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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?

schematic

small signal

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2 Answers 2

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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

schematic

simulate this circuit – Schematic created using CircuitLab

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

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

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  • \$\begingroup\$ Where did you get this equation from? \$\endgroup\$
    – Hector
    Feb 4, 2020 at 15:30

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