6.6.1. Iterative Method

So welcome back, I hope you have solve the numerical problem and as I said that you yourself have try to see, whether it is converging or not. But, interesting thing is that this kind of method is very impractical for an analysis, because even for simple circuit if we have to go through number of iteration and as I said that based on the slope. The convergence may or may be there or it may converge, but it may take more time based on this condition. So, it may not be good idea to stick to this one it is better to look out some other alternative ok.

The initial part of the iterative method emphasizes its impracticality. Solving a numerical circuit problem often requires several iterations to determine if the solution is converging to the correct value. This can be tedious and time-consuming, particularly for even simple circuits. The text suggests that relying solely on this iterative approach may not be efficient; thus, seeking alternative methods is advisable.

Consider trying to find the shortest route on a map by randomly following streets until you eventually reach your destination. While you may eventually get there, this method is tedious and could take a long time. A better approach would be to use a GPS or map app, which gives you the best route immediately. This analogy helps illustrate the inefficiency of the iterative method in circuit analysis.

Yes, if we consider the same numerical problem, namely if I consider the V here and in then we do have the resistance of 10 k, and then we do have the diode here, and then if we observe the corresponding output, by considering one initial guess. And, this initial guess it is not just arbitrary, typically we know that if it is silicon diode and if the diode is on the drop across this diode is roughly 0.6 V. And, with this guess, if I consider V = 0.6. The value of this I you will be obtaining it d R is . So, what you are getting here it is 0.94 mA.

In approaching the numerical problem, an explicit guess can be used to increase the likelihood of obtaining a quick and accurate solution. By assuming a typical voltage drop (0.6V) across a silicon diode, one can initially set the voltage, calculate the output current, and reach a value close to an expected result (0.94 mA in this case) quickly. This method demonstrates how informed initial guesses can enhance accuracy while reducing the number of iterations needed.

Think of baking a cake using a recipe. If you know to expect a specific temperature for the oven (say 350 degrees), you can start with that guess. Even if you're off by a few degrees, your cake might still turn out well enough, compared to starting from 0 and experimenting with various temperatures. Here, you used your knowledge of what typically works (like using a voltage drop of 0.6V) to guide your calculations.

So, this gives us one indication that probably we may have some practical method to replace this diode by a something call some model. So, what is that model? We may consider if the diode is on drop across this diode it is may be around 0.6 or 0.7 and let you call this voltage is Vγ. And, but then if depending on the current level, the voltage drop across this resistance diode it may not be remaining same.

The section introduces the idea of modeling the diode using a practical approach. Instead of relying on complex exponential functions, a simpler model of a diode can be established using a constant voltage drop (either 0.6V or 0.7V) represented as Vγ. Moreover, the voltage drop may vary based on the current flowing through the diode, indicating that real-life diodes do not always behave ideally. This model helps simplify the analysis of circuits involving diodes.

Imagine driving a car. The engine might work best at a specific RPM, and you're likely to shift gears based on accruing speed. Similarly, the diode model shows how we can represent its behavior with a simple voltage drop, making it easier to understand without getting bogged down by complex calculations.

So, we can say that this is the model will be using instead of using our exponential relationship for practical purposes. So, instead of this exponential relationship we will be going for this piece wise linear model.

The piecewise linear model offers a practical solution for representing diodes in circuit analysis. This model recognizes the behavior of a diode in two conditions: the 'on' state, where it has a voltage drop, and the 'off' state, where it is effectively an open circuit with a high resistance. By simplifying the diode's characteristics into linear segments, analysis becomes clearer and calculations more manageable.

Think of a traffic signal controlling a busy intersection. It changes colors at specific intervals. The red light can be thought of as a high-resistance (open) circuit, stopping all cars, while the green light allows traffic to flow (conducting state). By considering the stop and go states, rather than every nuanced change, makes controlling traffic much simpler.

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