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ELEC 350L
Electronics I Laboratory
Fall 2003
Lab 4: Electronic Thermometer
Introduction
Operational amplifiers are often used in “scaling” and “level-shifting” applications. Scaling is
simply the process of multiplying a signal voltage (or current) by a constant in order to change
its amplitude, and level-shifting is the process of adding or subtracting a constant voltage (or
current) value to or from a signal. In this lab experiment you will use a scaling and level-shifting
circuit to process the output signal from an electronic temperature sensor so that it produces
temperature readings in degrees Fahrenheit.
Theory of Operation
The National Semiconductor LM 35 is an electronic temperature sensor that produces an output
voltage that is proportional to the ambient temperature according to a scale factor of 10 mV/°C.
For example, if the temperature is 20°C, the LM 35 produces an output voltage of 200 mV. As
shown in Figure 1, the LM 35 is very easy to use. The device only requires an operating voltage
of 4−20 V and an external resistor (such as the 1 kΩ unit shown) to provide an appropriate load.
If the LM 35 drives a low-impedance load, the resistor shown in the circuit might not be
necessary, depending on the application. A temperature reading is obtained simply by
connecting a voltmeter between the output terminal and ground; the reading on the voltmeter (in
mV) gives the temperature in tenths of a degree Centigrade. For example, a reading of 200 mV
corresponds to a temperature of 20°C (200 tenths of a degree).
+4 to +20 V
vo
LM 35
1 k
Figure 1. Application of LM 35 temperature sensor.
If it is more desirable to have the circuit give the temperature in degrees Fahrenheit, then a
scaling and level-shifting circuit is required. Recall that Centigrade readings can be converted to
Fahrenheit readings using the formula
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TF  1.8TC  32 ,
where TF is the temperature in °F, and TC is the temperature in °C. The voltage produced by the
LM 35 would have to be scaled by a factor of 1.8 and then shifted by an amount corresponding
to 32°F (320 mV).
One approach to scaling and shifting a signal using a single op-amp is shown in Figure 2. The
circuit is a standard non-inverting amplifier, except that resistor R1 is connected to a reference
DC voltage source instead of directly to ground. It is straightforward to show that the output
voltage of the scaling and shifting circuit is given by (Try it!)
 R 
R
vo  1  2 vin  2 Vref ,
R1
 R1 
where the node labeled vin can be thought of as the output voltage of the LM 35 and as the input
voltage to the scaling and shifting circuit. Note that if Vref = 0, the circuit reduces to a standard
non-inverting amplifier. Resistor values R1 and R2 are chosen to obtain the appropriate voltage
scaling factor, then Vref is chosen so that, after it is scaled by the factor R2 / R1, it produces the
appropriate voltage shift. Note that the reference voltage must be negative if the overall shift is
to be positive.
+10 V
LM 35
+10 V
Rx
v in
+
_
vo
-10 V
1 k
R2
R1
Vref
(DC)
+_
Figure 2. Temperature sensor with scaling and level-shifting circuit.
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The purpose of resistor Rx is to mitigate the effects of the input bias currents (which you will
learn about later). It has no effect on the scale factor, but its presence improves the accuracy of
the voltage shift and consequently the accuracy of the Centigrade-to-Fahrenheit conversion. Its
value is chosen so that the output voltage of the op-amp is as close to zero as possible when all
other input sources (including Vref but excluding the power supplies) have values of zero.
Experimental Procedure
Design a scaling and level-shifting circuit like the one shown in Figure 2 to convert the output
voltage of an LM 35 from a 10 mV/°C scale to a 10 mV/°F scale. Use power supply voltages of
±10 V for the entire circuit. You will have to determine appropriate values for resistors R1 and
R2 and the voltage reference Vref. Initially use a short in place of Rx. (That is, set Rx = 0.) Note
that many combinations of values of R1 and R2 could be used to produce the correct scale factor.
Also, there are many ways to implement the voltage reference. However, do not simply use a
second power supply adjusted to the value of Vref; instead use the existing ±10 V supplies to
provide power to a voltage reference circuit of your own design. Keep in mind that the current
flowing through R1 is not negligible. You may design the voltage reference circuit around a
second op-amp. Be sure to record all of the details of your design in your notebook.
A data sheet for the LM 35 can be found at http://www.national.com/ds/LM/LM35.pdf. The
devices used in this lab exercise are manufactured in the TO-92 package style.
Test your circuit by using the bench-top multimeter to measure the voltages at the output of the
LM 35 and at the output of the op-amp. You will need to let the temperature of the LM 35
stabilize in order to get reliable readings. (The sensor’s temperature could change while you
move leads from one circuit location to the other.) If you wish, you may improve the correlation
of your measurements by teaming up with another group so that you can use your voltmeter and
theirs to measure both voltages at the same time. After you take readings at room temperature,
warm up the LM 35 by squeezing it with your fingers. If you can get the temperature to stabilize
again, take another pair of voltage readings at the higher temperature. Assuming that the output
of the LM 35 is an exact representation of the temperature in degrees Centigrade, determine the
percentage error of the Fahrenheit readings produced by the scaling and shifting circuit. What
are some possible reasons for any discrepancies observed?
If the resistor Rx is included in the circuit, it can help to mitigate any level-shifting errors caused
by the input bias currents of the op-amp. The resistor should have a value as close as possible to
Rx  R1 R2 .
You will find out at a later time how this equation is derived. Add the resistor to your scaling
and level-shifting circuit, and repeat the voltage measurements. Comment on any observed
improvement or degradation in the accuracy of the Centigrade-to-Fahrenheit conversion. (Keep
in mind the possibility that, without Rx present in the circuit, the error caused by the input bias
currents could offset the error caused by imprecise resistor values.)
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