Gain at an Arbitrary Cut in a Linear Bilateral Network, and Its Relation to Loop Gain in Feedback Amplifiers

General expressions are derived for the gain around the loop formed by cutting into an arbitrary linear bilateral network. A test signal is injected into one side of the cut, the other side is closed by an element which forces the voltages at the two sides to be equal, and the gain at the cut is the ratio of the test current to the closing current. In a dual situation the closing element forces the currents at the two sides to be equal, and the gain is the ratio of the voltages. If a cut isolates a single element, the resulting gain is Bode's return ratio for that element. In general, neither the gain at a cut nor return ratio meets a usual expectation for loop gain in a feedback amplifier.