# Step 1

- Construct the circuit showing in the diagram below:

- Here is a picture of the testbench setup:

- And here is a more detailed picture of the circuit on the breadboard:

# Step 2

- Connect Channel 1 of the oscilloscope to node A of the circuit and Channel 2 to node B, as shown in the diagram below:

- Set the function generator to rectangular wave mode with amplitude of about 2V and frequency of about 30kHz.

- Set Channel 1 and Channel 2 of the oscilloscope to DC coupling and 1V/div.

- Configure the trigger function to Auto mode, trigger on rising edge, source Channel 1, and adjust the trigger level to be within the range of Channel 1 waveform.

- Configure the built-in Math function of the oscilloscope to display Ch1 - Ch2 with 2V/div.

- The oscilloscope should display similar waveforms as shown in the screenshot below:

- Channel 1 (yellow trace) represents the output signal of the functions generator (node A). When this signal is high (at around 2V level) electric current flows through R1=1k and L1=1mH. This current can be determined using Ohm's law from the voltage drop on R1, which is measured by the Math trace (red trace).

- Immediately when the voltage at node A increases from zero to 2V these is no current flowing through the inductor and the voltage on the inductor (blue trace) follows Node A voltage.

- Then current starts flowing through the inductor (red trace) and settles to a value close to V(Node_A)/R1, since the resistance of the inductor is very low (we can approximate it to zero). As current starts flowing through the inductor the voltage o the inductor (Node B) starts decreasing towards zero.

- Insert a screenshot of the oscilloscope waveforms in this step.

- Why during discharge the voltage on the inductor becomes momentarily negative?

# Step 3

- Use the built-in cursor functions of the oscilloscope to measure the time constant of the current variation through the inductor during the charging phase, as shown in the screenshot below:

- In the example shown above cursor 1 has been placed at the beginning of the charging phase and cursor 2 has been placed so that delta V = 1.48V, which is close to 0.707*2.12V amplitude. The voltage of the Math trace can be translated into current through the inductor using Ohm's law as I = V_Math(t)/R1. This With these settings, delta T = 1.36us represents the time constant of the circuit, which theoretically should be equal to L/R. If we divide T=1mH / R=1kOhms = 10us; however, notice that the measured value is larger = 1.36us. The difference comes from additional inductance of the wires used in this circuit setup and from the variation of the L1 inductance and R1 resistance from the nominal values.

- Insert a screenshot of the oscilloscope displayed waveforms and cursor readings.

- From the delta V and delta T measurements in your experiment determine the measured time constant of the circuit.

- Calculate the time constant and compare the result with the measured value. Comment on any discrepancy between calculated and measured values.

# Step 4

- Construct the circuit showing in the diagram below:

- This circuit is derived from the previous one by adding a switch and replacing the function generator with a power supply. Here is a picture of the testbench setup:

- And here is a more detailed picture of the circuit on the breadboard:

# Step 5

- Connect Channel 1 of the oscilloscope to node A of the circuit and Channel 2 to node B, as shown in the diagram below:

- Set the power supply to 5V

- Set Channel 1 of the oscilloscope to DC coupling and 1V/div

- Set Channel 2 of the oscilloscope to DC coupling and 2V/div

- Configure the trigger function to Normal mode, trigger on rising edge, source Channel 2, and adjust the trigger level to about 2V.

- Configure the built-in Math function of the oscilloscope to display Ch1 - Ch2 with 2V/div.

- Set the timebase of the oscilloscope to 25us/div.

- Set the oscilloscope to single acquisition by pressing the "Single" button on the front panel.

- With these settings the oscilloscope will wait for a trigger event to happen and then it will acquire the signals and display them on the screen. The trigger event here is the rising of the voltage on node B after releasing the push-down switch.

- Push down the switch to close the electric circuit and hold it pushed.

- Release the switch. The voltage on node B increases quickly activating the trigger of the oscilloscope which displays a waveform similar to the one in the screenshot below. Notice that the timebase was set to 25us/div; you will need to magnify the timebase to 5us/div after the acquisition completes and the oscilloscope displays the waveforms.

- When the switch is pushed down electric current flows through the circuit resulting in almost zero volts at node B (blue trace in the first half of the screenshot above). The current can be determined using Ohm's law from the voltage drop on R1, which is measured by the Math trace (red trace), in this example I = 5.28V/1kOhm = 5.28mA. The energy stored by this inductor can be calculated as: W = 1/2 * L * I^2 = 1/2 * 1mH * (5.28mA)^2.

- Due to this current, energy is stored in the inductor during this time.

- After we release the push-down switch the electric circuit becomes open and current stops flowing. At this moment the energy stored in the inductor is released and it makes the voltage at node B increase above the power supply level of 5V. Due to parasitic capacitance and resistance in the electric path of the circuit and power supply the released energy generates resonance ringing as seen in the second half of the screenshot above. The ringing settles after all the energy stored in the inductor is dissipated, and the voltage at node B settles to 5V.

- Insert a screenshot of the waveforms measured in this step.

- Calculate the current flowing through the inductor during the time the switch is closed.

- From the value of the current calculate the energy stored in the inductor.