Engr 261 – Circuits and Devices Lab
Experiment # 10 – Bandpass Filter
Objectives:
After completing this lab, you will be able to
• calculate the cutoff frequencies of a bandpass filter by examining the individual low-pass and highpass stages of a filter,
• derive the transfer function for each stage of a bandpass filter,
• sketch the Bode plot of a bandpass filter from the transfer function of the individual stages.
Background
Bandpass filters permit a range of frequencies to pass from one stage to another. Many different types
of bandpass filters are used throughout electronics. For instance, the typical television receiver uses
several stages of filtering to achieve a bandwidth of 6 MHz, while an AM receiver has circuitry that
restricts the bandwidth to only 10 kHz. Although bandpass filters can be very elaborate, depending on
the application, they can also be constructed simply by combining a low-pass filter and a high-pass filter
as shown in Figure 1. Since expense and other design difficulties make RL filters impractical, RC filters
are used almost exclusively.
Figure 1. Simple bandpass filter
The bandpass filter of Figure 1 has two cutoff frequencies as determined by the cutoff frequencies of
the individual stages. The frequency below which the high-pass filter attenuates the signal is called the
lower cutoff frequency f1. The frequency at which the low-pass filter begins to attenuate is called the
upper cutoff frequency f2. As expected, the difference between the two frequencies is the bandwidth
BW. In order for the circuit to operate predictably, the cutoff frequencies should be separated by at least
one decade and the first stage must be the high-pass circuit.
The lower cutoff frequency ω1 in radians per second is found as ω 1 =
1
τ1
=
1
with a corresponding
R1C1
ω1
1
=
in hertz. The upper cutoff frequency ω2 in radians per second is found as
2π 2πR1C1
ω
1
1
1
with a corresponding frequency f 2 = 2 =
in hertz. The bandwidth of the
ω2 =
=
τ 2 R2 C 2
2π 2πR2 C 2
frequency f1 =
filter is BW = f 2 − f1 .
PreLab Calculations
1. Calculate and record the cutoff frequency (in radians per second and in hertz) for the high-pass
stage in the circuit of Figure 2.
Figure 2. Bandpass filter
2. Calculate and record the cutoff frequency (in radians per second and in hertz) for the low-pass stage
in the circuit of Figure 2.
3. Calculate and record the bandwidth of the filter circuit.
4. From the calculations of Steps 1 and 2 sketch the asymptotic Bode plots for the bandpass filter of
Figure 2 on a semilog scale.
Experimental Procedure:
1. Setup the circuit shown in Figure 2. Connect Ch 1 of the Oscilloscope to the output of the signal
generator and adjust the output to have an amplitude of 2.0 VP (4.0 VPP) at a frequency of 100 Hz.
2. Use Ch 1 as the trigger source and connect Ch 2 of the oscilloscope across the output of the circuit.
Measure the amplitude and phase angle of the output voltage vout
3. Repeat measurements and tabulate results for the following frequencies: 100, 200, 400, 800 Hz, 1
kHz, 2, 4, 8, 10 20, 40, 80 and 100 kHz.
4. For which frequency is the output voltage a maximum? Adjust the function generator to provide an
output of 2.0 VP, (4.0 VPP) at this frequency. While observing the oscilloscope, adjust the generator
frequency until voltage Vout is at the maximum value.
5. Decrease the frequency until the output voltage Vout is reduced to 0.707 of the maximum value found
in Step 4. Record the lower half-power frequency f1 and the corresponding output voltage
6. Increase the frequency above the center frequency until the output voltage Vout is again reduced to
0.707 of the maximum value found in Step 4. Record the upper half-power frequency f2 and the
corresponding resistor voltage Vout.
7. For each voltage measurement in Step 4, determine the voltage gain as both a ratio of amplitudes
V
AV = Vout / Vin and in decibels as given by the equation [AV ]dB = 20 log out
 Vin

 .

8. use the measured data to create a Bode plot on a semi-log scale. Compare theoretical gains and
phase shifts with the measured values.