How can I calculate Vout for a CMOS inverter?

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Discussion Overview

The discussion revolves around calculating the output voltage (Vout) for a CMOS inverter, focusing on the operational states of the NMOS and PMOS transistors under different input conditions. Participants explore the mathematical and logical reasoning behind the inverter's behavior, particularly when both the input voltage (Vin) and power supply voltage (Vdd) are at 5V.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that when Vin is 5V and Vdd is also 5V, the PMOS is in cutoff mode while the NMOS is in saturation mode, leading to confusion about how to calculate Vout.
  • Another participant suggests that if the PMOS is cut-off, then the NMOS current should be 0A, indicating that the NMOS is not in saturation but rather in triode mode.
  • A participant questions whether both MOSFETs in a CMOS inverter should have the same input at their gates, seeking clarification on the circuit configuration.
  • Another participant explains that the PMOS is in triode mode because the condition Vds < (Vgs - Vth) holds true, and since there is no current through the PMOS, Vds is 0V.

Areas of Agreement / Disagreement

Participants express differing views on the operational states of the NMOS and PMOS transistors under specific conditions, particularly regarding whether the NMOS is in saturation or triode mode. The discussion remains unresolved as participants explore these concepts without reaching a consensus.

Contextual Notes

There are limitations in the discussion regarding assumptions about the operating regions of the MOSFETs, as well as the dependence on specific definitions of saturation and triode modes. The mathematical steps to derive Vout are not fully resolved.

perplexabot
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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?
 
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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).
 
Last edited by a moderator:
Jony130 said:
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.
 
Last edited by a moderator:
perplexabot said:
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.
 
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?
 

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