LABORATORY AUTOMATION: DECAY OF A CAPACITOR
Purpose:
As an introduction to laboratory automation, the decay constant of
an RC circuit is measured using an IBM-PC computer. The computer
is programmed using the graphical language LabVIEW to control the
experiment, gather the data, and analyze the data.
References:
Using LabVIEW videotape, National Instruments, Austin, TX, 1996.
LabVIEW Tutorial Manual, National Instruments, Austin, TX, 1996.
(Refer to the other LabVIEW manuals as needed.)
Introduction:
Figure 1 illustrates the general idea of the experiment. When the
switch is in position 1, a power supply with internal resistance Ri
and emf E charges a capacitor C in series with a resistance R.
When the switch is set to position 2, the capacitor is discharged
through the resistor R. Rather than switching manually or
switching via a relay (a relatively slow device), a transistor
switch is employed. The transistor circuit (already constructed
for you) is illustrated in Figure 2. The transistor switch
position can be controlled by the computer’s logic. When a
2
A potential difference of 0 volts (logical False) is applied via
the digital output of the computer to the circuit, transistor A is
turned off and B is turned on. Logical False means that the
integer number zero is loaded into the register that controls the
transistor switch. Current then flows through the RC network,
charging the capacitor. When +3.5 volts (logical True) is applied
to the transistor circuit, the switching reverses causing current
to flow through the setup resistor to discharge the capacitor.
The decay of the voltage of this circuit during a discharge cycle
is exponential. An equivalent circuit for the network consists of
a resistor and a capacitor in series in a single loop. It follows
from Kirchhoff's second rule that IR + q/C = 0, where q is the
charge on the capacitor. Differentiating with respect to time,
one obtains R(dI/dt) + (dq/dt)/C = 0. Since dq/dt = I, then dI/dt
+I/RC = 0. Rearranging, dI/I = -dt/RC. Integrating yields I =
Ioexp(-t/RC). Using V = IR, we have V = Voexp(-t/RC). RC is often
called the time constant of the discharge circuit.
Experimental:
1. Programming with the Windows95 version of LabVIEW is presented
in the tutorial manual and the videotape. View the videotape
before coming to lab with the goal of obtaining an overview of
LabVIEW. During the first afternoon of the experiment, work
through the exercises in the first five chapters of the tutorial
manual. You can be selective with the material in the later
chapters. Let you use of the tutorial be guided by the tools
which you need to construct your virtual instrument. A list is
given below.
2. During the second afternoon, develop a LabVIEW virtual
instrument which accomplishes the following tasks:
a) charge the capacitor for ca. 5 seconds,
b) discharge the capacitor and measure the voltage across the
network as a function of time for several half lives,
c) determine the value of the RC constant and associated
statistics using linear regression,
d) plot the decay curve with axes on the monitor screen.
Change the color of the background so that it is a light
pastel color rather than black. You may need to change the
color of the line so that it is visible.
Please save your .vi file and your other work on a diskette that
you provide rather than on the hard drive.
3. Before you run the program, check the circuit connections.
electrical leads should be connected as follows:
The
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computer in:
cell:
power supply:
2-lead cable to the inputs on the connector
block for bit zero of the computer digital I/O
2-lead cable to the inputs on the connector
block for channel 0 of the ADC
2-lead cable to HP-6261a power supply
4. Turn on the power supply and the box with the circuit and the
transistor switch.
5. Set the voltage on the HP-6261A power supply to ca. 4.5 volts.
Do not exceed 5 volts. The Meter Selection switch MUST be in the
Volts position and NOT in the mA position. When the power supply
is configured as a current supply (i.e. in the mA position) rather
than as a power supply (in the Volts position), the voltage
required to deliver the selected current may be sufficiently high
to damage the acquisition board in the PC.
6. During the development phase of the experiment, you may wish to
use the Fluke multimeter to measure the voltage across the
capacitor. The multimeter will give you a quick indication of
whether you are charging or discharging the capacitor. However,
during your production runs, remove the multimeter leads as they
might change the RC constant of the circuit.
6. Once you have a functional program, use it to explore the art
of data sampling and experimental design. Normally one samples a
decaying waveform over 2-4 half lives. Note that the value RC and
the half life are related by the equation  = RC(ln 2). If the
sampling period is too short, the data will appear linear
irrespective of the actual relationship between voltage and time.
Recall that according to the Taylor theorem of calculus, any
continuous function will appear linear over a small interval. In
contrast, if the sampling period is excessively long, the dataset
is dominated by very small voltages that are heavily contaminated
by error and a biased value of RC will be obtained. This sinister
source of systematic error whereby one region of the dynamic range
(low voltages in this case) receives excessive weight is referred
to as stratified sampling. Use your program to explore the
dependence of RC on the measurement period (short, medium, and
long) and on the voltage output of the HP power supply. (Short,
medium and long are defined by the ratio of the actual sampling
period to the half life of the decay. Make multiple runs at two
acceptable sampling periods, e.g. two half lives and three half
lives. Calculate the mean value of RC and the 95% confidence
interval of the mean. Repeat the measurements at a different
setting of the power supply.
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Hardware Description and Programming Hints
The apparatus is interfaced to a National Instruments Lab PC+ DAQ
(digital acquisitions) board which is installed in slot 3 of the
PC bus. Windows95 assigned a DMA (direct memory access) channel
1, an IRQ (interrupt request) channel 5, and a base I/O address of
hex 140 to the device. You will not use these numbers in your
program. They are provided here in case the computer or the
interface card need to be replaced.
You will need the LabVIEW configuration data for the interface.
The LabVIEW device number for the card is 1 (one). The board has
one 12-bit analogue-to-digital converter (ADC) with 4 variablegain channels in differential mode, two 12-bit 5 V digital-toanalogue converters (DAC), a versatile clock, and digital
input/ouput (I/O). The DAC is also bipolar, i.e. the voltage
range is V Volts where the value of V depends on the gain
setting. The voltage range of the DAC without amplification is 5
V. The leads from the capacitor are connected to inputs 1 and 11
of the connector block which are assigned to channel 0 (zero) of
the ADC. The leads controlling the transistor switch are
connected to inputs 14 and 13 of the connector block which are
assigned to bit 0 (zero), port 0 (zero) of the digital I/O and
digital ground, respectively. You will address the digital I/O
device twice in the program, first to initiate charging and later
to initiate discharge. The device only needs to be configured
prior to the first use (i.e. set the Iteration parameter to 0
(zero)) and not on the second use (i.e. set the Iteration
parameter to 1 (one)).
With the aid of the Controls pallete, create a virtual instrument
panel with inputs for the acquisition rate and the number of
acquisitions and a graphical display of Voltage versus time. You
may wish to add other bells and whistles to your virtual machine.
To construct your diagram, you will use the following LabVIEW
ikons which are found via the Functions palette. The name, path,
and use of these ikons are summarized below.
path and name
Data Acquisition
Digital I/O
Write to Digital Line
function
configuring and controlling the
digital output of bit zero of
the digital I/O
Data Acquisition
Analogue Input
AI Acquire Waveform
configuring the ADC and
measuring Voltage at a
predetermined rate
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Structures
Sequence
performing the steps of the
experiment (charge, initiation
of discharge, measurement and
analysis)in a set order, one
frame per step
Structures
For Loop
generating an array of the times
at which the Voltage is measured
Analysis
Fit
Exponential Fit
fitting an arrays of Voltage and
to an exponential function and
calculating the RC constant
Time and Dialogue
Wait(ms)
determining the charging period
of the capacitor
Cluster
Bundle
connecting the output of the ADC
to the Waveform Graph ikon
The LabVIEW manuals provide examples of how to wire or connect the
ikons. The wiring tool and the on-line Help utility provide a
graphical display of the inputs and outputs of each ikon. The
exponential fit routine requires two arrays: Voltage and time.
The "AI Acquire Waveform" ikon has an output which produces the
Voltage array. However, you need to construct the time array with
the aid of a "For Loop" sequence from the number of acquisitions
and the time increment.
You will want to write, test, and develop your program in a
modular fashion. That is, write a section, save it, test it, and
modify it until the program works. Then move on to the next
section. A digital multimeter is available to monitor the voltage
across the RC network. Resist the temptation to write the entire
program first before testing. Use the sequence structure in your
program; this guarantees that the hardware is addressed in an
orderly manner and one does not attempt to control too many
features simultaneously. The first frame should set the digital
switch for charging and run a clock for the charging period. The
second frame should have one operation: set the digital switch for
discharged. The third and final frame should contain the code for
acquisition, processing, and display.
Experimental Report:
Print using the Print command under File the windows showing the
Panel of your virual instrument and the Diagram. The Diagram is
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the graphical equivalent of a conventional program. These
printouts, the answers to the questions on the report sheet, and
the entries from your laboratory notebook constitute your lab
report. If you are unable to complete this experiment by 5:00 p.m.
Friday, an additional afternoon can be scheduled. Much of the
work including in this experiment is performed before you begin
the lab. Write a flowchart (outline) for your experiment before
you come to lab.
decay-lv.doc, WES, 16 Aug. 1999
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DECAY OF A CAPACITOR
LAB AUTOMATION VIA LABVIEW
NAME:_____________________________________
1) VALUES OF THE MEAN VALUE OF RC
RC(sec)
95% C.I. (sec)
V0(Volt) sampling period (sec)
a)
b)
c)
d)
2) Did RC vary significantly with the sampling period when you
sampled over the time period of ca. 2-3 half lives? Discuss.
3) Did the value of RC depend on the voltage of the HP power
supply? What did you expect? Discuss.
4) Did you observe any anomalies in measurements over long sample
periods? Discuss and interpret the results.