5.1.4. Example of Non-Linear Circuit Analysis

So, dear students welcome to this course of Analog Electronic Circuits and today we are going to discuss some of our early topics namely how do we analyze a simple non-linear circuit. So, to start with we will be covering the diode circuits, but then whatever the concepts it will be discussed here, it is equally applicable in other non-linear circuits as well.

In this introduction, we outline the focus of our lesson on analyzing non-linear circuits, specifically starting with diode circuits. It is important to note that while we use diodes as our example, the analysis techniques we explore are applicable to various non-linear circuits. Non-linear circuits are characterized by their voltage-current relationships that are not straight lines, making their analysis different from linear circuits.

Imagine trying to drive a car along a winding road. Unlike a straight highway (linear circuit), the turns and slopes mirror the changing relationships in a non-linear circuit, like how a car speeds up or slows down depending on the incline.

So, what we are planning today, it is that we will start with non-linear circuit, we will try to seek how to find the circuit solution, namely the circuit voltage and circuit branch currents consistent with the KCL KVL of the circuit and also we will be seeing that the device characteristic need to be respected.

In this part, we identify our goals for the lesson: to determine circuit voltage and branch currents by applying Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL), alongside respecting the characteristics of circuit components like diodes. We'll learn how these laws help us understand how current and voltage behave in a circuit. KCL states that the total current entering a junction must equal the current leaving, while KVL states that the sum of potential differences (voltage) around a closed circuit must equal zero.

Think of KCL like water flowing in a pipe junction. The amount of water coming into the junction must equal the amount flowing out. KVL is similar to checking a budget: your expenses on one side of the equation should be balanced by income on the other.

So, then we will start with generalized methods namely graphical method or graphical interpretation of the method to find solution, then we will be covering iterative method which is finding numerical solution of a given circuit with known parameters and then we will be moving to practical methods.

We will explore several methods for analyzing non-linear circuits. One approach is the graphical method, which allows us to visually intersect various characteristics of circuit components to find solutions. Another approach is the iterative method, which progressively refines our guesses at the solutions using mathematical calculations until we approach the correct values. The goal is to apply these methods to effectively resolve the circuit analysis.

Consider trying to find the highest point on a hill. Using a graphical method would be like looking at a map to find where the slope meets the peak. Using an iterative method would be like taking small steps up the hill, each time checking your height and adjusting your path until you reach the top.

And that diode models the working model it today we will see that how it can be deployed for different examples and finally, will be giving a notion something called small signal equivalent circuit.

We introduce a diode model which helps us simplify our analysis of circuits involving diodes. This model captures the essential behavior of diodes and allows us to use it in various examples. Additionally, we'll explore the concept of a small signal equivalent circuit, a method for linearizing non-linear circuits so that they can be more easily analyzed. This concept is vital for understanding how small changes in voltage or current around a bias point affect circuit behavior.

Imagine trying to explain the rules of a complex game to a new player. Instead of sharing every detail, you create a simplified rulebook that captures the essence of the game but is easier to understand. Similarly, a small signal equivalent circuit distills complex behaviors into manageable forms for analysis.

So, let us see what is that method called, ok. So, this is what we already have just now we have discussed.

We move on to the iterative method, a step-by-step process to numerically approach the solution of the circuit. Starting with initial guess values, we calculate the current and voltage, refining these guesses iteratively until they converge on the actual solution that satisfies both KCL and KVL.

Think about baking a cake. Your first attempt might not be perfect, but each time you repeat the process, adjusting ingredients based on the taste and texture, you're iterating towards the ideal recipe. Similarly, in iterative circuit analysis, you're refining your guesses for voltage and current until they are just right.

--