# Calculating Resistance

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? • Please be specific ! – Long Pham Jul 12 '18 at 16:56
• @LongPham Updated. Cant be more specific than this – Sijaan Hallak Jul 12 '18 at 17:03

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

• Wait, how did you get that Vgs = 0? I know that Vg = 0. But why Vs=0 ? – Sijaan Hallak Jul 12 '18 at 17:14
• @SijaanHallak To turn-on VCCS you need Vgs voltage to appears first. Is this possible in your circuit? – G36 Jul 12 '18 at 17:17
• Doesnt Rs get some voltage from our test voltage? @g35 – Sijaan Hallak Jul 12 '18 at 17:22
• @SijaanHallak How? – G36 Jul 12 '18 at 17:25
• Do you agree with this Vs = Id*Rs and to Id current to flow you need Vgs first right? – G36 Jul 12 '18 at 17:30

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 $R_D$.