lecture Electronic BJT SMALL SIGNAL ANALYSIS

BJT SMALL SIGNAL ANALYSIS

1. Lecture 4-5:
BJT Small-Signal Analysis

2. Slide 1 BJT Small Signal Analysis
The re and hybrid models will be used to analyze AC small-signal transistor circuits.
The most fundamental of unbypassed
configurations appears in Fig. 29. The re equivalent
model is substituted in Fig. 1, but note the absence
of the resistance ro. The effect of ro is to make the
analysis a great deal more complicated, and
considering the fact that in

Fig. 1

5. Slide 2 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.

6. Slide 3 Removing DC effects of VCC and Capacitors

7. Slide 4 re Model
Determine , re, and ro:
 and ro: look in the specification sheet for the transistor or test the transistor using
a curve tracer.
re: calculate re using dc analysis:
E
e
I
25mV
r

8. Slide 5 Impedance Calculations
Input Impedance:
[Formula
8.1]
[Formula
8.2]
Output Impedance:
[Formula
8.3]
[Formula 8.4]
eBr||RZi 
eE
e
r10R
rZi


O
r||RZo
C

c

10ro
Zo
R
R
c



9. Slide 6 Gain Calculations
Voltage Gain (Av):
[Formula
8.5]
[Formula
8.6]
Current Gain (Ai):
[Formula
8.7]
[Formula
8.8]
Current Gain from Voltage Gain:
[Formula 8.9]
e
oC
r
)r||(R
Vi
Vo
Av 
C
e
C
10Rro
r
R
Av


)r)(RR(r
rR
Ii
Io
Ai
eBCo
oB



re10R ,10Rro
Ai
BC 

CR
Zi
AvAi

10. Slide 7 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. Slide 8 CE – Voltage-Divider Bias Configuration

12. Slide 9 re Model
You still need to determine , re, and ro.

13. Slide 10 Impedance Calculations
Input Impedance:
[Formula
8.10]
[Formula
8.11]
Output Impedance:
[Formula
8.12]
[Formula 8.13]
21
21
21
RR
RR
R||RR


er||RZi 
oCr||RZo
C
C
10Rro
RZo



14. Slide 11 Gain Calculations
Voltage Gain (Av):
[Formula
8.14]
[Formula
8.15]
Current Gain (Ai):
[Formula
8.16]
[Formula
8.17]
[Formula
8.18]
Current Gain from Voltage Gain:
[Formula 8.19]
e
oC
r
r||R
Vi
Vo
Av


C
e
C
10Rro
r
R
Vi
Vo
Av


)rR)(R(r
rR
Ii
Io
Ai
eCo
o



C
e
10Rro
rR
R
Ii
Io
Ai




re10R 10RC,ro
Ii
Io
Ai


CR
Zi
AvAi

15. Slide 12 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.

16. Slide 13 CE Emitter-Bias Configuration
Unbypassed RE

17. Slide 14 re Model
Again you need to determine , re.

18. Slide 15 Impedance Calculations
Input Impedance:
[Formula
8.20]
[Formula
8.21]
[Formula
8.22]
[Formula
8.23]
Output Impedance:
[Formula
8.33]
Ee 1)R(rZb 
)R(rZb Ee
eE
E
rR
RZb


Zb||RZi B
CRZo

19. Voltage Gain (Av):
[Formula
8.25]
[Formula
8.26]
or [Formula
8.27]
Current Gain (Ai):
[Formula
8.28]
Current Gain from Voltage Gain:
[Formula 8.29]
Slide 16 Gain Calculations
Zb
R
Vi
Vo
Av
C

)R(rZb
Rr
R
Vi
Vo
Av
Ee
Ee
C



E
E
C
RZb
R
R
Vi
Vo
Av


ZbR
R
Ii
Io
Ai
B
B



CR
Zi
AvAi

20. Slide 17 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.

21. Bypassed RE
This is the same circuit as the CE fixed-bias configuration and therefore can be solved
using the same re model.
Slide 18 CE Emitter-Bias Configuration

22. Slide 19 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.

23. Slide 20 re Model
You still need to determine , re, and ro.

24. Slide 21 Impedance Calculations
Input Impedance:
[Formula
8.37]
[Formula
8.38]
[Formula
8.39]
[Formula 8.40]
Zb||RZi B
Ee 1)R(rZb 
)R(rZb Ee
ERZb

25. Slide 22 Impedance Calculations (cont’d)
Output Impedance:
[Formula
8.42]
[Formula 8.43]
eEr||RZo
eE
e
rR
rZo



26. Slide 23 Gain Calculations
Voltage Gain (Av):
[Formula
8.44]
[Formula
8.45]
Current Gain (Ai):
[Formula
8.46]
Current Gain from Voltage Gain:
[Formula 8.47]
eE
E
rR
R
Vi
Vo
Av


EeEeE RrR ,rR
1
Vi
Vo
Av


ZbR
R
Ai
B
B



ER
Zi
AvAi

27. Slide 24 Phase Relationship
A CC amplifier or Emitter Follower configuration has no phase shift between input and
output.

28. Slide 25 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.

29. Slide 26 re Model
You will need to determine  and re.

30. Slide 27 Impedance Calculations
Input Impedance:
[Formula
8.54]
Output Impedance:
[Formula 8.55]
eEr||RZi
CRZo