4.3.3. Characteristic Curve Analysis

Now, we are going to talk about analysis of non-linear circuit and the corresponding approximation. We are considering a simple diode circuit as shown here. It consists of the input voltage V which is applied to a series connection of a resistor R and a diode. The output you are observing is the voltage across this diode V_D. Now, as you know that this diode I-V characteristic it is non-linear. So, we know that the current flowing through a diode I_D, it is a strong function of the voltage across this diode V_D to be more precise it is exponential, which can be written as I_D = I_O (e^(V_D/(n * V_T)) - 1).

In this part, we introduce the non-linear nature of diodes. When a voltage is applied to a diode, it doesn't produce a linear increase in current. Instead, it exhibits an exponential relationship between the voltage across it and the current flowing through it, known as the I-V characteristic. The equation describes how the diode's current, I_D, depends exponentially on the diode's voltage, V_D. Here, I_O represents the reverse saturation current, n is the ideality factor (generally close to 1 for silicon diodes), and V_T is the thermal voltage.

Imagine a garden hose: when you first open the tap, only a small amount of water flows out. As you increase the tap’s opening, the flow dramatically increases. Similar to how water pressure leads to more water flowing from the hose, increasing voltage leads to exponentially more current flowing through the diode.

We can split this characteristic curve into two parts; one is when V_D < V_γ the diode is OFF, and the other one it is when V_D > V_γ so we can say then the diode it is ON. So, you can see in OFF region this I_D = 0 and if it is ON we can say that this is exponential dependency.

Diode operation can be divided into two key states: OFF and ON. When the voltage across the diode (V_D) is less than the cut-in voltage (V_γ), the diode does not conduct current (I_D = 0), effectively acting like an open switch. Once V_D exceeds V_γ, the diode turns ON, and the current starts to flow exponentially. This behavior is crucial for understanding how diodes function in electronic circuits.

Think of a light switch: when the switch is off, no electricity flows (the light is off). When you turn the switch on (voltage exceeds a certain threshold), electricity flows, and the light turns on (current flows through the diode).

If the diode is ON then we can approximate this characteristic curve by a straight line. On the other hand, if it is less than V_γ then we can say the current ≈ 0. In this approximated straight line what we can say is that this I_D ≈ V_D / r_on, where r_on is the ON resistance of the diode.

When the diode is in ON state, its current can be approximated as a linear function of voltage. This simplification allows us to easily calculate the current flowing through the diode as a ratio of the voltage across it to its resistance when ON (r_on). If the voltage is below V_γ, no current flows, simplifying analysis in the OFF state to I_D ≈ 0.

Imagine a ramp leading to a flat surface. When you reach a certain height (cut-in voltage), the transition from the ramp to the level surface represents the ON state where movement is straightforward and linear. If you haven’t reached that height, you can’t move (no current). This linear approximation helps in calculating movement easily.

So, here we are going to analyze the same circuit, but then the diode we like to replace by its approximated I-V characteristic curve. If the voltage drop across the diode is V_D and it is more than this V cut-in voltage, then the corresponding current is given. So, if we replace this diode; by this circuit what we can get here it is the output voltage; output voltage as function of this input voltage that can be simply obtained by considering the V_out which is V_in - R * I.

To calculate the output voltage (V_out), we can use the relationship established by our approximated I-V characteristic curve for the diode. Under the assumption that the diode conducts, the output voltage can be obtained by subtracting the voltage drop across the resistor (determined by the current and resistor value) from the input voltage (V_in). This simplification results in a more manageable analysis of circuits with diodes.

Consider a reservoir where you have an inflow of water (input voltage). Some water is used to raise the level of water at a certain outlet (resistor and diode). The water level at the outlet (V_out) will be the inflow minus the amount that

Now, whenever in a non-linear circuit we are feeding the signal then what may be the situation? So, we have the resistor, we have the diode and then we do have DC ... Then the output voltage it will be same as the input voltage.

When both DC (steady voltage) and AC (varying signal) inputs are applied to the circuit, the analysis can vary significantly based on the diode's state. If the diode is OFF, the output voltage follows the input voltage precisely since no current flows through the diode. However, if the diode is ON, the output may be affected by the diode's characteristics and the resistor values, leading to potential attenuation of the AC signal superimposed on the DC.

Think of a two-lane highway where one lane represents DC traffic (steady flow) and the other represents AC traffic (periodic rush hours). When traffic is light (diode OFF), both lanes flow unhindered, and output (total traffic) is equal to input traffic. But when both lanes are busy (diode ON), the merging of steady and fluctuating traffic can create bottlenecks (signal attenuation), resulting in some delays at the output.

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