1
Electronics II
Laboratory #3
Frequency Response of RC Coupled Amplifiers
OBJECTIVES
The purpose of this experiment is to measure the overall low-frequency response
of a two-stage common emitter amplifier due to the coupling capacitors. You will be
able to demonstrate the effect of each coupling capacitors on the lower cutoff frequency
and learn to estimate this frequency.
EQUIPMENT LIST
1.
2.
3.
4.
5.
6.
7.
8.
9.
(2) 2N2222 silicone transistor
15-V DC Power Supply
Signal Generator
Resistors:
(2) 100 kΩ, (2) 12 kΩ, (3) 10 kΩ, (2) 1 kΩ
Capacitors:
(2) 100 µF, (1) 0.1 µF, (1) 0.01 µF, (1) 0.0022 µF
1 Breadboard
Jumper Cables
Multimeter
Oscilloscope with two probes
DISCUSSION
Whenever several amplifiers are RC coupled in order to furnish adequate gain,
there will be additional coupling capacitors affecting the lower frequency response. As
was the case with the single-stage amplifier in Experiment 2, there is a lower cutoff
frequency associated with each coupling and bypass capacitor. The calculations for the
lower cutoff frequency are the same as for the single-stage amplifier, except there are
additional capacitors that must be taken into account.
Figure 1 shows the equivalent circuit of a two-stage amplifier. A1 and A2 are the
open-circuit (unloaded) voltage gains of each stage. The capacitors C1, C2 and C3 are
coupling capacitors:
C1
C2
Rsource
Vs
C3
Ro1
Rin1
A1
Ro2
Rin2
A2
+
VL
RL
-
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04
2
Electronics II
Laboratory #3
The following equations are used to calculate the lower cutoff frequency due to
each coupling capacitor C1, C2 and C3 .
f c (C1 ) =
1
2 ⋅ π ⋅ (Rs + Rin1 ) ⋅ C1
f c (C2 ) =
1
2 ⋅ π ⋅ (Ro1 + Rin 2 ) ⋅ C2
f c (C3 ) =
1
2 ⋅ π ⋅ (Ro 2 + RL ) ⋅ C3
where
Rin = R1 // R2 // (rπ + (β + 1) ⋅ RE )
Ro = RC
The open-circuit (unloaded) voltage gains of each stage are calculated using the
following equation:
Av (unloaded ) =
− β ⋅ RC
rπ + (β + 1) ⋅ RE
The total voltage source gain (AS) of the two-stage amplifier is given by the following
equation:
 Rin1   Rin 2   RL 
 ⋅ 
 ⋅ 

As = A1 ⋅ A2 ⋅ 
R
+
R
R
+
R
R
+
R
 in1
s   in 2
o1   L
o2 
Provided that fc(C1), fc(C2) and fc(C3) are not close in value, the actual lower
cutoff frequency of the amplifier is approximately equal to the sum of the three individual
cutoff frequencies.
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04
3
Electronics II
Laboratory #3
PROCEDURE
1) Using the digital multimeter, measure the β of both BJT transistor and the
resistors values.
2) Connect the first stage of the amplifier and measure the bias currents (Icq).
Remember this current is DC. Determine the value of the dynamic resistance
of the transistor (rπ).
15V
VCC
100kohm
10kohm
0.0022uF
C2
Vout
+
50ohm
Rs
+
50mV
35.36mV_rms
Vin
15kHz
0Deg
Vs
0.1uF
C1
Vout
12kohm
1kohm
Figure 1
3) Set the signal generator voltage and frequency to 50 mV peak and 30 kHz.
Make sure that the signal generator termination is 50 Ω.
4) To determine the unloaded voltage gain of the first stage (A1) measure the Vin
and Vout voltages. The unloaded voltage gain is calculated using the following
equation:
A1 (unloaded ) =
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Vout
Vin
Rev: 09/23/04
4
Electronics II
Laboratory #3
5) Connect the second stage of the amplifier and measure the bias currents (Icq).
Remember this current is DC. Determine the value of the dynamic resistance
of the transistor (rπ).
15V
VCC
100kohm
10kohm
0.01uF
C3
Vout
+
50ohm
Rs
+
50mV
35.36mV_rms
Vin
30kHz
0Deg
Vs
0.0022uF
C2
Vout
12kohm
1kohm
Figure 2
6) Set the signal generator voltage and frequency to 50 mV peak and 30 kHz.
Make sure that the signal generator termination is 50 Ω.
7) To determine the unloaded voltage gain of the second stage (A2) measure the
Vin and Vout voltages. The unloaded voltage gain is calculated using the
following equation:
A2 (unloaded ) =
Vout
Vin
8) Now connect both stages as is illustrated in Figure 3.
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04
5
Electronics II
Laboratory #3
VCC 15V
100kohm
10kohm
100kohm
10kohm
0.0022uF
C2
50ohm
Rs
50mV
35.36mV_rms
15kHz
0Deg
Vs
0.01uF
C2
0.1uF
C1
+
VL
12kohm
1kohm
12kohm
1kohm
10kohm
RL
-
9) To verify that the amplifier is working. Measure with the oscilloscope the
peak-to-peak voltages of Vs, and VL. These values can be used to determine
the midband voltage gain from load-to-source AS = VL VS .
10) 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 30 kHz. This is the
overall lower cutoff frequency of the amplifier.
11) Return the signal generator frequency back to 30 kHz. Decrease the frequency
of the generator to each frequency in Table 4 measuring values of VL at each
frequency. These voltage values will be used to plot the low-frequency
response of the amplifier.
12) 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 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, C3 = 100 µF
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04
6
Electronics II
Laboratory #3
13) Return the signal generator frequency back to 30 kHz and again start
decreasing the frequency until the peak-to-peak voltage of the load decreases
to 0.707 times the value at 30 kHz. This frequency is fc(C1).
14) 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 = 0.0022 µF, C3 = 100 µF
15) Return the signal generator frequency back to 30 kHz and again start
decreasing the frequency until the peak-to-peak voltage of the load decreases
to 0.707 times the value at 30 kHz. This frequency is fc(C2).
16) To measure the cutoff frequency due to the coupling capacitor (C3) change the
following capacitors values (observe polarities as shown in Figure):
C1 = 100 µF, C2 = 100 µF, C3 = 0.01 µF
17) Return the signal generator frequency back to 30 kHz and again start
decreasing the frequency until the peak-to-peak voltage of the load decreases
to 0.707 times the value at 30 kHz. This frequency is fc(C3).
18) Calculate the overall cutoff frequency summing the individual cutoff
frequencies from steps 10, 12 and 14.
19) Using table 3, plot the amplifier frequency response (AV (dB) vs. freq.). The
 VL 
 . From the
 Vs 
voltage gain in decibels is equal to Av ( dB) = 20 ⋅ log
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: 09/23/04
7
Electronics II
Laboratory #3
DATA
Amplifier’s
Parameters
R1
R2
RC
RE
RL
β
ICQ
Table 1: Steps 1, 2 and 5
Measured Values
1st Stage
2nd Stage
Table 2: Midband Voltage Gain (f = 30 kHz). Step 9
Measured
Parameters
Voltages
Vs
VL
As = VL Vs
Table 3: Unloaded Voltage Gain (f = 30 kHz). Step 4 & 7
Voltages (Vp-p)
Parameters
1st Stage
2nd Stage
Vin
Vout
As = Vout Vin
Table 4: Frequency Response (Step 6)
Frequency (Hz)
VL (peak-to-peak)
As = VL VS
10 k
8k
6k
4k
2k
1k
950
900
850
800
700
600
500
400
300
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04
8
Electronics II
Laboratory #3
Table 5: Amplifier’s Cutoff Frequencies
Lower cutoff
Step Number
frequency
5 (overall)
10
12
14
15 (overall)
By: Prof. Rubén Flores Flores, Prof. Caroline González Rivera
Rev: 09/23/04