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Differential to single ended conversion
Introduction and Theory

In this experiment, we study an interesting combination of differential pairs and current mirrors that proves useful in many applications. To arrive at the circuit, let us first address a problem encountered in some cases. Recall that the op amps have a differential input but a single-ended output. Thus, the internal circuits of such op amps must incorporate a stage that “converts” a differential input to a single-ended output. We may naturally consider the topology shown in Figure as a candidate for this task.

pendulum

The circuit of Fig. above presents a quandary. While the transistors themselves are symmetric and the input signals are small and differential, the circuit is asymmetric. With the diode connected device, M3, creating a low impedance at node A, we expect a relatively small voltage swing—on the order of the input swing—at this node. On the other hand, transistors M2 and M4 provide a high impedance and hence a large voltage swing at the output node. (After all, the circuit serves as an amplifier.) The asymmetry resulting from the very different voltage swings at the drains of M1 and M2 disallows grounding node P for small-signal analysis.

The voltage gain is given by

pendulum

This is the exact expression for the gain.

pendulum