Noise Sources: Thermal, Atmospheric & Man-Made

Every receiver has a floor it cannot get under, and the floor has two halves that behave completely differently. One half is made inside the box — thermal agitation in resistances, shot noise in junctions, flicker noise in devices, and finally the quantizer — and you buy your way down it with better parts. The other half arrives through the antenna from lightning, from the galaxy, and from every switching power supply within a few hundred metres, and no amount of front-end money touches it.

Which half dominates is a function of frequency, and the crossover is sharp. Below roughly 100 MHz the sky is far noisier than any receiver you can build, so front-end noise figure is nearly irrelevant and the design problem is antenna siting and interference rejection. Above about 1 GHz the sky is quiet and cold, the receiver is the noise, and a tenth of a dB of noise figure is worth arguing about. Getting this backwards is the most expensive mistake in radio front-end design.

The floor: $kTB$ #

Johnson measured it in 1928 and Nyquist explained it the same year in the same volume of Physical Review: a resistor in thermal equilibrium generates a random EMF whose mean-square value is proportional to temperature, resistance, and bandwidth.

$$\overline{e_n^2} = 4kTRB \qquad\Longrightarrow\qquad v_n = \sqrt{4kTRB}$$

The consequence that matters for radio is the available power — the power that resistor delivers into a conjugate-matched load — because $R$ cancels out of it entirely:

$$\boxed{\;P_n = kTB\;}$$

$k = 1.380\,649 \times 10^{-23}$ J/K exactly (SI has fixed it since 2019). Source impedance is irrelevant; a 50 Ω termination and a 1 MΩ termination at the same temperature hand a matched receiver the same noise power. Only the voltage differs, and that only matters when you are not matching.

Where −174 dBm/Hz comes from #

Noise figure is defined against a standard reference temperature $T_0 = 290$ K — Friis's suggestion, adopted by the IRE and carried into the IEEE and ITU definitions ever since. It is not room temperature and not a physical constant; 290 K is 16.85 °C, chosen because it is close to the temperature an antenna sees looking across the atmosphere, and because it makes the arithmetic land on a round number:

$$kT_0 = 1.380\,649 \times 10^{-23} \times 290 = 4.0039 \times 10^{-21}\ \text{W/Hz}$$

$$10\log_{10}\!\left(\frac{4.0039 \times 10^{-21}}{1\times10^{-3}}\right) = 10\log_{10}\!\left(4.0039 \times 10^{-18}\right) = -173.98 \approx \boxed{-174\ \text{dBm/Hz}}$$

The same number in dBW is −204, which is why ITU-R P.372 writes the available noise power as $P_n = F_a + B - 204$ dBW with $B = 10\log b$. Everything downstream is that constant plus $10\log_{10} B$ plus the noise figure.

Noise factor, noise figure, noise temperature #

Three ways to write one quantity. Fluency in all three is not optional, because RF datasheets use one, satellite and radio-astronomy work uses another, and standards documents use the third.

Why two units. $NF$ compresses a huge range into a small one, which is exactly wrong when the antenna is cold. A 3 dB step in noise figure is a 3 dB step in output SNR only when the source is near 290 K — the terrestrial case. A satellite dish looking at cold sky may deliver an antenna temperature under 100 K, and there the same 3 dB of noise figure costs far more than 3 dB of SNR, because you are adding hundreds of kelvin to a source contributing tens. That is why satellite and radio-astronomy work quotes $T_e$, adds it directly to the antenna temperature as $T_{sys} = T_A + T_e$, and rolls the whole thing into the system figure of merit $G/T$ — antenna gain over operating noise temperature — rather than a noise figure.

The Friis noise formula: why stage one owns the answer #

Friis's 1944 paper defined the noise figure and gave the cascade rule in the same breath. For stages with noise factors $F_i$ and available gains $G_i$ (all linear, not dB):

$$F_{\text{sys}} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \cdots + \frac{F_n - 1}{G_1 G_2 \cdots G_{n-1}}$$

Read the structure, not the symbols. Every stage's excess noise factor $F_i - 1$ is divided by all the gain in front of it. Stage 1 is divided by nothing. Put 20 dB of gain in front of stage 3 and its contribution is scaled by 1/100 — which is why a mediocre mixer and a frankly bad IF strip barely register, and why the loss between the antenna and the first amplifier is the most expensive dB in the entire receiver.

In noise-temperature form the same statement is cleaner:

$$T_e = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1 G_2} + \cdots$$

flowchart LR
  ANT["Antenna"] --> FEED["Feed + filter<br/>L 1.5 dB"]
  FEED --> LNA["LNA<br/>NF 0.8 / G 21.5"]
  LNA --> SAW["SAW filter<br/>L 2.5 dB"]
  SAW --> MIX["Mixer<br/>CL 7 dB"]
  MIX --> IF["IF amp<br/>NF 4 / G 30"]
  IF --> ADC["ADC + back end<br/>NF 20 dB"]

A worked noise budget #

A representative 2 GHz receive chain, 20 MHz channel. The feeder between antenna and receiver is on the standard impairment inventory for exactly this reason — it both attenuates the signal and injects thermal noise, and it sits in the one position where that is unforgivable. Passive parts at ambient contribute a noise figure equal to their loss — that is not a convention, it follows from the ITU/IEEE definition: a lossy two-port at physical temperature $T_t$ has $f_t = 1 + (l_t - 1)\,T_t/T_0$, which collapses to $f_t = l_t$ when $T_t = T_0$.

Three readings of that table, and each one is a design decision:

1. The 1.5 dB of passive loss before the LNA contributes 73.5% of the total noise factor — more than everything else combined. It is the largest single line item and it does nothing but connect two components.
2. A 20 dB noise figure at the ADC costs 0.5%. Once 40 dB of gain sits ahead of a stage, its noise is essentially free. Chasing back-end noise while the feed loses 1.5 dB is misallocated effort.
3. Total $T_e = 290 \times (1.9209 - 1) = 267$ K, and the sensitivity floor in 20 MHz is $-174.0 + 73.0 + 2.84 = -98.1$ dBm.

Now move the LNA to the antenna — a mast-head or dish-mounted amplifier — so the 1.5 dB of feed loss sits after 21.5 dB of gain instead of before it. Nothing else changes:

1.29 dB recovered by relocating one part. Note it is not the full 1.5 dB: the feed loss still contributes its share downstream, just divided by the LNA's gain. This single line of arithmetic is why every serious VHF/UHF station, every satellite earth station, and every base-station tower puts the LNA at the antenna and runs the long cable afterwards.

Inside the box: thermal, shot, flicker #

Three distinct physical mechanisms, distinguishable by their spectra and by what they depend on.

Shot noise is the granularity of charge showing up as current fluctuation. Carriers cross a barrier as independent Poisson events, so a DC current $I_0$ carries a mean-square fluctuation

$$\overline{i_n^2} = 2qI_0 \quad \text{A}^2/\text{Hz}, \qquad q = 1.602\,176\,634 \times 10^{-19}\ \text{C (exact)}$$

At 1 mA that is 17.9 pA/√Hz; at 1 µA, 0.57 pA/√Hz. Two things follow. It scales as $\sqrt{I}$ while the signal current scales as $I$, so SNR improves with bias current — the opposite of the intuition people carry over from thermal noise. And it needs a barrier: shot noise requires the crossing events to be independent, which is why an ordinary ohmic resistor carrying DC shows no shot noise at all, only its thermal noise. Comparing the two for a junction with small-signal resistance $r = kT/qI$: thermal noise of an ohmic resistor of that value would be $4kT/r = 4qI$, exactly twice the junction's $2qI$. The junction is 3 dB quieter than a resistor of equal resistance.

Flicker noise is any noise whose power spectral density varies inversely with frequency. It dominates below a corner frequency where the $1/f$ slope crosses the white floor; that corner is a property of the device and the process, not of the circuit, and it ranges over orders of magnitude — significant at audio frequencies for op-amps, and important up to roughly 100 MHz for GaAs FETs. It matters in two places that look unrelated: DC-coupled and baseband instrumentation, where it sets the drift floor and is the reason chopping and correlated double sampling exist; and oscillators, where the device's $1/f$ noise is upconverted around the carrier and produces the steep close-in region of the phase-noise plot, which is why a low $1/f$ corner is a headline parameter for an oscillator transistor.

Quantization noise: the floor you choose #

Everything above is noise nature imposes. The quantizer's floor is one you pick, and it belongs in the same budget because it adds to the same total.

An ideal $N$-bit converter with LSB step $\Delta$ (written $q$ in most converter literature — not the electron charge above) produces an error uniformly distributed over $\pm \Delta/2$, giving an RMS error of $\Delta/\sqrt{12}$ spread over the Nyquist band DC to $f_s/2$. Against a full-scale sine wave that yields the standard result:

$$\mathrm{SNR} = 6.02N + 1.76\ \text{dB}$$

12 bits → 74.0 dB, 14 bits → 86.0 dB, 16 bits → 98.1 dB. Two riders on that number, both load-bearing:

• It is measured over the full Nyquist bandwidth. If your signal occupies only part of it and you filter digitally, you recover process gain $10\log_{10}\!\left(\frac{f_s/2}{BW}\right)$. A 14-bit converter at 250 MSPS gives 86.0 dB over DC–125 MHz, but 86.0 + 10 log(125/20) = 94.0 dB in a 20 MHz channel. Oversampling buys real dynamic range; this is the whole basis of sigma-delta conversion.
• The uniform-noise model assumes the error is uncorrelated with the input. When the sampling clock and the signal are harmonically related the quantization error stops looking like noise and concentrates into harmonics — the RMS value stays $\Delta/\sqrt{12}$ but it is now spurs, not a floor, and a spectrum plot looks nothing like the SNR figure predicts. This is why real converters are deliberately dithered. See quantization error for the mechanism and sampling and aliasing for what folds into the band in the first place.

The system rule is simple: set the analog gain so the analog noise floor sits a few LSBs above the quantization floor. Less and the ADC dominates and dithering fails; much more and you are burning dynamic range and clipping headroom for nothing.

Outside the antenna: atmospheric, galactic, man-made #

External noise is quantified by the external noise factor $f_a$ — the available noise power from a lossless equivalent antenna, referred to $kT_0b$:

$$f_a = \frac{p_n}{k T_0 b}, \qquad F_a = 10\log_{10} f_a\ \text{dB}, \qquad P_n = F_a + B - 204\ \text{dBW}$$

$F_a = 0$ dB means the antenna delivers exactly the 290 K thermal floor. The equivalent antenna temperature is $T_a = f_a T_0$. Everything below is from ITU-R P.372-17, the recommendation that holds the measured charts the whole industry works from.

Atmospheric noise from lightning #

Lightning is a broadband impulsive transmitter, and it never stops: satellite optical measurement puts the global flash rate at 44 ± 5 per second averaged over a year, 55/s in northern summer and 35/s in northern winter. Below the HF band the energy propagates enormous distances in the Earth–ionosphere waveguide, so what you receive is the aggregate of a planet's thunderstorms, not the local weather. P.372 does not model it with a formula: it publishes world charts of median $F_a$ at 1 MHz for each of four seasons × six four-hour local-time blocks, plus frequency-scaling curves and variability parameters for each block, referred to a short vertical monopole over a perfect ground plane. Season, hour, and geography each move it by tens of dB.

Two properties make it awkward beyond its raw level:

• It is not Gaussian. P.372 supplies amplitude probability distributions parametrized by $V_d$ precisely because the impulsive envelope, not the mean power, determines digital error rate. A modem designed against an AWGN assumption underperforms its predicted BER in atmospheric noise, and impulsive-noise blanking or interleaving is worth more than raw SNR. This is a channel-coding problem — see channel coding basics.
• It falls steeply with frequency, which is why it stops being the story above HF.

Atmospheric absorption noise, and rain #

At the other end of the spectrum a different atmospheric mechanism takes over. Oxygen and water vapour absorb — with resonances near 22 GHz (H₂O) and 60 and 120 GHz (O₂) — and, as the radio-systems course puts it, any body able to absorb energy also radiates it above 0 K. The sky brightness temperature a ground station sees follows directly from the total attenuation on the path:

$$T_B(f) = 2.73 \cdot 10^{-A_T/10} + T_{mr}\left(1 - 10^{-A_T/10}\right)\ \text{K}$$

with $T_{mr} = 275$ K in rain. The 2.73 K term is the cosmic microwave background leaking through; the rest is the atmosphere itself glowing at you in proportion to how much it is absorbing.

Galactic and cosmic background #

Below about 100 MHz the median galactic noise figure, neglecting ionospheric shielding, is

$$F_{am} = 52 - 23\log_{10} f \quad \text{(dB, } f \text{ in MHz)}$$

with 2 dB decile deviations; a narrow beam at the galactic pole sees about 3 dB less than the all-sky average, and pointing at the galactic centre sees considerably more. Above 2 GHz the galaxy has shrunk to a narrow bright band and only the Sun and a handful of strong sources (Cassiopeia A, Cygnus A, the Crab nebula) matter — the cosmic background contributes just 2.7 K. Background brightness scales as $T_b(f_i) = T_b(f_0)(f_i/f_0)^{-2.75} + 2.7$ K: 200 K at 408 MHz extrapolates to 19.7 K at 1 GHz.

The Sun is the exception that will ruin a link: about $10^6$ K at 50–200 MHz and at least $10^4$ K at 10 GHz even when quiet, far more when disturbed. Geostationary earth stations get a predictable outage twice a year when the Sun passes behind the satellite.

Man-made noise #

Aggregate emission from ignition systems, power lines, switching supplies, and everything else electrical. P.372 fits the median to a straight line in $\log f$:

$$F_{am} = c - d\log_{10} f \quad \text{(dB, } f \text{ in MHz)}$$

valid over 0.3–250 MHz for the populated categories.

Values are median $F_a$ in dB above $kT_0b$, computed from the ITU coefficients. The quiet-rural and galactic curves have narrower validity ranges than the other three — quiet-rural noise is ionospherically reflected and is only observed below the extraordinary-wave critical frequency, above which the ionosphere turns transparent and galactic noise takes over.

Read the spread rather than any single cell: a city site runs 23.2 dB above a quiet rural one at 1 MHz, widening to 25.0 dB at 100 MHz — a factor of 210 to 320 in noise power, and worth more than any receiver you can buy. P.372 also warns that this AWGN-like median is only one of three categories of man-made noise; the others are impulsive noise, and "single-carrier noise" — a discrete carrier or a hump in the spectrum from one nearby source, which is the typical indoor situation and which a median-power model does not describe at all.

Putting it together #

flowchart LR
  A["10 kHz - 30 MHz<br/>atmospheric + man-made<br/>Fa 25-77 dB"] --> B["30 - 300 MHz<br/>galactic + man-made<br/>Fa 6-36 dB"]
  B --> C["0.3 - 2 GHz<br/>receiver dominates<br/>Fa near 0 dB"]
  C --> D["above 10 GHz<br/>receiver + sky/rain<br/>Ta 10-250 K"]

The link budget is where all of this cashes out; radio propagation supplies the loss side of the same ledger, and transmission levels the dB arithmetic itself.