# Finding small signal resistance for MOSFET

I need to find the small signal parameter $$\r_{D1}\$$. I understand I must draw the small signal equivalent first, but I do not know where to label this resistance, or what exactly it is equal to. Also is $$\v_{dd}\$$ labeled correctly?

You just need to apply the usual method to determine the resistance seen from two terminals, here being $$\v_o\$$ (gate-drain terminal) and ground. Turn off all the sources. The circuit is

simulate this circuit – Schematic created using CircuitLab

Calculate $$\i_x\$$ and calculate vx/ix i.e. $$\r_{d1}\$$, which should be trivial.

• There should be an ac signal at the bottom of ro. $v_{dd}$ is not shorted in the small signal circuit. Feb 5, 2020 at 20:13
• So you're saying $r_{D1}$ is simply $r_{o}$? Feb 5, 2020 at 20:15
• @Hector No, it's r0 // 1/gm
– edmz
Feb 5, 2020 at 20:27

For that circuit, with diode-tied gate-drain connection, the dynamic resistance will be the transconductance.

For long-channel FETS, the transconductance is just the derivative of Idd(Vgate), or

2 * KW/L * Ve

where K = Mobility * Cox, and Ve = Vgs = Vt

To derive this maths, write the triode-region small-signal iout(vgate) equation, and apply your skills.

• Where did you get this equation from? Feb 4, 2020 at 15:30