Chap3 Utem (BJT Transistor Modeling)
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Transcript of Chap3 Utem (BJT Transistor Modeling)
![Page 1: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/1.jpg)
Chapter 7: BJT Transistor ModelingChapter 7: BJT Transistor Modeling
![Page 2: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/2.jpg)
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Topic objectives
• At the end of the course you will be able to– Understand about the small signal analysis of circuit
network using re model and hybrid equivalent model
– Understand the relationship between those two available model for small signal analysis
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INTRODUCTION:TRANSISTOR MODELING
• To begin analyze of small-signal AC response of BJT amplifier the knowledge of modeling the transistor is important.• The input signal will determine whether it’s a small
signal (AC) or large signal (DC) analysis.• The goal when modeling small-signal behavior is to make of a transistor that work for small-signal enough to “keep things linear” (i.e.: not distort too much) [3]• There are two models commonly used in the small signal analysis:
a) re modelb) hybrid equivalent model
![Page 4: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/4.jpg)
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How does the amplification be done?
• Conservation; output power of a system cannot be large than its input and the efficiency cannot be greater than 1
• The input dc plays the important role for the amplification to contribute its level to the ac domain where the conversion will become as η=Po(ac)/Pi(dc)
• Simply speaking…
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Disadvantages
• Re model– Fails to account the output impedance level of device
and feedback effect from output to input
• Hybrid equivalent model– Limited to specified operating condition in order to
obtain accurate result
![Page 6: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/6.jpg)
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VS
VCC
C1
C2
C3
+
-
Vo
RS
Vi
+
-RE
RCR1
R2
VS
+
-
Vo
RS
Vi
+
-
RCR1
R2
•I/p coupling capacitor s/c• Large values• Block DC and pass AC signal • Bypass
capacitor s/c•Large values
DC supply “0” potential
Voltage-divider configuration under AC analysis
Redraw the voltage-divider configuration after removing dc
supply and insert s/c for the capacitors
• O/p coupling capacitor s/c• Large values• Block DC and pass AC signal
![Page 7: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/7.jpg)
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VS
RSR2 R1
Rc
Transistor small-signal ac
equivalent cct
Vo
Zi
Ii
Zo
Io
Vi
+ +
- -
B
E
C
Redrawn for small-signal AC analysis
Modeling of BJT begin
HERE!
VS
+
-
Vo
RS
Vi
+
-
RCR1
R2
![Page 8: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/8.jpg)
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AC bias analysis :
1) Kill all DC sources
2) Coupling and Bypass capacitors are short cct. The effect of there capacitors is to set a lower cut-off frequency for the cct.
3) Inspect the cct (replace BJTs with its small signal model:re or hybrid).
4) Solve for voltage and current transfer function, i/o and o/p impedances.
![Page 9: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/9.jpg)
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IMPORTANT PARAMETERS
• Input impedance, Zi
• Output impedance, Zo
• Voltage gain, Av
• Current gain, Ai
Input Impedance, Zi(few ohms M)
The input impedance of an amplifier is the value as a load when connecting a single source to the I/p of terminal of the amplifier.
![Page 10: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/10.jpg)
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VS Two-portsystem
Vi
Rsense
IiZi
+
-
Determining Zi
+
-
sense
isi
R
VVI
i
ii
I
VZ
Two port system-determining input impedance Zi
• The input impedance of transistor can be approximately determined using dc biasing because it doesn’t simply change when the magnitude of applied ac signal is change.
![Page 11: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/11.jpg)
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Demonstrating the impact of Zi
VS=10mVTwo-portsystem
Vi
Rsource
Zi
+
-
+
-1.2 kΩ
600Ω
mV6.6600k2.1
)m10(k2.1
RZ
VZV
Ω600R impedance, sourceWith
system the toapplied 10mV Full
0ΩR source, Ideal
sourcei
sii
source
source
![Page 12: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/12.jpg)
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Example 6.1: For the system of Fig. Below, determine the level of input impedance
VS=2mV Two-portsystem
Vi=1.2mV
RsenseZi
+
-
+
-
1 k Ω
A8.0k1
m8.0
k1
m2.1m2
R
VVI
sense
isi
:Solution
k5.18.0
m2.1
I
VZ
i
ii
![Page 13: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/13.jpg)
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Output Impedance, Zo (few ohms 2M)
The output impedance of an amplifier is determined at the output terminals looking back into the system with the applied signal set to zero.
Two-portsystem
Rsource
Vs=0V
Rsense
V
+
-
+
-
Io
Zo
Vo
Determining Zo
sense
oo
R
VVI
o
oo
I
VZ
cctopen become ZRZ oLo RLZo=Ro
Iamplifier
IRo
IL
RoL
Lo
II
RRFor
![Page 14: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/14.jpg)
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Example 6.2: For the system of Fig. below, determine the level of output impedance
Two-portsystem
Vs=0V
Rsense
V=1 V
+
-
+
-
Zo
Vo=680mV
20 kΩ
A16k20
m320
k20
m6801
R
VVI
sense
oo
:Solution
k5.4216
m680
I
VZ
o
oo
![Page 15: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/15.jpg)
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Example 6.3: For the system of Fig. below, determine Zo if V=600mV, Rsense=10k and Io=10A
Two-portsystem
Rsource
Vs=0V
Rsense
V
+
-
+
-
Io
Zo
Vo
mV500
k1010m600
RIVVR
VVI
senseoo
sense
oo
:Solution
k5010
m500
I
VZ
o
oo
![Page 16: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/16.jpg)
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Example 6.4: Using the Zo obtained in example 6.3, determine IL for the configuration of Fig below if RL=2.2 k and Iamplifier=6 mA.
RLZo=Ro
Iamplifier
IRo
IL
mA747.5k2.2k50
)m6(k50RZ
)(IZI
:ruledivider Current
Lo
amplifieroL
:Solution
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Voltage Gain, AV
• DC biasing operate the transistor as an amplifier. Amplifier is a system that having the gain behavior. • The amplifier can amplify current, voltage and power.• It’s the ratio of circuit’s output to circuit’s input.• The small-signal AC voltage gain can be determined by:
i
ov
V
VA
![Page 18: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/18.jpg)
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VS AvNLVi
Rsource
Zi
+
-
+
-Vo
+
-
Determining the no load voltage gain
By referring the network below the analysis are:
cct)(open ΩRi
oLvNL
V
VA
load no
vNLARZ
Z
V
VA
:resistance sourcewith
si
i
s
ovs
![Page 19: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/19.jpg)
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Example 6.5: For the BJT amplifier of fig. below, determine: a)Vi b) Ii c) Zi d) Avs
VS=40mVBJT amplifier
AvNL=320Vi
Rs
Zi
+
-
+
-Vo=7.68V
+
-
1.2 kΩ
mV24320
7.68
A
VV
V
VA a)
vNL
oi
i
ovNL
:Solution
sources
s
isi
RR
A33.13k2.1
m24m40
R
V-VI b)
k8.133.13
m24
I
VZ c)
i
ii
192)320(k2.1k8.1
k8.1A
RZ
ZA d) vNL
si
ivs
![Page 20: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/20.jpg)
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Current Gain, Ai
• This characteristic can be determined by:
i
oi
I
IA
BJTamplifier
Vi
Zi
+
-
Vo
+
-
Ii
RL
Determining the loaded current gain
Io
L
ivi
R
ZAA
Li
io
ii
Lo
RV
ZV
Z/V
R/V
L
oo
RV
I
![Page 21: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/21.jpg)
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re TRANSISTOR MODEL
• employs a diode and controlled current source to duplicate the behavior of a transistor.• BJT amplifiers are referred to as current-controlled devices.
Common-Base Configuration
Common-base BJT transistorre modelre equivalent cct.
![Page 22: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/22.jpg)
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E
BB
C
Common-base BJT transistor - pnp
Ic Ie
e
b b
c
ec I αI
IcIe
re model for the pnp common-baseconfiguration
e
b b
c
ec I αI
IcIe
common-base re equivalent cct
re
current emitter
of level DC the isII
26mVr E
E(dc)
e
isolation part,Zi=re
e
b b
c
A0Ic
IcIe=0A
Determining Zo for common-base
reVs=0V
Zo
Therefore, the input impedance, Zi = re
that less than 50Ω.
For the output impedance, it will be as follows;
![Page 23: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/23.jpg)
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The common-base characteristics
![Page 24: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/24.jpg)
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e
b b
c ec I αI Ie
re
Defining Av=Vo/Vi for the common-base configuration
BJT common-basetransistor amplifier
Vi Vo
+
-
+
-
Zi
oZ RL
Io
LeLcLoo RIRIRIV
e
L
e
Lv
r
R
r
RA
gain, Voltage
eeiei rIZIV
ee
Lev
rI
RI
Vi
VoA
![Page 25: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/25.jpg)
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1A
gain,Current
i
e
e
e
c
i
oi
I
I
I
I
I
IA
e
b b
c ec I αI Ie
re
Defining Ai=Io/Ii for the common-base configuration
BJT common-basetransistor amplifier
Vi Vo
+
-
+
-
ZioZ RL
Io
![Page 26: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/26.jpg)
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Example 6.6: For a common-base configuration in figurebelow with IE=4mA, =0.98 and AC signal of 2mV isapplied between the base and emitter terminal:a) Determine the Zi b) Calculate Av if RL=0.56kc) Find Zo and Ai
e
b b
c
ec I αI
IcIe
common-base re equivalent cct
re
![Page 27: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/27.jpg)
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Solution:
5.6m4
m26
I
26mr Za)
Eei
43.845.6
)k56.0(98.0
r
RA b)
e
Lv
98.0I
IA
Ω Zc)
i
oi
o
![Page 28: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/28.jpg)
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e
b b
c
ec I αI
IcIe
common-base re equivalent cct
re
iI
![Page 29: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/29.jpg)
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Example 6.7: For a common-base configuration in previous example with Ie=0.5mA, =0.98 and AC signal of 10mV is applied, determine:a) Zi b) Vo if RL=1.2k c) Av d)Ai e) Ib
20m5.0
m10
I
V Za)
:Solution
e
ii
88mV5(1.2k)0.98(0.5m)
RIRIV b) LeLco
8.58m10
m588
V
VA c)
i
ov
98.0A d) i
A10
)98.01(m5.0
)1(m5.0
I-I
I-II e)
ee
ceb
![Page 30: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/30.jpg)
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Common-Emitter Configuration
Common-emitter BJT transistorre modelre equivalent cct.Still remain controlled-current source (conducted between collector and base terminal)Diode conducted between base and emitter terminal
Input Output
Base & Emitter terminal Collector & Emitter terminal
![Page 31: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/31.jpg)
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common-emitter BJT transistor
EE
B
C
Ib
Icbc I I
c
e e
b
Ic
Ib
re model npn common-emitter configuration
bc I I
c
e e
b
Ic
Ii=Ib
Determining Zi using re equivalent model
re
Ie+
-
Vbe
+
-
Vi
(1) Ii
ViZi
gives (1) into subtitute
and IbreIereVbeVi
b
eb
b
be
I
rI
I
VZi
erZi 7k~6 to hundred between ranges iZ
![Page 32: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/32.jpg)
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The output graph
![Page 33: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/33.jpg)
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bI
c
e
bIi=Ib
re model for the C-E transistor configuration
rero
e
0AbI
c
e
bIi=Ib
rero
e
Vs=0V
= 0A
oZ
impedance)high cct,(open ΩZ
the thusignored is r if
rZ
o
o
oo
Output impedance Zo
![Page 34: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/34.jpg)
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e
b b
cbco I II Ii=Ib
re
Determining voltage and current gain for the common-emitter amplifier
BJT common-emittertransistor amplifier
Vi Vo
+
-
+
-
oZ RL
Io
ei rZ
e
Lv
r
RA
Ib
Ib
Ib
Ic
Ii
IoA
gain,Current
i
LbLcLoo RIRIRIV
ebiii rIZIV
eb
Lb
i
ov
rI
RI
V
VA
gain, Voltage
iA
![Page 35: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/35.jpg)
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Example 6.8: Given =120 and IE(dc)=3.2mA for a common-emitter configuration with ro= , determine:
a) Zi b)Av if a load of 2 k is applied c) Ai with the 2 k load
975)125.8(120rZ
125.8m2.3
m26
I
26mr a)
ei
Ee
:Solution
15.246125.8
k2
r
Rb)A
e
Lv
120I
IA c)
i
oi
![Page 36: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/36.jpg)
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Example 6.9: Using the npn common-emitter configuration, determine the following if =80, IE(dc)=2 mA and ro=40 k
a) Zi b) Ai if RL =1.2k c) Av if RL=1.2k
k04.1)13(80rZ
13m2
m26
I
26mr a)
ei
Ee
:Solution
bI
cbIi=Ib
re model for the C-E transistor configuration
rero
e
RL
Io
![Page 37: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/37.jpg)
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67.77
)80(k2.1k40
k40
Rr
r
IRr
)I(r
A
Rr
)I(rI
I
I
I
IiAb)
(cont)Solution
Lo
o
b
Lo
bo
i
Lo
boL
b
L
i
o
6.8913
k40k2.1
r
rRvAc)
e
oL
![Page 38: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/38.jpg)
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Hybrid Equivalent Model
• re model is sensitive to the dc level of operation that result input resistance vary with the dc operating point
• Hybrid model parameter are defined at an operating point that may or may not reflect the actual operating point of the amplifier
![Page 39: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/39.jpg)
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Hybrid Equivalent Model
The hybrid parameters: hie, hre, hfe, hoe are developed and used to model the transistor. These parameters can be found in a specification sheet for a transistor.
![Page 40: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/40.jpg)
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Determination of parameter
0VVo
i12
0VVi
i11
o12i11i
o
o
VV
h
IV
h
VhIhV
0AIo
o22
0VVo
i21
o
o22i21O
o
o
VI
h
II
h
, 0VV Solving
VhIhI
H22 is a conductance!
![Page 41: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/41.jpg)
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General h-Parameters for any Transistor Configuration
hi = input resistancehr = reverse transfer voltage ratio (Vi/Vo)hf = forward transfer current ratio (Io/Ii)ho = output conductance
![Page 42: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/42.jpg)
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Common emitter hybrid equivalent circuit
![Page 43: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/43.jpg)
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Common base hybrid equivalent circuit
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Simplified General h-Parameter Model
The model can be simplified based on these approximations:
hr 0 therefore hrVo = 0 and ho (high resistance on the output)
Simplified
![Page 45: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/45.jpg)
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Common-Emitter re vs. h-Parameter Model
hie = rehfe = hoe = 1/ro
![Page 46: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/46.jpg)
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Common-Emitter h-Parameters
[Formula 7.28]
[Formula 7.29]
acfe
eie
h
rh
![Page 47: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/47.jpg)
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Common-Base re vs. h-Parameter Model
hib = rehfb = -
![Page 48: Chap3 Utem (BJT Transistor Modeling)](https://reader033.fdocuments.us/reader033/viewer/2022061516/554015a24a79593b1c8b4923/html5/thumbnails/48.jpg)
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Common-Base h-Parameters
[Formula 7.30]
[Formula 7.31]
1
fb
eib
h
rh