# Voltage Dividers:

## Introduction

In this project, we will design a circuit whose output voltage provides a crude temperature measurement. A thermistor—a device whose resistance changes with temperature—is used to sense the temperature. We will create an electrical circuit which uses this resistance change to output a voltage which indicates the temperature of the thermistor1. We want our system's output voltage to increase as temperature increases, and decrease if the temperature decreases.

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 10KΩ @ 25°C” thermistor. It's 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'll 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: Basic Design Assessment

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.

Use the voltage divider formula and the thermistor resistance data you acquired in Step 1 to verify that the voltage VOUT increases as temperature increases and decreases as temperature decreases.

## Step 3: Design the Fixed Resistor

Now we will choose a value for the fixed resistor in Fig. 2 which gives our temperature measurement system the best sensitivity. Sensitivity indicates the variation in a sensor's output parameter (VOUT, in our case) to its input (a temperature change, in our case). For us, sensitivity is the number of volts our output changes by, per degree of temperature change.

With R = 5 kΩ, use the voltage divider equation to determine the expected output voltage when the thermistor is warm and at room temperature. Record the expected change in voltage for this temperature change.

Repeat your calculation above, with R = 10 kΩ and R = 20 kΩ. Record the expected change in voltage for each of these cases. Which value of resistance results in the largest change in voltage? The resistor which results in the largest voltage change is the one you want to use—it results in a system with the highest sensitivity.

## Step 4: Build and Test Your System

Build the circuit of Fig. 2, with the resistor you chose in Step 3. Measure the output voltage at room temperature and under “warm” conditions (when you grip the thermistor between your fingers). Compare the measured voltage difference with your analytical predictions of Step 3. What is the percent error between your measured and expected voltage variations.

Cool the thermistor down (by, say, pressing a cold beverage can against the thermistor) and record the voltage change. Does the output voltage decrease as temperature decreases? Does this agree with your expectations from Step 2?

• 1 Resistance is not a common quantity to use to represent a physical parameter—engineers normally use voltage to represent the parameter being measured. Voltages are easier to use than resistance to represent information—they are easily recorded or used by other circuits. For example, digital logic circuits generally operate based on voltages applied to them; if we want to use a digital logic circuit to decide whether to turn on a heater when it gets cold, we will want to represent temperature as a voltage rather than as a resistance.