Operational amplifier: how does it work?

The operational amplifier, or op-amp, has great utility on electronics. In this post, it’s shown the operation of this integrated circuit (IC).

Operation

It has two inputs, one inverting and another non-inverting and, an output.

Op-amp can be supplied by a simple DC power source or a symmetric source. The latter type of source has three terminals: positive voltage, GND and negative voltage. To use a simple power source, Vee must be linked to GND. To supply op-amp with a symmetric power source, negative voltage terminal must be connected to Vee.

Operational amplifier supplied by a double power source. Source: Mundo Projetado.

Ideal op-amp and virtual ground

An ideal op-amp would have an infinite input impedance, output impedance equal to zero, an infinite voltage gain in open loop and the component would be immune to temperature variations.

In circuit analysis with this component, it’s common to use the concept of virtual ground. Consists in consider both voltage inputs as zero, even though V2 isn’t electrically connected to ground. Source: electroSome.

Operational amplifier equivalent circuit. Source: embarcados.

In an ideal operational amplifier, output impedance ( $Z_{out}$ ) is zero, therefore:

$V_{out}=A\cdot V_{in}$

V_{in}

is difference between the voltages

V_{p}

and

V_{n}

. Since voltage gain

A

is infinite,

$V_{in}=\frac{V_{out}}{A}=\frac{V_{out}}{\infty}=0$

$V_{in}=V_{p}-V_{n}$

$V_{p}=V_{n}$

Virtual ground is useful to analyze circuits with op-amp, whose gain is too high. Allowing simpler calculations with good approximation.

The real operational amplifier

A real op-amp has a very high impedance, low output impedance, high open loop gain, however are limited. Also exists an offset voltage, which is a voltage value on output when input terminals are in short-circuit. Real amplifiers have slew rate (SR), which is the maximum rate of output voltage variation, measured in $V/\mu s$ (voltages per microsecond).

operational amplifier transfer function — This graphic is real operational amplifier’s transfer function. vO and vD are output voltage and difference between two inputs respectively. In a real op-amp, for vO becomes zero, it’s necessary to apply a voltage difference on inputs ( $V_{OS}$ ). $VO_{min}$ and $VO_{max}$ are minimum and maximum values to amplifier obtains saturation. The region between saturation values is linear, where op-amp must operate. Source: Mundo Projetado.

Other important difference is the frequency range operation or band width. An ideal op-amp would have infinite band width, would operate in the same way in any frequency on input terminals. While the real has a limited frequency range, where it’s gain is constant and it’s decay when passes the limit of band width.