
*"
3%
0,5
6N
,5
6
."
?3%JΩ+"
3%G"
Fig. 59.33 Fig. 59.34
*"+,-/2#$
" +,-/2#$
."
Q
+,-/,#$%"
;
+,-/,#$
α )
)α
'
)0,,Ω(
)Ω(
)JΩ
rb
re rc
I/P O/P
E C
B
Fig. 59.35
rbrb ib
ie
rere re
rc
rc
ie
I/P O/P
EE
C
C
B B
(a) (b)
2254 Electrical Technology
; +,-/8
+,-/8 +,-/:
; +,-/>
Fig. 59.36 Fig. 59.37 Fig. 59.38
59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit59.11. Formulas for T-Equivalent of a CB Circuit
%+,-/-
;
3
F"
1
'
# $
# $# $
3
)α
'# $
$# $ # $ #
) )
0
# # $
6
0
# $ # $
6
)
Fig. 59.39
RS
Vin
rinVsrorb
rcre
ieib
ic
rinie
r L=
RL
+_
Transistor
B
E C
Vout
2255Transistor Equivalent Circuits and Models 2255
59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit59.12. Formulas for T-Equivalent of a CE Circuit
;
+,-2
1
'
# # $
)4#4β$
# $
3
)β # $
'# $
# $ # $
) )
0
# $=# # $?
0
# $=# # $ # $?
3
59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit59.13. Formulas for T-Equivalent of a CC Circuit
; +,-2
'
# $
)
4#;α$#
4
3$
# $
# $
3
# $# $
' )
)
# $# $
).
&
+,)-'B /&)Ω,/(1, /(8α/)'0 ##" %! $()1! ! ,! %
$# :60--$
1# #)α)->
-> "
# $ , #; ->$
'3
).ν
)2E->)/:
)
4
#;α$),4#;->$)93ΩΩΩΩΩ
+,)-)""B ! #!$ "
%! =))1! $ !
7))Ω
C5$! $#!$ ! !# $
;"%:#')>Ω"
):Ω"
)J
#)-:8D
$#$ &$ @
Fig. 59.40
Fig. 59.41
RS
rin
Vs
ro
reie
rcrb
ib
ic
Vout
rmie
r L=
RL
+_B
E
C
Vin
2256 Electrical Technology
1# #*"#)α#
4
$≅ α
∴ α )
#9
)-:8D9D)-:8
/0
-:8 /
# $ > : #; -:8$
4'3
/0 -:8 /
# $ 0 > : #; -:8$
'9
+,)-5! ! ,!! ,! %
$ $!!% "#'
/=)Ω,
/4))Ω,
/)2&8, α/)'&,
/()1
3/4))Ω
!, ! !% !
#@##7#0---
1# #2
/#; $ #; -,$
433ΩΩΩΩΩ
# $
3
-, :," 2
:," #; -,$ />">:#/ 2 2$
34/
-,
- # -,$
/
-,EE
# $ # $ 24 #/ 4 2$E,
< )
) .ν
)00,E-)'9)
H")
20:,)5$
59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?59.14. What are h-parameters ?
!.
!"
K!!
!+,-20.
" !
"
"0
"0
"00
% "
0 RQ
F " 0 0
A$$=#,1#. @
.+,-2/" 0)"
%
Fig. 59.42
2257Transistor Equivalent Circuits and Models 2257
0
5
6
00
6
!=#*$
0
!
?
)
4
0
0
0)
04
00
0
*"D
A$
$
=#,. @
.+,-22" )
0
0
0
0
6
000
0
6
."0
#09
$*"
00
#$
"3%!
N"
)
0
)
0
)
00
)
59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network59.15. Input Impedance of a Two Port Network
K !
+,-2,
."D
)
9
A#$.
,-2"
0 0
D
0 0
Fig. 59.43
Fig. 59.44
Fig. 59.45
2258 Electrical Technology
.+,-2,0);ν09
!0A#$.,-2"
000 00 0
;
0 0
00 9
A#$"
0 0
00
9
D
59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network59.16. Voltage Gain of a Two Port Network
#+ ,-2,$ )ν
09ν
Bν
)
D
*"
)ν
09
D
ν09
.,-,"
0
00# 9 $
D
+,)-9"#$ % &'46*+
1# #+"0
+"
+,-28#$
Fig. 59.46
!
)042@@2)'ΩΩΩΩΩ .+-28#$"
.
0);
90#
!
$
∴ 0 0
; 9 0
0
? 3)
B""
!0+,-2:%
02Ω
2Ω
.*")
090
∴ 0
00 0
9 0
0.50.50.50.50.5
Fig. 59.47
2259Transistor Equivalent Circuits and Models 2259
!
)242)>Ω
∴ 00
)9>)3)1,,#
*"!+,-28#$" '
)2Ω 0);, 0), 00)0,
59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors59.17. The h-parameter Notation for Transistors "
)
)
0
)$
)
0
)
)
00
))
)
.
+""'
$
"""
$"
"
"
$ "
59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor59.18. The h-parameters of an Ideal Transistor.""
"!
*""
' )
$
)
59.19.59.19.59.19.59.19.59.19. The h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB TransistorThe h-parameters of an Ideal CB Transistor
%+,-2>#$" !+"
,-2>#$%
A#*$,
+,-2-#$
∴ )
"
!
;
$
#%α$
!,
+,-2-#$
"%#$
Fig. 59.48
2260 Electrical Technology
RQ& "
""0*"
ν)
∴
0 0
""!
K"
#)9∞$
∴
)
SummarySummarySummarySummarySummary
)
(
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)(
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2261Transistor Equivalent Circuits and Models 2261
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2262 Electrical Technology
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2263Transistor Equivalent Circuits and Models 2263
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2264 Electrical Technology
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2265Transistor Equivalent Circuits and Models 2265
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2266 Electrical Technology
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2267Transistor Equivalent Circuits and Models 2267
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2268 Electrical Technology
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2269Transistor Equivalent Circuits and Models 2269
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2270 Electrical Technology
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2271Transistor Equivalent Circuits and Models 2271
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2272 Electrical Technology
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2273Transistor Equivalent Circuits and Models 2273
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2274 Electrical Technology
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OBJECTIVE TESTS – 59
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