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EE319 Lab 1 - Instrument Familiarization
1. Introduction. This lab is designed to familiarize you with the capabilities and limitations of the equipment that
we will be using in the course. We will focus on the two most important pieces of test equipment:
A Hewlett-Packard function generator and arbitrary waveform generator that will be our primary source of stimulus
signals for circuits under test.
A Hewlett-Packard oscilloscope, which will be used to display the response of the circuit to the stimulus source.
Neither the function generator, nor the oscilloscope is an ideal device. The function generator has an output
impedance and hence cannot deliver a voltage waveform to the circuit independent of frequency and test circuit
configuration. The oscilloscope has input impedance that loads the circuit under test, by placing an undesired
impedance across the measurement points.
We also need to consider the effects of the wiring used to connect the instruments to the circuit under test. So-called
"50 ohm" coaxial cable usually is used for this purpose. At the frequencies at which most of our circuits will
operate, this coaxial cable, if used for "straight through" connections will behave as a capacitor is connected across
the instrument terminals. This capacitor between the connection points will shunt the impedance of the circuit under
test.
The power supplies of our instruments (and powered circuits) are connected to the ac power lines and the power
lines are connected to earth ground. Hence we must consider the effects of "sneak" current paths that may exist via
the instrument common ground connections.
2. Circuit Model. Below is a sketch of a circuit that will account adequately for the effects discussed above, at least
for the experiments that will be performed in this course. (The model is adequate whenever the physical dimensions
of the circuit are a small fraction of the wavelength of the highest frequency of interest.)
3. Circuit Parameters. Use the manufacturer's manuals and/or component catalogs to find values for each of the
components used in the instrument and interconnect models above.
4. Impedance vs. Frequency Computation. Select two pieces of coaxial cable with BNC connectors on one end
and alligator clips on the other and measure the length of each piece. Look up the coax capacitance per foot and use
the measured lengths to estimate the capacitance of each piece of cable. we will use one piece of cable to connect
the function generator to the circuit and the other to connect the circuit to the oscilloscope.
a. Use the manufacturer's circuit model for the function generator and the measured capacitance of the interconnect
coax to develop a Thevinen equivalent circuit for the source and cable. Then compute and plot the equivalent source
magnitude and output impedance versus frequency. Your frequencies should span the range where the capacitive
reactance is significant, i. e., where it varies from about ten times to one-tenth the size of the source output
resistance. (A spreadsheet program or MATLAB could be used here.)
Compute the capacitive reactance from the source "low" terminal to ground versus frequency in decade increments
from 1 Hz to 10 MHz.
b. Next, compute the input impedance to ground of the oscilloscope and its coaxial cable probe in decade increments
also ranging from 1 Hz to 10 MHz.
c. We can increase the input impedance of the oscilloscope by using "10x" probes to connect test points to the scope
inputs, instead of using pieces of coaxial cable. Look up the description of the 10x probes used with the laboratory
oscilloscope. Then sketch an equivalent circuit for the combination of probe and scope impedances and calculate the
input impedance from probe tip to ground in decade increments over the same frequency range as before.
5. The Binary Attenuator. Sketched below is an R-2R circuit commonly used in digital-to-analog converters.
Verify that the input impedance of the circuit is 2R ohms and that the voltage at successive nodes is one-half of the
voltage at the previous nodes.
For noise rejection, attenuator circuits, such as the one described above are often built as balanced networks, where
the series arm resistance is split into two equal components and inserted in both the upper and lower branches of the
circuit (see below).
Build an approximation to a balanced R-2R attenuator using 510 ohm, 1000 ohm, and 2000 ohm resistors. The
attenuator should have three attenuation values (approximately 1/2, 1/4, and 1/8). Then drive it with the function
generator, and measure and record attenuation vs. frequency at the 1/2 and 1/8 attenuation points. Use the scope and
the pre-measured piece of coax to connect to the attenuator.
Your frequency range should run from 1 Hz to 10 MHz with your frequency points concentrated where the
attenuation vs. frequency curve changes rapidly.
Repeat the experiment with the piece of coax replaced by a 10x probe (properly compensated).
Next, use the sum and difference capabilities of the scope to construct a balanced measurement connection to the
attenuator output and repeat the above. You will need another piece of coax. Try to select a piece equal in length to
the original one.
Again repeat the above, now using two 10x probes to measure the attenuation.
6. Results. In your write-up, explain in each case above, why attenuation is not constant with frequency. Are the
errors dominated by the source impedance, the scope impedance, the connecting cable, the source capacitance to
ground, or what? Justify your explanation by comparing your experimental results with analytical results based on
the equivalent circuit models extracted from the instrument manufacturer's manuals and supplemented by your
estimates of the cable or probe capacitance. Sketch the equivalent circuit for each interconnect arrangement (coax to
scope, one 10x probe to scope, two 10x probes with the scope connected in difference mode).