21.1. Analog Electronic Circuits

Welcome back after the short break on the topic of Linearization of input or output transfer characteristic.

So, we are discussing about this a small signal equivalent circuit we are about to start that, and the intension there it is of course, to get the simplified circuit.

This section begins by welcoming students back and introducing the topic of linearization in analog circuits. Linearization is the process of simplifying complex, non-linear relationships in circuits to make analysis easier. The objective here is to transform a non-linear circuit into a small signal equivalent circuit for simplification.

Think of linearization like trying to predict the temperature change in your house on a day when it suddenly gets warmer. Instead of accounting for every fluctuation in temperature, you might average it out to get a simpler, easier-to-manage understanding of how warm your house will get over time.

So, this model it is referred as large signal equivalent circuit and so, this model it is large signal model of the transistor and the whole circuit it is large signal equivalent circuit. In contrast to that whenever we are doing the linearization what you are doing is we are simplifying this current equation.

In this chunk, a distinction is made between large signal and small signal models. The large signal equivalent circuit of a transistor encompasses the full behavior under high signal levels. When analyzing circuits for small signals, only the small variations around a bias point are of interest. Therefore, in linearization, we focus only on the small signal part of the circuit, simplifying the overall analysis.

Consider driving a car: when changing speed rapidly, your car's acceleration represents a large signal. However, if you're cruising at a constant speed, slight adjustments to maintain speed represent small signals. We don’t care about major changes when we are only fine-tuning our position.

So, one important thing is that, whenever instead of say this model. So, I should say this is, this portion is the model of the MOS transistor, and this is referred as large signal model whereas, in the small signal equivalent circuit whatever the small signal equivalent circuit we obtain for the transistor, it is the small signal model.

This chunk highlights the transition from large signal models to small signal models, emphasizing that small signal models focus on simplified parameters like transconductance (gₘ). These models are crucial for analyzing circuits near their operating point, where larger fluctuations are not taken into account.

Imagine adjusting a recipe. If you were to drastically change ingredients (a large signal), you'd have to rethink the whole dish. In contrast, if you're simply adjusting the salt by a small amount (a small signal), the dish remains fundamentally the same but is refined.

And this parameter it is referred as a trans conductance of the device, particularly for the small signal. This is one of the important parameters, so whenever you are talking about the small signal model of the device, it involves one new parameter or new set of parameters rather and one of them is the g.

Transconductance (gₘ) is defined as the ratio of output current to input voltage in small signal models. It conveys how effectively a transistor can control the flow of current, which is critical for the performance of amplifiers and switches in circuits.

Think of a water faucet controlling the flow of water: the turn of the handle represents the input (voltage), while the amount of water flowing out is the output (current). Transconductance measures how effectively the faucet (transistor) adjusts this flow with a small turn.

So, if you consider that, what we will be getting is that of course, this I is dependent through this ( ) part, we may get a drain to source one conducting element. And, that conducting element is nothing, but the output conductance or drain conductance.

Output conductance (gₖ) refers to the change in drain current (I_ds) due to changes in the drain-source voltage (V_ds). Understanding this concept helps designers predict how the drain current reacts under varying voltage conditions, which is vital for circuit stability.

Imagine a sponge soaking up water: the output conductance is like how much the sponge can soak up based on its pressure against the water. The higher the pressure (or voltage), the more water that can be accommodated—until the sponge becomes saturated.

So just to simplify it is normally referred as high frequency small signal model, on the other hand if we drop this to capacity of element it is simply said it is small signal model of the MOSFET.

This concludes the discussion on small signal models by highlighting the need for adapting models to higher frequencies. In high frequency applications, additional capacitive elements and parameters come into play, which affect circuit behavior and design considerations.

Think of radio frequencies; as you try tuning into a station, higher frequencies may require better antennas to capture the signal effectively. Similarly, circuits at high frequencies need more complex models to function correctly.

So, let me consider what are the parameters are given to us it is say this is 10 V, let you consider this may be 2 V and let you consider V = 1 V for simplicity of calculation.

Finally, an example is used to practically demonstrate the principles discussed. The task is to compute the output voltage (v_out) based on provided DC parameters and to validate the operating point before calculating small signal gain, illustrating the process of applying the small signal model.

Suppose you're setting a budget for a party and want to find out how much you can spend per person based on a total. You have a total budget (like a power source) and need to allocate it effectively, similar to how circuit parameters guide output choices.

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