Output Resistance dependency on Gate Length

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The output resistance is an important performance metric in a MOSFET. The output resistance is not an inherent property of a MOSFET. Rather, it is a characteristic that is used to justify the effect of channel-length modulation on a MOSFET’s small-signal behaviour. When the MOSFET is operating in the saturation region, the channel is ‘pinched-off’ in the drain end. The drain current is not affected by the drain-to-source voltage in the saturation region. The MOSFET acts like a current source controlled by the overdrive voltage VOV (VOV = VGS – VTH). This assumption is based on the idea that increasing the drain-to-source voltage does not alter the channel once it has become pinched-off.
In practicality, the drain-to-source voltage has a significant effect on the channel - the pinch-off point is moved toward the source, which results in more drain-to-source current as drain-to-source voltage is increased. This necessitates an additional circuit element to account for this additional current, and that is the output resistance RO.
This is akin to having a MOS device in conjunction with a resistor, which like regular resistor has a current flow equal to the voltage across the resistor divided by the resistance. As drain-to-source voltage increases, more current flows through the resistor, which indemnifies for the lack of change in the drain current (in the saturation region). The output resistance is given by the following equation.
The gate of the MOS reference device was varied and the output resistance was calculated using the output characteristic in each case. A plot of the output resistance versus the gate length was plotted. The output resistance seems to be increasing with the gate length, which is in accordance with the equation.

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