[SOLVED] problem in formulation of CMOS Schmittriger

[a.g.electronic96]

Hello everyone, I got a problem when I was calculating the voltage of circuit below. Assume that Vin is equal to zero so that TP and Tn2 are on and in non-saturated and saturated regions respectively. Moreover, Tn and Tn1 are off. it was written that the voltage of Vdsn1 is equal to :
Vsn=Vsn2=Vdsn1= Vdd-V'tn2
where V'tn2 is the threshold voltage, taking into account the influence of the substrate-source voltage.
but when you formulate it, it will not become true, because when you use a KVL trough the Tn2 and Tn1 by this assumption that the Vout is Vdd as it is proved, the formula below could be written:
Vdd-Vdsn2=Vdsn1 if you disregard of the small current coming from Tn (because of leakage current)
Beside:
vdsn2=Vgsn2 (because both of them are connected to vdd) and due to the fact that Tn2 is working in saturation region you will have : vdsn2>=vgsn2-Vt'n2
so the yielded equation is not correspond with that thing that author has been argued...
can anyone prove the author formula and explain it to me ....
Thanks in advance
I am in rush... please ...

Best regard...

 

[a.g.electronic96]

Thank you, I got the solution....