DAC Ladder Networks

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Inset A above is the symbol used for the collection of transistors that are, collectively, an operational amplifier. There are two inputs, + and -. The output voltage is equal to a gain A times the difference between the potentials of the two inputs. Typically, A is large, at least 10⁴ and usually 10⁶. Thus, a change of a few microvolts between the inputs can change the output by several volts. If we feed back some of the output to one of the inputs and anchor one input at a fixed potential, the only stable behavior is to have the potentials of the two inputs very close to each other. Thus, if we connect the output to the inverting (-) input, V_out = A(V⁺ - V_out) which, with a little algebra, gives V_out = A/(A+1) V⁺. Because A is big, A/(A+1) is close to 1, so the output potential equals the input. This re-enforces the point that the operational amplifier, properly wired, drives the potentials of its two inputs to nearly the same potential.