EE 212L: RC Time Constant, Square-waves and Probe
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
Pre-lab: Consider the RC circuit of Figure 5 shown below.
What is the theoretical time constant τ ("tau") for the
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
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.
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
Adjust your probe to be properly compensated before
Why would one choose to use a 10X probe versus one
without the built-in attenuation? (There are at least 3 possible
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
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.
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
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?
Measure the inductor provided in your kit. You'll need this value
for next week's lab.