Noise margins (NMH, NML): Foundations — Hardware deep dive

This page builds every symbol the parent note leans on, starting from "what is a voltage?" and ending at the four letters $V_{O H}, V_{O L}, V_{I H}, V_{I L}$ . Nothing is assumed. If the parent uses it, we earn it here first.

0. Voltage — the height of a signal

The ceiling and floor have names:

Look at the figure: the vertical bar is our ruler. A "1" wants to sit near the top rail; a "0" near the floor. The whole story of noise margins is about how much wiggle room a dot has before we can no longer tell which half it belongs to.

Why the topic needs it: noise margins are measured in volts. Without a ruler and two rails there is nothing to measure a cushion against.

1. Logic levels are RANGES, not points

Here is the single most important shift in thinking.

Look at the figure: the ruler is split into three coloured bands.

The top mint band = "definitely a 1".
The bottom lavender band = "definitely a 0".
The coral band in the middle = the forbidden / undefined region — voltages here are neither a clean 1 nor a clean 0.

Why the topic needs it: the noise margin is literally the width of the safe bands. If logic values were single points, there would be no cushion and no margin to speak of.

2. Input side vs Output side — the letters I and O

Two gates in a row: gate A drives, gate B receives. A voltage is an output at A and an input at B — the same wire, two viewpoints.

Why the topic needs it: the parent's mistake box warns "you must cross a gate boundary." That boundary is exactly the jump from an $O$ voltage on one gate to an $I$ threshold on the next.

3. Subscript H (high) vs L (low) — the four voltages

Combine each of ${I, O}$ with each of ${H, L}$ and you get the four numbers the whole topic runs on.

Look at the figure: four horizontal ticks on the ruler.

Near the top: $V_{O H}$ (driver's high promise) sits above $V_{I H}$ (receiver's high demand). The green gap between them is $N M_{H}$ .
Near the bottom: $V_{I L}$ (receiver's low demand) sits above $V_{O L}$ (driver's low promise). The green gap between them is $N M_{L}$ .

Notice the pattern that guarantees positive cushions: $V_{O H} > V_{I H} and V_{I L} > V_{O L} .$

Why the topic needs it: these four numbers are the topic. Every formula, every worked example, plugs into these four.

4. The VTC — where these four come from

The four voltages are not invented; they are read off a curve called the Voltage Transfer Characteristic.

The curve is built in detail in CMOS Inverter VTC. Here we only need to know two features of it.

4a. Slope — how steep the curve is

Why the minus sign? An inverter turns high into low, so raising the input lowers the output — the curve slopes downward, giving a negative slope everywhere.

4b. The slope $= - 1$ points define $V_{I L}$ and $V_{I H}$

Why does the parent insist $V_{I L}, V_{I H}$ are the points where slope $= - 1$ ? Because that is the exact boundary between shrinking noise and growing noise.

Where $∣ slope ∣ < 1$ : a small input wiggle produces an even smaller output wiggle → noise dies as it passes through the gate.
Where $∣ slope ∣ > 1$ : a small wiggle produces a bigger one → noise grows (amplified).
Where $∣ slope ∣ = 1$ : the gate breaks even — the crossover line.

Look at figure s04: the two coral dots mark where the tangent line has slope $- 1$ . Drop a vertical line from each dot to the input axis → those landing points are $V_{I L}$ (left) and $V_{I H}$ (right). Read the output at those same points → $V_{O H} = f (V_{I L})$ and $V_{O L} = f (V_{I H})$ .

The reason $∣ A_{v} ∣ > 1$ near the middle restores clean levels is developed in Static Gain and Regenerative Property.

Why the topic needs it: without the VTC and its slope, the four voltages would be arbitrary. The slope $= - 1$ rule derives them from the transistor physics.

5. Minimum, and why "both must be positive"

Prerequisite map

Equipment checklist

Test yourself — you should be able to answer each before moving to the derivation page.

What does a voltage represent on our vertical ruler?

The height of a signal, in volts, between the ground floor and the

V_{D D}

ceiling.

What are the two supply rails?

V_{D D}

(top rail, highest available voltage) and

0

V ground (floor).

Why are logic "0" and "1" ranges rather than exact numbers?

Real drivers and receivers cannot hit an exact voltage, so each logic value is a band of voltages with a forbidden gap between them.

What does subscript

O

mean vs subscript

I

O

= output voltage a gate produces (a promise);

I

= input threshold a gate requires (a demand).

What does subscript

H

mean vs subscript

L

H

= the HIGH (near-top-rail) case;

L

= the LOW (near-floor) case.

Name the four critical voltages.

V_{O H}

(output high),

V_{O L}

(output low),

V_{I H}

(input high threshold),

V_{I L}

(input low threshold).

What ordering makes the margins positive?

V_{O H} > V_{I H}

and

V_{I L} > V_{O L}

What is the VTC?

The graph

V_{o u t} = f (V_{in})

showing the output voltage for every input voltage of the gate.

What does

\frac{d V _{o u t}}{d V _{in}}

measure, and why is it negative here?

The slope (steepness) of the VTC; negative because an inverter lowers the output as the input rises.

Why are

V_{I L}

and

V_{I H}

taken at slope

= - 1

They mark the boundary between the gate attenuating noise (

∣ slope ∣ < 1

) and amplifying it (

∣ slope ∣ > 1

What does

min (N M_{H}, N M_{L})

tell you?

The overall robustness — the weaker of the two cushions limits the gate.

Connections

Noise margins (NMH, NML) — the parent this page prepares you for.
CMOS Inverter VTC — the full derivation of the curve these four voltages come from.
Static Gain and Regenerative Property — why $∣ A_{v} ∣ > 1$ near the middle restores clean levels.
Fan-out and Loading — how loading degrades $V_{O H} / V_{O L}$ .
Power Supply Scaling — how shrinking $V_{D D}$ shrinks the bands.
Static Noise Margin (SRAM butterfly curve) — the same cushion idea inside a bit-cell.
🇮🇳 Yeh note Hinglish mein padho →