Experiment Title:

Active Filter Design

Equipment List:
741 operational amplifier or the equipment
DC power suppliers (+/-V)
Analog signal generator (1Vpk sine at variable frequencies)
Resistors: 1-10k, 1-5.6k, 1-3.3k, 1-2.7k, 1-1,5k, 1-680Ω, 1-330Ω
Capacitors: 2-0.47μF, 1-0.015μF, 0.015μF (25V)
Dual-trace oscilloscope

Procedure:
We demonstrated the operational amplifier used in a VCVS, second order, low-pass filter with Butterworth characteristics by connecting the circuit below. C1 is parallel combination of the 0.015μF and 0.01μF capacitors.

Circuit #1

With Vs adjusted to produce a 1Vpk sine wave at 500Hz, we measured and recorded the peak value of Vo, which was 2Vpp. Since 500Hz is within the pass-band of this filter, these values can be used to determine the pass-band voltage gain Am.

At this juncture, we increased the frequency of the signal generator until the output voltage Vo equals 0.707 times that measured in the previous step. This was how we got the cutoff frequency f2 of the filter.

0.707 x 1.76(measured voltage)
= 1.2Vpp.

We now replaced 1.65k and 5.6k in circuit one with 2.7k and 10k respectively. With Vs adjusted to produce a 1Vpk sine wave at 100Hz, we again measured and recorded the peak value of Vo. Here it was 2Vpp. We also measured the cut off frequency f2 of the filter as described earlier above. F2 was measured to be 2MHz.

20log(0.88) = -1.11dB

To demonstrate the operational amplifier used in a VCVS, second order, high pass-filter with Chebyshev characteristics and 2Db ripple width, we connected the circuit below.

Circuit #2

With Vs = 1Vpk at 10kHz, we measured the peak value of Vo, which was 2.3Vpp. Then decreasing the frequency of the signal generator until Vo reaches maximum value yielded the 10kHz-15kHz. The peak value of Vo at this point when it is a maximum was 2.1V. The ratio of these two peak value can also be used to calculate the ripple width in dB like in the previous steps. Now, we continue to decrease the frequency of the signal generator until the output voltage Vo equals that measured at 10kHz. We also measured the frequency where this occurred, which is the cut off frequency f1 of the Chebyshev filter. It occurred at 7kHz when the voltage was 2.22V. Below is the table of the various frequencies used while trying to find the cut off frequency.

Frequency (kHz) Voltage output (Volts)
15 2.11
14.5 2.12
14 2.13
13.5 2.13
13 2.14
12.5 2.18
12 2.19
11.5 2.21
11 2.24
10.5 2.3
10 2.3
9.5 2.32
9 2.33
8.5 2.34
8 2.33
7.5 2.3
7 2.2
6.5 2.05
6 1.91

Conclusion:

Clearly, I saw that low pass filters are circuits that allow low frequency voltages to pass through them, while blocking high frequencies. High pass filters perform exactly opposite role; they pass high frequencies and block low frequencies. In the first circuit, all voltages whose frequencies are within the passband of a butterworth filter have approximately the same gain.. The cutoff frequency is the frequency at which the voltage gain drops by 3Db from the voltage gain in the passband. The attenuation produced by a chebyshev filter at any frequency outside the pass band is greater than the attenuation produced by a butterworth filter at the same frequency, assuming the filters have the same order and the same cutoff frequency.