### EE 212L: RC Time Constant, Square-waves and Probe Compensation

Objective: The purpose of this lab is to measure square-wave responses of an RC circuit to gain a better understanding of first-order circuits and time constants, and learn how to calibrate an oscilloscope probe.

Pre-lab: Consider the RC circuit of Figure 5 shown below.

1. What is the theoretical time constant τ ("tau") for the circuit?
2. Sketch one period of the output voltage vo on top of the input square-wave shown in Figure 1 when the input's period T is specified as
• T = 10 τ
• T = 1 τ
• T = τ / 10

3. Calculate the relationship between the 10% to 90% rise time (as shown in Figure 2 below), and the time constant τ for the circuit's step response. Hint: you'll need to solve for the step response of the circuit.

Laboratory Procedure:

1. Calibration and probe settings for the oscilloscope. A probe and its cable have an inherent resistance and capacitance that make the probe's behavior between the input (signal we wish to measure) and output (connection to oscilloscope) vary as a function of the signal's frequency. To enable more accurate measurements at low frequencies (say under 100kHz) probes come with an adjustable capacitor that can be used to match the inherent time constant of the probe and cable. It is good practice to calibrate your probe each time before use to ensure meaningful measurements.
• Display the 1kHz square-wave from the probe comp output of your oscilloscope as shown in Figure 3. Adjust the trigger, vertical scale and horizontal scale as needed to obtain a good view of a stable waveform.
• Measure the amplitude of the waveform with the scope probe in both the 1X and 10X positions. Note whether you adjusted the corresponding settings on the oscilloscope.
• Compensate the probe in the 10X position to by adjusting a small screw in the probe until the square wave is shown properly. Examples of measurements from under-, over- and properly compensated probes are shown in Figure 4 below.
Draw the shapes of your measured square wave when the probe is under-compensated and over-compensated.
• Why would one choose to use a 10X probe versus one without the built-in attenuation? (There are at least 3 possible reasons.)
2. Observe square waveforms using the oscilloscope and investigate effects of AC versus DC coupling.
• Set the frequency of your function generator to approximately 10 Hz and the waveform to a 5V peak-to-peak square-wave, and then a 5V peak-to-peak triangle-wave. Set up the oscilloscope to view these waveforms.
• Note and sketch differences for the two waveforms when the scope input is AC or DC coupled. Explain why the signal is degraded on AC coupling? Use DC coupling for the rest of this lab.
3. Measure rise time of a function generator square-wave.
• Set the frequency of a 5V peak-to-peak square-wave to 1MHz on the function generator and measure the rise-time of the square-wave (i.e., the time it takes to go from 10% to 90% of its final value while rising) using the oscilloscope by expanding the time base.
4. View and investigate RC circuit step responses.
• Construct the RC circuit shown in Figure 5 below on your breadboard and use your function generator to provide a 1V square-wave input vi for different periods (T = 10 τ, τ and τ / 10). Display both the input vi and output vo on the o-scope using Channels 1 and 2. Trigger on the rising edge of the input. Use the 10X probe and interpret your measurements accordingly.
• Sketch the output waveforms over a single period for signal input periods of T = 10 τ, τ and τ / 10. Label your axes. Explain the form of these plots and compare to your theoretical waveforms done in the prelab. For which pulse length does the output most resemble the input?
• For the input period T = 10 τ, the initial part of the waveform is equivalent to the step response of the circuit. Use the relationship obtained in the prelab to determine the time constant of this circuit by measuring the 10% to 90% rise time. Compare with the theoretical time constant.
• Repeat the previous two parts with the resistor and capacitor interchanged. Note this circuit setup can be thought of as similar to the AC coupling studied in part 1. Sketch the circuit, sketch the input and output waveforms as the input period is varied, and answer the following questions:
• For which pulse length does the output most resemble the input?
• Why does the output waveform go above the maximum and below the minimum values of the square-wave?
• Why isn't the output amplitude constant?
5. Measure the inductor provided in your kit. You'll need this value for next week's lab.