How can I calculate Vout for a CMOS inverter?

[perplexabot]

Hi all. I don't know if I have given this enough thought but I will ask anyway. I know that a CMOS is an inverter, so for input High you will get output Low, and for input Low you will get output High. I am trying to find this out mathematically (or even just logically) but I can't seem to do it.

Say Vdd (power supply to pMOS) is 5v and Vin is also 5v. In this case the PMOS will be in cutoff mode and the NMOS will be in saturation mode. Vgs of the NMOS will be 5v. I don't know what to do next. I know that the saturation current equation for the NMOS does not include Vd (or Vds) when channel length modulation is neglected, so I have no idea how to get Vd of NMOS (AKA: Vd of PMOS, AKA: Vout).

PS: Another thing that is bothering me, is when say Vin is 5v (and Vdd is also 5v), the NMOS should have current passing through it (since in saturation) but the PMOS should not have current passing through it (since in cutoff). Kind of a paradox in my opinion. But it kind of makes sense that Vo will be zero in order to negate this current.

Anyone?

 

[Jony130]

This short video should help you better understand the circuit .

Because if PMOS is cut-off then without the load NMOS current is 0A.
so NMOS is not in saturation but in triode mode (aka linear region).

 

[perplexabot]

This short video should help you better understand the circuit .

Because if PMOS is cut-off then without the load NMOS current is 0A.
so NMOS is not in saturation but in triode mode (aka linear region).

Hey. Thanks for the reply and the youtube link (probably going to watch it a couple more times). So the schematic in the video is a cmos? I thought for a cmos both mosfets would have the same input (Vin) at their gates? Thanks again.

 

[Jony130]

Hey. Thanks for the reply and the youtube link (probably going to watch it a couple more times). So the schematic in the video is a cmos? I thought for a cmos both mosfets would have the same input (Vin) at their gates? Thanks again.

Yes, it is a CMOS circuit. CMOS --->Complementary MOS. So we need nMOS and pMOS in the circuit and we have a CMOS circuit. And circuit you have in mind is a CMOS inverter.
Also read this
http://forum.allaboutcircuits.com/showthread.php?p=314871#post314871
This also should help you understand basic principles of how we analyse such circuits.

 

[perplexabot]

Hey, I have a question about the video. For part a) the professor said that the pmos is in triode because it is on but has no current. I understand that there is no current since nmos is in cutoff, i also understand that the pmos is on. my question is how do u know the pmos is in triode and not in saturation?

 

[Jony130]

We know that pMOS is in triode mode because Vds < ( Vgs - Vth).
No current is flow through pMOS, so there is no voltage drop across drain.
So Vds = 0V and 0V is smaller than (Vgs - Vth).
http://upload.wikimedia.org/wikipedia/commons/1/18/IvsV_mosfet.svg