75.4.1. Finding Differential Mode Gain

To find the differential mode gain of a circuit, we consider the stimulus where the common mode signal is set to zero. This means that the two signals applied to the input must be perfectly complementary, with no common mode component present.

Differential mode gain measures how effectively a differential amplifier amplifies the difference between two input signals while ignoring any signals that are common to both. To find this gain, we set the common mode component to zero, allowing only the differential signal to influence the output. This simplifies the analysis, enabling us to focus solely on how the amplifier responds to differences in input signals. Essentially, if we have an input signal at one terminal and its negative counterpart at the other, we are maximizing the amplifier’s ability to differentiate those signals.

Think of it like two people speaking to a judge about a dispute; only the differences in their stories matter. If they both were to say the same things, that would be similar to a common mode signal, and the judge's understanding would not change. However, when one person recounts an event differently, the judge can clearly see the essential differences, just as a differential amplifier highlights the variations in the input signals.

In this setup, if we denote the output voltage from one terminal as v_o1 and input voltage from the differential input as v_in_d, then the differential mode gain A_d can be expressed as A_d = v_o1 / v_in_d.

To calculate the differential mode gain (A_d), we take the output voltage from one terminal of the differential amplifier and divide it by the differential input voltage (v_in_d) that affected that output. This ratio gives us a clear understanding of how effectively the amplifier converts the voltage difference at its inputs into an amplified output. The gain should ideally be large, indicating that even small differences in the input signal can result in significant changes in the output.

Imagine you are using a pair of sensitive scales to measure the weight difference between two apples. If you place one apple on each side of the scale, a small weight difference will cause the scale to tip significantly. In a similar way, the differential mode gain reflects how a tiny difference in input voltage can lead to a large difference in output voltage, demonstrating the amplifier's sensitivity to input variations.

To determine the common mode gain A_c, we set the differential part of the input to zero. This means both terminals receive the same common mode signal, and we examine how the amplifier responds to this single input.

Common mode gain (A_c) is the measure of how much the amplifier amplifies signals that are present equally on both input terminals. To calculate this gain, we ensure that the differential input is zero, meaning we are applying the same voltage to both inputs. The output in this case should ideally be the same for both terminals, reflecting the inability of the amplifier to differentiate between them and thereby emphasizing its desired function of rejecting common signals while amplifying differences.

Think of it like a twin performance. If both twins dress the same and perform identically during a talent show, the judges can’t decide who’s better based solely on common outfits or actions. However, if one twin performs the song slightly worse or better than the other, it highlights a critical distinction. In this analogy, common mode gain illustrates the scenario when both twins (the input signals) are indistinguishable to the judges (the amplifier).

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