EC-22.3 Noise Figure, Gain, Linearity and Dynamic Range

What this is and why it exists

Four numbers decide what a radio can do, and they pull against each other.

The amplifier that hears the faintest signal is the one that distorts first when a strong signal arrives. That tension is why receiver design starts on a spreadsheet, before anybody chooses a component.

This topic is the arithmetic of that spreadsheet. The formulas are short. Their consequences are not obvious, and getting them wrong produces a radio that works in the laboratory and fails in a city.

The vocabulary

• Thermal noise — the noise any resistance produces because of its temperature.
• Noise floor — the noise power in the bandwidth of interest.
• Noise figure — how much a stage worsens the ratio of signal to noise.
• Cascade — a chain of stages, each with its own gain and noise figure.
• Compression — the point at which gain starts falling as input rises.
• Intermodulation — new frequencies created by two signals in a non-linear stage.
• Third-order intercept — an extrapolated figure predicting intermodulation.
• Dynamic range — the gap between the faintest and strongest usable signals.
• Chain budget — a table of every stage's gain, noise and linearity.

The mental model

Any resistance at any temperature above absolute zero produces noise, and the power of that noise is proportional to the bandwidth you look at. That sets a floor below which no receiver can detect anything. Every sensitivity figure in every specification is that floor plus whatever the electronics adds.

Noise figure measures what a stage adds. The important result is the cascade formula: each later stage's contribution is divided by the total gain in front of it. So the first amplifier decides almost everything. It also explains why a lossy component placed before the first stage is so expensive, since loss there costs noise figure directly.

Now the other end. Every amplifier eventually stops being proportional. The compression point is the input level at which its gain has dropped by one decibel. Above that the output no longer represents the input faithfully.

Intermodulation is worse than compression, because it creates signals where none were. Two strong signals in a slightly non-linear stage produce new frequencies, and some of them land very close to the originals. If two strong stations sit near your wanted channel, their intermodulation product can land exactly on it, where no filter can remove it. The third-order intercept point is an extrapolated figure predicting how bad this will be.

Dynamic range is the gap between the two. The floor is set by noise and the ceiling by distortion. More gain lowers the effective noise contribution of later stages and pushes the earlier ones towards compression. Improving one end usually worsens the other, and stating the range explicitly forces that trade into the open.

The tool that assembles all this is a chain budget: one row per stage, with gain, noise figure and intercept point. The system figures fall out of the arithmetic, and the row that is limiting becomes obvious. Almost every receiver design begins as one of these.

What you should now be able to explain or do

• Compute a noise floor from a bandwidth and explain what sets it.
• Apply the cascade formula and say why the first stage dominates.
• Define the compression point and say what happens above it.
• Explain how intermodulation puts energy where no filter can remove it.
• Derive a dynamic range from a noise floor and a distortion limit.
• Build a chain budget and identify the stage that limits the system.

Check yourself