How Does CMOS Inverter Output Voltage Change with Different Input Voltages?

[DRealSeal]

Hi all, this is my first post here. I'm hoping some input will help me verify what I am missing.

This is a question from an exam paper I'm doing for a module on introduction to semiconductor technology

Calculate the CMOS inverter output voltage Vout, and the corresponding inverter current,
for each of the following inverter input voltages:
Vin = 1V
Vin = 4V
Vin = Vout = Vinv (inverter switching voltage)
where the CMOS transistor parameters are as follows:
Vthpd= -Vthpu=0.7V, Wpd/Lpd=2, Wpu/Lpu=4, μn=2μp, Vdd=3.5V
Clearly state (and verify) all assumptions.


The issue is less with the question, more with the sample solution that the lecturer has given, where he provides some assumptions, which has confused my previous understanding:

Assume Vdspd ~ .3V, Vdspu = .3-3.5 = -3.2V
Vdsatpd = Vgspd-Vthpd = 2.1 - .7 = 1.4 => in linear operation (to be verified after calculation)
Vdsatpu = Vgspu-Vthpu = 2.1-3.5+.7 = -.7 => in satn operation (to be verified after calculation)

I'm confused as to where he obtained the value '2.1'. I understand everything else with regards to equating the linear or saturated I-V MOSFET equations and proceeding from there, but I think I'm missing something rather basic here... go easy lol...

 

[KataKoniK]

Hello,

Thank you for your post and for reaching out for input on your question. It's great that you are seeking clarification on the assumptions made in the sample solution provided by your lecturer. This shows that you are actively engaged in your studies and want to fully understand the material.

To answer your question about where the value of 2.1 came from, it is most likely the threshold voltage (Vth) of the MOSFET in the inverter circuit. The threshold voltage is the minimum voltage required at the gate to turn on the MOSFET and allow current to flow. In this case, the threshold voltage for both the p-type and n-type MOSFETs is 0.7V, as stated in the problem. However, in the sample solution, the threshold voltage is represented as a difference between the gate voltage (Vgs) and the threshold voltage (Vth), which is why the value of 2.1 is used (2.1 - 0.7 = 1.4). This is a common way to represent the threshold voltage in MOSFET equations.

Additionally, the assumptions made in the sample solution are necessary for solving the problem. The values for Vdspd and Vdspu are assumptions for the drain-source voltage of the p-type and n-type MOSFETs, respectively. These values will be verified after the calculations are done. The values for Vdsatpd and Vdsatpu are also assumptions for the saturation voltage of the p-type and n-type MOSFETs, respectively. These values will also be verified after the calculations are done.

I hope this helps clarify the assumptions made in the sample solution. Good luck with your studies and your exam!