Voltage Dividers

Imagine:

• You're designing a piece of audio equipment, and you need a volume control. You insert a "pot" - short for potentiomenter - into your circuit. The pot has a knob that will eventually let you adjust the volume.

• You're designing a measurement system for measuring small deflections in a cantilevered stairway in a performing arts center. You buy a strain gage and use it to measure the deflection as loads are applied to the stairway to test the stairway.

• You're measuring rotational velocity in a motor, and you use a resistor-capacitor combination to "filter" out the noise you experience in the tachometer measuring velocity.

These three situations have something in common. The circuitry you use in each of these situations will be some form of a common circuit - a voltage divider.

Goals

The goals for this lesson unit are:

Given a voltage divider,

Be able to predict the output voltage from the divider given the input voltage and values for the two resistors in the divider.

Be able to determine how the output voltage from the divider

changes when any of the resistance values change.

Voltage Divider Analysis

Just above, we presented three different places where voltage dividers were used.

• The first - the potentiometer - is a variable voltage divider and it is often used in volume controls, gain controls and other situations where an operator wants to be able to control some variable in a continuous fashion.

• The second example involved a strain gage and that sensor is very often used in a bridge circuit which is really two voltage dividers.

• The third example - a "filter" is an example of an AC voltage divider. You're going to need much more background in AC analysis before we can discuss filters meainingfully, but it gives us something to work toward.

In this lesson we will examine the simplest possible voltage divider, but let's remember that it is just the starting point for a whole family of circuits derived from it including bridges and filters. Here's a circuit diagram of a very basic voltage divider. It consists of two resistors, R_a and R_b. Those two resistors are in series. An input voltage is applied to the series combination and an output voltage is measured across one of the two resistors.

The output voltage will be some fraction of the input voltage, and the fraction is controlled by the values of the two resistors. Our first goal is to understand how the output voltage, V_out, depends upon the input voltage, V_in, and the values of the two resistors, R_a and R_b. We'll examine this problem and solve for the output voltage by using what we know about resistors and Kirchhoff's Laws. We'll guide you through this with a few questions.

Question

Q1. How much current (I_series) flows through the series combination of R_a and R_b?

Once we find that current, then we can calculate the output voltage using Ohm's Law. You have to notice that R_a and R_b are two resistors in series and divide the input voltage by the series equivalent.

Then, once you have the current you can find the voltage across either of the resistors because you know Ohm's Law. Doing that you should find the following expression for the output voltage of the voltage divider.

• I_series = V_in /( R_a + R_b )

  because the two resistors are in series if no current is drawn from the voltage divider circuit.

• V_out = V_in R_b/( R_a + R_b)

  because the voltage across the resistor can be obtained using Ohm's law.

Using a Voltage Divider to Measure Temperature

Let's say you want to measure a temperature. There are lots of devices there that vary somehow as temperature changes. One device is called a thermistor.

There are other devices somewhat like a thermistor - except that they measure other physical variables - not temperature.

• A photoresistor

  changes value when incident light intensity changes. It's used to measure light intensity in cameras, for example.

• A strain gage

  changes values when it is stretched. It's used to measure strain (small elongations due to stress) in bridges, buildings, parts of aircraft and many other areas.

Anyhow, you can use a thermistor to measure temperature. However, often you don't want to measure resistance. A voltage change is often easier to measure and display - compared to a change in resistance value. A voltage divider is a circuit that can be used to convert a resistance change to a voltage change.

Here's a voltage divider circuit.

In this circuit we have the following:

• A thermistor, shown as R_t.

• A constant input voltage, Vsource.

In the voltage divider circuit we can note some important facts.

• As R_t increases in value the output voltage increases in value. If R_t decreases in value, the output voltage decreases in value.

• There are some temperature sensitive resistors that increase in value as temperature increases, but a thermistor has smaller resistance as it heats up.

Let's look at a typical situation to get started. We'll assume that we have a thermistor that has a resistance of 5000W

at 25^oC. That turns out to be a typical thermistor. For this thermistor, we have the following values of resistance at the temperatures shown in the table below.