71.2.1. Representation of Signals

Suppose we do have say one signal something like this. See v in1. So, we do have one sinusoidal part and on top of that with respect to that we do have seen v in1. So, we may say that this pink colour is v in1 and then if I consider say v in2. So, that is also with respect to this dotted blue line and that is also sinusoidal, but it is in opposite phase. So, the pink one you may say it is true signal and the red one it is the complimentary signal.

In this chunk, we describe the characteristics of single-ended signals versus differential signals. Single-ended signals like v_in1 are represented in a simple sinusoidal waveform. Differently, v_in2 is also sinusoidal but is phase-inverted compared to v_in1. When we look at both, the pink signal (v_in1) represents the true or original signal, while the red signal (v_in2) reflects an inverted version, commonly referred to as the complementary signal. These concepts are foundational for understanding how differential signaling works, which uses two signals to carry the same information in opposite phases.

Consider a seesaw in a playground. One side going up represents the positive signal (v_in1), while the other side with its downward motion represents the negative or inverted signal (v_in2). Just as a seesaw relies on its two ends to function efficiently, differential signals rely on both v_in1 and v_in2 to ensure efficient data transmission and error correction in electronic circuits.

If you try to represent say these two signal namely the pink colour and red colour in terms of say differential and the common mode component. So, let me draw the differential part, let me use a colour say green. So, here you can see that the signal here it is large up to this point let me use different colour otherwise you may get confused.

In differential signaling, we also consider common mode and differential components. The common mode signal represents the average level of the two signals (like the blue line referred to), while the differential signal illustrates the difference between the two (represented by the green signal). The differential signal is essential for amplifying the desired information while the common mode signal helps to eliminate noise, enabling clearer signal processing.

Imagine two people speaking into two different microphones at a concert. The sound of both microphones represents the common mode (background noise). In contrast, the difference in their voices, like one saying 'hello' while the other says 'hi,' represents the differential mode signal that the sound system is designed to amplify. A good sound system reduces the common background noise, allowing the actual conversation to be heard clearly.

Now, suppose your main signal is this one the violet colour one, but then you do have a lot of disturbance getting represented by this blue signal and in case if you want to really find the find out this signal and if you extract this remove the noise part, the blue part then you can take help from this differential amplifier.

Differential amplifiers are designed to amplify the difference between two signals while rejecting any common signal (noise). The violet signal represents the desired information, while the blue part represents noise or disturbances. By feeding both signals into a differential amplifier, we can significantly enhance the true signal (violet) by diminishing the noise component (blue), resulting in a clearer output.

Consider a noise-canceling headphone. When activated, the headphones listen to the surrounding noise (like the blue signal) and create an opposite sound wave that cancels it out. This allows the user to hear their music or a podcast (the violet signal) much clearer without interference from the noisy environment.

If I say that it is a differential mode gain ad it is said high. So, if this is say high quote and unquote high and the common mode gain ac if I say it is having low value then at the output whatever the v you will get v o_d will be amplified. The amplified version of this signal and then if it is low common mode gain, it is low then this blue colour part it will be also coming here as common mode, but its strength it will be less.

This chunk contrasts the differential gain (A_d) with the common mode gain (A_c). For an ideal differential amplifier, the goal is to have a high differential gain—meaning it amplifies the desired signal effectively—while the common mode gain should be minimal. High differential gain amplifies the desired signal while low common mode gain minimizes unwanted noise. For example, if a signal produced at the input is 2V and the common mode gain is low, then noise components are substantially reduced at the output, equating to a clearer signal.

Think of a filter coffee maker. When coffee grounds (representing noise) are placed in the filter, the water (representing the signal) still passes through as a rich beverage while capturing only a few grounds in the filter (the common mode). A powerful filter ensures you get pure coffee (high differential gain) and only a little residue (low common mode), resulting in a delightful cup.

Now if I write this equation say this equation what we can say that v = A × v o_d d in_d. So, likewise if I see this equation, we can see that v = A × v o_c c in_c.

In this chunk, we discuss the mathematical representation of output signals from the different signal inputs. The output for the differential mode is represented as v_o_d = A_d × v_in_d (the differential input), while for the common mode it is v_o_c = A_c × v_in_c. These equations emphasize how the output is derived from both differential and common inputs, revealing the respective impacts of the gains applied to each type of signal.

Imagine a bakery. The amount of actual dough you let rise (differential input) determines the quality of bread produced (differential output). Meanwhile, any leftover flour or excess ingredients (common input) that tend to be wasted can lead to less efficient baking. Understanding and managing each input properly ensures a delightful end product!

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