75.3.1. Input and Output Relationship

So, to recapitulate whatever we have discussed in our previous lecture we do have say this is a main differential amplifier. Where we have the power supply DC supply and ground and then at the input we do have the differential input port having two terminals 1 and 2 and at this input we are given signal or I should say voltage signal and it is having a DC part meaningful DC part and on top of that we do have two signals. One is v in1 and v in2.

In a differential amplifier, there are two input terminals, typically referred to as terminal 1 and terminal 2. Signals are applied to these terminals, comprising both a meaningful DC component and an AC signal. The DC component of the input voltage ensures that the amplifier operates correctly, while the AC signals (v in1 and v in2) can vary to perform the amplification. It's crucial that the DC levels applied to both terminals are compatible to avoid distortion of the input signals.

Think of a differential amplifier as a person listening to two different conversations at a party. The DC part is like a common background noise level everyone needs to be aware of, while the actual conversations (v in1 and v in2) are the specific signals they want to hear and amplify. Properly adjusting the background noise level allows the person to focus on the conversations without getting confused.

Now, whenever we are talking about the DC level at the output and the DC level at the input, they may be having some relationship, but that relationship cannot be expressed by the two parameter what we have discussed is A and A. A and A they are essentially representing small signal relationship.

The output of a differential amplifier has a DC level that is influenced by the input's DC level. However, the relationship between these DC levels cannot simply be described by the amplifier's differential and common mode gains (A d and A c), which describe how the amplifier behaves with AC signals. Instead, understanding the output requires analyzing the overall nonlinear characteristics of the circuit, meaning both the DC and AC responses need to be considered.

Imagine the amplifier as a restaurant. The input DC signals are like the base prices of menu items, while the AC signals represent special toppings or ingredients that can change the overall dish price. While you establish the base price (DC level), the different combinations of toppings (AC signals) alter the final price dynamically. Knowing just one of these factors doesn’t give the entire picture; understanding both is essential for pricing the meal accurately.

So, in this circuit, whenever we will be talking about it is corresponding input and output what we will be talking is the input it is with respect to ground.

In analyzing differential amplifiers, we often focus on what is known as the small signal equivalent circuit. In this circuit, we simplify the analysis by assuming that the DC components do not change, leaving us to concentrate on the small AC signals around a ground reference level. This simplification allows easier calculations of gain and signal handling without concerning ourselves with the complexities brought in by large DC signals.

Consider small signal analysis like tuning a musical instrument. When tuning, the established pitch (DC signal) is your reference point. The small adjustments you make to bring the notes to harmony (AC signals) are what actually matter in the moment, allowing for a cleaner and clearer sound without distortion from external noise.

Now, once we are in small signal equivalent circuit, then it is basic parameters are differential mode gain and common mode gain.

In the small signal equivalent circuit of a differential amplifier, two important parameters are analyzed: differential mode gain (A d) and common mode gain (A c). Differential mode gain measures how well the amplifier enhances signals that appear differently at the two inputs, while common mode gain measures the amplifier's response to signals that are identical at both inputs. Ideally, you want A d to be as high as possible and A c to be as low as possible, ensuring that the amplifier effectively amplifies the wanted signal while ignoring noise or interference.

Imagine you're at a concert where a singer is performing on stage (the desired signal). The singer's voice is like the differential mode signal you want to amplify. Meanwhile, the background noise of the crowd (common mode signal) can inadvertently interfere. The goal of the sound engineer (differential amplifier) is to boost the singer's voice significantly, ensuring it overpowers the crowd's noise, making it clear and audible for everyone. The effectiveness of this task is what is quantified by the differential and common mode gains.

Now, to see the output in terms of whatever the input we are applying here and in case if we have say these two parameters namely the common mode gain and differential mode gain.

To determine the differential mode gain (A d) and common mode gain (A c) for a given circuit, we utilize specific configurations of input signals. For A d, we focus on input signals that are equal and opposite at the terminals (creating a pure differential signal), and for A c, we ensure the differential components are zero so only common signals are analyzed. This process allows us to calculate and characterize how well the amplifier performs in these conditions.

Calculating the amplifier's gains is like measuring the performance of athletes in different events. To evaluate a sprinter's speed (A d), you measure their sprint without the encumbrance of teammates (differential input). For a team relay (common mode gain, A c), you assess how well the team runs together, ensuring they are running under identical conditions. By isolating these performances, you can gauge individual capabilities effectively.

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