ENEE206 - Transient response in 1st and 2nd-order circuits

ENEE 206 Laboratory Week # 10

Transient response in 1st and 2nd-order circuits

Objective:

To characterize transient signals in circuits with energy-storing elements.

Pre-lab preparation:

Assume the following components are available to build your experiment:

Resistors:         51 Ohm    470 Ohm    1.0 k      2.0 k
Capacitors:	  100 nF      22 µF     220 µF   
Inductors:        4.7 mH      20 mH      50 mH
Diodes:           1N4007
Miscellaneous:    DIP-switch

Read about first and second-order circuits (Sections 7.1-7.3 in Mayergoyz and Lawson.) Also read about PSpice simulations in Section 7.7.
Draw wiring diagrams for the following circuits:
1. Switched RL circuit powered by a 5V battery.
2. Switched RC circuit powered by a 5V battery.
3. Switched RLC series circuit powered by a 5V battery. Given the available components, find RLC combinations that are overdamped, underdamped, and critically-damped (1 each).
4. Switched LC parallel circuit (with a series resistance R) powered by a 5V battery. Given the available components, find an RLC combination that is nearly critically-damped.
5. Simulate the circuit in (3) for the underdamped case. Plot the voltage across the capacitor as a function of time.
6. Simulate the circuit in (4). Plot the voltage across the capacitor as a function of time.
7. Extra Credit (5%): Simulate the circuit shown on the left when V1=5cos(12*pi*t). Plot the voltages across C1 and C2 as a function of time. Be certain that the initial conditions are correct. What is the maximum voltage on each capacitor and what is the peak voltage in steady-state (on each capacitor)?
8. Extra Credit (5%): Simulate the circuit shown on the right assuming that L = 50 mH, C = 22 µF, and the Quality factor (Q) of the inductor is 5 at the circuit's resonant frequency. Plot the voltage on the capacitor as a function of time. Short the diode and repeat the simulation and plot.

Experiment:

Ask the TA questions regarding any procedures about which you are uncertain.
Turn off all power supplies any time that you make any change to the circuit.
Make CERTAIN that you can answer all the questions in the post-lab analysis section.
Complete the following tasks:
1. Measure the dc resistances of all resistors and inductors to be used in the circuits.
2. Measure the inductances and capacitances with the LC meter.
3. Construct the switched RL circuit with a 51 Ohm resistor and the 4.7 mH inductor. Operate the oscilloscope in triggered mode and plot the voltage across the resistor as a function of time. Measure the time constant for the circuit.
4. Repeat the previous measurement with the 20 mH and 50 mH inductors (but do not make additional plots).
5. Construct the switched RC circuit with a 1 kOhm resistor and the 100 nF capacitor. Plot the voltage across the capacitor as a function of time. Measure the time constant for the circuit.
6. Repeat the previous measurement with the 22 µF and 220 µF capacitors (but do not make additional plots).
7. Construct the switched RLC series circuit with the values you selected for the underdamped circuit. Plot the voltage across the capacitor with time.
8. Repeat the above plot for the overdamped and critically-damped circuits.
9. Construct the switched RLC parallel circuit. Plot the voltage across the capacitor with time.
10. Extra credit (5%): Construct the circuit with the 2 capacitors. Trigger the circuit several times until you get a starting voltage near the input voltage maximum. Plot the voltage on each capacitor with time. Also plot the input voltage (after the switch). Measure the peak and steady-state voltage levels on each capacitor.
11. Extra credit (5%): Construct the circuit with a diode and plot the voltage on the capacitor with time. Replace the diode with a short and repeat the plot.

Post-lab analysis:

Generate a lab report following the sample report available on the Web page. Mention any difficulties encountered during the lab. Describe any results that were unexpected and try to account for the origin of these results (i.e. explain what happened). IN ADDITION, respond to the following questions/instructions:

What was the inductance of each inductor according to the RL circuit measurements? Compare with the results from the LC meter and comment.
What was the capacitance of each capacitor according to the RC circuit measurements? Compare with the results from the LC meter and comment.
Did all the RLC circuits behave as expected? If not, why not?
What was the oscillation frequency of the underdamped series RLC circuit?
What was the capacitor voltage overshoot of the underdamped series RLC circuit?
Which series RLC circuit approached steady-state most rapidly? Why?
What was the maximum voltage achieved on the capacitor in the parallel RLC circuit and how long after the switch closed did the maximum occur?
Compare the experimental and simulated results for both RLC circuits. Explain any differences that occurred.

Extra credit questions:

What was the maximum voltage across each capacitor in the two-capacitor circuit (in experimental step #10) and what was the difference between this value and the peak steady-state voltage?
Explain the operation of the circuit (in experimental step #11) with the diode present.
Estimate the inductance and quality factor Q of the inductor in the final (diodeless) problem assuming you know the correct value of the capacitor.