Operational amplifier characteristics

An operational amplifier (op-amp) produces an output voltage in response to the difference between two input voltages. Its signal connections are the non-inverting input, $$V_+$$, the inverting input, $$V_-$$, and the output, $$V_{\mathrm{out}}$$. These voltages are measured relative to a common reference.

Separate power-supply connections provide the energy needed for operation. They also limit the range of output voltages the op-amp can produce.

Ideal operational amplifier

An ideal op-amp has infinite input resistance, so no current enters either input. It also has infinite open-loop gain. In the ideal, unconstrained linear model, even an arbitrarily small non-zero difference between the inputs would demand an arbitrarily large output. In practice, the output cannot grow without limit because it is constrained by the power supplies.

Real open-loop behaviour

For a real op-amp operating in its linear open-loop region, the output voltage is proportional to the input difference:

Here, $$A_{\mathrm{OL}}$$ is the finite open-loop voltage gain. If $$V_+ > V_-$$, the input difference is positive and the output is positive. If $$V_+ < V_-$$, the difference is negative and the output is negative.

This proportional relationship applies only while the calculated output is within the op-amp’s practical output range. Beyond that range, the output reaches a limit rather than continuing to increase in magnitude.

Operational amplifier as a comparator

An operational amplifier can compare two voltages and indicate which is greater. Its two inputs are the non-inverting input, with voltage $$V_+$$, and the inverting input, with voltage $$V_-$$.

When the amplifier is used open-loop, its output is not fed back to either input. Its open-loop gain is very large, so even a small difference between the input voltages drives the output towards a saturation level:

• If $$V_+ > V_-$$, the output moves towards positive saturation.
• If $$V_+ < V_-$$, the output moves towards negative saturation.

The saturation levels are limited by the amplifier’s power supplies. They are not necessarily exactly equal to the supply voltages.

Comparing a signal with a reference voltage

One input can be held at a fixed reference voltage, while the other receives a changing signal. As the signal crosses the reference, the output changes between its two saturation states.

• Signal at the non-inverting input: when the signal rises above the reference, $$V_+ > V_-$$, so the output moves towards positive saturation.
• Signal at the inverting input: when the signal rises above the reference, $$V_+ < V_-$$, so the output moves towards negative saturation.

Swapping the inputs therefore reverses the output state produced by the same signal.