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Getting exact values of VIL, VOL, VIH and VOH ?

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Robotduck

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I am reading couple of books on calculating the values of VIL, VOL, VOH, VIH for basic NMOS inverter. I notice there are 2 methods to calculate these values.
One is an approximate method: where it is assumed that VOL is basically equal to Vmin that a given circuit can achieve and set VOH to Vmax.

Second method is standard method: to get the -1 slope points to calculate VOL,VOH,VIL, VIH.

My question is : which method is more accurate ? I can see the first one is approximation but the voltage at the output can go to Vmin and standard method does not take this into account. Noise margins are different in both cases. First method has wider noise margins. I am having a hard time understanding the standard method ??:x
 

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