1. Chapter 7: BJT Transistor Modeling
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

2. Transistor Modeling Slide 1
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:
• re model
• hybrid equivalent model
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

3. Important Parameters Slide 2
Zi, Zo, Av, Ai are important parameters for the analysis of the Ac characteristics of a transistor circuit.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

4. Input Impedance, Zi Slide 3 [Formula 7.1]
To determine Ii: insert a “sensing resistor”
then calculate Ii: [Formula 7.2]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

5. Output Impedance, Zo Slide 4 [Formula 7.5]
To determine Io: insert a “sensing resistor”
then calculate Io: [Formula 7.4]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

6. Voltage Gain, Av Slide 5 [Formula 7.6] For an amplifier with no load:
Note: the no-load voltage gain (AVNL) is always greater
than the loaded voltage gain (AV).
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

7. Current Gain, Ai Slide 6 [Formula 7.9]
The current gain (Ai) also be calculated using the voltage gain (Av):
[Formula 7.10]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

8. Phase Relationship Slide 7
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
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

9. re Transistor Model Slide 8
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.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

10. Common – Base Configuration
Slide 9
Using a PNP transistor the Common-Base configuration and the re model:
The emitter is the input and the collector is the output.
This model indicates: Ic = Ie
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

11. re Slide 10 [Formula 7.11] where IE is the DC current.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

12. Common-Base re Model Slide 11
The diode in the previously shown re model can be replaced by the resistor re.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

13. Impedance in Common-Base Configuration
Slide 12
The re model indicates:
The input impedance (Zi) is quite small:
[Formula 7.12]
The output impedance (Zo) is quite large:
[Formula 7.13]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

14. Gain calculations for the Common-Base
using the re model
Slide 13
Voltage Gain:
[Formula 7.14]
Current Gain:
[Formula 7.15]
The phase relationship between input and output is 0 degrees.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

15. NPN Common-Base Configuration
Slide 14
The npn transistor will use the same calculation. The only difference is that the voltage polarities and current directions will be the opposite.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

16. Common-Emitter Configuration
Slide 15
The base current is the input and the collector is the output.
This model indicates:
[Formula 7.16]
[Formula 7.17]
[Formula 7.18]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

17. Impedance in Common-Emitter Configuration
Slide 16
The input impedance (Zi):
[Formula 7.19]
The output impedance (Zo):
[Formula 7.20]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

18. Gain calculations for the Common-Emitter
using the re model
Slide 17
Voltage Gain (Av): [Formula 7.21]
Current Gain (Ai): [Formula 7.22]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

19. Common-Collector Configuration
Slide 18
The Common-Emitter Model is used for Common-Collector.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

20. Hybrid Equivalent Model
Slide 19
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.
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

21. General h-Parameters for any Transistor Configuration
Slide 20
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)
hf = forward transfer current ratio (Io/Ii)
ho = output conductance
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

22. Simplified General h-Parameter Model
Slide 21
The above model can be simplified based on these approximations:
hr  0 therefore hrVo = 0 and ho  
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

23. Common-Emitter re vs. h-Parameter Model
Slide 22
hie = re
hfe = 
hoe = 1/ro
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

24. Common-Emitter h-Parameters
Slide 23
[Formula 7.28]
[Formula 7.29]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

25. Common-Base re vs. h-Parameter Model
Slide 24
hib = re
hfb = -
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

26. Common-Base h-Parameters
Slide 25
[Formula 7.30]
[Formula 7.31]
Robert Boylestad Digital Electronics
Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.