21.2. Prof. Pradip Mandal

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.

In this chunk, the focus is on what linearization means in the context of electronic circuits, specifically when dealing with transistors. Linearization involves simplifying the input/output characteristics of a circuit to more easily analyze its behavior under small changes in operating conditions. By considering a small signal equivalent circuit, we can eliminate complexities while maintaining accuracy for small signal variations around a certain operating point.

Think about how you might simplify a complicated recipe when cooking. Instead of focusing on every little detail, such as exact timing and temperature, you might create a simplified version that emphasizes the key steps. Similarly, linearization in circuits helps engineers focus on the parts of the circuit behavior that matter the most for small changes in input.

So, you may recall the equivalent circuit if I consider the large signal behavior, what we said it is and the transistor may be replaced by a current source dependent current source.

A large signal equivalent circuit represents how a MOSFET behaves under larger input signals. In this model, the MOSFET is often represented by a current source whose output depends on the voltage across it (gate-source voltage). This allows for an understanding of how the transistor operates when significant signal variations are present.

Imagine a water faucet. When you turn the tap open a lot (large signal), the water flow is strong and corresponds to how a large signal circuit behaves. However, when you're just making small adjustments to the flow (small signal), the nuances of control become simpler to manage.

In contrast to that whenever we are doing the linearization what you are doing is we are simplifying this current equation, namely the drain to source current we are considering only the small signal part.

During linearization, we focus only on small signal variations when analyzing the MOSFET. This means calculating how slight changes in the gate-source voltage affect the drain-source current, thereby forming a small signal equivalent circuit. This version of the circuit simplifies analysis and provides a clearer understanding of the device's linear behavior.

Consider a light dimmer switch. If you're only adjusting the light slightly, you can ignore the more significant fluctuations of the entire light setup and focus on how small tweaks change the brightness just a bit. The same principle applies when transitioning from analyzing large signals to focusing on small changes in a circuit.

So, this factor it is it depends on the size of the transistor, it depends on the device parameter, it depends on the operating point also.

Transconductance (gm) is a crucial parameter in small signal models. It indicates how much the drain current changes in response to changes in gate-source voltage. This value is not constant; it shifts with the transistor's size, its material properties, and its operating point, which is the DC bias level the circuit is set to. Therefore, gm is essential for understanding and predicting the behavior of a MOSFET in a circuit.

Think of transconductance like the responsiveness of a lever. The heavier the load on the lever (or the size of the MOSFET), the more effort (or gate voltage change) you need to exert to move it. This responsive adjustment is vital for efficient control in electronic circuits.

If you consider that, what we will be getting is that of course, this I is dependent through this (λ) part.

Output conductance (gd) describes how the drain-source current varies with changes in the drain-source voltage while keeping other variables constant. It's represented mathematically, and it also significantly impacts the performance of the transistor, particularly concerning its ability to maintain stable operations under various output conditions.

Consider driving a car on a hilly road. The car's speed (drain current) changes with the incline (output voltage). If the incline changes (or there's an output variation), how well the car can maintain its speed without you accelerating (output conductance) shows how responsive the system is to changes in road conditions.

So, this model of course, it is I should say it is a simple enough part then, if this model it is sufficient for mid frequency range and low frequency range.

The small signal model developed for the MOSFET is simple yet effective for low to mid-frequency applications. However, in high-frequency scenarios, additional elements like capacitances must be considered to capture the complete behavior of the transistor. This model aids in circuit simplification and helps in determining gains in practical applications.

Think of this simplification as using a basic map for local navigation; it's great for low-speed driving. But as you approach a busy highway (high frequency), you need a more detailed map (adding capacitances) to navigate the complexities of more significant signal variations effectively.

--