4.6. MOSFET Equations

In Saturation Region (E-MOSFET):
ID=12k(VGS−Vth)2
I_D = rac{1}{2} k igg(V_{GS} - V_{th} igg)^2

In this equation, I_D represents the drain current flowing through the MOSFET when it is in the saturation region. The parameters involved are:

• k, which is a process-dependent constant that describes the MOSFET's characteristics.
• V_GS (Gate-Source Voltage) is the voltage difference between the gate and the source terminals.
• V_th (Threshold Voltage) is the minimum gate voltage required to create a conductive channel between the source and drain.
  This measurement indicates that the drain current is proportional to the square of the difference between the gate-source voltage and the threshold voltage. This relationship highlights that small changes in the gate voltage can lead to significant changes in the drain current, which is fundamental in the operation and design of MOSFETs.

Think of the MOSFET as a water tap. The gate voltage (V_GS) acts like the handle of the tap that controls the flow of water. The threshold voltage (V_th) is like the point at which you have to turn the tap before any water flows out. Once you turn the tap (apply voltage) beyond the threshold, water (current) starts flowing, and the more you turn it (increase V_GS), the more water (current) flows out. The equation shows how dramatically the flow increases once the tap is turned beyond the threshold, illustrating the sensitive nature of the MOSFET's operation.

Where:
● IDI_D: Drain current
● VGSV_{GS}: Gate-Source Voltage
● VthV_{th}: Threshold Voltage
● k=μCoxWLk = BCC_{ox} rac{W}{L}: Process-dependent constant

In this section, we define the variables used in the drain current equation:

• I_D (Drain Current): This refers to the current flowing from the drain terminal to the source terminal when the MOSFET is active.
• V_GS (Gate-Source Voltage): The voltage that exists between the gate and the source. It is crucial for determining if the MOSFET will allow current to flow.
• V_th (Threshold Voltage): The specific gate-source voltage that must be exceeded for the MOSFET to conduct current fully. If V_GS is less than V_th, the MOSFET will not conduct.
• k is derived from the process parameters - it involves the mobility of charge carriers (μ), oxide capacitance per unit area (C_ox), and the width-to-length ratio of the transistor (W/L). This indicates how effectively the MOSFET can control the flow of current.

Imagine baking a cake as an analogy. The ingredients (k, V_GS, and V_th) all need to be in the right amounts for your cake (the current) to rise perfectly (conduct well). If you don’t add enough baking soda (threshold voltage) or mix the ingredients (gate-source voltage), your cake won’t rise. The k factor would be analogous to the specific baking instructions that can change based on the recipe or brand of ingredients used.

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