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ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit

ECEN 214-516

Post-Lab 8

Sinusoidal Steady State Response of a 2nd Order Circuit

Procedure

Task 1: Sinusoidal Steady-State Response of a 2nd Order Low-Pass Circuit

  1. First we built the Sallen-Key circuit as shown in Figure 1.1. We used the values found in prelab for the values of R1, R2, C1,and C2.
ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img1

Figure 1.1: Sallen-Key 2nd Order Circuit

  1. We set up test probes so we would be able to test the input voltage, output voltage, and the phase difference between the input and output.
  2. Next, we made those three measurements for thirteen different input frequencies.
  3. Then, we changed the frequency to result of an input:output ratio of about 0.707.
  4. Once the cut-off frequency was determined, the phase difference was also recorded.
ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img2

Task 2: Sinusoidal Steady-State Response of a 2nd Order High-Pass Circuit

  1. First we built the Sallen-Key circuit as shown in Figure 2.1. We used the values found in prelab for the values of R1, R2, C1,and C2.

Figure 2.1: Modified Sallen-Key 2nd Order Circuit

  1. We set up test probes so we would be able to test the input voltage, output voltage, and the phase difference between the input and output.
  2. Next, we made those three measurements for thirteen different input frequencies.
  3. Then, we changed the frequency to result of an input:output ratio of about 0.707.
  4. Once the cut-off frequency was determined, the phase difference was also recorded.

Data and Results:

Task 1: Sinusoidal Steady-State Response of a 2nd Order Low-Pass Circuit

Task 1

Frequency [Hz]

Input Amplitude [V]

Output Amplitude [V]

Phase Diff [ms]

10

10

0.34101

50.962

18

10

0.10499

27.441

32

10

0.03326

16.470

56

10

0.01142

8.976

100

10

0.00403

4.833

178

10

0.00168

2.922

316

10

0.00134

1.583

562

10

0.00101

1.015

1000

10

0.00101

0.502

1778

10

0.00101

0.264

3162

10

0.00101

0.152

5623

10

0.00101

0.089

10000

10

0.00101

0.050

Cut-Off

2.5

1.41

1

147.73

ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img3 ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img4

Task 2: Sinusoidal Steady-State Response of a 2nd Order High-Pass Circuit

Task 2

Frequency [Hz]

Input Amplitude [V]

Output Amplitude [V]

Phase Diff [ms]

10

2

1.8566

92.898

18

2

1.9507

53.125

32

2

1.9833

30.303

56

2

1.9950

17.661

100

2

1.9990

10.210

178

2

2.0001

5.914

316

2

1.9990

2.920

562

2

1.9927

1.818

1000

2

1.9782

1.004

1778

2

1.9036

0.545

3162

2

1.7793

0.320

5623

2

1.3496

0.168

10000

2

0.4287

0.424

Cut-Off

5000

1.41

1

378.29

ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img5 ECEN 214-516 Sinusoidal Steady State Response of a 2nd Order Circuit img6

Discussion

The lab went pretty much as expected over all. For task 1, the pass and stop band started at around 100 Hz and goes to the highest frequency we had. For task 2, the pass and stop band starts at 10 Hz, the lowest frequency, and ho to about 1000 Hz. This shows that the two circuits pretty much behave exact opposite of eachother. I would say that I would change the values of the resistors and/or capacitors to shift the pass and stop bands. In our lab, we didn’t find any values where the output is higher than the input. Even though we did not get these values, I can see how it could occur given the data that we observed. The reason it can happen considering the conservation of energy is because the op-amp has an additional power source. Over all the lab was pretty good, maybe some changes would be to try frequencies higher/lower to get a more leveled off curve. In addition, we couldn’t find a feature to measure the phase difference of the output and input, if we had a better way to test that we would have had much better results.

Conclusion

Over all, this lab was very insightful into the way that the Sallen-Key Circuit works. I find it very interesting that there are so many ways to use op amps to achieve different effects. I noticed that simply flipping the placement of the resistors and capacitors had such a dramatic impact on the way the circuit worked. It is also useful to know how to find the cut-off frequency because that would be important to know when possibly making some type of wired communication circuit.

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