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5. Operational Amplifiers

Introduction
In many electronic circuits, the signals (voltage differences) that are generated and manipulated are very small. Therefore, amplification is often essential. When playing a CD for instance, the signals generated in the CD player are quite small and will not adequately drive a speaker system. The signals from the CD player are therefore passed into the stereo amplifier (which often comes as a tuner/amplifier combination in modern home stereo systems). The heart of the stereo amplifier is the operational amplifier, or op-amp, which takes low level voltage signals as inputs and produces large output voltages that vary linearly with the input voltage.

Operational Amplifiers
The op-amp is a simple example of an integrated circuit. The common 411 op-amp used in this laboratory contains 24 transistors on a single silicon chip. Many integrated circuits are much larger: a computer's microprocessor can contain several million separate elements. Each transistor is a three terminal semiconductor device that controls a large current with a small one. If you later study electronics, you will learn about transistors. In this course, we will omit that stage and show how the functioning of op-amp circuits can be understood without knowing anything about the individual transistors of which op-amps are composed. You need only understand a few basic principles (explained below) and Kirchoff's circuit laws. Our reason for doing this lab is to show you how practical problems can be solved using electronic devices. These days, most scientists solve practical instrumentation problems using op-amps and other integrated circuits rather than discrete components.

An op-amp has three main terminals. The circuit symbol for an op-amp is shown in figure 1. The V- input is called the inverting input, the V+ input is called the non-inverting input, and Vout is the output voltage. All voltages are measured relative to the ground line of the power supply for the op-amp. All op-amps need a power supply in order to provide the amplification, since without a voltage higher than the input voltages it would be impossible to produce amplification. Generally the power supply is provided by connections at +15 V and -15 V to the op-amp. (Note that by convention, these power supply connections are not shown on the circuit symbol for the op-amp. However, you must always connect them up in the lab.) The supply voltages determine the maximum output voltage range of the op-amp, and if Vout reaches one of the supply voltages the op-amp is said to be in "saturation". This situation is to be avoided since if the op-amp is in saturation, its output cannot be varying linearly with the inputs.

[pic]
Figure 1: Op-amp inputs and output

The op-amp will amplify both AC and DC signals, although there is a high frequency f3dB (analogous to the f3dB or “cutoff frequency of a low-pass filter) determined by the type of op-amp; frequencies beyond this value will be amplified less and less as the frequency increases. We describe the signal amplifying properties of the op-amp by giving its gain, the ratio between the output signal and the input signal. In the so-called "open loop" configuration shown in figure 1, the output voltage is given by

[pic],(1)
where the open loop voltage gain A0 characterizes the op-amp. Note that the voltage difference between the inputs is amplified and not the voltage between an input and ground. If you add 5 volts to both inputs, this does not affect the output at all! Equation 1 makes it clear why V- is called the "inverting" input; it contributes negatively to the output signal.

The input impedance of an op-amp is typically 106 Ω although it can be as high as 1012 Ω in some models. The output impedance is usually very small. The gain A0 is extraordinarily high, typically 106 at low frequencies, so that an op-amp hooked up solely with two inputs and its supplies...
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