Noise temperature — where it appears
Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.
The loss in front, counted twice
A decibel of cable before an amplifier costs a decibel of signal, which everybody expects, and a decibel of noise figure, which is a separate decibel arriving from a separate place. Measured across the slider it is exact: 1.31 dB of chain noise figure becomes 2.31 with one decibel of cable and 9.31 with eight, every time, while the 8.70 dB that stage ordering is worth does not move at all. A lossless reactive network in the same position costs nothing, because only the real part of an impedance is warm.
Which way the noise goes
Two warm resistors joined together each drive the other, and the net flow is 4kΔT·R₁R₂/(R₁+R₂)² per hertz. At the match that is kΔT exactly — 1.5187 zeptowatts per hertz between 400 K and 290 K — and a kilohm pair and a gigohm pair at the same two temperatures exchange the same, which is why noise is quoted as a temperature. At one temperature the net is zero at every ratio to a part in 10³⁷, and that zero is the second law rather than a tolerance.
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.
The resistance colder than the room
In a passive network the noise at a port is 4kT times the real part of its impedance, and reciprocity is why: the transfer from each resistor to the port equals the transfer from the port to that resistor, so one solve from the output gives every resistor's share and the shares add to Nyquist's expression, here to 4.4 × 10⁻¹⁶. With gain in the network both fail. A 50-ohm termination made by feedback around an amplifier of gain A presents 50.000 Ω and has the noise of a 50-ohm resistor at 290/(1 + A) kelvin — 2.90 K at a gain of 99 — but only where the amplifier still has its gain.
The end a lossy line looks like
A line running from room temperature into a 4 K stage is a chain of pads, each at its own temperature, and its noise at the cold end is each piece's emission attenuated by everything after it. Cut into forty pads along a linear gradient, a 20 dB line fed from a 300 K source delivers 67.7 K to the cold end, where the continuous closed form says 67.63; its cold half supplies 46.7 K of that and its warm half 18.0. Read from the warm end, the same line's own noise is 184 K at 10 dB against 89.7 at the cold: a lossy line looks like the end it is read from. And twenty decibels placed as one attenuator at the 4 K stage deliver 6.96 K, where at room temperature they deliver 300.
Named alongside it
The objects these essays reach for when they reach for this one.
Johnson noiseAvailable powerNoise figureVerificationFriis cascadeImpedance matchingTransmission lineControlled sourceGain–bandwidth productInput impedanceInsertion lossMaximum power transfer