Introduction

Operational amplifiers (op amps) are used in a variety of instrumental applications. These devices have the advantages of high input impedance, high open-loop gain, and low impedance output. Their name derives from the fact that a variety of circuits incorporating them can be assembled which perform mathematical operations on the input signal supplied to the circuit. Several circuits of this type will be constructed in this laboratory. The general configuration of an op amp is given in Figure 1. The device is supplied power (usually ±15 V) at the connections labelled +PS and -PS. The two signal inputs are labelled (+) and (-) and are called differential inputs. The potential at these two inputs is given by ₊ and _- respectively. Operational amplifiers are designed such that the device manipulates the output such that the following condition is met:

Thus, with the application of the appropriate circuit elements at the input(s) and in a feedback loop, circuits can be constructed which will carry out operations such as addition, subtraction, multiplication, division, differentiation and integration.

Equipment

The following items are required for this laboratory:

(1) Assorted resistors 
(2) A small dc power supply
(3) Digital multimeter (DMM)
(4) Function generator
(5) Hook-up wire
(6) Oscilloscope
(7) Operational amplifiers
(8) Thermistor

Procedure

I. Voltage Follower with Gain

The schematic for this circuit is shown in Figure 2.
 

This circuit amplifies the input voltage by a factor dependent on the values of R₁ and R₂. Because the input signal is applied to the noninverting input of the op amp, the sign of the output is the same as that of the input. The relationship between the input voltage and the output voltage is given by:

Construct this device choosing values for R₁ and R₂ such that the gain of the circuit is 2x, 5x, and 10x. Record all resistor values used and show gain calculations. Measure the actual gain of each circuit and compare it to the calculated gain. Calculate the %error between the actual and calculated gain.

II. Inverting Amplifier with Gain

The schematic for this circuit is given in Figure 3, along with the expression describing the output.

(1) Assemble this circuit with input and feedback resistors such that the gain of the circuit is -2x, -5x, and -10x. Record all resistor values used and show gain calculations. Measure the actual gain of each circuit and compare it to the calculated gain. Calculate the %error between the actual and calculated gain.

(2) A thermistor is a device with a temperature-dependent resistance. Using beakers of heated and chilled water, measure the resistance of the thermistor at several temperatures between 0 C and 50 C. Plot this resistance against the actual temperatures (as measured with a laboratory thermometer). Arrange the inverting amplifier with a thermistor as one resistor in such a way that the output voltage becomes more positive as the temperature increases. Set the gain so that the ouput changes 10mV/C around room temperature. Using beakers of heated and chilled water, plot the output voltage as a function of the actual temperature (as measured with a laboratory thermometer) for several points between 0 C and 50C. Determine whether or not the circuit response is linear with respect to temperature. Explain this behavior.

III. DAC

Assemble the circuit shown in Figure 4 using the output of the two 5V power supplies as the inputs to the DAC.
 
 

(1) Determine the voltages output by the DAC for the decimal numbers 0, 1, 2, and 3.