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Can somebody tell me why R_o2 is RD Why dont we take Rs into consideration ?

Their answer is Ro2=vt/it = Rd

My question is why didnt they take in consideration Rs and the current source?

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  • \$\begingroup\$ Please be specific ! \$\endgroup\$ – Long Pham Jul 12 '18 at 16:56
  • \$\begingroup\$ @LongPham Updated. Cant be more specific than this \$\endgroup\$ – Sijaan Hallak Jul 12 '18 at 17:03
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In your diagram, we can see a voltage controlled current source.

The control voltage is \$V_{GS}\$. And \$V_{GS}\cdot g_m\$ current can only flow if \$V_{GS}\$ voltage is larger or smaller than \$0V\$. But in your circuit \$V_{GS} = 0V\$ therfore \$V_{GS}\cdot g_m\$ also must be zero.

The situation will be different if you add \$r_o\$ resistor between the drain and the source terminal. In this case \$V_{GS}\$ is no longer equal to \$0V\$. Because now \$r_o\$ provides a path for a current from \$V_t\$ to GND. So the voltage at \$V_S\$ is larger than \$0V\$

I/O Resistance of common source MOSFET with source degeneration

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  • \$\begingroup\$ Wait, how did you get that Vgs = 0? I know that Vg = 0. But why Vs=0 ? \$\endgroup\$ – Sijaan Hallak Jul 12 '18 at 17:14
  • \$\begingroup\$ @SijaanHallak To turn-on VCCS you need Vgs voltage to appears first. Is this possible in your circuit? \$\endgroup\$ – G36 Jul 12 '18 at 17:17
  • \$\begingroup\$ Doesnt Rs get some voltage from our test voltage? @g35 \$\endgroup\$ – Sijaan Hallak Jul 12 '18 at 17:22
  • \$\begingroup\$ @SijaanHallak How? \$\endgroup\$ – G36 Jul 12 '18 at 17:25
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    \$\begingroup\$ Do you agree with this Vs = Id*Rs and to Id current to flow you need Vgs first right? \$\endgroup\$ – G36 Jul 12 '18 at 17:30
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R_o2 is the impedance looking into the drain node from the perspective of \$V_t\$. That drain has two other connections: -

  1. A current source that has infinite impedance (irrespective of what is connected to the source) i.e. it is the actual drain connection and,
  2. Resistor \$R_D\$

Hence the signal impedance R_o2 is \$R_D\$.

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