6.4.1. Using the Model in Circuits

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 issue with iterative methods (like trying to calculate current through a circuit step-by-step) is that they can be impractically slow. Engineers often find themselves repeating steps multiple times before getting an accurate result. Instead of relying on these time-consuming methods, it's suggested to seek out a more efficient alternative.

Imagine trying to bake a cake by tasting the batter repeatedly until you get the right flavor instead of following a tested recipe. This would take much longer than just using the recipe, similar to how iterative methods can unnecessarily prolong circuit analysis.

Yes, if we consider the same numerical problem, namely if I consider the V here and 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.

By using a calculated guess, such as assuming a silicon diode has a voltage drop of around 0.6V, we can significantly simplify our calculations. This guess allows us to find a solution to our problem in one step rather than going through many iterations.

Think about guessing the right temperature for a cup of coffee. Instead of checking the temperature a hundred times, you just take a good guess based on experience (like knowing coffee usually feels right at a certain warmth) to save time.

So, then just by one step itself we can find the solution. This is of course, one indication that how we are trying to get a practical method by the virtue of guess and proceed by one iteration, but then some people may say that no I do have a diode, it may be silicon diode, but I know that it is diode drop it is roughly 0.7. And, if we use a instead of 0.6 if you use 0.7, then also if you see the corresponding value of this I is . Of course, it is slightly different from this value; it is not as close as this one, but still if you compare this value and this value. I should say this amount of error it is in the order of just 1 % slightly above 1 %.

Using different guesses for voltage drop (like 0.6V vs 0.7V), we can track how close our answers are to the actual current. These calculations show that even with different initial guesses, the error in our final answer is small, remaining within an acceptable percentage range.

This is like estimating how many pages are left in a book. If you guess there are about 100 pages left, but reality is 102, your estimate is still quite close. It shows that sometimes a reasonable guess can lead to surprisingly accurate results.

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.

We can simplify our analysis by using a model for the diode that accounts for its behavior instead of the complex exponential characteristics. This model takes into account a threshold voltage Vγ and introduces a resistance that varies with current, thus allowing for more straightforward circuit analysis.

Consider how you might model the behavior of traffic lights. Instead of calculating the exact time each light stays green based on traffic conditions (which can vary), you’d assume a standard timing model for how long a light is typically green based on observed data.

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.

To make diode analysis easier, we adopt a piecewise linear model. This model simplifies calculations by breaking down the nonlinear behavior of the diode into segments that can be analyzed using linear equations. It helps engineers work within practical limits without needing complex calculations.

Imagine trying to estimate the cost of a taxi ride. Rather than using a complicated pricing algorithm based on time and distance, you might say a ride costs $5 for the first mile and an additional$2 for every subsequent mile. This way, you can more easily estimate the total fare.

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