LabExperimentNo.9 RC, RL, and RLC Transient Analysis

I. Introduction

The purpose of this lab is to introduce the use of capacitors and inductors, and to analyze the transient response of RC, RL, andRLC circuits. During the lab, the following data will be obtained:

a)The current and voltage response of an RC series circuit to a pulse

b)The current and voltage response of an RL series circuit to a pulse

c)The underdampednatural response of a series RLC circuit

II. Componentsand Instruments

Thecomponentsandinstrumentsrequiredforthis labarelisted below.

Resistors:

1 KΩ Resistor

Inductors:

680 uH Inductor

Capacitors:

470 uF electrolytic capacitor

330 nF foil capacitor

Other parts:

2 pushbutton switches

Instruments:

NI myDAQ

Additional:

Breadboard Tool Box Hook-up Wire

III. Lab Measurements

This lab assignment has three different circuits, TWO different power supplies, and TWO oscilloscope traces. You can use your NI myDAQ for ALL of them, at once if you choose. The first circuit is a typical RC series circuit. In your prelab you should have already calculated the time constant of the circuit. You will confirm this calculation and measure the voltage and current response due to a pulse.

The second circuit is a typical series RL circuit. Once again you should have calculated in your prelab the time constant of this circuit. You will also measure the voltage and current response of the RL circuit to a pulse. Note that to actually see the response to the pulse, we will use a 5V DC (only positive voltage) square wave as a source. A square wave at the correct frequency will imitate a long pulse (in terms of the time constant) being applied again and again, so the behavior of the circuit is periodic, but also reaches steady state. This means an oscilloscope can capture the full response in a continuous fashion, and each cycle of the square wave shows the complete behavior of the circuit due to a pulse.

The final circuit is a series RLC circuit. You should have done the calculation of the response of a series RLC circuit in the prelab. The values from the prelab are the same for this circuit. You will not put a resistor in this circuit; the series resistance of the inductor will act as the resistive component (R = 0.6 Ohms). The measurements in this circuit will be different from the first two. You will be measuring the natural response of the circuit, that is, the circuit without a power source. However, there will be an initial condition of voltage across the capacitor. To accomplish this, you will charge the capacitor to 5V using the 5V supply on your myDAQ, and thendischarge it through the inductor. This will imitate the underdamped natural response of a series RLC circuit.Measurements to be made for the post-lab are in bold. Pay attention to the BOLD text.

a)RC CIRCUIT:

Build the circuit shown in Figure 1 on your breadboard. Use your myDAQ as the square wave source. Make the period of the square wave at least 20 times longer than the calculated time constant. This will yield a pulse that is 10 times as long as the time constant, which will ensure that the circuit reaches a steady state. Also remember to add the correct DC offset to maintain a purely positive DC pulse.

Figure 1: RC circuit

Open the myDAQ oscilloscope, and set it up for dual channel acquisition (activate Channel 1 and Channel 2). Then make four connections to the board: Connect one channel (2 wires) to measure voltage across the resistor, and connect the other channel (2 more wires) to measure voltage across the capacitor.Record the waveforms obtained. It is recommended to take a screenshot of the output for the lab report. Determine the time constant from the waveform on the oscilloscope.

The time constant is the time that it takes the system to rise to 1-1/e = 63.2% of the steady state value on the rising edge of a pulse, or the time it takes it to fall 1-1/e = 63.2% (to 36.8%) of the final value on the falling edge of a pulse. This information can be used to calculate the time constant from the waveform obtained.

NOTE: You are measuring the voltage across the capacitor directly, and the current through the capacitor indirectly, by measuring the voltage across the resistor. Recall that the current through a resistor is DIRECLY proportional to current, at ANY time. Therefore the voltage across the resistor is an accurate representation of the current through the capacitor over time (and the resistor, as they are in series).

b)RL CIRCUIT:

Build the circuit shown in Figure 2 on your breadboard. Use your myDAQ as the square wave source.Use the same calculation as the RC circuit.

Figure 2: RL circuit

Open the NI ELVIS oscilloscope, and set it up for dual channel acquisition (activate Channel 1 and Channel 2). Then make four connections to the board: Connect one channel to measure voltage across the resistor, and connect the other channel to measure voltage across the inductor.Record the waveforms obtained, as before.Determine the time constant from the waveform on the oscilloscope. Once again the voltage across the resistor accurately represents the current through the inductor.

c) RLC CIRCUIT:

Build the circuit shown in Figure 3 on your breadboard. Use your myDAQ as 5V source (connect to the 5V terminals, not the function generator).

Figure 3: RLC circuit

Deactivate one channel on the oscilloscope and connect the remaining channel to measure voltage across either the inductor or the capacitor. Since the behavior of this circuit is not periodic, it is necessary to obtain a single oscilloscope frame that is timed to obtain the desired underdamped response after the capacitor is discharged into the inductor, but before it is completely damped. To do this, you must:

  1. Stop the oscilloscope acquisition.
  2. Make these changes to the oscilloscope settings:
  3. Time/Div = 20 ms
  4. Volt/Div = 2V
  5. Acquisition = Single shot
  6. Charge the capacitor using pushbutton 1.
  7. Then, wait about three seconds, and start the single shot acquisition. Be sure and wait THREE seconds first!
  8. IMMEDIATELY press pushbutton 2 after starting the single acquisition. This will discharge the capacitor into the inductor. The time between the start of acquisition and the button press should be 1-2ms. It may take a few tries to accomplish this, but it is not difficult. Simply push the start button and IMMEDIATELY push pushbutton 2. It is best if one person does both, one with each hand.
  9. The scope should show 5 volts, then a sharp fall to 0V very close to the left side of the screen. If it is not close to the left side you must try again, starting from step 3. Once you have the fall to 0V very close to the left side of the screen, decrease the Time/Div setting one level at a time. This will zoom the scope toward the left side of the screen, and at some point the oscillation should become visible. If you wish you may attempt to use a different time division, such as 10ms, and the same operation applies. However, if you use a time division setting larger than 20ms you will not be able to zoom sufficiently to see the oscillation, and if you use one that is much smaller it will zoom too quickly toward the left side and the waveform will not be visible.

Determine the frequency of the oscillation from the displayed waveform. If you cannot do so you must acquire the waveform again. Once this can be done, record the waveforms obtained, as before. Also to record the approximate amplitude of each peak, and the approximate time that it takes reach steady state.

IV. Post-lab Report

In your lab report make sure you discuss the following:

a)Explain the behavior of an inductor and capacitor (with formulas for current and voltage for each).

b)Calculate the time constant or characteristic frequency for the circuits given in lab (from prelab).

c)Explain the characteristic behavior of RC, RL, and RLC circuits based on in-lab observations.

d)Explain the natural response of a circuit, and define underdamped, critically damped, and overdamped responses.

e)Record the formula for the characteristic response for each of the three circuits fabricated in lab.

f)On the graphs of voltage obtained in lab, indicate the time constant and steady state value for the RL and RC circuits, and indicate the time period of oscillation and settling time. Also explain what each graph represents (they are not both voltage only).