Operational Amplifiers: The Ideal Op-Amp

the virtual ground

In an inverting amplifier, the minus input sits at 0 V even though no wire connects it to ground. The op-amp actively holds it there. It is called a virtual ground because, for the currents in the circuit, that node behaves exactly like ground, yet it is maintained by the op-amp's output rather than by a real connection.

Here is the mechanism in steps. The plus input is tied to real ground, so V+ equals 0 V. Negative feedback drives the minus input to match it, so V- becomes 0 V too (golden Rule 2). Meanwhile no current flows into the input itself (Rule 1), so any current you push toward this node has only one place to go: onward through the feedback resistor. Concretely, 1 V applied through a 10 kilohm resistor delivers 1 V over 10 kilohm equals 0.1 mA into the virtual ground, and that exact 0.1 mA continues through the feedback resistor.

This makes the inverting node a perfect summing junction: currents arriving from different sources simply add, because the node never changes voltage and the sources never see each other. That single fact is the foundation of the summing amplifier, the integrator, and the transimpedance amplifier. The caveat: it is only a ground while feedback is working. Disconnect the feedback or let the op-amp saturate against a rail, and the virtual ground is no longer at 0 V.

Feed 5 V through a 5 kilohm resistor into the virtual ground. The node stays at 0 V, so the resistor sets 5 V over 5 kilohm equals 1 mA, and that 1 mA flows on through the feedback resistor to form the output.

Because the node is pinned at 0 V, each input resistor sets a clean, independent current.

A virtual ground is held by feedback, not connected to ground. It cannot sink real load current to ground, and it collapses the instant the op-amp saturates.

Also called
virtual earth虛擬接地虛地