University of Pennsylvania
Department of Electrical and Systems Engineering
ESE 206: Electrical Circuits and Systems II - Lab
AC MEASUREMENTS - IMPEDANCE
I. Purpose and Equipment:
Purpose: Examine the frequency dependent behavior of R, L, and C impedances.
Equipment Required
1 - Fluke Digital Multimeter (with RMS function)
1 - HP33120A Function Generator
1 - HP54600B Oscilloscope
1 - RCL Meter (shared)
1 - Protoboard
1 - l kΩResistor
1 - 0.1 µF Capacitor
1 - 100 mH Inductor
II. Introduction:
The s-domain impedance can be expressed in the phasor domain by substituting jfor s. In the
sinusoidal steady state, the impedance of the three passive components varies with frequency according
to the following ideal relationships or models:
ZR = R
(1)
ZL = jL
ZC = 1/jC
(2)
(3)
In this laboratory exercise you will verify these element constraints by comparing the impedance
calculated from the relationships above, to the magnitude of the impedance calculated from the
measured voltage across and the current through the elements at different frequencies.
III. Pre-lab Assignment (Please note that all Pre-lab written (or computer) assignments are to be
completed (and/or printed) on paper separate from the lab notebook and handed in to the
instructor at the start of your Lab session); if you write the pre-lab down in your lab notebook you
should make a copy of it and hand the copy in at the start of the lab.:
1. Read Section 8.5 in the text (D. Irwin and R. M. Nelms).
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2. Prepare a table using an Excel Spreadsheet with thirteen columns, labeled Freq, vR, iR, |ZRmeas|,
|ZRtheo|, vC, i C, |Z Cmeas|, |ZCtheo|, vL, i L, |ZLmeas|, and |ZLtheo|. Fill in the first column, starting at a
frequency of 10 Hz. Enter the remaining frequencies in standard logarithmic frequency steps (1, 2, 5,
and 10) up to 100 kHz.
The meas subscript indicates the value is computed from the measured values of the voltage and current.
The subscript indicates the impedance is calculated from the appropriate equation, i.e. Eq. 1, 2 or 3,
depending on the circuit element. The vertical bars serve as a reminder that these measurements
represent the magnitude of the impedance, without regard to the phase angle between the current and
voltage.
3. Using Excel compute the values for |ZRtheo|, |ZCtheo| and |ZLtheo| at all the frequencies listed in the
table prepared in item (2) for the component values R = 1 k, C = 0.1 F and L = 100 mH. Print a copy
of the table for you to record your data during lab. Using Excel plot and print graphs of |ZRtheo|, |ZCtheo|
and |ZLtheo| with a logarithmic horizontal axis for frequency; for the magnitude of the impedances,
|ZCtheo| and |ZLtheo | use also a logarithmic scale.
4. Error Analysis (see also the write up on Data and Error Analysis):
Consider the following circuit, used to measure the voltage Vo. The resistors have a tolerance
of ±5% and the voltage source an accuracy of ±1%. In addition the voltmeter has an accuracy of
±1%. Determine the possible error (in V or mV) of the measured output voltage Vo.
R1=5k 
+
Vi=5V
R2=
10k 
Vo
-
IV. Experimental Procedure:
1. Prepare the circuit for measurement.
a. Use the RCL meter to measure and record the value of each of the elements. Also, measure and
record the series parasitic series resistance Rs of the inductor and parallel resistor of the capacitor.
-3-
.
A
Ammeter
Irms

Function
Generator

Vrms
-
-
Device
Under
Test
Vrms
Scope
.
Figure 1
b. Build the circuit of Figure 1. Put the 1 kΩ resistor in the circuit location indicated by the box labeled
Device Under Test.
c. Set the function generator to produce a 10 Hz sine wave. The amplitude of the signal produced by the
function generator should be set so that convenient scales on the ammeter (use the Fluke multimeter) and
the oscilloscope can be used.
2. Measure the impedances
As the frequency of the signal from the function generator is changed, the impedance equations for the
inductor and capacitor (Eqs. 2 and 3) predict that the current through and the voltage across these two
elements will also change. Freely adjust the ranges on the ammeter and the oscilloscope, and the
amplitude of the signal from the function generator so that signal levels are readily measured by the
ammeter and the oscilloscope.
a. Measure and record the current, Irms and the voltage Vrms. Adjust the input frequency to the next data
point. Use the frequency counter on the oscilloscope to verify that the frequency is correct, and then remeasure the current and voltage. Continue in this manner until the resistor v-i data is complete through
100 kHz.
b. Remove the resistor from the circuit, and insert the capacitor in its place. Fill in the data columns for
the capacitor current and voltage.
c. Replace the capacitor with the inductor. Use the 10x probe when measuring the voltage over
the inductor with the oscilloscope. Fill in the data columns for the inductor current and voltage.
V. Conclusion:
1. Plot the data:
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On one graph plot both the theoretical and the empirical (measured) impedance for all three elements.
Both axes should be logarithmic, with the frequency on the horizontal axis and the impedances on the
vertical axis.
To help identify the curves, set up the line format so that the theoretical curves are of one line type, or
color, and the empirical curves are of a different line type or color. Print out the graph. Clearly label
each curve and tape the sheet into your journal.
2. Questions to be Answered:
In part l a of Section IV Experimental Procedure you measured the parasitic resistance Rs of the
inductor. At what frequencies does this resistance create a significant difference between |ZLmeas| and
|ZLtheo|?
Can the calculated inductor impedance, |ZLtheo|, be corrected to eliminate the separation between the
plots of |ZLmeas| and |ZLtheo|? Discuss your answer. If the answer is yes, describe how you would
correct the estimate.
At very low and high frequencies, it is likely that the measured impedances of the inductor and capacitor
will deviate from the ideal theoretical impedance models in Eqs. 2 and 3. Suggest reasons for this
behavior.
Kenneth R. Laker
Revised 20 January 2003
Updated Jan. 16, 2006 (JVdS)