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BJT Transistor Modeling
Transistor Modeling
A model is an equivalent circuit that represents the AC characteristics of the transistor.It uses circuit elements that approximate the behavior of the transistor.
There are 2 models commonly used in small signal AC analysis of a transistor:
• hybrid equivalent model
2
Important Parameters
Zi, Zo, Av, Ai are important parameters for the analysis of the AC characteristics of a transistor circuit.
Input Impedance, Zi
To determine Ii: insert a “sensing resistor”
then calculate Ii:
i
ii I
VZ =
sense
isi R
VVI −=
3
Output Impedance, Zo
To determine Io: insert a “sensing resistor”
then calculate Io:
o
oo I
VZ =
sense
oo R
VVI −=
Voltage Gain, Av
For an amplifier with no load:
Note: the no-load voltage gain (AVNL) is always greaterthan the loaded voltage gain (AV).
i
ov V
VA =
it)(opencircu Ri
oVNL
LVVA
Ω∞=
=
4
Current Gain, Ai
The current gain (Ai) also be calculated using the voltage gain (Av):
i
oi I
IA =
L
ivi R
ZAA −=
Phase Relationship
The phase relationship between input and output depends on the amplifier configuration circuit.
Common – Emitter : 180 degrees
Common - Base : 0 degrees
Common – Collector: 0 degrees
5
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.
• hi = input resistance
• hr = reverse transfer voltage ratio (Vi/Vo)
• hf = forward transfer current ratio (Io/Ii)
• ho = output conductance
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
6
Simplified General h-Parameter Model
The above model can be simplified based on these approximations:
hr ≅ 0 therefore hrVo = 0 and ho ≅ ∞
Common-Emitter h-Parameters
acfe
EQ
fe
BQie
βhI
mV25hImV25h
=
≅=
7
Common-Base h-Parameters
1hImV25h
acfb
EQib
−≅−=
=
α
BJT Small-Signal Analysis
8
Common-Emitter (CE) Fixed-Bias Configuration
The input (Vi) is applied to the base and the output (Vo) is from the collector.
The Common-Emitter is characterized as having high input impedance and low output impedance with a high voltage and current gain.
Removing DC effects of VCC and Capacitors
Hybrid Equivalent Circuit
⇒
9
Hybrid Equivalent Circuit
Determine hfe, hie, and hoe:
hfe and hoe: look in the specification sheet for the transistor or test the transistor using a curve tracer.
hie: calculate hie using DC analysis: EQ
feBQ
ie I25mVh
I25mVh ≅=
Impedance Calculations
Input Impedance:
Output Impedance:
ieBi h||RZ =
ie10hR iei B
hZ ≥≅
oeCo h
1||RZ =
R101/h Co CoeRZ ≥≅
10
Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
ie
oeCfe
i
ov h
)1/h||(RhvvA −==
Coe 10R 1/hie
Cfev
hRhA
≥
−=
)h)(RR(1/h)(1/hRh
iiA
ieBCoe
oeBfe
i
oi ++
==
ieh10 R ,10R 1/hfeiBCoe
hA≥≥
≅
C
ivi R
ZAA −=
Phase Relationship
The phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion.
11
CE – Voltage-Divider Bias Configuration
⇓
You still need to determine hfe, hie, and hoe.
Impedance Calculations
Input Impedance:
Output Impedance:
21
2121 RR
RRR||RR+
==′iei h||RZ ′=
oeCo h
1||RZ =
Coe 10R 1/h Co RZ ≥≅
12
Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
ie
oeCfe
i
ov h
1/h||RhvvA −==
Coe 10R 1/hie
Cfev
hRhA
≥
−≅
( ))hR)(R(1/h
1/h RhiiA
ieCoe
oefe
i
oi +′+
′==
Coe 10R 1/hie
fei
hRRhA
≥+′
′≅
ie10h R ,10R 1/hfeiCoe
hA≥′≥
≅
C
ivi R
ZAA −=
Phase Relationship
A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.
13
CE Emitter-Bias Configuration
Unbypassed RE
Again you need to determine hfe, hie.
Impedance Calculations
Input Impedance:
Output Impedance:
Efeieb 1)Rh(hZ ++=
1 h ,h 1)R(hEfeb
feieEfeRhZ
>>>>+≅
bBi Z||RZ =
Co RZ =
14
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
Gain Calculations
b
Cfe
i
ov Z
RhvvA −==
Efeb Rh ZE
Cv
RRA
≅
−≅
bB
Bfe
i
oi ZR
RhiiA
+==
C
ivi R
ZAA −=
Phase Relationship
A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias.
15
Emitter-Follower Configuration
You may recognize this as the Common-Collector configuration. Indeed they are the same circuit.
Note the input is on the base and the output is from the emitter.
Hybrid Equivalent Model
You still need to determine hfe and hie.
16
Impedance Calculations
Input Impedance: bBi Z||RZ = Efeieb 1)Rh(hZ ++=
1 h ,h 1)R(hEfeb
feieEfeRhZ
>>>>+≅
Impedance Calculations (cont’d)
Output Impedance:1h
h||RZfe
ieEo +
=
1 h , h 1)R(hfe
ieo
feieEfe
hhZ
>>>>+
≅
17
Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
Current Gain from Voltage Gain:
)1h/(hRR
vvA
feieE
E
i
ov ++
== 1AieEfe h 1)R(hv >>+
≅
bB
Bfe
i
oi ZR
RhiiA
+−≅
E
ivi R
ZAA −=
Phase Relationship
A CC amplifier or Emitter Follower configuration has no phase shift between input and output.
18
Common-Base (CB) Configuration
The input (Vi) is applied to the emitter and the output (Vo) is from the collector.
The Common-Base is characterized as having low input impedance and high output impedance with a current gain less than 1 and a very high voltage gain.
Hybrid Equivalent Model
You will need to determine hfb and hib.
EQfe
ieib I
mV251h
hh =+
= 1αh acfb −≅−=
19
Impedance Calculations
Input Impedance:
Output Impedance:
ibEi h||RZ =
Co RZ =
Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
ib
C
ib
Cfb
i
ov h
RhRh
vvA ≅==
1hiiA fb
i
oi −≅==
20
Phase Relationship
A CB amplifier configuration has no phase shift between input and output.
CE Collector Feedback Configuration
This is a variation of the CE Fixed-Bias configuration.
21
Hybrid Equivalent Model
You will need to determine hfe and hie.
Impedance Calculations
Input Impedance:
Output Impedance:
F
Cfe
iei
RRh1
hZ+
=
FCo R||RZ ≅
22
Gain Calculations
Voltage Gain (Av):
Current Gain (Ai):
ie
Cfe
i
ov h
RhVVA −==
CfeF
Ffe
i
oi RhR
RhIIA
+==
C
F
i
oi R
RIIA ≅=
Example
According to the figure above– Perform DC analysis and find the Q-point.– Evaluate the voltage gain Avs and the current gain Ai.– Sketch vo on the AC+DC load line graph when
• vs = 100 sin(wt) mV.• vs = 900 sin(wt) mV.
hfe = hFE = 200ICO = 0 AVBE = 0.7 VVCEsat = 0 V
⇒
ICQ = 0.39 mA
VCBQ = 6.8 V