Open-loop gain

The open-loop gain of an amplifier is the gain obtained when no overall feedback is used in the circuit. Open loop gain, in some amplifiers, can be exceedingly high. An ideal operational amplifier (op-amp) has infinite open-loop gain. Typically an op-amp may have a maximal open-loop gain of around ${\displaystyle 10^{5}}$. The very high open-loop gain of the op-amp allows a wide range of feedback levels to be applied to achieve the desired performance.

Normally, feedback is applied around an amplifier with high open loop gain so that the effective gain circuit is defined and kept to a desired figure.

Definition

The definition of open-loop gain (at a fixed frequency) is

${\displaystyle A_{\text{OL}}={\frac {V_{\text{out}}}{V^{+}-V^{-}}},}$

where ${\displaystyle V^{+}-V^{-}}$ is the input voltage difference that is being amplified. The dependence on frequency is not displayed here.

Role in non-ideal gain

The open-loop gain is a physical attribute of an operational amplifier that is often finite in comparison to the usual gain, denoted ${\displaystyle G}$. While open-loop gain is the gain when there is no feedback in a circuit, an operational amplifier will often be configured to use a feedback configuration such that its gain will be controlled by the feedback circuit components.

Take the case of an inverting operational amplifier configuration. If the resistor between the single output node and the inverting input node is ${\displaystyle R_{2}}$ and the resistor between a source voltage and the inverting input node is ${\displaystyle R_{1}}$, then the ideal gain for such a circuit at the output terminal is defined, ideally, to be:

${\displaystyle G=-{\frac {R_{2}}{R_{1}}}}$

However, with the use of open-loop gain, the equation becomes:

${\displaystyle G={\frac {-{\frac {R_{2}}{R_{1}}}}{1+(1+{\frac {R_{2}}{R_{1}}}){\frac {1}{A}}}}}$

Notice that the equation becomes effectively the same for the ideal case as ${\displaystyle A}$ approaches infinity.

In this manner, the open-loop gain is important for computing the actual gain for a given non-ideal operational amplifier network in situations where the ideal model of an operational amplifier begins to become inaccurate.

Operational amplifiers

The open-loop gain of an operational amplifier falls very rapidly with increasing frequency. Along with slew rate, this is one of the reasons why operational amplifiers have limited bandwidth.