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Noise Margins
The transfer function of a digital inverter will typically look something like this: vO V+

d vO = −1 dv I
Transition Region

d vO = −1 dv I vO = f (vI )
I III II
V+

vI

Note that there are essentially three regions to this curve: I. The region where vI is relatively low, so that the output voltage vO is high. II. The region where vI is relatively high, so that the output voltage vO is low. III. The transition region, where the input/output voltage is in an indeterminate state (i.e, an ambiguous region between high and low.

Jim Stiles

The Univ. of Kansas

Dept. of EECS

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Note that the transition region is rather arbitrarily defined by the points on the transfer function where the magnitude of the slope is greater than one (i.e., where d vO dv I > 1.0 ). Although this transfer function looks rather simple, there are actually several parameters that we use to characterize this transfer function—and thus characterize the digital inverter as well! 1. First of all, let’s consider the case when vI=0. The output of the digital inverter in this condition is defined as VOH (i.e., OH “output high”), i.e.:

VOH

vO when v I = 0

Thus, VOH is essentially the “ideal” inverter high output, as it is the output voltage when the inverter input is at its ideal low input value vI=0. Typically, VOH is a value just slightly less than supply voltage V+.
2. Now, let’s consider the case when vI =V+. The output of the digital inverter in this condition is defined as VOL (i.e., OL “output low”), i.e.:

VOL

vO when v I = V +

Jim Stiles

The Univ. of Kansas

Dept. of EECS

11/5/2004

Noise Margins

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Thus, VOL is essentially the “ideal” inverter low output, as it is the output voltage when the inverter input is at its ideal high input value vI =V+. Typically, VOL is a value just slightly greater than 0. vO VOH

vO = f (vI )
VOL
0 V+

vI

3. The “boundary” between region I and the transition region “input of the transfer function is denoted as VIL (i.e., IL low”). Specifically, this is the value of the input voltage that corresponds to the first point on the transfer function where the slope is equal to -1.0 (i.e., where d vO dv I = −1.0 ).

Effectively, the value VIL places an upper bound on an acceptably “low” value of input vI—any vI greater than VIL is not considered to be a “low” input value. I.E.:

Jim Stiles

The Univ. of Kansas

Dept. of EECS

11/5/2004

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vI considered "low" only if vI < VIL

4. Likewise, the “boundary” between region II and the transition region of the transfer function is denoted as VIH “input high”). Specifically, this is the value of the (i.e., IH input voltage that corresponds to the second point on the transfer function where the slope is equal to -1.0 (i.e., where d vO dv I = −1.0 ).

Effectively, the value VIH places a lower bound on an acceptably “high” value of input vI—any vI lower than VIH is not considered to be a “high” input value. I.E.:

vI considered "high" only if vI > VIH vO V+

d vO = −1 dvI
Transition Region

d vO = −1 dvI vO = f (vI )
I
VIL
Jim Stiles

III
VIH

II
V+
The Univ. of Kansas

vI

Dept. of EECS

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Note then that the input voltages of the transition region (i.e., VIL < v I < VIH ) are ambiguous values—we cannot classify them as either a digital “low” value or a digital “high” value. Accordingly, the output voltages in the transition region are both significantly less that VOH and significantly larger then VOL. Thus, the output voltages that occur in the transition region are likewise ambiguous (cannot be assigned a logical state). Lesson learned Stay away from the transition region!

In other words, we must ensure that an input voltage representing a logical “low” value is significantly lower than VIL, and an input voltage representing a logical “high” value is significantly higher than VIH.
Q: Seems simple enough! Why

don’t we end this exceedingly dull handout and move on to something more interesting!?

A: Actually, staying out of the transition region is sometimes more difficult than you might first imagine!

The reason for this is that in a digital system, the devices are connected together—the input of one device is the output of the other, and vice versa.
Jim Stiles The Univ. of Kansas Dept. of EECS

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For example: V+ V+

vI1

vO1 =vI2

vO2

output of that inverter is therefore vO 1 = VOL . Thus, the input

Say that the input to the first digital inverter is v I 1 = V + . The

to the second inverter is likewise equal to VOL (i.e., vI 2 = vO 2 = VOL ). V+ V+

vI1 =V+

vO1 =vI2 =VOL

vO2

be a problem—after all, isn’t VOL much lower than VIL??

Q: So? This doesn’t seem to

Jim Stiles

The Univ. of Kansas

Dept. of EECS

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A: True enough! The input vI2=VOL is typically well below the maximum acceptable value VIL. In fact, we have a specific name for the difference between VIL and VOL—we call this value Noise Margin (NM):

NML = VIL − VOL

Volts ⎤ ⎡ ⎣ ⎦

The noise margin essentially tells us how close we are to the ambiguous transition region for a typical case where v I =VOL . Of course, we do not wish to be close to this transition region at all, so ideally this noise margin is very large! Now, consider the alternate case where vI1 =0.0 V. The output of the first inverter is therefore vO 1 = VOH . Thus, the input to the second inverter is likewise equal to VOH (i.e., v I 2 = vO 2 = VOH ). V+ V+

vI1 =0.0

vO1 =vI2 =VOH

vO2

be a problem—after all, isn’t VOH much larger than VIH??

Q: This still doesn’t seem to

Jim Stiles

The Univ. of Kansas

Dept. of EECS

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A: Again, this is true enough! The input vI2=VOH is typically well above the minimum acceptable value VIH. We can again specify the difference between VIH and VOH as a noise margin (NM):

NMH = VOH − VIH

Volts ⎤ ⎡ ⎣ ⎦

This noise margin essentially tells us how close we are to the ambiguous transition region for a typical case where v I = 0.0 V . Of course, we do not wish to be close to this transition region at all, so ideally this noise margin is very large!
Q: I don’t see why we care

about the values of these “noise margins”. Isn’t the simple fact that VOLVIH sufficient?

A: Ideally yes. However, in our example we have made one important assumption that in fact may not be true! It turns out that in a real digital circuit, vI2 may not be equal to vO1 !!

Jim Stiles

The Univ. of Kansas

Dept. of EECS

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V+

V+

vI1

vO 1 ≠ v I 2

vO2

possible? It appears to me that vI2 must be equal to vO1 !?

Q: What! How can this be

A: It turns out that for a real digital circuit, a lot can happen between the output of one device and the input to another. The voltage at the input of a device might be affected by many sources—only one of which is the output device connected to it!

Examples of these “extra” sources include: 1. Thermal noise 2. Coupled signals 3. Power supply transients We will combine the effect of all of these sources together into one “noise” source vn(t). Thus, a better model for our digital circuit example is:
Jim Stiles The Univ. of Kansas Dept. of EECS

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V+

vI 2 =

V+

vI1

vO1

+

vO 1 + vn (t )

vO2

*

vn(t)

Now, let’s reconsider the case where vI1= V+. We find that the input to the second digital inverter is then vI 2 = VOL + vn (t ) : V+

vI 2 =
VOL

V+

vI1 =V

+

+

VOL + vn (t )

vO2

*

vn(t)

Now we see the problem! If the noise voltage is too large, then the input to the second inverter will exceed the maximum low input level of VIL—we will have entered the dreaded transition region!!!! To avoid the transition region, we find that the input to the second inverter must be less than VIL:
Jim Stiles The Univ. of Kansas Dept. of EECS

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VOL + vn (t ) VIH −VOH
−vn (t ) < NMH

vn (t ) > −NMH

Note that the noise vn(t) is as likely to be positive as negative—it is in fact negative valued noise that will send vI2 to a value less than VIH!

Jim Stiles

The Univ. of Kansas

Dept. of EECS

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Thus, we can make the statement that the magnitude of the noise vn(t) must be less than the noise margins to avoid the ambiguous values of the disturbing transition region! I.E., make sure that:

vn (t ) < NM

for all time t

Jim Stiles

The Univ. of Kansas

Dept. of EECS