1. LECTURE 1: BASIC BJT AMPLIFIER -AC ANALYSIS-

2. Lecture’s Content
BJT LINEAR AMPLIFIER - BJT small signal operation - BJT AC equivalent circuits

3. Objectives
Understand the concept of an analog signal and the principle of linear amplifier.
Investigate the process a single-transistor circuit can amplify a small, time-varying input signal.

4. Introduction Signals contain some type of information.
The electrical signals in form of time-varying current and voltage are analog signal.
Electronic circuit that process analog signal – analog circuit, example linear amplifier.
Linear amplifier – magnify an input signal and produce an output signal whose magnitude is larger and directly proportional to input signal.

5. Example of linear amplifier
Block diagram of a compact disc player system.

6. Cont.. From figure, a dc voltage source connected to amplifier.
The amplifier contain transistors that must be forward biased so that they can act as amplifying devices.
We want the o/p signal to be linearly proportional to input signal o/p of speaker is an exact reproduction of signal from compact disc.
So, we need a linear amplifier.

7. Cont.. 2 type of amplifier analysis:
dc analysis due to applied dc voltage source.
ac analysis due to time-varying signal source.
dc analysis is performed by ac source set to zero ~ large signal analysis.
ac analysis is performed by dc source set to zero ~ small signal analysis.

8. Bipolar linear amplifier
Transistor -- heart of an amplifier.
Bipolar transistors is used in linear amplifier cct because of their high gain.
Figure (a) – cct where input signal vI contain dc and ac signal. Figure (b) – VBB is dc voltage to bias transistor at Q-point and vs is ac signal that is to be amplified. Figure (c) – voltage transfer characteristic graph.
To become amplifier, transistor need to be biased with dc Q-point  transistor biased in forward-active region.
A time-varying (sinusoidal) signal is superimposed on dc input voltage, VBB, o/p voltage change along the curve producing a time-varying o/p voltage.

9. Figure c
Figure a
Figure b

10. Cont bipolar linear amplifier
If o/p voltage directly proportional to and larger than i/p voltage  linear amplifier cct.
If transistor is not biased (in cutoff or saturation), o/p voltage doesn’t change with a change in i/p  cct is not an amplifier.
Summary of notation
Variable
Meaning
iB, vBE
Total instantaneous values
IB, VBE
DC values
ib, vbe
Instantaneous ac values
Ib, Vbe
Phasor values

11. Graphical analysis & ac equivalent circuit
Fig d) Common-emitter cct
with a time-varying signal
source in series with
dc source.
Fig e) Common-emitter transistor
characteristic, dc load line and sinusoidal
variation in base current, collector current
and collector-emitter voltage.

12. Graphical analysis cont..
The graph shows collector current, iC vs c-e voltage, vCE for different values of iB.
Q-point is chosen where distance between iB curves are even to get linear amplification.
Line between VCC / RC and VCC –- dc load line.
Signal source, vs produce ac base current superimposed on quiescent base current.
ac collector current produce a time-varying voltage across RC, that induces an ac c-e voltage, vCE.
vCE or vO will be larger than i/p to produce signal amplification.

13. Graphical Analysis & AC Equivalent Circuit
Based on Fig. d & e
(time-varying signals linearly related & superimposed on dc values)
If signal source, vs = 0:

14. Graphical Analysis & AC Equivalent Circuit
For B-E loop, considering time varying signals:
Rearrange:
Base on (5), left side of (7) is 0. So:
For C-E loop, considering time varying signals:
Base on (6), left side of (11) is 0. So:

15. Graphical analysis cont..
Signal source, vs in base cct generate time-varying component in base cct –- iB and vBE.
Figure f) shows the exponential relationship between iB and vBE.
If magnitude of time-varying signal superimposed on dc quiescent pt is small => develop a linear r/ship between ac vBE and ac iB.
This r/ship corresponds to the slope of curve at Q-point.
Slope at Q-point is inversely proportional to a small-signal parameter, rΠ.

16. Cont.. From figure above, relation between vBE and iB is:
If vBE is composed of dc term with sinusoidal component superimposed, vBE=VBEQ + vbe, then
The term [IS/β].exp (VBEQ / VT) is quiescent base current, we can write

17. Cont..
The base current eq. is not linear and can’t be written as ac current superimposed on dc quiescent value.
If vbe << VT, we can expand the exponential term in a Taylor series, keeping only linear term which lead to small signal approximation.
Where ib is the time-varying base current

18. AC equivalent circuit of C-E with npn transistorRB vs vO
vce
vbe ic ib + -
AC equivalent circuit of C-E with npn transistor

19. Equations Input loop: Output loop: 0.026 V
Set all dc current and voltage
to zero – voltage become
short cct & current become
open cct.

20. Rules for ac analysis Replacing all capacitors by short circuits
Replacing all inductors by open circuits
Replacing dc voltage sources by ground connections
Replacing dc current sources by open circuits

21. SMALL-SIGNAL HYBRID-Π EQUIVALENT CIRCUIT OF BIPOLAR TRANSISTOR (BJT)
Definition of small signal
Small signal : ac input signal voltages and currents are in the order of ±10 percent of Q-point voltages and currents.
e.g. If dc current is 10 mA, the ac current (peak-to- peak) < 0.1 mA.

22. Small signal hybrid-π equivalent circuit of bipolar transistor cont..
Figure shows iB vs. vBE with small-time varying signal superimposed at Q-pt.
Since sinusoidal signals are small, the slope at Q-pt treated as a constant, has units of conductance.
The inverse of this conductance is small- signal resistance, rπ

23. Small signal hybrid-π equivalent circuit of bipolar transistor cont..
We can relate small-signal input base current to small- signal input voltage by:
Finding rπ from Q-point slope lead to:
rπ also known as diffusion resistance and is a function of Q-point parameters. VT is known as thermal voltage.

24. Small signal hybrid-π equivalent circuit of bipolar transistor cont..
Now, we consider the output terminal characteristic of BJT.
Assume o/p collector current is independent of collector- emitter voltage collector-current is a function of base- emitter voltage, so the equation:
From eq 5.2 in Chapter 5 Neaman,

25. Small signal hybrid-π equivalent circuit of bipolar transistor cont..
After substitution and rearrange the above, we obtain:
The term ICQ / VT is a conductance. Since this term relates current in collector to a voltage in B-E circuit, it is called transconductance and is written:
Transconductance also a function of Q-pt parameters and directly proportional to dc bias current.

26. Small signal hybrid-π equivalent circuit of bipolar transistor cont..
Using these new parameters  develop a simplified small-signal hybrid-π equivalent cct for npn BJT.
Phasor components given in parentheses.
This circuit can be inserted into ac equivalent circuit shown previously.

27. Small-signal hybrid- equivalent circuit using transconductance
gm=ICQ/VT
r=VT/ICQ
Transconductance parameter

28. Small-signal hybrid- equivalent circuit using transconductance cont..
We can relate small-signal collector current to small- signal base current for o/p of equivalent cct.
Where
β is called ac common-emitter current gain.
Thus:

29. Current gain parameter
Small-signal hybrid- equivalent circuit using common-emitter current gain
Current gain parameter

30. Small-signal voltage gain cont..
Combine BJT equivalent cct to ac equivalent cct.
Small-signal hybrid-π model

31. Small-signal voltage gain cont..
Voltage gain, Av = ratio of o/p voltage to i/p voltage.
Small-signal B-E voltage is called the control voltage, Vbe or V.
The dependent current source is gmV flows through RC produce –ve C-E voltage at the output.

32. Small-signal voltage gain cont..
From the input portion of the circuit, using voltage divider:
The small-signal voltage gain is:

33. Example 1 Given :  = 100, VCC = 12V
VBE = 0.7V, RC = 6k, VT=0.026V, RB = 50k and
VBB = 1.2V
Calculate the small-signal
voltage gain.

34. Solutions 1. 2. 3. 4. 5. 6.

35. Example 2
Given VCC=5V, VBB=2V, RB=650kΩ, RC=15kΩ, β=100 and VBE(on)=0.7V.
Determine:
a) Q-points,
b) gm and r
c) voltage gain.

36. Hybrid-π equivalent circuit including Early effect
Early Voltage
(VA)

37. Hybrid-π equivalent circuit including Early effect **Early voltage**
Figure above show current-voltage characteristic for constant values of B-E voltage.
The curves are linear with respect to C-E voltage in forward-active mode.
The slope is due to base-width modulation effect  Early Effect.
When the curves extrapolated at zero current, they meet a point on –ve voltage axis, vce = -VA. VA --- Early voltage with typical value in range of 50 < VA < 300V.

38. Hybrid-π equivalent circuit including Early Effect
Early Effect => collector current, iC is dependent to collector-emitter voltage, vCE (refer Chapter 5- Neaman):
The output resistance, rO:
Substitute and rearrange both equation,

39. Hybrid-π equivalent circuit including Early effect cont..
Hence, small-signal transistor output resistance, rO become:
rO is equivalent to Norton resistance  rO is parallel with dependent current sources.

40. Modified bipolar equivalent circuits including rO due to Early Effect.
Transconductance
parameter
ro=VA/ICQ
Current gain
parameter

41. Self study for pnp transistor
From Neaman textbook,
Ac equivalent circuit – pg 386
Transconductance and current gain – pg 386 & 387
Small-signal hybrid-π equivalent circuit – pg 387
Do example 6.3

42. Expanded hybrid-π equivalent circuit
Include 2 additional resistance, rb and rμ.
rb  series resistance of semiconductor material.
Since rb << rμ., rb is neglected (short cct) at low freq.
rμ  reverse-biased diffusion resistance of B-C junction. Typically in megaohms and neglected (open cct).
Normally, in hybrid-π model, we neglect both rb and rμ.