18.1. Linearization of Non – Linear Circuit Containing BJT

So, dear students welcome back to this course on Analog Electronic Circuits. Myself Pradip Mandal from IIT Kharagpur, I am associated with the Department of E and ECE. Today’s topic for this course is Linearization of Non-Linear Circuit Containing BJT.

In this introduction, Professor Pradip Mandal welcomes the students back to the course on Analog Electronic Circuits and states that the focus of today's lesson is on linearization techniques applied to circuits that contain Bipolar Junction Transistors (BJTs). Linearization is important because it simplifies the analysis of circuits that are inherently non-linear, especially when dealing with small fluctuations around a given operating point.

Think of trying to understand the path of a ball thrown into the air. While the trajectory is actually a complex curve, if you only focus on a small part of the journey (like just after the throw), you can simplify the analysis to a straight line. This is similar to how engineers look at small signal variations in non-linear circuit behaviors.

So, what are the concepts we are going to cover in today’s presentation? As I said that we will be covering the linearization of non-linear circuit containing BJT, then the notion of small signal equivalent circuit...

In this segment, the professor outlines the key topics that will be addressed. The discussion will include how to linearize the characteristics of a non-linear circuit—especially focusing on BJTs. The concept of small signal equivalent circuits will also be introduced, which allows engineers to simplify their analysis of signals that are small compared to a larger operating point.

Imagine checking the blood pressure of a patient. In a healthy individual, if you take a reading, the pressure may fluctuate. However, if you focus on small changes just around a person's normal range, you can simplify your analysis instead of factoring in extreme fluctuations. This simplification is akin to linearization in electronics.

When we say linearization of a non-linear circuit we are primarily focusing the narrow range of the input or output transfer characteristic...

This chunk explains the core concept of linearization: focusing on a narrow bandwidth of the input-output characteristic curve of a non-linear device, like a BJT. Essentially, even when the characteristics of the circuit are non-linear across larger ranges, within this narrow band, we can treat them as if they were linear. This facilitates easier mathematical treatment and prediction of circuit behavior.

Think of how a car's speedometer works. It's designed to give you an accurate reading when you're within normal driving speeds. If you're speeding or slowing down very rapidly, the reading might not be accurate. In a similar way, linearization takes a 'snapshot' of normal operating conditions to create simple models.

Then we will see the notion of small signal equivalent circuit... the non-linear circuit characteristic can be linearized.

In this chunk, the concept of small signal equivalent circuits is put forward. This involves taking the non-linear characteristics of the circuit and translating them into a linear form for analysis, under the condition that signal variations remain within a small range. The small signal models allow engineers to apply simpler linear circuit analysis techniques.

Consider a bendy straw. If you’re drinking a normal amount of liquid, it works perfectly. However, if you try to drink a massive amount too quickly and the straw bends at an angle, it becomes ineffective. The small signal equivalent is like ensuring you're only trying to draw small gulps of liquid, maintaining effective performance.

This circuit contains the BJT NPN transistor and it is having a base bias with a voltage...

This part dives into the practical example of a circuit with a BJT. Here, the relationship between the input voltage (base-emitter voltage) and the output voltage (collector-emitter voltage) is discussed. The output response is dependent on changes to the input signal, and the professor details how these characteristics can be plotted to form an input-output graph.

Imagine a dimmer switch for a light. Gradually increasing the switch increases light output, but if you crank it too quickly, the light may flicker unexpectedly. A similar relationship exists here where small changes in input can cause proportional changes in the output, especially in linear regions.

Let me go a little more detail of the linearization. So, what we are doing is basically we are making use of these two equations...

This section focuses on the mathematical side of linearization, highlighting the specific equations used when calculating the output voltage based on small signal variations. The essence is that by keeping track of changes in voltages, we can determine the overall effect on the circuit's output, thereby simplifying the complex behavior of the transistor to a manageable analysis.

Think about baking a cake. If you add a little too much of one ingredient, a small change can be easily accommodated. However, if you change the amounts drastically, it can ruin the cake. The same goes for linearization: small changes are easy to calculate and manage, unlike large fluctuations.

To summarize then v , v , it is the small signal part... of the transfer characteristic and considering only the small signal part.

In conclusion, the focus is reiterated on translating the input-output non-linear relationships into linear terms, centering around the operating point (Q-point). This few-point focus simplifies analysis and helps in drawing meaningful conclusions from the circuit's behavior under small signal conditions.

Imagine guiding a ship through a foggy sea. You can only see a short distance ahead, so you navigate carefully based on what’s directly in front of you. Linearization is like navigating through small increments of visibility, ensuring you reach your destination safely while avoiding the unpredictable aspects of the ocean.

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