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In order to satisfy the static discipline,
a circuit must produce outputs that are better

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than the acceptable inputs.

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This ensures that if you concatenate multiple
gates together, for example one buffer followed

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by another buffer, then the input to each
gate will be valid even if a small amount

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of noise was introduced by the previous gate.

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So taking a closer look at that, what that
means is that if I have a valid input at my

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first buffer, and I am guaranteeing that the
output that I produce is slightly better than

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my original input, then even if a little bit
of noise was introduced, the input to the

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second buffer is still going to be considered
a valid input.

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More concretely, to satisfy the static discipline,
a valid low output must be less than a valid

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low input.

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The way that we specify this is that is that
Vol il.

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Also, a valid high output must be greater
than a valid high input.

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So Voh must be greater than Vih.

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If we put this all together, we have Vol
il and Vih oh

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and of course we want our low inputs to be
less than or equal to our high inputs, so

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Vil ih.

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Another way to think about this is to look
at the orange and green arrows which show

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the ranges of valid inputs which are wider
than the ranges of valid outputs.

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The other thing that is shown here are the
noise margins which correspond to the area

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of valid inputs but invalid outputs.

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As we said earlier, a valid input must always
produce a valid output.

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A valid input has Vin il
if its low or Vin > Vih

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if its high.

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A valid output has Vout ol
if its low and Vout > Voh

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if its high.

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In this problem, we want to determine whether
specifications 1, 2, and 3 (which provide

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0.3 volt noise margins) satisfy the static
discipline given the voltage transfer curve

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shown here.

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For each specification, we need to check the
following two constraints:

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1) Is Vol il ih
oh - satisfying this constraint

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guarantees that the outputs produced are better
in quality than the inputs.

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The second constraint is: Does a valid input
produce a valid output?

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Since this curve shows an inverting function,
this translates to:

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a) Does a valid input (where Vin
il) always produce a valid high

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output (where Vout > Voh)?

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And b) Does a valid high input (where Vin
> Vih) always produce a valid low

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output (where Vout ol)?

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If all of these constraints are satisfied,
then that specification obeys the static discipline.

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If not, it doesn't.

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For all three specifications, we see that
indeed Vol il ih

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oh, so the first constraint
is satisfied for all three specifications.

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Now let's check the second constraint.

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For specification #1: If Vin il
which is equal to 0.4, then Vout

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= 5 which is greater than Voh which
is 4.9, so a valid low input produces a valid

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high output.

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If Vin > Vih which equals
4.6 then Vout equals 0 which is

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less than Vol which is 0.1, so
a valid high input produces a valid low output.

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Since all of the constraints are satisfied,
specification #1 satisfies the static discipline.

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For specification #2: If Vin out >= 4 which is not greater

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than> Voh which is 4.4.

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So this specification does not satisfy the
static discipline.

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For specification #3: If Vin out >= 4 which in this case

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is greater than Voh which is 3.9.

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So the first part of the constraint checks
out.

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Now we need to check what happens when we
have a valid high input.

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In this case, if Vin > 3.6 then
Vout ol

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or 1.1, so this part of the constraint checks
out as well.

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Since all the constraints are satisfied, that
means that specification #3 also satisfies

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the static discipline.