Amplifier Teaching Aid (DED Philippinen, 86 p.) 
Lesson 7  Small Signal Amplifier 

Title: Small Signal Amplifier
Objectives:
 Know the purpose of capacitors in amplifier circuits
 Able to calculate the voltage gain in an CE amplifier
Figure
AC Signals
After the transistor has been biased with the Qpoint near the middle of the load line, we can put a small acvoltage on the base (V_{in}). That procedures a large ac voltage at the collector (V_{out}). This increase is called amplification. For two reasons we have to use capacitors. First, to couple or transmit ac signals (coupling). Second, to short ac signals to ground (bypass).
A capacitor is open at low frequencies and shorted at high frequencies.
_{}
Capacitive reactance (X_{C}) is inversely proportional to frequency (f) and to capacitance (C). For a coupling capacitor to work properly, it has to act like an ac short at the lowest frequency that the ac source can have. To realize that we can use the following rule:
X_{C} < 10 R
Make the reactance at least 10 times smaller than the total resistance in series with the capacitor.
Ex: Calculate the capacitance of C_{1} for a proper ac transmittance. Frequency range: 2020000 Hz
Fig. 71: Use of coupling
capacitor
Total resistance: 1KW + 500W = 1.5KW
_{}
_{}  > _{}
_{}C = 53mF
The capacitor to choose should be bigger than 53mF. The next standard value is:
C = 56mF
It is connected in parallel across a resistor. The reason for doing this is to bypass an ac current away from the resistor. The capacitor provides a short for the ac. You can use the following rule to calculate the capacitance:
Make the reactance at least 10 times smaller than the total resistance in parallel with the capacitor.
From a given amplifier circuit first do the dc analysis (recall lesson 6) and than do the ac analysis.
Fig. 72: CE amplifier circuit
DC equivalent circuit
For dc, all capacitors are acting like open switches; therefore we can draw the following dc equivalent circuit:
Fig. 73: DC equivalent
circuit
Now the dc analysis can easily be done: (see Lesson 6)
V_{B} = 1.8V
V_{E} = 1.1V
I_{E} = 1.1 mA
V_{C} = 6.04V
V_{CE} = 4.94V
AC equivalent circuit
For the ac all capacitors are shorted and the dc sources are reduced to zero:
Fig. 74: Ac equivalent,
circuit
The top of the 10K and 3.6K resistors are grounded. The resistors 10K/2.2K and 3.6K/10K are in parallel so we can combine them:
Fig. 74: Simplified ac equivalent
circuit
Now we got a really simple circuit for the ac analysis.
Voltage Gain
One of the most important characteristics for small signal amplifiers is the voltage gain (A_{V}).
_{}
The lowercase letters are used to indicate ac values. The output voltage is given by:
V_{out} = i_{c} * r_{c}
The input voltage is given by:
V_{in} = i_{e} * r_{e}
Substitute of these two expressions:
_{}
Because i_{c} approximately equals i_{e}:
_{}
AC emitter resistance (r_{e})
The first step in calculating the voltage gain is to estimate the ac emitter resistance (r_{e}).
_{} (formula derived by using calculus)
This relation applies to all transistors that means it is a universal formula.
Let's remember our example circuit (Fig. 74):
_{}
AC collector resistance
Due to the ac analyzing method we easily get the ac collector resistance (re). See Fig. 74:
r_{c} = 2.65KW
So now we are ready to calculate the voltage gain:
_{}
HO: What will be the voltage gain for the following circuit?
Fig. 75: CE amplifier circuit
Solution:
DC analysis
V_{B} = 3.6KW, V_{E} = 2.9 KW, I_{E} = 2.9 mAV_{C} = 9.5V, V_{CE} = 6.6V
AC analysis
r_{c} = 2.65KW
_{}
_{}
Figure
No. 1 (circuit above) Calculate the capacitance of C_{1}, to design a proper working bypass capacitor for the load R_{L}. Frequency range: 20  20000 Hz
No. 2 (circuit below)
a) Draw the dc equivalent circuit.
b) Calculate the following dc values: I_{C}, V_{CE}
c) Draw the ac equivalent circuit.
d) Calculate the ac emitter resistance (r_{e}) and the ac collector resistance (r_{c}).
e) What is the voltage gain A_{V}?
f) What happens to the voltage gain if the supply voltage doubles?
Figure
Figure
Procedure:
1. Connect the circuit
2. Connect an signal generator to the input. Set it to 1000 Hz (sinewave) and minimum output. Connect an oscilloscope to the output terminals of the amplifier. Adjust the oscilloscope for proper viewing.
3. Set the output of the generator to the maximum undistorted
amplifier output.
Measure the peak to peak input and output amplitude and
record it in the table. Draw the input and output waveforms in the table.
4. Set the generator to the minimum undistorted amplifier
output.
Measure the peak to peak input and output amplitude and record it in
the table. Sketch the input and output waveforms in the table.
Step 

Input 
Output  

I_{C} 
V_{pp} 
Waveform 
V_{pp} 
Waveform 
3      
4      