This next topic focuses on the operational amplifier, which is one
of the most widely used electronic components in the analog world. The operational amplifier, also known as an
op-amp, is a type of differential amplifier.
The output voltage of an op-amp is:

Op-amps are used in a variety of applications, which perform many
different operations, hence the name. External
passive elements – such as resistors, caps, inductors, etc – are used to
determine the end function. Before continuing
into any applications, you should consider the following properties of an ideal
op-amp.

__Ideal OP-AMPs have:__

Infinite input impedance

Zero Output Impedance

Infinite Differential Gain

Zero Offset Voltage

Zero Input Bias Current

Zero Common Mode Gain

Recalling our previous equation and substituting Aol=∞ produces
the following relationship for the non-inverting and inverting inputs.

This equation merely demonstrates that for an ideal op-amp, both
inputs are the same voltage value, so in a sense both inputs are virtually
shorted to each other.

Using these properties, you can solve any ideal op-amp circuit
configuration. To get you started in
op-amp analysis, I’ve provided a simple circuit below, which is an inverting
op-amp configuration.

Using KCL, let’s guess the current direction and solve for node 2.

What happens when I substitute a voltage for the V+ input?

I’ll leave this next configuration as homework:

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