75.4.2. Finding Common Mode Gain

The basic operation and most important thing is that characterization of a differential amplifier. So, this is what we have discussed and this is what the corresponding small signal equivalent circuit and it is stimulus which is having combination of the common mode part and the differential parts.

In this chunk, we emphasize the distinction between differential and common mode gains. The differential amplifier analysis involves two important gains: the differential mode gain (Ad) and the common mode gain (Ac). The differential mode gain pertains to the amplification of the difference between two input signals, whereas the common mode gain deals with signals that are applied equally to both inputs. For accurate characterization, it is crucial to understand how the amplifier responds to both of these kinds of signals.

The terminology of 'equivalent circuit' refers to a simplified version of the actual complex circuit, which helps in analyzing behavior without the intricacy of the full system. This circuit illustrates how common mode and differential signals are treated separately to evaluate their gains effectively.

Think about how a pair of microphones can pick up both a conversation (differential signal) and background noise (common mode signal). When you want to record a conversation, you want to amplify the voices while minimizing the background noise. In this analogy, the microphones serve as the differential amplifier: they amplify the differences in sound (voices) while also measuring how much of the noise (common mode) is present. A good microphone setup would ideally have a high sensitivity to the conversation but low sensitivity to the noise.

To find Ad of this circuit, we take this circuit and then we consider that this part = 0. So, then the corresponding stimulus what you can see here it is common mode signal it is 0, we do have only the differential signal coming to the circuit. So, this kind of stimulus it is referred as differential mode of stimulus which means that the common mode component it is completely 0 and the signal coming here and here, they are perfectly complimentary to each other.

In this chunk, we focus on how to determine the differential mode gain (Ad). We 'turn off' the common mode signal component by setting it to zero, leaving the amplifier with just the differential signals at the inputs. This isolation enables the measurement of how well the circuit amplifies differences between the inputs.

The current through each input signal is complementary (opposite in direction), and this configuration allows us to measure the output specifically due to the difference, rather than any shared signals—demonstrating the amplifier's effectiveness in distinguishing between the two inputs.

Imagine a seesaw with two children of different weights sitting on opposite ends. The seesaw is balanced when the children hold the same weight of gifts each. Here, the weights are analogous to the inputs to the differential amplifier. If one child adds a large gift, the seesaw will tilt, representing the differential mode gain—showing the reaction to the differences in weight. The seesaw's behavior enables you to focus purely on this difference, ignoring any uniform weights they might both possess, akin to ignoring the common mode signal.

In this the second circuit, to find the common mode gain we are making these differential particles to 0. So, naturally, the v = Av whatever the vin we are applying and v on the other hand Av. Now v = 0, so that gives us v = 0. And hence the corresponding output v is just v and v, it is also v.

This chunk describes determining the common mode gain (Ac). We achieve this by removing differential components (setting them to zero), allowing us to analyze solely how the amplifier reacts to signals that are the same at both inputs. In this configuration, both input signals experience the same voltage, and therefore the output voltages will also be the same, as they reflect the input directly without any difference to amplify.

By calculating the output from these shared input signals, we can effectively determine how well the differential amplifier suppresses common signals, which ideally should yield a low output (indicating high common mode rejection).

Consider a scenario of two identical speakers playing music at the same volume in a room. If a listener positioned between them experiences balanced sound from both sides, the amplifying system is effectively managing common audio levels well. However, if one speaker fails, and both sounds become unbalanced, the listener may only hear music coming from one direction. In this case, to evaluate the speaker system's ability to handle equal sound inputs, you'd measure the resultant volume level to gauge how much the failure affects perception, paralleling how common mode gain is evaluated in the differential amplifier context.

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