Delay on cmos inverter while increasing W of nMOS and pMOS

cmosmosfet

We have one CMOS inverter and a fixed capacitance as load , for example 0.1pF . As an experiment we increase W of nMOS and pMOS and each time we increase W, we find the delay of the inverter (using spice). We notice that while increasing W, the rate of decreasing delay is dropped. Why is this happening ?

Best Answer

I'll assume you are reffering to the charging/discharging delay. Let's take the discharge time delay. That is TpHL (H-L) trasition. This happens when you are applying Low-to High input, your Output changes from High to Low.

This is the image of a regular CMOS inventor. enter image description here

Now to calculate for TpHL, it is by definition the times it takes the capacitor to discharge from Q such that the output voltage changes from VDD to VDD/2. During this period, a High input is applied, therefore, the PMOS acts as an open circuit and we will only need to analyze the NMOS.

When C is fully charged "at the beginning of the discharge", the N-mos is in saturation.

Therefore; you can apply the saturation current equation. When the the output voltage reaches VDD/2, the NMOS is in linear and you have to apply the linear current equation.

Now you've calculated the currents. we find average current Iavg = (I(0) + I(at Q = Q/2) /2

Therefore; TpHL = C * (V2-V1)/2 /Idn av

Note now, increasing W will increase the current>> which will therefore decrease TpHL.

enter image description here

In short words: Increasing the W, will increase the average current either in saturation or linear, which will increase the charging/discharging rate >> which will decrease the delay