Laboratory 3
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Laboratory 3
Measuring Capacitor Discharge with the BLIP
Parts List
100 µF electrolytic capacitor
BLIP board (soldering completed)
3 chips for BLIP
1. PIC16C765 microprocessor
(programmed with BLIP 1.2)
2. AD557 8-bit D/A converter
3. TC7662A DC/DC converter
various 5% resistors
Introduction
In this lab you will finish construction of your BLIP by inserting
the chips (integrated circuits). You will then use the BLIP in its
data acquisition mode to record the voltage over time across a
capacitor discharging through a resistor. The BLIP will enter
these voltage readings at a constant sampling rate directly into a
word processor or spreadsheet (the BLIP does this through USB
as if it were typing on a keyboard). With these readings you will
calculate the time constant RC, and compare it to the expected value from the actual resistor and capacitor.
First, procure the chips for your BLIP and insert them into their respective sockets. Be sure to observe
proper orientation of the chips (the AD557 is inverted). Follow the instructions in the BLIP User Manual. Be
careful not to bend the pins, especially on the 40-pin microprocessor chip. Line up one row of 20 pins first
and then press evenly at an angle as you line up the other edge of 20 pins for insertion into their holes. Then
press straight down to insert the chip. Inspect the pins visually by looking down edge from the end to make
sure no pins are bent. Have your TA validate proper completion of the BLIP before proceeding further. (A)
The BLIP’s mode of operation is selected by 4 “jumpers” that connect between the two rows of 4 header
pins. These 4 jumpers set the voltages on pins 40, 39, 38, and 37 of the microprocessor to 0 V (clear) when
present or 5 V when absent. They determine the mode that the BLIP enters upon power-up or when the reset
button is pushed. In the figure to the right, two jumpers are shown
connecting pins 38 and 37 to ground, putting the BLIP into Data
Acquisition Mode, which you will use for this lab.
Be careful not to place the BLIP on a metal surface, as the pins
on its underside could short out and damage the BLIP. Always
place the BLIP on a non-conductive surface free from any stray
pieces of wire.
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© 2013 George Stetten
40 39 38 37
Laboratory 3
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Connecting the BLIP to the Breadboard
First, remove the 9 V battery used in previous
labs. The BLIP can deliver +/- 5 V to power the
breadboard. You must never use the 9 V battery
and the BLIP at the same time, as this may
damage the BLIP and possibly the computer
beyond it.
6
The BLIP gets power from
the USB hub. Using colorcoded
22-gauge
single
conductor wire, connect +5 V
power (red) and ground (black)
from the BLIP to the top power
busses on the breadboard.
These wires are inserted
directly into the holes of the
BLIP’s power connector (see
figure to left). Connect the top
ground bus of the breadboard
to the lower ground bus as
shown.
The circuit shown in the
photo to the right (schematic
on following page) will be used
to record the discharge of a capacitor. The white
wire running from pin 6 of the BLIP I/O (inputoutput) connector carries the voltage to be
measured to the BLIP’s “analog input”.
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Touch wire to top of resistor to charge
capacitor.
© 2013 George Stetten
Laboratory 3
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Discharging a Capacitor
In this lab, we will record the voltage across a discharging
capacitor. To do this, we will use a capacitor with the fairly large
capacitance of 100 µF. To procure such large capacitance, one
normally uses “electrolytic” capacitors, whose plates are
manufactured to be very close together by a chemical process.
Electrolytic capacitors are fairly sensitive to breakdown (the one
shown in the picture to the right is only guaranteed to tolerate
16 V before the material between the plates breaks down).
Furthermore, electrolytic capacitors must be connected with the
proper polarity, otherwise they may leak a great deal. The
negative lead (marked by large negative signs “-“ in the gray
stripe) must be maintained at a lower voltage than the other (+)
lead. In our circuit the (-) terminal will therefore be connected
to ground. The symbol for the electrolytic capacitor has a
curved (-) plate and a “+” by the other plate.
The schematic to the right shows how to build a simple
circuit and connect it to the BLIP to monitor the discharge of a
capacitor. The pushbutton “switch” shown in the schematic is
actually just a wire from the +5 V power bus that you will
momentarily touch to one end of the 100 Ω resistor. The 100
Ω resistor prevents overloading the power supply while
charging the capacitor, since at the commencement of charging
a capacitor presents an effective short circuit. Although not
dangerous to the BLIP, the sudden loss of power could have
the unexpected result of resetting the microprocessor. Consult
the picture on the previous page to build this circuit and have
your TA check it before plugging the BLIP into the USB hub (not directly into the computer). (B)
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Once the wire that was temporarily touched to the top of the 100 Ω resistor is removed, the capacitor is
discharging, and the schematic representation may be simplified to the figure below. The voltages across the
two components are both functions of time: VC ( t ) is the voltage across the capacitor and VR ( t ) is the voltage
across the resistor. Likewise, the current I( t ) , which must be identical through both components, is a function
of time. This current through the resistor by Ohm’s law is
I( t ) =
VR ( t )
R
(1)
and the current through the capacitor (negative since the
capacitor is discharging) is
I ( t ) = −C
by
dVC ( t )
dt
(2)
the
fundamental law of the capacitor. Since
VC ( t ) = VR ( t ) by Kirchhoff’s Voltage Law, equations 1 and 2
can be combined into a single differential equation for
VC ( t ) . Derive that differential equation and show that
VC ( t ) = VC (0)e
−
t
RC
(3)
is a solution for it, where t = 0 at the moment the wire is removed from the top of the 100 Ω resistor. (C)
The time constant RC represents the time at which VC ( t ) has fallen to VC (0) /e , or 37.8% of the initial
voltage. We will record a series of measurements of VC ( t ) to estimate RC.
Recording measurements of the discharging capacitor with the BLIP
Open a new document in Microsoft Word on your lab computer and click the mouse within the new
document. Then plug your BLIP into a serial port of the hub on the desktop. Never plug it directly into the
computer, to avoid potential damage to the computer. Press the BLIP reset button. The BLIP should type its
identification (e.g., “BLIP v1.2”) and then begin typing numbers between 0 and 255 (28-1). The 0 means “0
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Laboratory 3
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volts” and 255 means “5 volts”. Other readings are linearly interpolated between these two voltages. Using
the potentiometer on the BLIP, adjust the data rate to 2 samples per second. Then touch the wire from the
+5 V bus to the top of the 100 Ω to charge the capacitor. Estimate the time (order of magnitude) required to
charge the capacitor through this resistor (D). Estimate the voltage (in units of 0-255) to which the capacitor
should be charged. This will not be the full 255, because of the voltage divider made up of the 100 Ω and 24
K resistors. (E) Does this correspond to what you see on the computer readout?
After you charge the capacitor and remove the wire, you should see the list of numbers typed by the BLIP
starting near 255 and decreasing towards 0. Copy (control-C) the first 25 readings from where it just starts to
decline, and paste (control-V) them into the indicated box in the Microsoft Excel worksheet provided on the
Class schedule website next to these laboratory instructions. The worksheet will provide a graph of the
readings, which should appear to be the decaying exponential described by equation 3 above.
To estimate RC, we first take the natural logarithm of the voltage readings
t ⎞
⎛
−
t
RC
ln(VC ( t )) = ln⎜VC (0)e ⎟ = ln(VC (0)) −
RC
⎝
⎠
(4)
and use the excel “Slope” function. Use the Excel “help” feature to see what the Slope function is actually
doing (a linear regression to find the best fit of a straight line through the data points). Thus the slope is
actually −ΔT /RC . Explain why this is true. (F) To relate the slope (which is relative to samples) to the actual
time constant, RC, we must consider the sampling rate of 2 samples per second ( ΔT = 0.5 seconds). The
spreadsheet takes this into account in computing the value in cell D35.
Familiarize yourself completely with the Excel worksheet and be prepared to answer questions from the
TA. With your meter, measure the actual resistance and capacitance of the nominal 24 K resistor and 100
µF capacitor. To measure capacitance, insert the capacitor leads into the “Cx” slots and dial up the 200 µF
capacitance range. Conveniently, the meter does not care about the polarity of electrolytic capacitors.
Compute a new time constant RC from these values. Compare this to your value for RC computed from your
measurements on the excel sheet. Why does the logarithm of the voltage appear to be a straight line, but get
more wiggly at the lower end? (G)
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© 2013 George Stetten