# Operational Amp Model

## Introduction

All operational amplifiers (op amps) tend to follow the same basic model (shown in Fig. 1). Component modeling like this is commonly used to abstract and simplify circuit designs. This way we can think of the device as simply an individual component, and do not have to consider all of the sub-components within the op amp IC.

In general, op amps are governed by the following equation:

$$\Large V_{Output}= G_{open\;loop\;gain}*(V_{Non-inverting\;Input} - V_{Inverting\;Input})$$

$V_{Non-Inverting}$ and $V_{Inverting}$ represent the input voltages to our component (the voltages measured at each terminal with respect to ground). Terminal four in Fig. 1 is our non-inverting input terminal, and likewise terminal three is our inverting input. Overall the input to the op amp is really just the difference between these two terminals.

The output of the op amp (terminal 5) is then simply the difference between the two input terminals times a constant term called “open loop gain”. In General, “gain” is a measurement of the ratio of output signal compared to the input signal (a circuit with a gain of 2, means the output is twice as large as the input).

Open loop gain then is just the gain of the op amp by itself (without taking into consideration any external circuit configuration). Ideally, open loop gain is considered to be infinite, and in fact is made as large as possible on purpose to help performance of the circuit. This may seem confusing and quite impractical at first to have a component that tries to amplify an input signal to a theoretically infinite voltage. Op amps are almost always configured to have either “positive” or “negative” feedback loops. A feedback loop helps to stabilize the gain of an op amp at any desired level (below the open loop gain). The gain of an op amp circuit that utilizes feedback loops is known as “closed loop gain”.

You probably also noticed the $V_{cc}$ and $V_{ee}$ terminals in Fig. 1, these terminals are known as “rails”, “voltage rails”, or “supply rails”. Normally rails are not shown on schematics, but all op amps require them. “Rails” can be thought of as the power source for the output signal. When building an op amp circuit $V_{cc}$ (some op amps manufactures refer to $V_{cc}$ as “V+”) should always be connected to a positive voltage source, where $V_{ee}$ should be connected to a negative voltage source (alternately can be referred to as “V-”). The link to the right shows an example of negative voltages. Some op amps (like the TCA0372 for example) are designed to work with either one or two source voltages (in the case of using just one source, Vee is tied to ground).

It is very important to understand that the output voltage of an op amp comes from the “rail” voltage source and not from the input to the op amp. So accordingly, output voltage can never exceed rail voltage. The rail voltage can be thought of as the maximum and minimum bound of the output signal. Whenever the output signal does try to exceed the rail voltage, it is clipped (or limited) at the rail voltage. This property is called “saturation”, and is common to all op amps. The link to the right shows an example of saturation.

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