1
Electronics II
Laboratory #2
Lower Cutoff Frequency of a Bypassed CommonEmitter Amplifier
OBJECTIVES
The purpose of this experiment is to measure the lower cutoff frequency of a commonemitter amplifier due to coupling and bypass capacitors. You will be able to demonstrate the
effect of these capacitances on the lower cutoff frequency and learn how to estimate this
frequency.
EQUIPMENT LIST
1.
2.
3.
4.
2N2222 silicone transistor
15-V DC Power Supply
Signal Generator
Resistors:
(1) 82 kΩ, (1) 15 kΩ, (1) 6.8 kΩ, (1) 2.2 kΩ, (1) 1.5 kΩ, (1) 5.6 kΩ
5. Capacitors:
(2) 100 µF, (1) 4.7 µF, (1) 0.22 µF, (1) 0.1 µF
6. Two oscilloscope probes
7. 1 Breadboard
8. Jumper Cables
9. Digital Multimeter
10. Oscilloscope
DISCUSSION
Since the impedance of coupling capacitors increases as frequency decreases, the voltage
gain of a BJT amplifier decreases as frequency decreases. At very low frequencies, the
capacitive reactance of the coupling capacitors may become large enough to drop some amount
of the input or output voltage. Also, the emitter bypass capacitor may become large enough so
that it no longer shorts the emitter resistor to ground decreasing the amplifier voltage gain.
The following equations can be used to determine the lower cutoff frequency, where the
voltage gain drops 3 dB from the midband value or 0.707 times the midband AV.
f c (C1 ) =
1
2 ⋅ π ⋅ C1 ⋅ (Rs + Rin )
Rin = R1 // R2 // rπ
where:
fc (C1) = lower cutoff frequency due to C1
C1 = input coupling capacitance
Rin = input resistance of the amplifier
Rs = source resistance
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/16/05
2
Electronics II
Laboratory #2
f c (C2 ) =
1
2 ⋅ π ⋅ C2 ⋅ (Ro + RL )
Ro = RC
where
fc (C2) = lower cutoff frequency due to C2
C2 = output coupling capacitance
Ro = output resistance of the amplifier
RL = load resistance
f c (C E ) =
1
2 ⋅ π ⋅ C E ⋅ Rth
 r + R1 // R2 // Rs 
Rth = RE //  π

β
+
1


β ⋅ VT
rπ =
I CQ
where
fc (CE) = lower cutoff frequency due to CE
CE = emitter bypass capacitance
Rth = Thevenin resistance parallel to the bypass capacitor
RE = emitter resistance
Rs = source resistance
R1 and R2 = input bias resistors
β = short circuit current gain of the transistor
VT = thermal voltage (26 mV @ 300 K)
ICQ = DC bias current of the transistor’s collector.
Provided that the cutoff frequencies are not close in value, the overall lower cutoff
frequency is approximately equal to the sum of the three individual cutoff frequencies.
PROCEDURE
1) Using the digital multimeter, measure the β of the BJT transistor and the resistors
values of the circuit resistors. Complete table 1.
2) To measure the bias current (Icq) of the amplifier, connect the following circuit.
Remember this current is DC. Determine the value of the dynamic resistance of the
transistor (rπ). Complete table 1.
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/16/05
3
Electronics II
Laboratory #2
VCC 15V
82kohm
R1
6.8kohm
Rc
0.22uF
C2
5.6kohm
Rs
50mV
35.36mV_rms
10kHz
0Deg
Vs
+
+
0.1uF
C1
VL
Vin
15kohm
R2
-
1.5kohm
Re
4.7uF
Ce
2.2kohm
RL
-
3) Set the signal generator voltage and frequency to 50 mV peak and 10 kHz
respectively. Make sure that the signal generator termination is 50 Ω.
4) To verify that the amplifier is working, measure with the oscilloscope the peak-topeak voltages of Vin , VL and Vs. These values can be used to determine the midband
voltage gain AV = VL Vin and the voltage gain from load-to-source
AS = VL VS .
Complete table 2.
5) Now decrease the frequency of the signal generator until the peak-to-peak voltage of
the load decreases to 0.707 times the value at 10 kHz. This is the overall lower cutoff
frequency of the amplifier. (Table 4).
6) Return the signal generator frequency back to 10 kHz. Decrease the frequency of the
generator to each frequency in Table 3 measuring values of VL at each frequency.
These voltage values will be used to plot the low-frequency response of the amplifier.
7) By making two capacitors very large, the effects of those capacitors on the lower
cutoff frequency can be made negligible. The cutoff due to the third capacitors can
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/16/05
4
Electronics II
Laboratory #2
then be measured. With this in mind, change the capacitor values to measure the
individual cutoff frequency of each capacitor. To measure the cutoff frequency due to
the input coupling capacitor (C1) change the following capacitors values (observe
polarities as shown in Figure):
C1 = 0.1 µF, C2 = 100 µF, CE = 100 µF
8) Return the signal generator frequency back to 10 kHz and again start decreasing the
frequency until the peak-to-peak voltage of the load decreases to 0.707 times the
value at 10 kHz. This frequency is fc(C1). (Table 4)
9) To measure the cutoff frequency due to the output coupling capacitor (C2) change the
following capacitors values (observe polarities as shown in Figure):
C1 = 100 µF, C2 = 0.22 µF, CE = 100 µF
10) Return the signal generator frequency back to 10 kHz and again start decreasing the
frequency until the peak-to-peak voltage of the load decreases to 0.707 times the
value at 10 kHz. This frequency is fc(C2). (Table 4)
11) To measure the cutoff frequency due to the bypass capacitor (CE) change the
following capacitors values (observe polarities as shown in Figure):
C1 = 100 µF, C2 = 100 µF, CE = 4.7 µF
12) Return the signal generator frequency back to 10 kHz and again start decreasing the
frequency until the peak-to-peak voltage of the load decreases to 0.707 times the
value at 10 kHz. This frequency is fc(CE). (Table 4)
13) Calculate the overall cutoff frequency summing the individual cutoff frequencies
from steps 8, 10 and 12.
14) Using table 3, plot the amplifier frequency response (AV (dB) vs. freq.). The voltage
gain in decibels is equal to
V 
Av (dB) = 20 ⋅ log L  .
 Vin 
From the graph identify
the overall cutoff frequency. Remember this happen when the gain drops 3 dB from
the midband voltage gain in decibels.
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/16/05
5
Electronics II
Laboratory #2
DATA
Table 1: Steps 1 and 2
Amplifier’s
Measured
Parameters
Values
R1
R2
RS
RC
RE
RL
Β
ICQ
Table 2: Midband Voltage Gain (f = 10 kHz). Step 4
VL (peak-to-peak)
AV = VL Vin
As = VL VS
Table 3: Frequency Response (Step 6)
Frequency (Hz)
VL (peak-to-peak)
As = VL VS
AV = VL Vin
10 k
8k
6k
4k
2k
1k
950
900
850
800
700
600
500
400
300
200
100
50
Table 4: Amplifier’s Cutoff Frequencies
Lower cutoff
Step Number
frequency
5 (overall)
8
10
12
13 (overall)
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/16/05