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2.2.8 Worked Examples: The Static Discipline


In order to satisfy the static discipline,
a circuit must produce outputs that are better than the acceptable inputs. This ensures that if you concatenate multiple
gates together, for example one buffer followed by another buffer, then the input to each
gate will be valid even if a small amount of noise was introduced by the previous gate. So taking a closer look at that, what that
means is that if I have a valid input at my first buffer, and I am guaranteeing that the
output that I produce is slightly better than my original input, then even if a little bit
of noise was introduced, the input to the second buffer is still going to be considered
a valid input. More concretely, to satisfy the static discipline,
a valid low output must be less than a valid low input. The way that we specify this is that is that
Volil. Also, a valid high output must be greater
than a valid high input. So Vohmust be greater than Vih. If we put this all together, we have Voliland Vihohand of course we want our low inputs to be
less than or equal to our high inputs, so Vilih. Another way to think about this is to look
at the orange and green arrows which show the ranges of valid inputs which are wider
than the ranges of valid outputs. The other thing that is shown here are the
noise margins which correspond to the area of valid inputs but invalid outputs. As we said earlier, a valid input must always
produce a valid output. A valid input has Vinil
if its low or Vin>Vihif its high. A valid output has Voutol
if its low and Vout>Vohif its high. In this problem, we want to determine whether
specifications 1, 2, and 3 (which provide 0.3 volt noise margins) satisfy the static
discipline given the voltage transfer curve shown here. For each specification, we need to check the
following two constraints: 1) Is Volilih
oh- satisfying this constraint guarantees that the outputs produced are better
in quality than the inputs. The second constraint is: Does a valid input
produce a valid output? Since this curve shows an inverting function,
this translates to: a) Does a valid input (where Vinil) always produce a valid high output (where Vout>Voh)? And b) Does a valid high input (where Vin
>Vih) always produce a valid low output (where Voutol)? If all of these constraints are satisfied,
then that specification obeys the static discipline. If not, it doesn’t. For all three specifications, we see that
indeed Volilihoh, so the first constraint
is satisfied for all three specifications. Now let’s check the second constraint. For specification #1: If Vinil
which is equal to 0.4, then Vout=5 which is greater than Vohwhich
is 4.9, so a valid low input produces a valid high output. If Vin>Vihwhich equals
4.6 then Voutequals 0 which is less than Volwhich is 0.1, so
a valid high input produces a valid low output. Since all of the constraints are satisfied,
specification #1 satisfies the static discipline. For specification #2: If Vinout>=4 which is not greater than>Vohwhich is 4.4. So this specification does not satisfy the
static discipline. For specification #3: If Vinout>=4 which in this case is greater than Vohwhich is 3.9. So the first part of the constraint checks
out. Now we need to check what happens when we
have a valid high input. In this case, if Vin>3.6 then
Voutolor 1.1, so this part of the constraint checks
out as well. Since all the constraints are satisfied, that
means that specification #3 also satisfies the static discipline.

Reynold King

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