ELEC 226, Spring 2003
Prof. Rich Kozick
RC Circuits, Time Constants, and an Oscillator
In this lab, we will begin with an exercise with RC
circuits and time constants. You will learn how to use the
oscilloscopes to capture transient events and measure the time
constant. Then we will analyze and build an "astable multivibrator"
or clock circuit using a 741 op amp. The circuit output will be a
square wave and a triangle wave, and the frequency of the wave can be
adjusted by changing the resistor and capacitor values in the circuit.
RC Circuits and Time Constants:
We will work with the RC circuit in Figure 1. The purpose of the
Rs resistor is to prevent a surge of current into the
capacitor when the switch is closed. We will use
C = 1 micro F and Vs = 12 volts.
Please answer the following questions in your lab notebooks.
These answers should not take very long, since we have discussed this
in class recently.
- If the switch has been closed for a long time so that the
capacitor is fully charged, what is the voltage v(t) across the
- Suppose that the switch opens at time t = 0 seconds. Analyze the
circuit and find an equation describing the voltage v(t).
- What is the time constant for this circuit, in terms of
Rs, R, and C? Make a sketch of v(t), indicating the value
of v(t) after 1, 2, 3, 4, and 5 time constants.
- You should be able to see from your plot where the following two
facts and "rules of thumb" about time constants come from:
- The response decays to 36.8% of its original value after one time
- The response has decayed to "zero" after 5 time constants,
since the amplitude is less than 1% of the original value.
- What value of R should be used to obtain a time constant of 1
Please choose R to achieve a time constant of approximately 1 msec,
and choose Rs so that most of the 12 volts appears across the R-C
parallel combination when the switch is closed. Consider the case of
opening the switch at time t = 0. We will use the oscilloscope to
measure the time constant of the circuit.
Please set up the circuit in Figure 1 on your protoboard. The lab
assistant and I will help you to use the scopes in order to measure
the time constant. Record notes in your lab notebook so you can refer
to them in the future when we use the scopes.
An outline of the procedure that you can use to measure the time
constant is as follows.
As you know, the scopes are digital instruments, so they
can be programmed to perform a lot of useful functions. The steps
below allow a single "trace" of the capacitor discharge to be
displayed on the oscilloscope. Measurements can then be performed on
- Adjust the horizontal (time) axis scaling and the vertical
(voltage) scaling to values that are appropriate for the value of
Vs and the time constant.
- Open and close the switch a few times. Make sure the v(t) you
observe on the scope matches the sketch you made earlier.
- Use the MODE key on the scope to set it to record a single trace
when you open the switch. Also set the scope to trigger at a level
just below v(0), and set the scope to trigger on a negative slope.
- Use the STOP, RUN, and ERASE keys to record a trace of v(t) after
you open the switch.
- Use the cursors on the oscilloscope screen to measure and compute
the time constant. If you use the "%" option in a clever way, then
you can get the scope to do all the computations for you in checking
the time constant.
Below are some specific activities and measurements to make.
- Measure the time constant of the circuit using the oscilloscope.
Compare the measured value with the expected value based on the R and
C component values.
- Consider the case in which the switch is initially opened and
then closed to charge the capacitor.
Use the oscilloscope to capture one trace of the charging capacitor.
Note that the procedure needs to be modified slightly to capture
- Modify the circuit to achieve a time constant on the order of one
second. Use the oscilloscope to verify that the time constant is
indeed about one second.
Op Amp Clock Circuit:
Look at the circuits in (a) and (b) of Figure 2.
How will each circuit operate?
Which one will oscillate?
How is the period (or frequency) of oscillation related to the
R and C values?
Please note that the circuits may not be connected with
negative feedback, so consider whether the op amps are saturated.
Perform the following activities.
- Please sketch on a single plot the capacitor voltage
vc(t) and the op amp output voltage vout(t)
versus time for the oscillator circuit. How is the period of the
wave related to the values of R and C?
What value should you choose for the resistor Ra? Why? If R is a
potentiometer that varies from 0 ohms to 100 k ohms, what value of C
should you use to produce a clock frequency as low as 1000 hertz? How
can you modify the circuit to produce clock frequencies in the range
from 100 to 1000 hertz?
Set up and test your circuit. Demonstrate how the frequency of your
clock circuit varies as you change the potentiometer. Observe both
vc(t) and vout(t) on the oscilloscope.
What if the pair of resistors with value Ra are replaced by
resistors with values that are not identical? Can you make a triangle
wave generation circuit? Try it!!