Supplementary material for “The bug: a temperaturecontrolled experiment on a protoboard”
Paul K. Dixon
Department of Physics, California State University at San Bernardino, San Bernardino,
California 92407
1
In this document, the supplementary material is organized by section with a oneto-one correspondence with the section headings in the primary article. The sub-headings
refer to the particular topic of relevance in the primary article.
II. Sample Construction
Capacitor choice: Commercial ceramic capacitors are made with high dielectric
constant materials, most typically titanates; doped barium titanate and doped strontium
titanate are the most common ingredients [1]. The large dielectric constant in these
materials is a result of a ferroelectric transition [2-4]. In a pure single crystal material,
this results in power-law divergent dielectric susceptibility at the transition temperature.
This divergent susceptibility is suppressed and broadened with impurity doping, resulting
in a material that has a very high dielectric susceptibility over a fairly broad operational
temperature range near room temperature, but at the expense of an unusually strong
variation with temperature. This allows for the construction of low-cost nonpolar
capacitors in the 1 pF – 1 µF range in very small packages. Such capacitors are used in
electronics for situations where the value tolerance in the design is very loose, usually a
factor of 2 or more. This unsuitability in regards to temperature variation is exactly the
property that makes them interesting for our use.
For our experiment, we wanted the largest capacitance variation possible. The
primary criterion for choosing the capacitor was to pick the one with the largest dielectric
constant, and thus hopefully the weakest doping and strongest variation with temperature.
We also wanted to avoid values in the pF range to make the measurement easier. Another
issue was that we wanted a capacitor package that was similar in size and shape to the
thermistor package to create a symmetric geometry for the bug. This helps to balance the
temperature gradients on both sides of the heater resistor, thus minimizing the difference
of the temperature measurement of the thermistor on one side to that actual temperature
of the capacitor on the other side. Within our collection of ceramic capacitors on hand,
the apparent best choice was 10 nF. This choice has turned out to work quite well, and
the cost is negligible, just a few cents per capacitor. After the fact, we have since deduced
that we chose a capacitor made of the material Z5V, which is a relatively lightly doped
2
barium titanate mixture with a peak dielectric susceptibility of ~ 20,000 and transition
temperature of ~ 25 oC. Those wishing to choose a capacitor with such sharp
temperature-dependent properties should acquire capacitors specified as Z5V, Y5V, or
with temperature specifications: +20% to -80% [5].
Thermistor choice and temperature calibration: The thermistors that we use
are standard Vishay Dale NTC 10 kΩ @ 25 oC silicon thermistors. They can be obtained
from a variety of electronics vendors, both calibrated and uncalibrated. The uncalibrated
version is under $1; the calibrated version typically is 5-10X more expensive. We
purchase the uncalibrated model and do a calibration against a NIST-traceable platinum
resistance thermometer ourselves. We find that a three point calibration over the active
temperature range of the experiment (25 oC – 85 oC) is adequate to obtain ±100 mK
accuracy consistently with the widely-used Steinhart-Hart equation [6]
(
)
3 −1
T = A + B [ ln( R) ] + C [ ln( R) ]
.
(1)
We improve the accuracy of the calibration to ±30 mK by using a 20 (or more) point
measurement and our own ad-hoc fitting form
T = C1 + C2 e− C3 R + C4 e− C5 R .
(2)
Although it would be very instructive to have the students do the calibration
themselves in the lab, we do it beforehand and give them the calibration curves to use.
They learn a variety of thermometry calibration procedures in their senior-level advanced
laboratory course, and this experience would be redundant.
Heater resistor choice: The choice of the ½-Watt 60-Ω metal-film resistor for
the heater was motivated by a variety of considerations. The 60-Ω resistance value was
chosen as a rough impedance match to the ~ 50-Ω output impedance of the power
amplifier that we use to drive it; the amplifier will be described in detail below. In
addition, the 60-Ω value allows us to overdrive the resistor to a desired maximum power
of 1.2 Watts at an applied voltage of 8.5 Volts, well within our working voltage band.
3
This results in a temperature in the neighborhood of 85 oC, which is our target maximum
temperature. At this temperature, all three components show no long term degradation
effects. Even with our maximum possible applied voltage of 10 Volts resulting in a
power of 1.7 Watts, the ½-Watt metal film package design is robust enough to survive
with just a little discoloration. This typically is not the case for carbon resistors, and they
should be avoided for this application. As is the case with the capacitor, the cost is
negligible, just a couple of cents per resistor.
Adhesive choice: The three components are bonded together with an adhesive.
We have tried a wide variety of readily available adhesives over the years and have found
just a couple of good choices. Standard 5-minute epoxy is adequate, but it tends to yellow
after a few cycles and become brittle after repeated use for a month or so. The best
adhesive that we have found is Plastic Fusion Adhesive, product #15277, from the Super
Glue Corporation, a division of Pacer Technology. It is a 2-component adhesive that is
available in “big-box” home centers. We have found that it doesn’t show any degradation
even after repeated cycles to 125 oC. As can be seen in Fig. 1b in the primary article, we
try to minimize the amount of adhesive so that the structure of the bug is visible to the
students. Including the cost of the adhesive, a set of 25 bugs can be constructed for under
$20.
III. Temperature Measurement and PID Feedback Power Control
Temperature measurement and manual power control set-up: The first
experiment that the students do with the bug is to set up a simple circuit for manual
control of the power, and measurement of the thermistor resistance. The bug is placed on
a prototyping breadboard, raised above the board to a height of 2-3 cm. The component
leads are left at their full length so that there is adequate stand-off from the board; if
pushed down to the surface, the bug can discolor and even melt the breadboard at its
maximum temperature. The heater resistor is connected to a simple variable voltage
4
power supply capable of delivering at least 150 mA of current at a voltage of 8.5 Volts.
The thermistor resistance is measured with a Hewlett Packard HP34401A digital
multimeter (DMM) that communicates with a PC via an IEEE-488 parallel bus interface.
When we started this series of experiments 10 years ago, we used a low-cost
Elenco 550 breadboard trainer and used the on-board power supply. Since then, we
designed the NI-ELVIS workstation [7] for our applied physics curricula partly with this
series of experiments in mind, and now use NI-ELVIS instead. Its variable power supply
is more than adequate to the task. Even though we use NI-ELVIS for these experiments,
they can still be done with standard electronics instructional tools. In fact, for
pedagogical reasons, we avoid using many of the integrated hardware/software features
of NI-ELVIS that could be applied to these experiments. For example, we use the
Hewlett Packard 34401A digital multimeter to measure the resistance of the thermistor
even though we could do it using the ohmmeter capability integrated into NI-ELVIS. The
reason for this is that we want the students to gain the valuable experience of interfacing
a standard measurement instrument to the PC.
The first major LabVIEW (LV) student software project in this series of
experiments is the development of an instrument driver for the HP34401A. The students
start with a series of in-class exercises to establish communication with the instrument
over the IEEE-488 interface using the basic “VISA” ASCII read and write commands
included in LabVIEW. The VISA tools are a wrapper for ASCII communication over a
range of protocols including parallel IEEE-488, serial RS-232, Ethernet, etc. The now
almost-ubiquitous use of Standard Commands for Programmable Instruments (SCPI) for
instrument control on all of these ASCII-based interfaces makes developing an IEEE-488
instrument driver a skill that is easily transferable to these other protocols as well. After
the students establish communication with the instrument, they then proceed through a
series of given command sets to configure the instrument, perform a measurement, and
return the data. One of the issues that we address at this point in the lab is the tradeoff of
speed and resolution. This then leads to a discussion of the issue of 60 Hz power line
noise rejection via line cycle integration – in our opinion, an important but often
overlooked topic in measurement instruction.
5
Once they have learned the basic communication protocol, they then proceed with
a relatively large project to build an instrument driver for the DMM capable of a variety
of basic measurements including voltage, current, and resistance. The instrument driver is
a stand-alone virtual instrument (VI) that can be used in a one-shot mode or can return
measurements continuously in response to a software trigger over the bus.
To keep the amount of new coding to a minimum, we take advantage of earlier inclass programming exercises to do some of the work ahead of time. For example, one of
the critical components of the driver is a command generator. The command generator is
a subVI that creates command sequences of the proper syntax in response to a series of
menu choices made by the user (or the higher level program); for example, a sequence of
the two commands “CONF:RES DEF,DEF” and then “TRIG:COUN 1” sets the
instrument in a state ready for the software triggering of a resistance measurement with a
default range of 10-kΩ and a default resolution of 5½ digits using 10 line cycle
integration. We have the students build this subVI three weeks earlier as an in-class
exercise in string manipulation. The same is true for the subVI that converts the returned
measurement string to a floating point numeric value. In fact, numerous subVIs in this
project and the projects to follow are developed earlier in the course as programming
exercises in array manipulation, signal averaging, string manipulation, file I/O, etc. This
helps to make this series of projects manageable in the allotted three weeks.
Once the instrument driver is complete, the students then integrate it into a toplevel VI called “Temperature Chart” that measures the resistance of the thermistor every
half-second, converts the resistance to temperature using Eq. 2, and charts the
temperature versus time. For this assignment and all of the other homework assignments
in this sequence of projects, the students are given LabVIEW VIs with fully designed
front panels but empty block diagrams. They spend quite a bit of time earlier in the
course learning how to design front panels; at this stage in the course, their time is put to
better use on the coding. In addition, the students are given working versions of the VIs
with block diagrams that have been password protected. This allows them to both test
their hardware and explore the features that they are being asked to re-create. Once a
6
given assignment is complete, they are then given the password and can inspect our
solution.
Power control and measurement interfacing: The next major student project is
to interface the power control and power measurement to the PC via the multifunction
DAQ card that is part of the NI-ELVIS system. The students then incorporate both
features into the temperature charting software. They start by building a power amplifier
and interfacing the electronics as shown in Fig. 1. The current-boosted DAC outputs on
NI-ELVIS have enough current capability without enhancement, but we choose to have
them build the power amplifier anyway. In part, this is to refresh their memories and
reinforce the interfacing techniques that the learned in the freshman electronics course
that is a prerequisite to this one.
Fig. 1. (a) A circuit schematic for
interfacing the heater resistor to
automatic power control. (b) A detailed
schematic of the power follower (1XP).
The power amplifier is a conventional design in which the relatively low-current
push-pull output transistors inside the op-amp are effectively replaced with a pair of
discrete transistors capable of much higher current capability. Note that the discrete pushpull transistors are still inside the feedback loop, making this a power voltage-follower
design. This power booster can deliver up to 200 mA of current to the 60-Ω resistor,
much in excess of the 2 mA capability of typical DAQ card analog outputs. Even with
very inexpensive components like the 741 op amp, 2N3904 NPN transistor, and 2N3906
PNP transistor, the power-follower has an output impedance of ~ 50 Ω and an effective
bandwidth in excess of 1 kHz.
One of the analog outputs of a PC multifunction DAQ card is used to set the
voltage across the heater. The actual voltage across the heater resistor is measured using
one of the DAQ card differential analog input pairs.
7
The students build and test this circuit in a matter of minutes. The component cost
is well under $1. If they make a mistake, the most common failure mode is an easily
replaced blown transistor, at a cost of 10 cents or so.
A basic PID algorithm: The PID algorithm presented below is a rudimentary
version with a somewhat standard improvement in the integral power calculation. The
integral power is cleared (reset to zero) if the system leaves the control band to avoid
“integral windup”; this leads to much smaller temperature overshoots and quicker settling
for setpoint changes larger than the control bandwidth. An added feature is that the
integral term is only reset to zero if the system leaves the control bandwidth for two
consecutive temperature measurements, thus avoiding inadvertently clearing the integral
due to measurement noise or an occasional unexplained spike in the measurement.
Definition of terms (memory elements in Italics):
Counting indices:
j
=
represents the index of the current cycle
j -1
=
represents the index of the previous cycle
Temperature measurement:
Tj
=
current temperature of this cycle [oC], also can be written as just T
Tj-1
=
temperature of the last cycle [oC]
δT
=
Tj – Tj-1
temperature change since the last cycle [oC]
Time measurement:
tj
=
current time of this cycle (sec), also can be written as just t
tj-1
=
time of the last cycle (sec)
δt
=
tj – tj-1
elapsed time since the last cycle (sec)
Control Parameters:
Ts
=
Setpoint (desired temperature) [oC]
8
∆
=
Control bandwidth [oC]
S
=
Settle bandwidth [oC]
τi
=
Integral time (sec)
Ion
=
Integral control on, Boolean, True = on, False = off
τd
=
Derivative time (sec)
Don
=
Derivative control on, Boolean, True = on, False = off
ts
=
Settle time [sec]
TH
=
Ts + ∆/2
High limit of control band [oC]
TL
=
Ts - ∆/2
Low limit of control band [oC]
TSH
=
Ts + S/2
High limit of settle band [oC]
TSL
=
Ts - S/2
Low limit of settle band [oC]
Power terms:
Pp
=
Proportional power [normalized 0-1]
kj
=
current count of the number of cycles outside of the control band
kj-1
=
previous count of the number of cycles outside of the control band
PIj
=
current integral power [normalized], also can be written as just PI
PIj-1
=
integral power of last cycle [normalized]
Pd
=
Derivative power [normalized]
Pr
=
Pp + PIj + Pd
Pt
=
Final total power [normalized]
Raw total power [normalized]
Settle terms:
Go
=
Temperature is settled, Boolean, True = on, False = off
tej
=
current elapsed running time in the settle band [sec]
tej-1
=
elapsed running time in the settle band of the previous cycle [sec]
Power algorithm:
Proportional power:
Pp
=
or
1/2 +(Ts-Tj)/∆
if
9
TL < Tj < TH
=
or
1
if
Tj < TL
=
0
if
TH < Tj
Derivative power:
Pd
=
or
-[τd/∆]*[δT/δt]
if
Don = True
=
0
if
Don = False
=
kj-1 + 1
if
Tj < TL
=
0
if
TL < Tj < TH
Out counter:
kj
and
kj-1 = 0
or
TH < Tj
Integral power:
PIj
=
PIj-1 - [(Tj-Ts)*δt]/[∆∗τi]
if
TL < Tj < TH and Ion = True
=
0
if
kj > 1
and PIj-1 = 0
or
Raw power:
Pr
=
Pp + PIj + Pd
Final total power:
Pt
=
Pr
if
0 < Pr < 1
Pt
=
1
if
1 < Pr
Pt
=
0
if
Pr < 0
Settle algorithm:
Settle time tracking:
tej
=
tej-1 + δt
if
TSL < Tj < TSH
=
0
if
Tj < TSL
=
0
if
TSH < Tj
Determination of settled condition:
10
Ion = False
Go
=
True
if
ts < tej
Initialization:
Tj-1
=
Tj
tj-1
=
tj
kj-1
=
0
PIj-1
=
0
tej-1
=
0
Pd
=
0
PIj
=
0
Reasonable starting values for loose control of “the bug”:
∆
=
4
Control bandwidth [oC]
S
=
1
Settle bandwidth [oC]
τi
=
30
Integral time (sec)
τd
=
0.5
Derivative time (sec)
ts
=
100
Settle time [sec]
11
PID power control exploration: In addition to exploring the PID control
concepts in lecture, we explore the behavior of the actual bug system under PID control
using a password protected version of the VI “temp chart with PID” that the students will
be coding for this specific project. Figure 2 shows the front panel of this VI.
Fig. 2. The front panel of the “temp chart with PID” LabVIEW
virtual instrument (VI) used in the bug experiments. Also
shown is the minimized version obtained by activating a
“shrink” feature.
Fig. 3. The temporal autocorrelation of the
temperature deviations from the setpoint for To
= 50 oC and for a variety of conditions. Each
autocorrelation was produced from a data set in
excess of 2 hours: the original control
parameters [∆ = 4 oC, τi = 30 s, and τd = 0.5 s]
for an unwrapped and exposed bug (bold
dotted line), the ZN control parameters [∆ =
0.833 oC, τi = 3.5 s, and τd = 0.875 s] for the
wrapped and shielded bug (bold solid line),
both ZN time constants doubled (dashed line),
both ZN time constants cut in half (dotted line),
and doubling just the integral time while leaving
the derivative time unchanged (solid line).
Autocorrelation of the temperature fluctuations: In Fig. 3, we show the
temporal autocorrelation of the temperature fluctuations from the long data sets used to
produce Fig. 7 in the primary article. As can be seen in the figure, the overshoot and
settling time are both much more sensitive than the size of the fluctuations to these
12
control parameter changes. Doubling just the integral time leads to a slightly more
underdamped response than the ZN response, but at the benefit of smaller fluctuations
from the setpoint as demonstrated in Fig. 7 of the primary article. On the other hand,
cutting the time constants in half leads to instability as was seen in the step response
experiments shown in Fig. 5 of the primary article.
Fig. 3 is instructive, but the correlation analysis that it presents is beyond the
mathematical prerequisites for this course. Because of this, we prefer to present
essentially the same information to the students in a more tractable fashion, using the
simple large step response measurements shown in Fig. 5 in the primary article. The step
response measurements have the added benefit of clearly illustrating the effects of the
derivative time on the maximum ramping rate outside of the control band.
V. Fully Automated Experimental Control
Fig. 4. The C(T) data viewer VI that launches at the end of an experimental sequence. This VI
automatically does a simple linear exponential fit to the RC decays to obtain an estimate of the
capacitance at each temperature, and displays the results.
Student C(T) experiments: Once the students finish the development process,
we have them use their resulting software to execute a series of C(T) experiments. In Fig.
4, we show the C(T) data viewer VI after the execution of a sequence from To=80 oC to
13
To=35 oC in steps of 5 oC. This experiment takes ~ 20 min and is typical of the runs that
the students perform in the lab. The data shows a significant variation of capacitance with
temperature, increasing from ~ 7 nF to ~ 13 nF as the temperature drops from To=80 oC
to To=35 oC, as well as a suggestion of a possible peak in the capacitance below 35 oC.
14
References
[1] G.H. Haertling, “Ferroelectric Ceramics: History and Technology”, J. Am. Cer. Soc.,
Volume 82, Number 4, pp. 797-1615, 1999.
[2] D. Hennings, “Barium Titanate Based Ceramic Materials for Dielectric Use”, Int. J.
High Technol. Ceram. Vol. 3, no. 2, pp. 91-111, 1987.
[3] K. Uchino, Ferroelectric Devices (Marcel Dekker, 2000).
[4] D. Damjanovic, “Ferroelectric, dielectric and piezoelectric properties of ferroelectric
thin films and ceramics” Rep. Prog. Phys. 61, pp. 1267-1324, 1998.
[5] M. Khan, AVX Corp., “Multilayer Ceramic Capacitors – Materials and Manufacture”,
http://www.avxcorp.com/docs/techinfo/mlcmat.pdf.
[6] Vishay Components, “NTC Thermistor Overview” and “NTC Accuracy Line”,
vishay.com.
[7] P. K. Dixon and T. D. Usher, “Universal Laboratory Prototyping and Interfacing
System (ULIS)”, United States Patent # 6,895,563 (2001).
15