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Introduction & Theory
With the exception of superconductors, all conductors have electrical resistance. The resistance of a conductor varies with composition, geometry, temperature, pressure, fields, and other factors. In this experiment, the variation of resistance with temperature will be investigated.
For most common conductors, the dependance of resistance on temperature is minimal under mild conditions; however the resistance of some materials varies strongly with changes in temperature. These materials are useful in thermistors, electronic devices used to determine temperature.
The flow of electricity through a circuit is similar to water in a pipe in many respects. The addition of pressure at one point in the pipe can cause flow and ejection of water at some distant point in the point. Similarly, electrons are pushed through a circuit by applied potentials. The difficulty in moving an electron from one molecule to another gives rise the resistance. In materials such as metals with a sea of electrons, resistance is very low. In insulators such as glass and rubber, it is difficult to transfer electrons between atoms and resistance is high. Other materials, known as semiconductors, can have high or low resistances depending on the conditions. In the case of the thermistor, the increase in molecular motion due to temperature increases allows electrons to be transferred between molecules easier. As a result, the resistance is relatively high at low temperatures and lower at high temperatures.
The use of a thermistor as a temperature reading device has several advantages. The use of small amounts of semiconductor material, and the small heat capacity that accompanies it, results in short response times to temperature changes. In addition, the use of electrical current in measurement lends itself directly to technological applications. Using a computer and other available electronic instruments, plots of conditions versus temperature and temperature versus time can be quickly, accurately, and repeatedly created and stored for future analysis.
One problem with computerized analysis using thermistors involves the nature of the signal obtained. The source signal exists as a resistance, which a computer has no inherent means of determining. The most straightforward measurement of resistance involves applying a potential across the resistor and measuring the effects. Fortunately, the voltages and currents computers are designed to work with are not sufficient to heat the resistor merely by measuring it. The problem still remains however, of how to turn an analog resistance into a digital form that the computer can use. While many methods exist for this purpose, three are outlined below. These employ an analog to digital converter (commonly written as A/D converter) to translate a signal that may take arbitrary values (between a fixed maximum and minimum) to ordered sets of on and off values that a computer can use. One method also employs a D/A converter, which changes sets of on and off values to a voltage.
The joysticks found on modern computers face, and overcome, a situation similar to that of a thermistor. The stick is mechanically connected to a variable resistor, so a change in position results in a change in resistance. This resistor serves as a part of a one shot monostable vibrator, which is in essence an RC circuit. When a reading is desired, a voltage is applied to the circuit. This charges a capacitor, which is discharged slowly through the variable resistor in the joystick. Through the use of transistorized circuits, a voltage above a predefined level is seen as being "on" and below is "off". By determining the time between application of the voltage and the transition of circuit state from "on" to "off". Thus the resistance is found as a function of elapsed time. Simply using a thermistor instead of the mechanical rheostat allows temperature to be measured. While this method is accurate enough for games and fairly inexpensive, the types and tolerances of common components hamper the precision and speed of this method. A typical computer obtains between 20 and 100 readings from a joystick in a second, depending on the specifications of the circuit itself and the resistance being measured. (Note that resistance affects the discharge time of the capacitor so high resistances take longer to read than low resistances.)
Another method involves placing the thermistor in an oscillating circuit in such a way that the frequency of the circuit was determined by the thermistor. Using a comparative circuit similar to the one used above would cause the computer to read an alternating off/on signal. The time between transitions may then be calibrated to indirectly obtain readings of temperature readings. This method has several shortcomings as well, however. The computer must be able to read the signal very rapidly and without interruptions. This may require a significant percentage of processing power going to simply acquire the data. One time interruptions as the computer handles keys being pressed on the keyboard, redrawing the cursor when the mouse is moved, or other background tasks can cause readings to be missed, resulting in wild readings. General insufficiencies in processing power or other component latency can cause invalid data to appear correct if oscillations are missed systematically.
The previous two methods use a single on/off condition (bit) along with a time measurement to come up with a reading. Another method converts the applied resistance directly into a binary number that the computer can immediately process.
As an aside, binary (base 2), octal (base 8), decimal (base 10), and hexidecimal (base 16) are number systems frequently encountered in computer systems. The binary number system is based upon only groups of zeros and ones. This corresponds to the on and off states that the transistors in the processor, the charged and discharged states of capacitors in RAM, and the magnetic polarities of material in drives. As a result, it is common to see numbers expressed in binary when two states are being compared. The conversion between binary and the more familiar decimal is given by the following formula, where bases are denoted by subscript and n is the number of bits (indexed from zero, not one)
The third method uses switching transistors in a voltage divider network to form a digital to analog (D/A) converter and compares the voltage obtained with the voltage being measured. By successive approximations, the output is made to match the input within the resolution of the device.
The precision of the first two methods is dependant on time, while the third method is dependant upon the number of bits the converter can handle. A 4 bit converter has a range of values from 0000 to 1111 (0-16) while a twelve bit converter may range from 0000 0000 0000 to 1111 1111 1111 (0-4095). Thus, the 4 bit device is limited to ± 6.25% precision at best, while the 12 bit device may be reliable to ± 0.024%.
The goal of this experiment is to create a calibration curve for a thermistor using a computer equipped with an A/D converter.
A thermistor, variable temperature water bath, thermometer calibrated to NIST standards from 0C to 40C, low voltage regulated power supply, testing circuit (one can be built from wire, prototyping board, and one 5k resistor), and a computer equipped with an A/D board and software.
The resistance of the thermistor will be measured at many temperatures, so that a calibration curve may be constructed.
Place the thermistor in the water bath and attach to a testing circuit as shown in Fig. 2. The variable resistor labeled sensitivity may be replaced by a 5k resistor in this experiment (which ranges from 0C to 40C). Adjustment of this resistor allows the most sensitive readings to be obtained for arbitrary temperature ranges, and should generally be the average of the minimum and maximum resistances expected for the temperature ranges. This resistor must be left constant throughout a run if the results are to be meaningful.
Place the thermometer in the bath near the thermistor, set the bath to its coolest setting, and allow the system to come to thermal equilibrium within the calibration limits of the thermometer (0-40 C). Adjust the bath so that it warms slowly, and note the readings obtained by the computer and the temperature at at least every 2C change. It may be necessary to adjust the bath so that it continues to rise, but be sure that the temperature may be considered constant while readings are being taken. Once the temperature has reached its maximum, the data may be plotted to yield a calibration curve.
Some systematic error is introduced by measuring the temperature as it is changing, due to the heat capacity of the thermometer bulb. This is necessary however if a large number of data points are to be measured in a reasonable amount of time, and can be minimized by ensuring that the temperature changes slowly.
The use of a simple voltage divider to manifest changes in resistance as voltage changes limits the precision measurement. With a 5 V source and resistances given for the thermistor(1) at 0C and 40C, a voltage change of only 2.1 V may be expected. As a result, for temperatures to be accurately resolved to the nearest 0.5C, the voltage must be able to be resolved to at least 0.05 V, assuming an ideal linear relationship. Deviations from linearity result in even smaller voltage changes with temperature over some intervals. The use of a circuit taking advantage of high-gain transistors would allow a greater change in voltage with temperature changes, with a penalty of increased cost and complexity.
Avoid contact with electronics and water, especially those connected to 120 volt sources. Always use a grounded receptacle, preferably one with ground fault interruption. In the event of a shock, turn of the power at the source; do not attempt to remove the victim until the power is off! Treat for shock, and administer CPR if necessary. If severe, seek medical attention promptly.
Mercury and mercury vapor are highly poisonous. Inhalation of vapor may lead to fever, nausea, vomiting, diarrhea, headache, chest pain, and possibly death. Skin contact may lead to a rash or allergic reaction, and if extensive may also cause the same effects as inhalation of vapor. Affected persons should be removed to fresh air and contaminated clothing removed. Necessary first aid techniques should be performed. Seek medical attention immediately.
1. Specification sheet for Yellow Springs Instrument Company glass encapsulated thermistor, provided in handout.
2. Chemical safety data taken from the internet at "http://hazard.com/msds"