Electronics 1 : Chapter # 07 : AC Analysis BJT

BJT Transistor Modeling
• A model is an equivalent circuit that represents the AC
characteristics of the transistor.
• A model uses circuit elements that approximate the
behavior of the transistor.
• There are two models commonly used in small signal AC
analysis of a transistor:
– re model
– Hybrid equivalent model

BJT Transistor Modeling
Remove capacitors and replace it
with short circuit equivalent

Small signal Analysis- AC equivalent model
• Output impedance Z0= Vo/ I0
•Input impedance Zi= Vi/ Ii
•Current gain Ai= Io/ Ii
•Voltage gain Ao= Vo/ Vi

The re Transistor Model
• BJTs are basically current-controlled devices; therefore the re model
uses a diode and a current source to duplicate the behavior of the
transistor.
• One disadvantage to this model is its sensitivity to the DC level. This
model is designed for specific circuit conditions.

Common-Base Configuration
Input impedance:
Output impedance:
Voltage gain:
Current gain:
ec II 
e
e
I
mV26
r 
ei rZ 
oZ
e
L
e
L
V
r
R
r
R
A 


1Ai 

Common-Emitter Configuration
  bbe III   1
The diode re model can be
replaced by the resistor re.
more…
e
e
I
mV26
r 
for Ac is generally greater
than 1.


Common-Emitter Configuration
Input impedance:
Output impedance:
Voltage gain:
Current gain:
ei rZ 
 oo rZ
e
L
V
r
R
A 
 oriA

Common-emitter characteristics

Example
• 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
125.8
m2.3
m26
I
26m
ra)
ei
E
e
:Solution
15.246
125.8
k2
r
R
b)A
e
L
v 
120
I
I
Ac)
i
o
i 

Common-Collector Configuration
Input impedance:
Output impedance:
Voltage gain:
Current gain:
ei rZ )1(  
Eeo RrZ ||
eE
E
V
rR
R
A


1 iA

Simplified General h-Parameter Model
• hi = input resistance
• hf = forward transfer current ratio (Io/Ii)

re vs. h-Parameter Model
acfe
eie
h
rh


Common-Emitter
Common-Base
1h
rh
fb
eib



The Hybrid p Model
The hybrid p model is most useful for analysis of high-
frequency transistor applications.
At lower frequencies the hybrid p model closely
approximate the re parameters, and can be replaced by
them.

16
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

17
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

18
Common-Emitter re vs. h-Parameter Model
acfe
eie
h
rh



19
Common-Base re vs. h-Parameter Model
1

fb
eib
h
rh

Electronics 1 : Chapter # 07 : AC Analysis BJT

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Electronics 1 : Chapter # 07 : AC Analysis BJT