ELEC 101, Spring 2001

Prof. Rich Kozick

Prof. Rich Kozick

Voltage Dividers, Temperature Sensors, and Bridge Circuits

We have several objectives in lab this week. Some of the things we will do include:

- Continue to learn how to use the laboratory equipment and how to build circuits on your breadboard
- Analyze a voltage divider to determine the best resistance value to use in a sensor configuration
- Set up and test a voltage divider and a bridge circuit using a thermistor to measure temperature

Designing a Voltage Divider Sensor

Voltage divider circuits are often used in measurement instruments to convert a physical quantity such as light intensity, temperature, or elastic strain into a voltage. An example circuit is shown below.

A material that changes its resistance in accordance with light is called a
*photoresistor*, and a material that changes its resistance in accordance with temperature is called a *thermistor*. The resistor R_{sensor} in the above circuit represents such a device. Voltage dividers are also used for things like volume controls on radios and televisions, dimmer switches on lights, and intensity controls on computer screens. In these applications, the resistance of a *potentiometer* (or "pot" for short) is varied by the user to change the output voltage.

The above circuit produces an output voltage V_{out} that
lies between the source voltage and ground.
In your lab notebook, please derive the relationship between the output voltage and the source voltage, as determined by the resistance values. (You should have done this exercise before, but make sure you understand it.) Note that V_{out} will vary with the physical variable that we are measuring as R_{sensor} changes.

Please answer the following questions in your lab notebook.

- Assuming that the sensor has a resistance that increases as the physical variable increases,
does the output voltage of the circuit increase or decrease?
- If the resistance decreases as the physical variable increases, how does the output
voltage vary?
- Devise a circuit in which the variation is the opposite of that in the above circuit.

Sometimes the sensor is exposed to only two values of the physical
variable, and an instrument must distinguish between the two levels.
For example, a light might shine or not shine on a photoresistor.
Then we might want to design the circuit in order to obtain the
largest difference between the two voltages produced. If the supply
voltage V_{s} is 5 volts, and if we can make the output
voltage close to 5 volts and 0 volts in the two conditions, then we
have designed a circuit that produces levels close to the standard
levels in digital logic. Determine the resistance R_{0} that
gives the greatest difference between the output voltages when
R_{sensor} = R_{max} and R_{sensor} =
R_{min}. Then determine the maximum difference, and how close
you can get to 0 and 5 volts.

**During the lab period, be sure that you understand how to set up
this analysis and the approach used to find the best value for
R _{0}.
You may want to finish the steps in the analysis after the lab session.
**

Consider an application of your result. Suppose that you have a sensor for which the resistance varies between R_{min} = 1000 ohms and R_{max} = 5000 ohms for two fixed conditions. In digital logic circuits, anything above 3.5 volts is sensed as logical "1", and anything below 1.5 volts is sensed as logical "0". However, the more you exceed these limits, the more reliable the circuit will be. For the sensor described above, can you achieve reliable operation? We will check your prediction later in the lab by building the circuit.

Testing the Voltage Divider Circuits

Next we will construct some voltage divider circuits in order to test the results from previous sections. First let V_{s} = 5 volts and replace R_{sensor} by a resistance value of 1000 ohms. Next replace R_{sensor} by resistance value of 5000 ohms. Choose R_{0} to achieve maximum voltage difference for the two values of R_{sensor}. Measure the actual voltage levels for the two cases, and compare with your earlier predictions.

Second, we will use a *thermistor* as R_{sensor}. Measure the resistance of the thermistor at room temperature, and when you heat it by squeezing between your fingers. Choose a value for R_{0}, and set up the voltage divider circuit. What values of V_{out} correspond to room temperature and body temperature? What would happen to your measurements if the source V_{s} deviated from 5 volts?

Bridge Circuits

Let us consider a bridge circuit, which is shown below. The bridge circuit is really just two voltage dividers, and it has some practical advantages over a simple voltage divider.

In this bridge, the output voltage V_{out} is now a difference between the two
sides of the bridge. If the circuit components are chosen properly, the voltage
difference will be zero.
Show the conditions for a "balanced bridge,"

Please do the following exercises with the bridge circuit.

- Build the bridge with the thermistor as R
_{sensor}and R_{0}(R_{0}is the value you chose in testing the voltage divider), R_{A}, and R_{B}chosen for balanced operation at room temperature. Note that in practice, the bridge can be "calibrated" by making R_{A}= R_{0}and using a variable R_{B}that is adjusted until V_{out}= 0. (A bridge circuit is often connected to the calibration knob on devices that you use!) - Now measure the output voltage at room temperature and at body temperature.
How do the measurements compare with the voltage divider?
- Will your circuit measure a temperature below room temperature? Explain what you expect.
- What advantage does the bridge provide over a single voltage divider?
(You might consider what happens in the bridge if V
_{s}changes, perhaps due to a weakening battery. How does V_{out}change if the bridge is nearly balanced?)

E-Lessons

A number of interesting E-Lessons are available on voltage dividers and bridge circuits. Feel free to browse them whenever you would like. The path to the E-Lessons is described in Lab 2, and the voltage divider lessons are under "Elements -> Resistors -> Voltage Dividers".