INDIANA UNIVERSITY, DEPT. OF PHYSICS, P400/540 LABORATORY
FALL 2008
Laboratory #2: Voltage divider, oscilloscope, capacitors, RC circuits, and
filters
Goal: Get some practice with voltage dividers, the oscilloscope and capacitors;
Use and measure the behavior of capacitors in RC circuits and applications such as highand low-pass filters.
1. Voltage Divider
+5 V
10k
V
10k
Vout
Gnd.
Construct the voltage divider shown above. Apply Vin = +5 V (use the fixed DC
voltage on the breadboard). Measure the (open circuit) output voltage Vout. Then attach a
10k load and see what happens.
Now measure the short circuit current. This means "short the output to ground,
but make the current flow through your ammeter. Don't worry: in this case the "short" will
only cause a modest amount of current.
From Ishort-circuit and Vopen-circuit you can now calculate the Thevenin equivalent
circuit.
Now build the Thevenin equivalent circuit, using the variable "+V" DC supply as
the voltage source, and check that its open circuit voltage and short circuit current match
those of the circuit that it models. Then attach a 10k load, just as you did with the original
voltage divider, to see if it behaves identically.
2. Getting familiar with the oscilloscope
We will be using the oscilloscope ("scope") in many labs from now on, so you
should become familiar with its operation.
You can also become familiar with the function generator on the breadboard that
puts out time-varying voltage waveforms: sine waves, triangle waves, and square
waves. Generate a ~1000 Hz sine wave with the function generator and display it on the
scope. Connect to the terminal of the scope using coaxial cables to the coaxial inputs of
the breadboard (ask me if you don't know what "coaxial" means).
Play with the scope's sweep and trigger controls. Specifically, try the following:
o
o
o
The vertical gain knob. This controls "volts/div"; note that "div" or
"division" refers to the centimeter marks on the screen, not the tiny 0.2 cm
hash marks.
The horizontal sweep speed selector: time per division (make sure the
knob is in its CAL position, not VAR or "variable".)
The trigger controls. Don't feel dumb if you have a hard time getting the
scope to trigger properly. Triggering is by far the subtlest part of scope
operation. Beware of the tempting so-called "normal" settings (usually
labeled "NORM"). They rarely help, and instead cause much misery when
misapplied. "AUTO" is almost always the better choice.
Switch the function generator to square waves and use the scope to estimate the
"risetime" of the square wave (defined as the time to pass from 10% to 90% of its full
amplitude). It may appear to rise instantaneously, but zoom in using the time per division
controls.
Set the function generator to some frequency in the middle of its range, and then
try to make an accurate frequency measurement with the scope. Directly, you measure
period of course, not frequency, i.e., f = 1/T.
3. AC Voltage Divider
How would the analysis of the voltage divider be affected by an input voltage that
changes with time (i.e., an input signal)? Hook up the voltage divider from section 5, and
see what it does to a 1 kHz sine wave, comparing input and output signals.
10k
1 kHz
Sine Wave
Signal
10k
Vout
Explain in detail, to your own satisfaction, why the divider acts as it does.
4. RC Circuit
Build the circuit below and verify that it behaves in the time domain as expected.
Drive the circuit with a 500 Hz square wave from the external (Agilent) function
generator and look at the output with the oscilloscope. Be sure to use the scope's DC
input setting.(Aside, how to set up the scope for this: (i) Hit "CH1 Menu" button close to
CH1 control knobs. (ii) The column of buttons to the right of the screen control various
aspects. Select "DC" for the "Coupling" option. (iii) To initially set up, set "Coupling" to
"Gnd", i.e., it will ground CH1. Now move the flat trace vertically up and down until it lies
on top of the x-axis – this establishes your zero voltage level. (iv) Go back to "DC"
coupling.)
R = 10k
Input
Output
C = 0.01 µF
Measure the time constant by determining the time for the output to drop to 37%.
Does it equal the product RC?
Measure the time to climb from 0% to 63%. Is it the same as the time to fall to
37%? Check what happens if you vary the frequency of the square wave.
5. RC Differentiator
C = 100 pF
Input
Output
R = 100 Ω
Construct the RC differentiator shown above. Drive it with a square wave at
100 kHz using the function generator on the breadboard. Does the output make sense?
(sketch it) Try a 100 kHz sawtooth (ramp) wave. Try a sine. Again, does the output make
sense in terms of what the circuit should be doing?
6. RC Integrator
R = 10k
Input
Output
C = 0.01 µF
Now construct the integrator above (hmmmm, seen this one before, but we will
be driving it in a different frequency regime). Drive it with a 100 kHz square wave at
maximum output level and sketch the result.
Drive it with a sawtooth wave at the same frequency. What is the output
waveform called? Does it make sense?
To expose this only as an approximate or conditional integrator, try dropping the
input frequency. Are we violating the condition (see text and notes) that Vout<<Vin?
When we work with operational amplifiers later, we will see how to make "perfect"
differentiators and integrators that let us lift the restrictions we place on these RC
versions.
7. RC Low-pass Filter
R = 15k
Input
Output
C = 0.01 µF
Construct the low-pass filter shown above. What do you calculate to be the filter's
–3dB frequency? (Reminder: f3dB = f-3dB = 1/(2πRC)). Drive the circuit with a sine wave,
varying the frequency over a large range to observe its low-pass property. The 1 kHz
and 10 kHz frequency ranges should be most useful.
Find f3dB experimentally, i.e., use the scope to find the peak (or peak-to-peak)
amplitude of the input and the peak (or peak-to-peak) amplitude of the output. Measure
the frequency at which the filter attenuates by 3 dB (Vout down to 70.7% of full
amplitude). Make a table and linear-linear plot of Vout/Vin vs. frequency (and at least use
frequencies approximately those of 0.25f3dB, 0.5f3dB, 2f3dB, 4f3dB, 10f3dB, 20f3dB, etc.)
Now make your own Bode plot by plotting it on log-log scale (use provided paper,
or else feel free to use your favorite computer plotting application, frequency on
horizontal scale, Vout/Vin on vertical scale) to demonstrate the rolloff behavior at high
frequencies.
8. RC High-pass Filter
C = 0.01 µF
Input
Output
R = 15k
Using the same components, construct the high-pass filter shown above. Where
is this filter's –3dB point? Check out how the circuit treats sine waves: check to see if the
output amplitude at low frequencies (well below the –3 dB point) is proportional to
frequency.