Electrical Circuits Essay, Research Paper

SUMMARY

Unlike the last lab on RL, RC and RLC circuits, we measured the frequency characteristics of these circuits. We observed the steady-state sinusoidal response of an high-pass RL circuit, a low-pass RC circuit and a band-pass RLC circuit.

PROCEDURE

10.4.1 Steady-State Sinusoidal Response of High-Pass RL Circuit

This part of the lab consisted of constructed an high-pass RL circuit shown below in Figure 10.1. We used the scope to measure the phase and the gain of the circuit. Also, we used the Gain-Phase meter to measure the phase and the gain of the circuit.

Figure 10.1: High-pass RL circuit.

A Bode plot is shown below from the measurements of the scope, gain in dB versus log f and, separately, phase shift in degrees versus log f.

90 Y = 90?

20log|jw|

-20log |1+j (w/170212)|

AdB,q 0

-90 -b = -tan-1(w/170212)

170212 log f

10.4.3 Steady-State Sinusoidal Response of Low-Pass RC Circuit

We did the exact same procedure as above except the data was for a low-pass RC circuit. This circuit is shown below in Figure 10.2.

Figure 10.3: Low-pass RC circuit

A Bode plot is shown below from the measurements of the gain-phase meter, gain in dB versus log f and, separately, phase shift in degrees versus log f.

90

-20log |1+j (w/2500)|

AdB,q 0

-90 -b = -tan-1(w/2500)

250 log f

10.4.5 Steady-State Sinusoidal Response of Band-pass RLC Circuit

Again, the exact same procedure as above was done for this circuit. This circuit, a band-pass RLC circuit, is shown below in Figure 10.3.

Figure 10.3: Band-pass RLC circuit

A Bode plot is shown below from the measurements of the gain-phase meter, gain in dB versus log f and, separately, phase shift in degrees versus log f.

@ 1 kW

90

-20log |1+j (w/461265)|

AdB,q 0

-90 -b = -tan-1(w/461265)

461265 log f

@ 10 W

90

-20log |1+j (w/46126)|

AdB,q 0

-90 -b = -tan-1(w/46126)

46126 log f

WRITE-UP

2. Compare the theoretical transfer functions with what what you measured:

My theoretical transfer function agrees with my measured values.

3. For the two RLC circuits, calculate the bandwidth in Hz (2pb) the center frequency wo and the quality Q from your measured data.

With 1 kW:

Bandwidth = 1.33E1012

wo = 461265 rad/sec

Q ? 5

With 10 W:

Bandwidth = 1.33E1011

wo = 46126 rad/sec

Q ? 4

How do they agree with your theoretically-calculated values? The values are close.

Can you explain any differences? There really is no difference.

4. Comment on the gain from Vi and point A, especially near the resonant frequency wo.

A is between the cutoff frequencies.

CONCLUSION

This lab was a difficult one due to the fact that I forgot what a Bode plot was. Also, we only had one day to work on it. As a result, we had to take data really quick in order to finish in time. I do not know if our data is right.