Chapter 5
RC and RL First-Order Circuits

m5.4 Response of the RL Circuit

The circuit of Figure m5.4 demonstrates how an inductor can produce a high-voltage pulse across a load resistance Rload that is considerably higher than the circuit’s power supply V batt, a 1.5-V “AA” battery. High-voltage pulses drive photo flash bulbs, strobe lights, and cardiac defibrillators, as examples.

Resistor Rs models the finite resistance of an electronic analog switch and Rw models the finite winding resistance of the inductor. Component values are: Rs = 16 Ω, Rw = 90 Ω, Rload = 680 Ω, L = 33 mH, and V batt = 1.5 V.

  1. Determine the load voltage v after the switch had been closed for a long time.
  2. Determine the equation that describes v(t) after the switch opens at time t = 0.
  3. Determine the magnitude of the peak value of v(t). How many times larger is this value compared to the battery voltage V batt?
  4. State the value of the circuit time constant τ with the switch open. Plot v(t) over the time range -τ ≤ t ≤ 5τ.

PIC


Figure m5.4: Circuit for Problem m5.4

NI Multisim Measurements

  1. Enter the circuit of Figure m5.4. Use the interactive switch SPST (single pole, single throw) and a measurement probe to determine v with the switch closed for a long time.
  2. Connect the oscilloscope to monitor the voltage v(t). Run interactive simulation, adjusting the oscilloscope settings to make the waveform fill a reasonable amount of the available display in both the vertical and horizontal directions. Use edge triggering and the “Normal” triggering mode to capture the transient when the switch opens. You may wish to decrease the time step size of interactive simulation to achieve higher resolution; see the tutorial video linked at the end of this section.
  3. Use the oscilloscope cursor to measure the magnitude of the peak value of v(t).
  4. Measure the time constant using the half-life technique described in Figure E.1 in Appendix E.
NI Multisim video tutorials:

NI myDAQ Measurements

  1. Construct the circuit of Figure m5.4 using the normally-closed Switch 2 contained in the Intersil DG413 quad analog switch described in Appendix D. Refer to the pinout diagram of Figure D.1 and connect power according to the photograph of Figure D.2. Do not place actual resistors for Rs and Rw because these simply model the finite resistance of the analog switch and inductor winding resistance. Create the 1.5 volt source with the LM317 variable voltage circuit of Figure B.2 in Appendix B and connect it to the DG413 “Source (Input)” terminal; connect the “Drain (Output)” terminal to the inductor.

    Establish the following myDAQ signal connections to the DG413:

    Use the NI ELVISmx Digital Writer (“DigOut” on the NI ELVISmx Instrument Launcher) to operate DIO0 as an output. Toggle the button for Line 0 to operate the analog switch. Use the NI ELVISmx DMM voltmeter to measure v when the switch is closed.

  2. Change the switch control voltage to AO0, Analog Output 0. Create the switch control voltage with the NI ELVISmx Function Generator. Choose the squarewave shape and adjust the amplitude and offset to make the squarewave swing between 0 and 5 volts. Observe this waveform on the oscilloscope to confirm your correct setup before you connect it to the analog switch.

    Adjust the NI ELVISmx Oscilloscope settings to display the voltage v(t) so that the waveform fills a reasonable amount of the available display. Use a combination of edge triggering and the “Horizontal Position” control. You may find it helpful to set the “Acquisition Mode” to “Run Once” and then click the “Run” button repeatedly until you capture a good trace. Alternatively, try increasing the squarewave frequency to keep the oscilloscope from timing out; a squarewave frequency of about (5τ)-1 Hz allows the voltage transient to reach its final value before the switch closes again.

  3. Use the oscilloscope display cursors to measure the magnitude of the peak value of v(t).
  4. Measure the time constant using the half-life technique described in Figure E.1 in Appendix E.
NI myDAQ video tutorials:

Further Exploration with NI myDAQ

The switch model resistance Rs and the inductor winding resistance Rw values used in the circuit of Figure m5.4 were based on measurements taken with actual equipment, but may not necessarily match the values for your devices.

Measure the on-resistance of your analog switch and also measure the resistance of your inductor. Recalculate your theoretical time constant value using your measurements. Report the degree to which you see closer agreement between your theoretical and measured values for the time constant τ.