Concept

Friis cascade — where it appears

The rule that a chain of stages has a noise factor equal to the first stage's plus each later stage's excess divided by the gain ahead of it. It is why the first stage decides a receiver's noise, and why a lossy element placed first costs its whole loss in noise figure.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The usable range of one stage, in a 10 kHz measurement. computed by solving, not by drawing. The floor is the Johnson noise of a 1 kΩ source in the measurement's own noise bandwidth — 501.6 nV, using 15.7 kHz rather than the 10 kHz corner. The ceiling is the drive at which an exponential's distortion reaches one per cent, 1.03 mV. Between them is 66.3 dB, and nothing a designer does moves either number without changing the circuit.

A floor and a ceiling

Every other boundary these essays measure is a ceiling. This one puts a floor underneath and measures the distance between them — 4.00 nanovolts per root hertz at the bottom, one per cent of harmonic distortion at 1.03 millivolts at the top, and 66.3 decibels of range in a ten-kilohertz measurement. Both ends are computed, neither is on a datasheet, and the arrangement of the stages decides which one moves.

noise · Dynamic range

A 6 dB pad at 290 K turns a cold source into 217.2 K and a 290 K one into 290 K. computed by solving, not by drawing, every resistor's Johnson noise carried to the pad's open output. A matched 50 Ω T-pad of 6 dB (arms 16.61 Ω, shunt 66.93 Ω) at 290 K, fed from a 50 Ω source at the temperature on the horizontal axis. The output's noise temperature (dots) is Tₛ/L + T·(1 − 1/L), with T the pad's own temperature, to nine figures (line): a slope of 1/L = 0.2512 and an intercept of 217.2 K — the pad's own noise, (1 − 1/L)·290 K, seen at its output. The dotted diagonal is no pad at all. The two cross at 290 K, where the source is at the pad's temperature and the output is too.

The noise a pad adds is its temperature

A matched resistive pad of loss L at physical temperature T presents a noise temperature of Tₛ/L + T(1 − 1/L) at its output, for a source at Tₛ,, and summing its four resistors' Johnson noise to the open output confirms it to nine figures. Referred to its input its own noise is (L − 1)·T — 288.6 K at 3 dB, 28,710 K at 20 dB — so its noise figure in decibels is its loss in decibels at 290 K, which Friis states from the definition and the resistors reach by themselves. At its output a pad can never add more than its own temperature: cooled to 4 K, a 20 dB pad adds 3.96 K there, and still 396 K referred to its input. Most of a heavy pad's noise is made in its last resistor — 82.6% at 20 dB. And set between a 400 K source and a 290 K load, a pad stops the net flow of noise power at a temperature that depends on its loss, or, below 1.40 dB, at none.

noise · Johnson noise

Named alongside it

The objects these essays reach for when they reach for this one.

Noise figure Available power Averaging Dynamic range Johnson noise Noise temperature Signal-to-noise ratio Thermal equilibrium

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