1. BJT Transistor Modeling1

2. 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 2

3. 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 model
b) hybrid equivalent model 3

4. 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… 4

5. Disadvantages Re model Hybrid equivalent 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 5

6. DC supply  “0” potential O/p coupling capacitor  s/c Large values
Block DC and pass AC signal
I/p coupling capacitor  s/c
Large values
Block DC and pass AC signal
Bypass
capacitor  s/c
Large values
Voltage-divider configuration
under AC analysis
Redraw the voltage-divider
configuration after removing dc supply and insert s/c for the capacitors 6

7. Modeling of BJT begin HERE!7

8. 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. 8

9. Input Impedance, Zi(few ohms  M)
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. 9

10. 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. 10

11. Demonstrating the impact of Zi11

12. Example 6. 1: For the system of Fig
Example 6.1: For the system of Fig. Below, determine the level of input impedance 12

13. 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. 13

14. Example 6. 2: For the system of Fig
Example 6.2: For the system of Fig. below, determine the level of output impedance 14

15. Example 6. 3: For the system of Fig
Example 6.3: For the system of Fig. below, determine Zo if V=600mV, Rsense=10k and Io=10A 15

16. RL=2.2 k and Iamplifier=6 mA.
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. 16

17. The amplifier can amplify current, voltage and power.
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: 17

18. By referring the network below the analysis are:18

19. Example 6. 5: For the BJT amplifier of fig. below, determine:. a)Vi
Example 6.5: For the BJT amplifier of fig. below, determine: a)Vi b) Ii c) Zi d) Avs 19

20. This characteristic can be determined by:
Current Gain, Ai
This characteristic can be determined by: 20

21. Common-Base Configuration
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 transistor
re model
re equivalent cct. 21

22. Zo   isolation part, Zi=re Therefore, the input impedance, Zi = re
that less than 50Ω.
For the output impedance, it will be as follows;
isolation part,
Zi=re
Zo   22

23. The common-base characteristics23

24. 24

25. 25

26. Example 6.6: For a common-base configuration in figure
below with IE=4mA, =0.98 and AC signal of 2mV is
applied between the base and emitter terminal:
Determine the Zi b) Calculate Av if RL=0.56k
c) Find Zo and Ai 26

27. Solution: 27

28. 28

29. 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:
Zi b) Vo if RL=1.2k c) Av d)Ai e) Ib 29

30. Common-Emitter Configuration
Common-emitter BJT transistor
re model
re 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 30

31. 31

32. The output graph 32

33. Output impedance Zo 33

34. 34

35. Example 6.8: Given =120 and IE(dc)=3.2mA for a common-
emitter configuration with ro=  , determine:
Zi b)Av if a load of 2 k is applied c) Ai with the 2 k load 35

36. Example 6.9: Using the npn common-emitter configuration,
determine the following if =80, IE(dc)=2 mA and ro=40 k
Zi b) Ai if RL =1.2k  c) Av if RL=1.2k  36

37. 37

38. 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 38

39. 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. 39

40. Determination of parameter
H22 is a conductance! 40

41. General h-Parameters for any Transistor Configuration
hi = input resistance
hr = reverse transfer voltage ratio (Vi/Vo)
hf = forward transfer current ratio (Io/Ii)
ho = output conductance 41

42. Common emitter hybrid equivalent circuit42

43. Common base hybrid equivalent circuit43

44. 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 44

45. Common-Emitter re vs. h-Parameter Model
hie = re
hfe = 
hoe = 1/ro 45

46. Common-Emitter h-Parameters
[Formula 7.28]
[Formula 7.29] 46

47. Common-Base re vs. h-Parameter Model
hib = re
hfb = - 47

48. Common-Base h-Parameters
[Formula 7.30]
[Formula 7.31] 48