1. SMALL SIGNAL BJT AMPLIFIER
SMALL SIGNAL OPERATION

2. INTRODUCTION
One of the primary uses of a transistor is to amplify ac signals.
This could be an audio signal or perhaps some high frequency radio signal.
It has to be able to do this without distorting the original input.
Most transistors amplifiers are designed to operate in the linear region
The common-emitter amplifier has high voltage and current gain

3. Definition of Small Signal
ac input signal voltages and currents are in the order ±10% of Q-point voltages and currents. eg
If dc current is 10mA, the ac current (peak to peak) is less than 0.1 mA.

4. HOW BJT AMPLIFIES?
When a weak ac signal is given to the base, a small ac base current start flowing.
Due to BJT, a much larger ac current flow through RC
Therefore a large voltage appear across the collector circuit.

5. R1, R2, RE – form the biasing circuit & stabilization.
C1(Coupling capacitor) – couple the signal to the base.
C2(Bypass capacitor) - use in parallel with RE to provide low reactance path to amplified ac signal
C3(Coupling capacitor)- couple the signal to the next stage

6. Circuit Diagram IC VCE IB VCC Common-Emitter Biasing(CE)
input = VBE & IB
output = VCE & IC + _ IC
VCE IB
VCC
= Common-emitter current gain =
= Common-base current gain =
The relationships between the two parameters are:

7. Example
Given the common-emitter circuit below with IB = 25A, VCC = 15V and  = 100. Find the ideal collector current.
 = 100 = IC/IB
IC = 100 * IB = 100 * (25x10-6A) = 2.5 mA

8. Collector-Current Curves
Common-Emitter
Collector-Current Curves IC
Active Region IB
Saturation Region
Cutoff Region
IB = 0
Region
of Operation
Description
Active
Small base current controls a large collector current
Saturation
VCE(sat) ~ 0.2V, VCE increases with IC
Cutoff
Achieved by reducing IB to 0, Ideally, IC will also equal 0.
VCE

9. DC Analysis of Transistor Circuits Common-Emitter Circuit
Common-emitter circuit with an npn transistor
Assume B-E junction: forward biased  V drop is the cut-in / turn-on V [VBE (on)]
IC represented as a dependent I source (function of IB)
Neglect reverse-biased junction leakage current & Early effect

10. dc equivalent circuit, with piecewise linear parameters

11. Base-emitter Junction Characteristics And The Input Load Line

12. Common- Emitter Transistor Characteristics And The Collector-emitter Load Line

13. Common-emitter circuit Load Line

14. Kirchoff’s voltage law equation (around B-E loop):
Both load line & quiescent IB change as either or both VBB & RB change
Kirchoff’s voltage law equation (around C-E loop):
IC & VCE relationship represents DC load line

15. Amplifier Operation
The boundary between cutoff and saturation is called the linear region.
A transistor which operates in the linear region is called a linear amplifier.
Only the ac component reaches the load because of the capacitive coupling and that the output is 180º out of input phase.
Fig 6-2 amplifier circuit

16. Example
Assume Q-point value of iB=10A, ac signal peak value is 5A and β=100.
So at any instant, iC =100iB iB
iC=100iB
VCE=VCC-iCRC
Output voltage
15A
1.5mA
4 V
Positive peak value
10A
1.0mA
6 V
Signal current zero
5A
0.5mA
8 V
Negative peak value

17. dc equivalent circuit of transistor amplifier
Only dc condition are to be considered
No signal is applied (All ac source reduce to zero)
dc cannot flow through a capacitor (open circuit)
To calculate the dc currents & voltages

18. DC Equivalent for the BJT Amplifier
DC Equivalent Circuit
All capacitors in the original amplifier circuit are replaced by open circuits, disconnecting vI, RI, and R3 from the circuit and leaving RE intact. The the transistor Q will be replaced by its DC model.

19. ac equivalent circuit of transistor amplifier
Only ac condition are to be considered
dc voltage not important, considered zero or ground. (VCC=0)
the capacitors used to couple or bypass the ac signal. (short circuit)

20. AC Equivalent for the BJT Amplifier
The coupling and bypass capacitors are replaced by short circuits.
The DC voltage supplies are replaced with short circuits, which in this case connect to ground.

21. (continued)
By combining parallel resistors into equivalent RB and R, the equivalent AC
circuit above is constructed. Here, the transistor will be replaced by its
equivalent small-signal AC model (to be developed).

22. Graphical Analysis & AC Equivalent Circuit
Equations
Input loop
Output loop RC RB vs vO
vce
vbe ic ib + -
0.026 V
AC equivalent circuit of C-E with npn transistor

23. Small-signal hybrid- equivalent circuit
vbe = ibrπ rπ
= diffusion resistance /
base-emitter input resistance
1/rπ
= slope of iB – VBE curve
gm=ICQ/VT
r=VT/ICQ
Using transconductance (gm) parameter

24. Small-signal hybrid- equivalent circuit
Using common-emitter current gain (β) parameter

25. Small-signal equivalent circuit
Small-signal hybrid- equivalent circuit
Small-signal equivalent circuit r Vs RB RC Vo Ic Ib
gmVbe
Vbe
Vce + -
Output signal voltage
Input signal voltage

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

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

28. Hybrid- Model and Early Effect
transconductance
parameter
ro=VA/ICQ
current gain
parameter
ro = small-signal transistor output resistance
VA = early voltage

29. Hybrid- Model and Early Effect
Early Voltage (pg 109)
Early Voltage
(VA)

30. Example vs Given :  = 100, VCC = 12V VBE(on) = 0.7V, RS = 0.5k,
RC = 6k, R1 = 93.7k, R2 = 6.3k
and VA = 100V.
Calculate the small-signal voltage gain. vs RS R1 R2 RC CC vO
VCC

31. Solution
R1 \\ R2 Vs RS RC rO r
gmV Vo Ri Ro

32. Exercises Neamen book: Ch. 4 Question 4.1 (pg. 177)