# Voltage Dividers:

## Introduction

This project is a variation of the temperature measurement system created in the first design problem associated with the Voltage Dividers project. In this exercise, we will again design a circuit whose output voltage provides a crude temperature measurement. However, in this system we want the output voltage of the system to be zero at room temperature, increase as temperature increases, and decrease as temperature decreases.

A thermistor—a device whose resistance changes with temperature—is used to sense the temperature. Thermistors are classified as Negative Temperature Coefficient (NTC) or Positive Temperature Coefficient (PTC) depending on whether their resistance decreases or increases with temperature. Thermistor specifications also include their nominal resistance at some temperature. The thermocouple in the Digilent Analog Parts kit is an “NTC 10 kΩ @ 25°C” thermistor. Its physical appearance is shown in Fig. 1.

This exercise uses concepts introduced in our project on Voltage Dividers. A link to this project is provided at the right.

## Step 1: Characterize the Thermistor

In order to design our circuit, we will first need to understand how the thermistor behaves. In this step we will characterize the thermistor's resistance change resulting from a temperature change.

1. Measure the thermistor's resistance at room temperature. Record this value.

2. Grip the resistor firmly between two fingers to warm it up. (We are assuming that your body temperature is above room temperature.) Measure and record the resistance of the thermistor under “warm” conditions.

3. Cool the thermistor by (for example) pressing a cold beverage container against it. Measure and record the resistance of the thermistor under “cold” conditions.

## Step 2: Design the Fixed Resistor

We will use the circuit of Fig. 2 to implement our temperature measurement system. The resistor R is a fixed resistor—we need to choose an appropriate value for this resistor to make the system perform well. The resistance RTH is the thermistor resistance—this resistance varies with temperature. The voltage VOUT is the voltage we will use to indicate the temperature. This voltage should increase or decrease as temperature increases or decreases. Notice that we are using two voltage supplies, and measuring the output voltage relative to ground in order to allow our output voltage to go both positive and negative.

Use the voltage divider formula and the thermistor resistance data you acquired in Step 1 to determine what value of R is necessary to make the output voltage equal zero2. This resistance is the value you want to use for the resistor R in the circuit of Fig. 2.

## Step 3: Implement and Fine-tune the System

The resistance value you determined in Step 3 will be unlikely to be readily available as a standard resistor in the parts kit. Implement the fixed resistor using a potentiometer from the Analog Parts kit. Potentiometers are described in the page on practical resistors in the related materials section above. Set the potentiometer to approximately the resistance value you determined in Step 2. Implement the circuit of Fig. 2, apply power to the circuit and measure the voltage VOUT at room temperature. This should be zero volts, but it is more likely that this will be a small—but nonzero—voltage.

To fine-tune your system, monitor the output voltage while adjusting the potentiometer resistance. Once you are measuring a zero volt output voltage, the potentiometer has the desired value.

## Step 4: Test the System Response at Warm and Cool Temperatures

Measure and record the output voltage at room temperature and under “warm” conditions (when you grip the thermistor between your fingers). Verify that the output voltage becomes positive when you warm the thermistor.

Cool the thermistor down (by, say, pressing a cold canned beverage against the thermistor) and record the output voltage. Verify that the output voltage becomes negative when you cool the thermistor.

• 1 If you've already done design problem 1, you can skip this step. Just use the data you acquired previously.
• 2 Hint: the total voltage difference across the voltage divider is 10V. However, if you use this information in the voltage divider formula to solve for the voltage at node a, you will get a voltage that is relative to negative 5V. To make VOUT = 0V, we want Va = 5V (relative to negative 5V).