Exp. 1 USE OF BASIC ELECTRONIC MEASURING INSTRUMENTS, PART I
PURPOSE:
•
•
•
To become familiar with some of the instruments used in this and subsequent labs.
To develop proper laboratory procedures relative to collecting, recording, and analyzing data.
To clearly understand and differentiate between the accuracy of measurement (or instrument) and
the precision of measurement (or instrument).
This experiment relates to the following learning objectives of the course
1. Ability to interconnect equipment and devices such as multimeter, counters, and oscilloscope to
achieve required results.
2. Acquire practice in recording data and results and maintaining a proper engineering notebook.
3. Ability to analyze and evaluate data.
LAB EQUIPMENT:
HP/Agilent E3640A DC Power Supply
1
1
1
1
1
Decade Resistance Box
Agilent 34410A Digital Multimeter/Timer/Counter
Potentiometer (100Ω)
Resistive Circuit on Plexiglass Board
STUDENT PROVIDED EQUIPMENT:
1
2
2
Meter leads (one pair)
Pairs, long banana-to-banana leads
Pairs, short banana-to-banana leads
Experiment Sections:
1)
2)
3)
4)
Multimeter Resolution
Resistance Measurements
Verifications of Kirchhoff’s Circuit Laws
The Potentiometer
Section 1) Multimeter Resolution
In this section we learn about the “accuracy” and “precision” of a measurement from an
instrument (an Agilent 34401A multimeter in this case). Accuracy and precision are two important
concepts in measurement and we must tell them apart.
Accuracy1 is defined as the difference between the values obtained from measurement and the
real "true" value of a quantity. It can be expressed in absolute numbers, such as 5 mV, or in
relative numbers, such as 0.5%. In the former case, the measured voltage cannot be different
from the actual voltage by more than 5 mV, in the latter the measured voltage may be off from
the actual value by no more that 0.5%.
Precision (or Resolution) of a measurement is related to the smallest difference between the
measured values that can be distinguished. For example, if a voltmeter precision is 0.1 V we
1,
Partially adopted and edited from “Measurement Errors,” New Jersey Institute of Technology, ECE dept.
1
could measure the difference between 10.2 V and 10.3 V, but we would not be able to measure
10.24. However, just because an instrument has a finely divided scale on which we can read
numbers "precisely," as is the case for digital instruments, it does not necessarily mean that the
measurement is accurate. For instance the instrument may not be well calibrated. It is generally
true, however, that more accurate instruments are designed with finer scales or more digits in
their numerical display.
In considering the effect of an instrument’s precision on measurement errors, we are usually
concerned with relative rather than absolute numbers. An absolute error of 0.1 V for
measurement of a power line voltage of 117 V is very acceptable, since it gives a relative error
of 0.1/117 < 0.1 %. The same absolute error in the measurement of an amplifier output of 1 V
gives a large relative error of 10%.
a) Set the “Auto/Manual” key of the Agilent 34401A multimeter to Manual (“Man”).
b) Set the decade box dials to provide a resistance of 123Ω.
c) Measure and record the resistance of the decade as follows. For each number of digits (use the
shift key to select 4, 5, or 6 digits) displayed, observe (but don’t record) the effect of changing the
range of the display; then, choose the range that gives the best accuracy and record the complete
readout (i.e., all of the digits displayed). As will be seen below in the User’s Guide (i.e.,
“manual”), the “range” of the meter, for a given display setting, is expressed as the highest possible
readout of the form”1.00 …0”, “10.00 …0”, or “100.00 … 0” ( Ω, kΩ, or MΩ), with the total
number of 0’s being the “number of digits” displayed. .
e) Set the multimeter to autorange and measure and record the decade resistance again. Again, make
measurement for 4, 5, and 6 digits of precision
Questions: Section 1
1) Which is the most accurate measurement you made in parts c and d, and what is its accuracy (see
User’s Guide)? Note: In the User’s Guide, use the specification given for after 1 year of use. Also,
express your accuracy as both an absolute value (in ohms) and a relative value (in %), showing your
calculations.
2) Make a general statement about which meter resistance range should be used for maximum precision
and best accuracy. Assume the meter is not in the autoranging mode.
Section 2) Resistance measurements
a) In the lab notebook, set up a table with seven rows and five columns. The titles of the columns
should be as follows:
column 1:
column 2:
column 3:
column 4:
column 5:
Resistance range of meter scale presented
Resistance setting of the decade box
Measured value of decade resistance
Measured value of decade – measured meter lead resistance
% difference between nominal and measured resistance values
2
Seven different resistance measurements will be taken; thus, there should be room for at least seven
rows in the table. Note that seven is the minimum; you may take as many measurements as you
would like.
b) Set the Agilent 34401A multimeter to the manual (“Man”) position.
c) Set the meter on the lowest range and measure the resistance of the meter leads. Record the
measured value.
d) Set the decade box switches to provide resistance values of 1, 2, 5, 10, 20, 50, and 100Ω. At
each of these values, measure and record the resistance in the table you created. For each of
the decade box settings, verify that the meter provides the greatest resolution and record that
scale in the table.
Note: Since this experiment specifically addresses error calculations, state the formula by
which you calculated the percent difference. (Appearing in your formula should be the
variables Rmeasured, Rleads, and Rdecde box.) For future experiments, though, providing such a
formulas will not be necessary.
e) In the lab notebook, set up a table with seven rows and four columns. The titles of the
columns should be as follows:
column 1:
column 2:
column 3:
column 4:
Resistance setting of the decade box
Measured value of decade resistance
Measured value of decade minus meter lead resistance
% difference between nominal and measured resistance values
*Note: The table should include seven rows to accommodate the seven resistance measurements.
f) Repeat part d), but use the autoranging (not “man”).
Questions: Section 2
1) At what resistance setting of the decade box does it make little sense to include the resistance
of the meter leads in the % difference calculations? Hint: consider the relative magnitude of
the meter leads (which you can measure using the multimeter)
2) Compare the two tables of data. Does the multimeter’s autorange function change the
precision and accuracy of the measurements in any way?
3) Take a moment and list a few reasons why the measured decade resistances differed from the
decade box settings.
Section 3) Verification of Kirchhoff’s Circuits Laws
Recall that the Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL) state:
1. The algebraic sum of the currents into any junction point is zero.
2. The algebraic sum of the voltages around any closed path in the network is zero.
Now follow the procedure below:
a) Locate and obtain the plexiglass board which contains the 200Ω, 680Ω, and 1.2kΩ resistors.
3
b) Verify that the HP E3640A Power Supply (a.k.a. “Agilent E3640A Power Supply”) is turned
off. If not, switch the output ON/OFF key to OFF.
c) Connect the meter leads as shown in the circuit below. The positive terminal of the power
supply should be connected to the shared terminals of the 680Ω and 1.2kΩ resistors which is
not connected to the 200 Ω resistor (see diagram below). The negative terminal of the power
supply should be connected to one terminal of the 200Ω resistor, which is not connected to
the other two resistors.
+
10.0V
+
-
R2
R1
200Ω
-
V1
680Ω
R3
1.2kΩ
V2
-
+
d) Turn the power supply output key to the “ON” position.
e) HP E3640A DC Power Supply has 2 voltage ranges. The “Voltage Range” key can be set to
“High” or “Low.” At the “Low” range, the voltage range is 0-8V with a current limit range of
0-3A. At the “High” range, the voltage range is 0-20V with a current limit range of 0-1.5A.
The desired voltage can be obtained within the selected range by:
•
•
•
•
Setting the “Voltage/Current” key to Voltage.
Using the resolution selection Key (< >) to highlight the voltage display digit requiring
modification.
Using the Knob to adjust the voltage to the desired value.
Setting the “Voltage/Current” key to Current and following similar steps, the current
limit can be set to the desired value. Use the display/limit button to get “limit” flashing,
then use the knob and direction buttons to set each of the digits.
Adjust the voltage to 10V with a 1A current limit.
f) Set the current limit on the power supply to 20mA. Use the multimeter to measure the
voltage supplied to the circuit. Make sure the voltmeter is reading in the DC Volts mode.
g) Measure and record the voltage V1 and V2 and quickly verify that these two voltages add up
to the voltage provided by the power supply. If V1 + V2 does not equal VS, an error exists
within the circuit and/or the measurement. Correct the error before continuing. Record the
current being supplied by the power supply.
h) Turn off the power supply and disconnect the leads from the circuit.
i)
Measure the resistances on the circuit board and record their values. Note that only the
parallel combination of the 680Ω and 1.2kΩ resistors is accessible.
4
Questions: Section 3
1) Did KVL (Kirchhoff’s Voltage Law) hold for the above circuit? Explicitly show your results
and account for any differences.
2) Did KCL (Kirchhoff’s Current Law) hold for the above circuit? Explicitly show your results
and account for any differences. Note: You should specifically Ohm’s law to verify KCL at
the node where all three resistors meet.
3) Using the nominal resistance values, calculate the current you would have expected through
the 200Ω resistor when power was supplied to the circuit. Do not use the measured value for
this calculation. Compare this current value with the actual amount of current which flowed
through the resistor (use Ohm’s law). Why are these two values the same or different?
4) Could you have made the resistance measurements with power still connected to the circuit?
5) In step f) above, the “loaded” value of the voltage supplied by the meter was measured. Do
you think it might have been different if you first set the power supply to 10V and then
remeasured it after you “loaded” it with the circuit? You can verify your answer
experimentally (optional)!
Section 4) The Potentiometer (optional)
a) In your lab notebook, construct a table with five columns and with the following headings:
column 1:
column 2:
column 3:
column 4:
column 5:
Desired value of I
Measured value of V1
Measured value of V2
Calculated value of I
% difference between desired and measured (by calculation) current
b) Switch the power supply ON/OFF key to the OFF position.
c) Using nominal values for the decade resistances, construct the circuit shown below (do not
turn on the power supply yet).
500 Ω
+
V2 Potentiometer
5.0V
+
-
R2
I
100 Ω R1
+
10kΩ
V1
-
5
d) Switch the power supply ON/OFF key to the ON position and adjust its output voltage to 5V
(leave the current limit at 1A). Use the multimeter to measure the loaded supply voltage and
record the value of this voltage.
e) Adjust the pot so that I = 0.070mA. Do this by measuring the voltage V1 and applying
Ohm’s Law to the 10kΩ resistor. This may be a little tricky, but do the best you can (without
taking too long) to obtain the desired current. Record V1 and V2.
f) Without changing any other part of the circuit, repeat step e) for I = 0.059mA, 0.033mA, and
0.018mA. Record all of your results.
g) Turn off the power to the circuit.
h) Remove the decade resistances from the circuit and measure their resistances with the
multimeter. Record these values.
Questions: Section 4:
1) Both pots and decade boxes are forms of variable resistances. What is the major difference
between the two devices? (It is not the size or shape).
2) For each of the four current values in this section, use KVL to model the pot as two resistors.
Explicitly state the value of the two resistors for each current value.
3) Compare the R1 and R2 values calculated in question 2 above to the Pre-Lab values.
6