11.1.2. Department of Electronics and Electrical Communication Engineering

So, welcome back here again the second part of today’s module. What we are looking for it is the expression of the current as function of the W’s and L’s and V and V. And V and V of course, they are applied here. And also, just to get an idea that how this current depends on the device parameters.

In this introduction, the focus is on understanding how the output current of a MOSFET (metal-oxide-semiconductor field-effect transistor) is determined by various factors. Specifically, it highlights that the current depends on the dimensions of the transistor (width W and length L), and the voltages at the gate (Vgs) and drain (Vds). This sets the groundwork for analyzing the MOSFET's behavior under different conditions and helps students understand the significance of these parameters.

Imagine a water pipe: the width of the pipe (like the width W of the MOSFET) allows more water to flow through if it's wider, while the length of the pipe (similar to L) affects the ease of flow. The water pressure at the entry of the pipe (analogous to Vgs) determines how much water can flow out.

So, on the other hand if the W is increasing the corresponding resistance it will decrease. So, you may say directly that I is proportional to the W/L aspect ratio of the channel.

This chunk discusses how the dimensions of the MOSFET affect its current output. It states that when the width (W) of the MOSFET increases while the length (L) remains constant, the resistance decreases, leading to an increase in current. Conversely, increasing the length results in higher resistance, which reduces current. Thus, the ratio W/L is crucial for determining how effectively the MOSFET can conduct electricity.

Think of this like a highway: a wider road (larger W) allows more cars (electrons) to travel compared to a narrow road. However, if the road gets too long (larger L), it can lead to congestion, slowing down the traffic (decreasing current).

This will be proportional to the conductivity in the channel regions which is controlled by this V - Vth, which means that whatever the excess voltage you do have beyond the threshold voltage that is effectively contributing to the conductivity or it is helping to increase the conductivity in the channel.

This section explains how the difference between the gate-source voltage (Vgs) and the threshold voltage (Vth) contributes to the conductivity within the MOSFET. The excess voltage above the threshold enhances the channel's ability to conduct, effectively increasing the overall current. This dynamic is critical for understanding how manipulation of voltages can control the MOSFET's performance.

Consider this like a light switch: the threshold voltage (Vth) is the point at which the switch needs to be flipped. If you apply more voltage (like further pressing a switch) past this threshold, it effectively increases the brightness of the light (the current). Hence, the more you push past the threshold, the brighter it gets.

So, if I combine all of them, so what we can say here it is I is proportionality constant say × (V - Vth) × Vds.

Here, the relationship derived mentions that the output current (I) is shaped by a constant that encompasses various device parameters multiplied by the excess gate-source voltage (V - Vth) and the drain-source voltage (Vds). This formula gives students a concrete understanding of how all these parameters interact to determine the current flowing through the MOSFET.

This can be likened to a recipe: you have a 'recipe constant' that tells you how many ingredients (the parameters) and in what proportions you need to mix them (the behaviors of V and Vth) to create the final dish (the current). The right balance means you end up with something great, while the wrong balance can ruin the outcome.

However, whenever we say that Vds is higher than Vth and whatever the excess amount we have it is contributing towards the conductivity of the channel, this is valid only when Vds is low compared to Vgs - Vth.

This chunk emphasizes that the relationship discussed holds true as long as the drain-source voltage (Vds) remains relatively small compared to the difference between gate-source voltage (Vgs) and threshold voltage (Vth). If Vds approaches or exceeds this threshold, the assumptions made in earlier calculations may no longer apply, highlighting the importance of this condition in accurate circuit design.

Imagine a spring: if you stretch it gently, it behaves predictably. But if you pull too hard (like increasing Vds too much), it could break or function unpredictably. Proper analysis requires knowing how much you can safely stretch the spring.

We need to correct our calculations and consider both this part as well as that part and take an average.

This segment reveals that as Vds becomes significant, the conductivity characteristics of the channel need to be recalibrated to get accurate current expressions. The need to average factors during high Vds conditions ensures the model reflects reality more closely, representing how the channel's conductivity varies along its length. Adjustments in calculations are essential to maintain accuracy under different voltage conditions.

Think of it as adjusting a recipe after tasting: you might need to add more salt or sugar based on how the dish tastes, just like recalibrating calculations based on varying conditions to get the best outcome.

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