HF Noise Factor and SNR: Why the Decibels Do Not Simply Add Up

A useful discussion about adding an amplifier after an active receive array brought us back to a familiar question: if one amplifier has a noise figure of 1.5 dB and another has 2.8 dB, will the first give us 1.3 dB better reception?

Sometimes it can. Often, on HF, the difference is much smaller. And an amplifier that does not have the lowest noise figure can still make a considerable improvement when placed before a long cable or a relatively noisy receiver.

This follows our active-HF-antenna measurement guide. Here I want to make the arithmetic tangible: what the numbers mean, why a Beverage can receive well despite substantial loss, and why counting noise-figure decibels is not a receiving-system calculation.

First separate three different things called “noise”

Signal-to-noise ratio, or SNR, tells us how far the wanted signal stands above the noise in a stated receiving bandwidth. An SNR of 10 dB means ten times as much signal power as noise power. Twenty decibels means one hundred times as much. Both powers must refer to the same point in the system.

Noise factor, F, describes the noise performance of a receiving device or network under a defined source condition. Noise figure, NF, is that factor expressed in decibels. The usual reference source has a noise temperature of 290 kelvin, approximately 17°C. Under those reference conditions, F is the input SNR divided by the output SNR.

A 3.01 dB NF means a factor of two: the device doubles the noise relative to what an ideal noiseless device would deliver from that reference source. It does not mean that it halves the SNR of every antenna signal, whatever noise the antenna already supplies. The distinction follows directly from the standard noise-factor and noise-temperature definitions.

External noise is what the antenna receives from its surroundings: atmospheric noise, human-made interference and radiation from the wider radio environment. ITU-R also uses an external noise factor, referenced to an equivalent loss-free antenna. That is a measure of the received environment, not a component’s added-noise figure. A large external noise factor does not prove that the antenna is inefficient. See ITU-R P.372, Radio noise.

On many lower-HF installations, this received noise dominates. But a quiet site, an antenna that rejects the dominant noise directions, substantial loss, or operation toward the quieter upper HF bands can change the balance. “It is HF” is not a complete noise budget.

Two noise sources do not add like two gain settings

Suppose the existing noise at one point is −110 dBm and a second, independent contribution is −120 dBm, in the same bandwidth and referred to that same point. Here dBm expresses a power relative to one milliwatt; dB expresses a ratio between powers. The second contribution is one tenth of the first. Adding them gives 1.1 times the original noise power, or −109.59 dBm. The increase is only 0.41 dB.

We add the powers, then convert the result to decibels. Two equal independent noise powers give a 3.01 dB increase; a much smaller contribution produces a much smaller increase. Adding the printed dBm values would have no useful physical meaning.

There is nothing wrong with decibels. Consecutive signal gains and losses can be added in dB. Actual SNR degradations across successive stages, evaluated under their actual operating conditions, also add in dB. The mistake is treating separately specified, 290 K noise figures as those actual on-air degradations.

A 1.3 dB NF advantage can become a 0.02 dB SNR advantage

Compare two amplifiers with the same gain and suitable input matching. One has 1.5 dB NF; the other has 2.8 dB NF. Assume that later receiver noise is negligible and neither amplifier overloads.

Use the noise from the standard 290 K source as one unit. The quieter amplifier adds approximately 0.413 units of input-equivalent noise. The other adds 0.905 units. If the antenna or preceding system already supplies 100 units, we are comparing 100.413 with 100.905—not deducting 1.5 or 2.8 dB from the signal.

These are calculated examples, not measurements of a particular antenna or amplifier. The input noise is what actually reaches the stage being compared, after any earlier antenna electronics, transformers, filters, delay lines and combining network.

A higher SNR from a directional antenna does not, by itself, tell us that this absolute noise level is low. We need both pieces of information. Nor does the presence of an active antenna automatically make every following amplifier’s noise irrelevant.

Why a lossy Beverage can still be an excellent receiving antenna

A Beverage is a long, low travelling-wave receiving antenna. Its relationship with the ground and its termination help establish a directional response. The termination absorbs travelling energy that would otherwise reflect; real ground and conductor losses also dissipate energy. It is not designed to maximise radiation efficiency as a transmitting antenna.

That sacrifice can be useful. The antenna may retain enough response toward the wanted station while accepting substantially less noise from other directions. The original Beverage patent describes the directional principle; our Beverage and BOG comparison discusses its practical dependence on the installation.

The loss is not what improves reception. The useful pattern and placement can improve the signal-to-external-noise ratio; tolerable loss is a price paid for obtaining them. Loss itself attenuates signal and received noise, adds thermal noise and can leave too little output to overcome receiver noise.

Some specialist receiving antennas accept substantial efficiency loss in exchange for a useful pattern. Ordinary efficient antennas need not have a large loss-equivalent noise figure. And a Beverage has no single universal NF: its length, height, frequency, soil, termination and feed system all matter.

A low or negative gain in dBi is not enough to calculate antenna NF either. Gain contains the effect of directivity as well as efficiency; realised gain also includes mismatch. A weak S-meter reading is not an efficiency measurement.

A quieter signal can be easier to read

Consider two hypothetical antennas in the same receiving bandwidth. The numbers below are powers delivered at the receiver input; they already include each antenna’s response and losses. The receiver adds an equivalent −140 dBm of noise at that input in either case.

The second signal is 10 dB weaker, yet its SNR is approximately 9.59 dB better. The antenna has reduced the unwanted noise more than the wanted signal. Turning up a noiseless amplifier after the first antenna would raise both together and would not create that improvement.

This is an illustration of discrimination, not a claimed Beverage measurement. If the unwanted noise arrives from the same direction and with the same polarization as the wanted station, a directional antenna may offer much less advantage.

What “antenna noise figure” can mean in a defined model

For a passive antenna, we can separate a loss-free version of its receiving pattern from an equivalent dissipative loss. If its efficiency is η, all of that modeled loss is at 290 K, and we use a matched available-power reference, its loss-equivalent noise factor is 1/η. Ten per cent efficiency corresponds to 10 dB; one per cent corresponds to 20 dB.

This follows from the antenna efficiency and thermal-noise relationship in NIST Technical Note 1551, page 7. Mismatch and different physical temperatures require their own treatment.

Take the deliberately severe one-per-cent-efficiency example, and use an ideal noiseless receiver to isolate the antenna loss. Its 20 dB loss-equivalent NF stays the same, but its actual SNR penalty depends on the external noise entering the loss-free reference antenna:

With a very noisy external field, much of the signal and noise are attenuated together, and the antenna’s own thermal noise is a small addition. With a quiet field, that thermal contribution becomes decisive. A real receiver adds another contribution after the loss, so excessive loss can still make a low-noise preamp necessary. These are model inputs, not predictions for every HF location.

A useful preamp is not necessarily an exceptionally low-NF preamp

Now consider a practical reason to add gain: a receive antenna or array is followed by a long coaxial cable and then the receiver. An amplifier before that cable raises the wanted signal and the existing antenna noise before the cable and receiver add their own contributions.

Assume 2 dB of matched cable loss at 290 K, a receiver with 10 dB NF, and an added amplifier with 14 dB power gain. Here is the electronic chain’s reference NF, referred to the point before the cable/amplifier arrangement:

The 2.8 dB NF amplifier already makes a large difference to the chain. Its position matters too: placed after the cable, it cannot recover the SNR already lost there.

Do not read the change from 12.00 to 3.97 dB as an automatic 8.03 dB on-air improvement. With existing input noise 10 dB above the 290 K reference, the calculated SNR improvement is 3.35 dB. Substituting the same-gain 1.5 dB NF amplifier then gains only another 0.19 dB. All these values assume linear operation and the stated matching.

That explains how an operator can honestly report much better readability with a preamp switched on, without that observation establishing a need for an NF of 1 or 1.5 dB. It also explains why “a preamp never helps on the low bands” is an equally poor rule.

Gain protects against following noise. It cannot erase noise or restore SNR lost before the amplifier. Once following noise is already small enough, extra gain mainly increases levels and reduces the remaining margin before overload.

Apply the budget at the right place in an active array

In a VerticalVortex3-based receiving array, for example, an additional amplifier after the element electronics, delay lines and combiner is a later stage. Its input contains the signal and noise that survive that complete preceding system. Evaluate the additional stage there; do not treat it as though it were connected directly to a bare antenna element.

Four branches are not four amplifiers in series. Do not add the losses of four parallel cables, or call an ideal four-way combiner an automatic 6 dB loss for a correctly phased wanted signal. Wanted signals combine according to amplitude and phase; independent amplifier-noise powers combine with the corresponding power weights. External noise can also be correlated between elements.

A voltage-gain figure from a high-impedance probe is not automatically the available power gain needed in a conventional matched-chain calculation. Likewise, a 50 Ω amplifier NF does not fully describe its behaviour on a highly reactive antenna source. Amplifier voltage noise, current noise and the actual source impedance matter, as explained in Analog Devices’ discussion of op-amp noise. This is relevant to short electric probes and dipoles as well as loop interfaces.

One more trap: a warm lossy cable generates thermal noise, but it also attenuates the noise entering it. When the incoming noise is much higher than the cable’s thermal noise, the cable’s output noise can fall while the system noise figure gets worse. “There are long delay lines, therefore the next amplifier’s noise must be swamped” does not follow.

The arithmetic, when you want to go further

The examples use matched available powers and independent added noise. All gains and factors inside these equations are ordinary ratios, not decibels.

A genuine dB-addition case: matched passive loss at 290 K before an amplifier gives F_total = L × F_amp. Therefore the loss in dB does add to that amplifier’s NF. Move the loss after sufficient gain, and its contribution changes. The ordering is part of the answer.

What I would compare at the station

Start with the wanted signal and the noise in the same bandwidth. Compare antennas with rapid switching or simultaneous recordings so fading does not masquerade as an improvement. Keep receiver gain, bandwidth and signal processing controlled; a louder speaker or taller waterfall trace is not an SNR measurement.

For two amplifiers, compare at equal net gain. Otherwise the test mixes two questions: whether more gain helps, and whether less added noise helps. Include strong-signal conditions, because a low-NF stage that compresses or creates intermodulation can make reception worse.

To decide whether downstream noise matters, characterize the receiving chain with a suitable matched termination, then measure what the installed antenna or array actually delivers to that same reference plane. A noise rise with the antenna connected is a useful initial clue; a changed source impedance, receiver AGC or uncalibrated display can make it misleading.

Absolute NF can be measured with a calibrated Y-factor setup or an appropriate gain-and-output-noise method. Both require attention to bandwidth, matching, calibration and the measuring receiver’s own noise. A component datasheet or an arbitrary noise-generator setting is not a measurement of the finished HF system.

The question I want answered is: what is limiting this station’s SNR? If external noise dominates, improve the receiving pattern, location or the interference environment. If antenna/feed losses and receiver noise dominate, reduce avoidable loss before the first useful gain stage, then improve that stage and its placement. If strong signals cause overload, solve the linearity and filtering problem. A single NF number cannot make those decisions for us.

Noise figure belongs in the design. It becomes misleading when we ask it to stand in for the entire antenna, environment and receiving chain.

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