Download DC Measurements Y1 Physics Lab 2016/17 V R A + - I V R A +

DC Measurements
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Y1 Physics Lab 2016/17
Aims of the experiment
To understand the basic principles of DC resistance measurements
To measure the current-voltage characteristic of a diode
To use a four-terminal measurement to determine the resistance of a piece of copper wire
To use a Wheatstone Bridge to study a thermistor and a load cell
Skills checklist
At the end of this experiment, check that you have mastered and understood the following:
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DC measurements of current, voltage and resistance
Using a myDAQ for voltage measurements and signal averaging
Extracting results by fitting experimental data to a theoretical model
Introduction
Figures 1a and 1b illustrate the basic principle for measuring an unknown resistance R in a DC
circuit using a voltmeter and an ammeter. An ideal voltmeter has an infinite resistance and therefore
draws no current from the circuit, whilst an ideal ammeter has zero resistance and hence there is no
voltage drop across it. For ideal meters, both circuits are equivalent. However, real voltmeters have
a finite input resistance RV (usually >1 MΩ and possibly much higher), whilst real ammeters have a
non-zero resistance RA. In fact, most ammeters work by measuring the voltage across a known
resistor (the ‘shunt’ resistor), which is connected internally across the ammeter’s input terminals.
The voltmeter and ammeter in figure 1 therefore present additional resistances RV and RA in parallel
or series with the unknown resistor R.
To minimize the effect of meter resistance, when the unknown resistor R << RV (the most common
situation), we use the circuit in figure 1a. In that case, the ammeter is excluded from the voltage
measurement, and the value of its resistance RA is not important. Moreover, the current through the
voltmeter is negligible (since RV >> R), so the ammeter measures the current flowing through R.
However, this approximation breaks down when R is very large: the current flowing through RV is
then no longer negligible. In that case, we use the circuit in figure 1b for measuring very high
resistances. With this circuit, current flowing through the voltmeter does not affect the ammeter
measurement, and, provided that RA << R, the voltage dropped across the ammeter is negligible.
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R
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R
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DC
Supply
DC
Supply
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Figure 1. (a) Circuit for low/medium resistance
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(b) Circuit for high resistance
Particular care must be taken when measuring low resistances or when we need to determine the
resistance R to very high accuracy. In that case, we must exclude the resistance of connecting leads
and solder joints from the measurement of R. Lord Kelvin devised an elegant solution to this
problem in the form of the four-terminal resistance measurement shown in figure 2. Here,
connecting wires are attached at A and B so that current I can flow through the sample. However, a
separate pair of voltage-sensing wires is also attached to the sample at C and D as shown. The
voltage between C and D is therefore not affected by resistance in either the current-carrying leads
or the joints at A and B. Moreover, the very high resistance of the voltmeter means that negligible
current flows through the voltage-sensing leads. Hence, the resistances of all the leads and solder
joints are excluded from the measurement. The voltmeter therefore reads the voltage V1 – V2
between C and D, and Ohm’s Law tells us that the resistance is R = (V1 – V2)/I.
V1
V2
A
B
I
C
D
R
I
Figure 2. Kelvin four-terminal resistance measurement
In practice, the current I through R in figures 1 and 2 is often determined by measuring the voltage
V0 across a known resistance R0 (using the 4-terminal technique for the most accurate
measurements). The current is therefore I = V0/R0, and R is then given by
R = (V1 − V2 ) I = R0 (V1 − V2 ) V0 .
(1)
This method is fine for determining an accurate value for the resistance R (e.g., for a platinum
resistance thermometer). However, we sometimes need to measure a very small resistance change.
In that case, we generally use the Wheatstone Bridge shown in figure 3. Here, we use a sensitive
voltmeter as a ‘null detector’. You should be able to show that the bridge is in balance (i.e., with no
voltage across the null detector) when
R1 R2 = R3 R4 .
(2)
A small change in any of the resistors produces a small out-of-balance voltage, which can then be
measured accurately by the sensitive null detector. (This voltage change would be too small to
measure in the presence of the much larger DC voltage across the resistor in figure 1.)
R3
R1
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DC
Supply
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R2
R4
Figure 3. Wheatstone Bridge
DC measurements may be affected by small offset voltages (e.g., thermoelectric emf’s). We can
take account of them either by reversing the current or by measuring the DC offset before applying
a measuring current (the usual choice for automated measurements).
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The National Instruments myDAQ
This experiment uses a National Instruments myDAQ in conjunction with a dedicated breadboard
(myProtoBoard), as shown in Figure 4. The NI myDAQ is specially designed for students to learn
electronics∗. It plugs into a PC via USB, and the myProtoBoard, in turn, plugs into the myDAQ.
Figure 4. NI myDAQ and myProtoBoard (photos by National Instruments)
The myDAQ is equipped with:
• 2 analogue-input channels (AI0 and AI1) for measuring voltages
• 2 analogue-output channels (AO0 and AO1) for producing voltages
• 8 digital channels for use as digital outputs (DIO0-DIO3) or inputs (DIO4-DIO7)
• 5V digital and ±15V analogue power supplies (with respective grounds DGND and AGND)
• Audio input and output channels
• A built-in digital multimeter (DMM)
The myDAQ is controlled by running a program to display a virtual instrument (VI) on a PC. NI
provide ready-made VIs that mimic benchtop test equipment, such as an oscilloscope, a function
generator, a DMM, etc. They are accessed through the ‘NI ELVISmx Instrument Launcher’ shown
in Figure 5a. (You can find it through the Start Menu inside the National Instruments folder.)
Figure 5b shows the ELVISmx oscilloscope.
Figure 5. (a) ELVISmx Instrument Launcher
(b) ELVISmx Oscilloscope
The myDAQ oscilloscope can measure voltages from DC to about 30 kHz. This is much lower than
the bandwidth of a real oscilloscope (typically 20 MHz or more), but it is fine for learning basic
electronics.
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As a student, you can buy your own myDAQ and software for home use from Studica at an academic discount.
SAFETY NOTE: The myDAQ must
not be used as a test instrument
connected to other mainspowered instruments or circuits:
only use it with circuits on the
myProtoBoard that are powered
by the myDAQ itself.
Figure 6 shows a plan view of the
myProtoBoard. On the right-hand side is an
ordinary piece of solderless breadboard. On
the left, is the black connector that plugs into
the myDAQ together with six white ‘quads’
that provide a row of four connections to each
myDAQ input and output. The quads group
together related channels (labelled by white
lettering on the green base) such as analogue
outputs (AO) and analogue inputs (AI).
Analogue-output channel 1 produces a signal
voltage between AO1 and AGND (analogue
ground or earth, which acts as the 0V
reference point in the circuit). In contrast,
analogue-input channel 1 measures the
difference in voltage between AI1+ and AI1-.
Figure 6. my Protoboard
(photo from Studica)
The differential voltage measurement is an extremely useful feature of the myDAQ’s analogueinput channels. You do not find this capability with an ordinary oscilloscope: it allows you to
measure the voltage across any component in the circuit (not just the voltage of one end of a
component relative to AGND). Also, the input resistance of a myDAQ analogue-input channel is
extremely high (>10 GΩ, compared to 1 MΩ for an oscilloscope). The analogue-input channel
therefore acts as an almost-ideal voltmeter.
Figure 7. myDAQ DMM: (a)DC Volts
(b) Resistance
Figure 7 shows the myDAQ’s built-in DMM, selected by ‘Digital Multimeter’ in the ELVISmx
Instrument Launcher. Just like a real multimeter, it can be used as a digital voltmeter (DVM) for
measuring DC voltages or as an ohmmeter for measuring resistance.
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Experiments
5.1
Diode Resistance (45 mins)
The circuit in figure 8 is a practical realization of the resistance-measuring circuit in figure 1a. Here,
a diode D1 replaces the unknown resistance R. The voltage across the diode is measured using
myDAQ analogue-input channel AI1 (connected differentially across the diode to measure the
voltage difference between AI1+ and AI1-). The current through the diode is determined by
measuring the voltage across resistor R0 (nominally 1 kΩ) using myDAQ analogue-input channel
AI0. Hence, R0 and AI0 play the role of the ammeter in figure 1a. The myDAQ also supplies a DC
voltage from analogue output AO0, with the current returning to the analogue ground AGND
(which acts as the 0V reference for the voltage measurements).
Your first task is to check the components using the myDAQ’s DMM:
• Connect the 1N4148 silicon diode in series with a 1 kΩ resistor on the myProtoBoard.
• Connect the red and black DMM leads across the diode (replacing AI1 in figure 8).
• Start the DMM by clicking ‘Digital Multimeter’ in the ELVISmx Instrument Launcher.
• Select the diode tester by pressing the diode symbol on the DMM front panel (see figure 7)
and clicking ‘Run’. The diode’s forward-bias voltage should be about 0.6 V.
• Now, connect the DMM across the (nominal) 1 kΩ resistor and measure its value R0 on the
2 kΩ ohmmeter range, as in figure 7b. We use R0 as a ‘standard resistor’ in this experiment.
(The myDAQ is calibrated to an accuracy of ±0.8%. In critical applications, we would use a
high-precision standard resistor as R0.)
• Stop the DMM (red button), close its window and disconnect the DMM leads.
Figure 8. Diode-resistance measurement
Now, investigate the diode resistance:
• Connect the diode and R0 to the myDAQ as shown in figure 8 via the quads on the
myProtoBoard.
• To reduce the likelihood of errors (and to help the demonstrators!) use orange, blue and
green wires (two of each colour) as shown.
• In the ELVISmx Instrument Launcher, click on ‘Oscilloscope’ to launch the VI shown in
figure 5b. Enable Channel 1 as well as Channel 0.
• Click on ‘DC Level’ in the ELVISmx Instrument Launcher to launch the VI shown in figure
8. Select channel AO0.
• Click ‘Run’ on the scope. In addition to the two traces, the scope displays the values of the
RMS voltage for each channel. In a DC experiment, the RMS value is the same as the DC
voltage. Hence you can use the scope here as a convenient two-channel DC voltmeter.
• Click ‘Start’ on the DC Level Output VI. When the DC level is 0V, the scope will show just
a small offset voltage and some noise (about 1 mV).
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Use the up/down arrows on the DC level to change the voltage from 0V to 1.5 V in steps of
0.3 V. Note down the readings for CH0 and CH1 at each bias voltage. (To save time, you
can take single measurements here.) Then press ‘Stop’ on both VIs and close their windows.
Construct a table to show current I and resistance R as a function of the bias voltage V across
the diode.
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5.2
Diode Current-Voltage Characteristic (45 mins)
The silicon diode is a nonlinear electrical device, i.e., its resistance varies with the applied voltage.
It is more useful to characterize such a device by its current-voltage (I-V) characteristic, as shown
in figure 9.
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Figure 9. I-V Characteristic for an ideal p-n junction diode
The current I through an ideal p-n junction diode at bias voltage V and absolute temperature T obeys
the Shockley equation:
(
I = I 0 eeV
kT
)
−1 ,
(3)
where e is the charge on the electron and k is Boltzmann’s constant. When it is forward biased, the
diode current increases exponentially with voltage, whilst a reverse bias (V << 0) produces only a
small ‘leakage current’ I0, as shown in figure 9. The diode therefore acts as a rectifier, as you have
seen in the Introduction to Electronics experiment.
We could plot the diode I-V characteristic by manually taking many point-by-point measurements.
However, it is better to get the myDAQ to take the measurements for us, as follows:
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Download the file myDAQ-DC-DiodeIV.vi from Canvas. Double click on this file to start
LabVIEW. (If they open, close LabVIEW’s context-help and Toolbox windows.) Click the
‘Data Acquisition’ tab and enter the value of R0 measured in the previous section in the first
text box. To start the VI, click the white arrow just below the menu bar (see Figure 10).
Figure 10. myDAQ-DC-DiodeIV.vi (Data Acquisition tab)
The left-hand graph in figure 10 shows a diode I-V characteristic similar to that in figure 9.
• Press ALT+PrintScreen to capture a screenshot of the VI.
• Open Windows Paint and paste the image from the clipboard.
• You can then print the image and stick it in your lab notebook.
(You can also right-click on the graph and select ‘Export’ to save a simplified image as a bitmap for
printing, and you can export the data to Excel for later analysis.)
The right-hand graph in figure 10 shows the data with the current plotted on a logarithmic scale.
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Why does the logarithmic plot produce almost a straight line? (Note that we generally use
straight-line plots wherever possible to compare experiment and theory.)
In semiconductor physics, we often represent the I-V characteristic of a real diode by an equation of
the form
(
I = I 0 e eV
nkT
)
−1 .
(4)
If n = 1, then the diode obeys the ideal Shockley equation in equation (3). We can use the
LabVIEW VI to determine the value of n for the 1N4148 silicon diode:
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Click on the ‘Data Analysis’ tab in the VI (see figure 11).
Figure 11. myDAQ-DC-DiodeIV.vi (Data Analysis tab)
LabVIEW fits the experimental data to a function of the form
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y = a1 e a2 x − 1 ,
(5)
where x represents the voltage V and y represents the current I. This equation has the same
functional form as equation (4) above. The main graph in figure 11 shows experimental data
(crosses) and the best-fit curve (red line). (The graph of residuals shows the small differences
between the data and the fitted curve.)
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Use the best-fit value of a1 (and its error) to determine the leakage current I0 (and its error)
for the 1N4148.
Use the best-fit value of a2 (and its error) to determine the value of n (and its error) in
equation (4) for the 1N4148. To find the absolute temperature T, you will need to measure
room temperature.
Does the 1N4148 obey the ideal Shockley equation? (Close the VI and LabVIEW to finish.)
If you have time, repeat the above measurements and analysis for a BAT43 Schottky diode,
which uses a metal-semiconductor junction (a ‘Schottky barrier’) instead of a p-n junction.
5.2
Four-terminal resistance measurement (1 hr 30 mins)
The myDAQ can also be used to measure a very small resistance (as small as 0.01 Ω) using the
four-terminal method shown in figure 12.
Figure 12. myDAQ four-terminal resistance measurement
You are provided with a sample of enamelled copper wire with a resistance of about 0.1 Ω. Two
jumper leads have been soldered to it to act as the voltage-sensing leads, as in figure 2.
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Insert the bare ends of the copper wire into the Protoboard to act as current leads for the
sample in figure 12, and connect a 1 kΩ resistor R0 in series as shown.
Use an orange jumper lead to connect the top end of R0 to the myDAQ analogue output
AO0 and a green lead to connect the lower end of the sample to AGND∗.
Connect the voltage-sensing leads on the sample to myDAQ analogue inputs AI1+ and AI1-,
and connect AI0+ and AI0- across R0. Sketch the circuit in your notebook.
Download the file myDAQ-DC-LowResistance.vi from Canvas and double-click the file to
start LabVIEW.
Click the ‘Data Acquisition’ tab and enter the value of R0 in the first text box. To start the
VI, click the white arrow just below the menu bar (see Figure 13).
Figure 13. myDAQ-DC-LowResistance.vi (Data Acquisition tab)
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For correct operation of the myDAQ’s analogue inputs, the low-resistance sample must be connected to AGND.
The I-V characteristic in figure 13 shows some random errors because the maximum voltage across
the copper wire is only ~0.2 mV (since the myDAQ analogue output delivers a maximum current of
2 mA). To improve the accuracy of the measurements, the myDAQ takes the average of 10,000
measurements (known as ‘oversampling’). The VI also measures the offset voltages for channels
AI0 and AI1 (typically < 1 mV) and subtracts them from the measurements. The text boxes at the
bottom of the VI display the average of 10,000 readings for the offset voltages together with their
standard deviation, which is due to a small amount of electrical noise in the system. The standard
deviation is an estimate of the accuracy that we could expect for a single reading.
• Take a screenshot and print it for your notebook.
• Write down the values for the offsets and their standard deviations.
• Estimate the accuracy that you would expect for AI1 averaged over 10,000 readings∗. (You
may need to consult the summary of statistical formulae in the Laboratory Manual.)
Figure 14 shows the Data Analysis tab for the myDAQ-DC-LowResistance VI. In this case, we
make an unweighted least-squares fit of the data to a straight line of the form
y = a1 x + a2 ,
(6)
where x now represents the current I and y represents the voltage V. The slope of this line, given by
the parameter a1, is the resistance R of the sample.
Figure 14. myDAQ-DC-LowResistance.vi (Data Analysis tab)
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Take a screenshot and print it for your notebook.
From the best-fit parameters, find R and the error on R.
Taking the copper wire to be of diameter 0.315 mm and length 50 cm between the voltagesensing leads, find the resistivity ρ of copper at room temperature.
Does your measured value of ρ agree with the standard value of 1.7 x 10-8 Ω m?
Note down the fitted value of a2 and its error. What is the significance of this parameter?
If you have time, repeat the measurement of R with only 10x oversampling and explain the
effect on the error.
Close the VI and LabVIEW.
Note that, by oversampling 10,000x in the presence of a small amount of noise, we can measure voltages more
accurately than the intrinsic resolution of the myDAQ’s analogue-input channels, which is about 60 µV.
5.3
Wheatstone Bridge (1 hr)
We now use the myDAQ to explore the operation of the Wheatstone Bridge circuit in figure 3,
connected as in figure 15. The myDAQ 5V supply provides DC power for the bridge, which is
connected at its bottom end to the myDAQ digital ground DGND. One arm of the bridge consists of
an unknown resistor R1 in series with a fixed 4.7 kΩ resistor as R2. We also choose R4 in the other
arm to be 4.7 kΩ, whilst a 10 kΩ multiturn potentiometer is used as a variable resistor for R3.
The myDAQ’s analogue-input channel AI1 acts as the null detector, and the bridge is balanced by
adjusting R3. Since R2 = R4, it follows from equation (2) that the balance condition is R1 = R3.
Figure 15. myDAQ Wheatstone Bridge circuit
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Start by using a 4.7 kΩ resistor for R1, as well as R2 and R4, on the myProtoBoard.
Insert the 10 kΩ potentiometer into the breadboard so that its three pins are in adjacent rows.
The central row is the wiper of the potentiometer. To use the potentiometer as R3 in figure
15, connect to the central row and one other row.
Connect AI1+ and AI1- from the myProtoBoard quads to the bridge using orange and blue
jumper leads.
Connect the myDAQ 5V supply and DGND to power the bridge, as shown in figure 15.
Start the myDAQ Oscilloscope from the ELVISmx Instrument Launcher, enable channel 1
and click ‘Run’.
Balance the bridge by adjusting R3 (with a small screwdriver) to make the voltage on CH1
as close to zero as possible. You should be able to increase the sensitivity of CH1 to the
maximum (10 mV/div).
Estimate how accurately you can balance the bridge using CH1 of the myDAQ oscilloscope.
Hence, estimate how small a change in resistance R1 you could measure with this bridge.
Now, replace R1 by a bead thermistor, whose nominal resistance at 25 °C is 4.7 kΩ.
Touch the thermistor briefly with your fingertip. How does this affect the voltage on CH1?
According to the manufacturer’s datasheet, the resistance of the thermistor decreases by
approximately 4.5% for a temperature increase of 1 K at room temperature. Estimate how
small a temperature change you could measure with this bridge.
How could you increase the sensitivity of the bridge?
5.4
Load-cell Wheatstone Bridge (time permitting)
Wheatstone bridges are also widely used inside digital balances. You are provided with a ‘load cell’
that is fitted with four thin-film strain gauges (of nominal resistance 1 kΩ) connected together to
form a Wheatstone bridge, as shown in figure 16 (on the next page). The load cell in figure 16a is
an aluminium-alloy bar, drilled with two large holes to make a ‘binocular beam’ that bends at its
centre under an applied load. The strain gauges R1 to R4 are glued tightly to either side of the load
cell to sense the bending: the resistances of R1 and R4 on one side of the bar increase and the
resistances of R2 and R3 on the other side decrease. Operating the four strain gauges in a bridge
configuration provides an out-of-balance voltage that is proportional to the applied load (up to 1 kg
in this case).
Since the strain gauges are already connected as a bridge, connecting the load cell’s four leads to
the myDAQ in figure 16b is very simple: Red = 5V, Black = DGND, Green = AI1+, White =
AI1-. This produces a circuit that is equivalent to the Wheatstone bridge in figure 3, with myDAQ
analogue input AI1 acting as the null detector.
Clamped
end
Figure 16.
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Load
R1
R4
R2
R3
(a) Load cell
(b) Strain-gauge bridge
Using the myDAQ oscilloscope, show that the bridge is approximately balanced at zero load.
Measure the out-of-balance signal produced by a 100 g load.
Allowing for the zero-load offset, what is the sensitivity of the bridge (in mV/kg)?
Using the myDAQ oscilloscope, how small a weight could you measure with this bridge?
(In practice, a digital balance uses a DC amplifier to amplify the out-of-balance voltage
~100x before it is measured by a microcontroller.)
Neil Thomas (September 2016)