6.1.1. Lecture - 06

So welcome back, I hope you have solve the numerical problem and as I said that you your self 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.

This section introduces the topic of analyzing simple non-linear circuits and emphasizes the difficulty associated with using iterative methods for solving these circuits. Iterative methods often require multiple calculations to reach a solution, which can be time-consuming, especially in practical scenarios. The lecture indicates that while this approach can yield accurate results, there are more efficient methods available that can give accurate solutions in a single step.

Imagine trying to find the right temperature for cooking a dish by tasting it multiple times—taking bites and adjusting the heat each time. It's tedious! Instead, using a kitchen thermometer provides a quick check, allowing you to cook perfectly without guesswork. Similarly, in circuit analysis, finding better methods is akin to using a thermometer rather than relying solely on iterative tasting.

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.

In this chunk, the discussion revolves around making an initial guess for the voltage drop across the diode in the circuit. It is noted that for silicon diodes, a common initial guess for the voltage drop when the diode is in the 'on' state is about 0.6 volts. This forms the basis for calculating the current in the circuit, which is a crucial step in solving the numerical problem discussed earlier.

Consider starting a game with a known score—if the average score to win is around 60, beginning with a guess of 60 helps you focus your strategy effectively. Similarly, using a known value for the voltage drop helps streamline calculations in electrical circuits.

And, with this guess, if I consider V = 0.6. The value of this I you will be obtaining it is . So, what you are getting here it is 0.94 mA. Now, if you compare our previous numerical value, which it was close to if, I recall correctly 0.94023 something like this mA. So, if I compare this value, this value after third iteration you obtain versus this one, what we have it is the amount of error it is in fact, less than I should say 0.03 %.

Here, the calculated current based on the initial voltage guess of 0.6 V results in approximately 0.94 mA. This value is very close to a value obtained through a previous numerical procedure, indicating that our initial guess was quite accurate. The small error margin of less than 0.03% demonstrates the effectiveness of using informed guesses in circuit analysis, particularly when systems are non-linear.

Imagine predicting delivery times based on past experience—if 95% of the time, deliveries take just under an hour, your estimate will likely be pretty spot-on if you estimate around that same time. Similarly, making an educated guess about the voltage drop leads to a current calculation that is very accurate.

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.

This chunk explains how accuracy can be influenced by the initial guess. If a different guess of 0.7 V is used, the current calculation yields a value of 0.93 mA. Although this is slightly less accurate than the previous guess, it is still within an acceptable error margin of about 1%. This illustrates that small variations in initial assumptions can lead to differences in results but may still fall within practical limits for engineer calculations.

Think of estimating the distance to a destination. If you guessed it’s 10 miles but it's actually 10.3 miles, you’re still quite close! In engineering, being within even a small percentage can often be considered good enough.

So, this gives us one indication that probably we may have some practical method to replace this diode by a something call some model.

The lecturer suggests that instead of relying on complex iterative methods or empirical values, we can develop a simplified model for the diode. This model incorporates an ideal voltage drop and a small resistance, which allows for more straightforward calculations and can lead to quicker solutions without losing much accuracy.

Much like engineers might use models to predict structural reactions instead of constructing prototypes from scratch, here we’re looking at simplifying the circuit with a practical model that captures the essential behavior of the diode without convoluted 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 proposal of using a piecewise linear model means approximating the non-linear characteristics of the diode with linear segments. This method allows circuit analysts to tackle diode behavior in a way that simplifies calculations by treating different regions of operation linearly, thus facilitating easier analysis of the circuit's response.

Think about how you might approximate a curved path with straight lines for ease of navigation—by doing so, while you lose a bit of precision, you gain a much simpler route to follow. Similarly, the piecewise model simplifies the analysis of diode circuits while providing sufficient accuracy for engineering purposes.

So, let us see the application of this simple model. Let me redraw this circuit by replacing this diode assuming this V is higher than cutting voltage and hence the diode is in on-condition.

In this segment, the lecturer discusses applying the piecewise linear model to represent the diode when it’s turned on. The term 'on-condition' indicates that the diode conducts electricity, and its behavior can be modeled simply with its equivalent circuit to facilitate easier calculations in practical scenarios.

When driving, you adjust your speed based on traffic lights—when the light is green (on-condition) you can simplify your driving strategy as you don’t have to stop. Similarly, understanding when the diode is on allows for simplifications in circuit analysis.

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