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

V_{ol}

than a valid high input. So V_{oh}must be greater than V_{ih}. If we put this all together, we have V_{ol}_{ih}

less than or equal to our high inputs, so V_{il}ih. 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 V_{in}

if its low or V_{in}>V_{ih}if its high. A valid output has V_{out}

if its low and V_{out}>V_{oh}if 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 V_{ol}

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 V_{in}_{out}>V_{oh})? And b) Does a valid high input (where V_{in}

>V_{ih}) always produce a valid low output (where V_{out}

then that specification obeys the static discipline. If not, it doesn’t. For all three specifications, we see that

indeed V_{ol}

is satisfied for all three specifications. Now let’s check the second constraint. For specification #1: If V_{in}

which is equal to 0.4, then V_{out}=5 which is greater than V_{oh}which

is 4.9, so a valid low input produces a valid high output. If V_{in}>V_{ih}which equals

4.6 then V_{out}equals 0 which is less than V_{ol}which 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 V_{in}out>=4 which is not greater than>V_{oh}which is 4.4. So this specification does not satisfy the

static discipline. For specification #3: If V_{in}out>=4 which in this case is greater than V_{oh}which 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 V_{in}>3.6 then

V_{out}olor 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.