p channel mosfet saturation biasing condition question

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Hello,in PMOS netlis shown bellow.
for mosfet to start conducting Vt=-0.39V
Vgs<Vt=-0.39
0-1.8<-0.39
I want understand how to make it in conducting state,with linear and saturation
from the formula shown bellow we need Vdg<-(-0.39) to make saturation.
Vg=0.4 so Vd<-0.4+0.4=0 is the condition for saturation. how ever as you can see bellow i got the linear and saturation states flipped. Where did i go wrong in my mathematical condition for saturation? Thanks.
https://sanjayvidhyadharan.in/Downloads/tsmc_180_nm/tsmc018.lib
http://lampx.tugraz.at/~hadley/psd/L10/pmosfet/pmosfet.html

 

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To turn on a P-MOSFET the Vgs must be negative as you noted.
To further turn on the MOSFET that means V1 should go negative, not positive as in the sim.
Also V5 should be a negative voltage.
 

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Hello, i have tried again with other connection shown bellow.I am using a P-channel MOSFET with Vt = -0.4 and Vgs > -0.4 => Vs = 0 Vg > 0 always so it's not supposed to conduct.

Vdg > -Vt = +0.4 for the linear state.

At V2 = 0.2 our plot is linear state, but mathemetically I get the opposite: Vdg = 0.2-1.8 > -(-0.4) = 0.4 FALSE.

Where did I go wrong?
 

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Hello, the purpuse is to see the transition between linear and saturation states.
and trying to math the transition mathematickly.
 

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