paraphrase

b. The resonant frequency is ωr=6.1kHz. This matches the graph but, it is difficult to see because more points should have been plotted near the peak. The graph gives a resonant frequency of 5.12kHz.

c. The theoretical bandwidth of this circuit is 11.6kHz, which cannot be accurately confirmed from this plot because too few data points were taken.

d. PSPICE was used to plot the magnitude of V2 versus frequency. These results match the results from step “a” above.

R2

10k

C1

.01uF

L1

68mH

0

RL

84.3

V1

1Vac

0Vdc

R1

10k

V

R2

10k

C1

.01uF

L1

68mH

0

RL

84.3

V1

1Vac

0Vdc

R1

10k

V

Discussion

While doing this experiment, several calculations needed to be done which involved concepts learned in the lecture. The students needed to be able to find H(jω), |H(jω)|, resonant frequency (ωr) and bandwidth. Not knowing how to apply these mathematical models would have drastically slowed down the process of completing the experiment.

All four circuits had the same resonant frequency because they had the same capacitor and inductor values. The theoretical and experimental values were different by about 16%. This is because not enough data points were taken as the values approached the peak. There was a similar problem when finding bandwidth from the graphs. Not enough points were plotted to accurately find the bandwidth. Graphs can be a helpful way to make sure the experimental values of resonant frequency and bandwidth match the theoretical values. Therefore, in future experiments like this, several more data points must be taken near the cutoff and peak frequencies.

Conclusion

In this lab, the students observed how the output voltage varies with frequency in band pass filters. The students gained experience taking measurements with the oscilloscope, as well as, using several mathematical models to make calculations. It was observed just how important it is to take an adequate number of data points so that the theoretical values can be verified with the experimental values.