ECEN 326 Lab 8

Frequency Response of a Common-Emitter BJT Amplifier

Circuit Topology
Circuit schematic of the common-emitter amplifier is shown in Fig. 1. Capacitors CB and CC are used for AC
coupling, whereas CE is an AC bypass capacitor used to establish an AC ground at the emitter of Q1 . CF is a small
capacitance that will be used to control the higher 3-dB frequency of the amplifier.

VCC
Rout
CF RC
RB1
RS CB Vo
Q1 CC RL

Vs RB2
Rin RE CE

Figure 1: Common-emitter BJT amplifier.

DC Biasing and Mid-band Frequency Response

For this section, assume that CB = CC = CE = ∞ and CF = Cπ = Cµ = 0. You can find the DC collector current (IC ) and
the resistor values following the analysis provided in Lab #1. Since the topology and the requirements are slightly
different, you need to make minor modifications to the design procedure and equations.

Low Frequency Response

Figure 2 shows the low-frequency small-signal equivalent circuit of the amplifier. Note that CF is ignored since its
impedance at these frequencies is very high.

RS CB CC
vo
vs RB rπ vπ gm vπ RC RL

CE RE

Figure 2: Low-frequency equivalent circuit.

Using short-circuit time constant analysis, the lower 3-dB frequency (ωL ) can be found as
1 1 1
ωL ≈ + + (1)
R1s CB R2s CE R3s CC
where
R1s = RS + (RB k rπ ) (2)
 
rπ + (RB k RS )
R2s = RE k (3)
β+1
R3s = RC + RL (4)

High Frequency Response

At high frequencies, CB , CC and CE can be replaced with a short circuit since their impedances become very small.
Figure 3 shows the high-frequency small-signal equivalent circuit of the amplifier.
c Department of Electrical and Computer Engineering, Texas A&M University

1
 RS rb Cµ +CF
vo
vs RB Cπ rπ vπ gm vπ RC RL

Figure 3: High-frequency equivalent circuit.

The higher 3-dB frequency (ωH ) can be derived as

1
ωH =    (5)
RCL
RT Cπ + (Cµ + CF ) 1 + gm RCL +
RT
where
RT = rπ k (rb + (RS k RB )) (6)
RCL = RC k RL (7)

Thus, if we assume that the common-emitter amplifier is properly characterized by these dominant low and high
frequency poles, then the frequency response of the amplifier can be approximated by
vo s 1
(s) = Av (8)
vs s + ωL 1 + s
ωH

Calculations and Simulations

Assuming CB = CC = CE = ∞ and CF = Cπ = Cµ = 0, and using a 2N3904 BJT, design a common-emitter amplifier
with the following specifications:
VCC = 5 V RS = 50Ω RL = 1 kΩ
Rin ≥ 250 Ω Isupply ≤ 8mA |Av | ≥ 50 0-to-peak unclipped output swing ≥ 1.5 V

1. Show all your calculations, design procedure, and final component values.
2. Verify your results using a circuit simulator. Submit all necessary simulation plots showing that the specifica-
tions are satisfied. Also provide the circuit schematic with DC bias points annotated.
3. Using a circuit simulator, find the higher 3-dB frequency (fH ) while CF = 0.
4. Determine Cπ , Cµ and rb of the transistor using DC operating point analysis (Cπ , Cµ and rb are usually listed as
Cpi, Cmu and rx (or 1/gx),respectively). Calculate fH using Eq. (5) and compare it with the simulation result
obtained in Step 3.
5. Calculate the value of CF to have fH = 20 kHz. Simulate the circuit to verify your result, and adjust the value
of CF if necessary.
6. Calculate CB , CC , CE to have fL = 500 Hz. Simulate the circuit to verify your result, and adjust the values of
capacitors if necessary.

Measurements
1. Construct the amplifier you designed.
2. Measure IC , VE , VC and VB . If any DC bias value is significantly different than the one obtained from simula-
tions, modify your circuit to get the desired DC bias before you move onto the next step.
3. Measure Isupply .
4. Obtain the magnitude of the frequency response of the amplifier and determine the lower and higher 3-dB
frequencies fL and fH .
5. At midband frequencies, measure Av , Rin , and Rout .
6. Measure the maximum un-clipped output signal amplitude.

2
Report
1. Include calculations, schematics, simulation plots, and measurement plots.
2. Prepare a table showing calculated, simulated and measured results.

3. Compare the results and comment on the differences.

Demonstration
1. Construct the amplifier you designed on your breadboard and bring it to your lab session.

2. Your name and UIN must be written on the side of your breadboard.
3. Submit your report to your TA at the beginning of your lab session.
4. Measure Isupply .

5. Obtain the magnitude of the frequency response of the amplifier and determine the lower and higher 3-dB
frequencies fL and fH .
6. At midband frequencies, measure Av , Rin , and Rout .