3.5. Non-linear Circuit and Approximation

Now we will be moving to another topic the non-linear circuit and its corresponding approximation. So, we may start with simple DC diode circuit and the corresponding I-V characteristic.

In this chunk, we introduce the concept of non-linear circuits, particularly focusing on diodes and their characteristics. Non-linear circuits do not have a direct output-to-input proportionality, meaning their response changes with input levels. Diodes are a common example of non-linear components, as their current-voltage relationship does not follow a straight line but instead forms a specific curve.

Think of a non-linear circuit like a garden hose with a nozzle. When you partially cover the nozzle with your thumb (like applying a diode in reverse bias), the flow of water diminishes dramatically (like reverse saturation current). Conversely, when you completely remove your thumb, the hose flows freely, representing forward bias where the diode conducts. The varying flow illustrates how non-linear circuits behave differently based on the amount of input, similar to how voltage affects current in a diode.

And then we can see that what may be the input to output transfer characteristic. So, just to give you as an example let you consider one simple circuit containing one resistor and one diode and then we do have a voltage applied across this one.

In this chunk, we explain how to analyze the input-output relationship using a simple circuit with a resistor and diode. The current-voltage (I-V) characteristic of a diode describes how the current flowing through the diode changes as the voltage across it varies. This relationship is typically represented in a graph where the x-axis is voltage and the y-axis is current. As the voltage increases in the forward direction, the current rises exponentially after a certain threshold known as the cut-in voltage. In contrast, if the voltage is reversed, only a small leakage current flows until a breakdown point.

Imagine a rollercoaster (the current) that only starts moving when the climb (voltage) reaches a certain height (cut-in voltage). Below that height, the coaster remains stationary (no current). Once the rollercoaster reaches that height, it gains speed rapidly, illustrating how diodes only start to conduct current above that threshold voltage.

And, then what you may say about the voltage; the obvious answer probably you may be knowing the diode characteristic and the diode characteristic which is I equals to diode current equals to I_0(e^(VD/q)-1), reverse saturation current e to the power the voltage across this diode divided by n Boltzmann constant k and then temperature in Kelvin; typically, this non ideality factor n we consider 1, q is charge.

This chunk delves into the mathematical representation of the diode's I-V characteristics, particularly the ideal diode equation: I = I_0(e^(VD/q) - 1), where I_0 represents the reverse saturation current. The equation demonstrates that as the voltage (VD) across the diode increases, the current (I) flowing through it will increase exponentially. The reverse saturation current (I_0) indicates how much current flows through the diode when it’s reverse biased at zero voltage.

Think of the diode as a fountain. When there’s no water (voltage) in the fountain, a small amount of water (reverse saturation current) might leak out. But as you turn the faucet (apply voltage), water starts gushing out more and more vigorously as you open the valve further (higher voltage), representing the exponential increase in current.

So, of course, we do have another part minus one. Particularly this minus 1 part is very important if the diode is in reverse bias condition.

This last chunk focuses on the significance of the '-1' in the diode equation. This term indicates the current flow when the diode is reverse-biased. In practical applications, knowing how a diode behaves under reverse bias is crucial for designing circuits that require specific performance characteristics, such as protection against back voltage or reverse currents.

Consider a locked gate (the diode in reverse bias). When closed, only a tiny trickle of water can seep through (reverse saturation current). But if you open the gate fully (forward bias), a flood of water rushes in. Understanding both scenarios helps determine how to set up a security system that allows flow in one direction while minimizing escape through the locked gate, similar to how diode functions in electrical circuits.

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