Cable loss before the first low-noise amplifier can damage a GNSS receive chain's noise performance much more than the same loss after it. Early low-noise gain reduces the relative contribution of later stages. It does not recover signal-to-noise ratio already lost upstream. Consequently, two chains with the same net conducted gain can have different noise figures.
This distinction explains why a cable-loss budget alone cannot establish receiver sensitivity. The useful question is not simply how many decibels an amplifier adds, but where it adds them and how much noise accompanies that gain.
Noise figure measures a different property from gain
Power gain describes a device's output-to-input signal-power ratio. Noise figure describes its added-noise penalty under a specified reference condition. An amplifier raises the input noise as well as the wanted signal, and contributes noise of its own. A larger output signal is therefore not evidence of an improved signal-to-noise ratio. Keysight's noise-figure explanation distinguishes these effects.
Use F for linear noise factor and NF for its decibel form. For the matched, thermal-noise model used here, with the input source at the standard reference temperature T₀ = 290 K:
F = SNRᵢₙ / SNRₒᵤₜ; NF = 10 log₁₀(F).
For example, NF = 1 dB means F ≈ 1.259, not F = 1. The decibel number is not a noise power in dBm. Nor does a quoted noise figure specify antenna directional gain or the received satellite signal power.
The reference temperature defines the noise measurement. It is not a claim that the antenna sees a 290 K sky, or that every component is physically at that temperature.
Why a passive cable adds a noise penalty
A cable attenuates the wanted signal and incoming noise. A real lossy cable also generates thermal noise. In a matched system with both the source and cable at T₀, the cable's available output noise remains kT₀B, while the signal is attenuated. Here k is Boltzmann's constant and B is the noise bandwidth.
Under those conditions, a cable with linear power loss L has gain G = 1/L and noise factor F = L. Thus a 3 dB cable has a 3 dB noise figure. That equality is conditional on temperature and matching, not a universal identity for every installation. Michael Steer's Noise Characterization, attenuator example explains the passive-loss result and the cascade model.
Scaling the signal and existing noise powers by the same factor would preserve their ratio if no noise were added. A real lossy cable also contributes thermal noise.
Read the chain in order, using linear quantities
For three matched, linear stages at a common signal frequency, the conventional Friis noise equation is:
Fₜₒₜ = F₁ + (F₂ − 1) / G₁ + (F₃ − 1) / (G₁G₂).
F₁, F₂ and F₃ are linear noise factors. G₁ and G₂ are linear power gains. Convert gain and noise figure with 10 raised to their dB values divided by 10. For a positive cable-loss figure, L = 10^(loss_dB / 10), so its gain is 1/L. Do not put decibel values directly into this equation or use a voltage-gain conversion.
The denominators explain the importance of order. Noise added later is referred back through the preceding gain. When an early stage has gain below one, it makes the following stages' noise contributions more significant at the chain input.
Analog Devices' cascade analysis derives the linear-block case. It also explains why frequency-converting receivers need careful treatment of mixer and image-noise definitions. A bare mixer specification should not be inserted into a simple RF cascade without checking those definitions.
Hypothetical example: equal net gain, unequal noise figure
Consider three invented arrangements at one GNSS-band frequency. They are mathematical examples, not product specifications or measurements.
Assume matched ports, linear small-signal operation, uncorrelated added noise, consistent noise bandwidth and a 290 K source. The cable is also physically at 290 K. The LNA has 20 dB gain and 1 dB NF. The cable has 3 dB loss. The receiver is represented by an equivalent input noise factor corresponding to 5 dB NF for the same signal and noise convention. Its internal conversion stages are not modeled separately.
The reference plane for total noise figure is the input of the first listed element. The gain column stops at the receiver input and excludes the receiver's internal gain.
| Order from the common source toward the receiver | Conducted gain before receiver | Total noise figure, including receiver |
|---|---|---|
| LNA → receiver; no cable loss | 20 dB | 1.074 dB |
| Cable → LNA → receiver | 17 dB | 4.074 dB |
| LNA → cable → receiver | 17 dB | 1.179 dB |
The linear inputs are Fₐ ≈ 1.258925, Gₐ = 100, L ≈ 1.995262 and Fᵣ ≈ 3.162278. Subscript a denotes the amplifier and r the equivalent receiver.
Without the cable, Fₜₒₜ = Fₐ + (Fᵣ − 1)/Gₐ ≈ 1.280548.
With the cable first, Fₜₒₜ = L + (Fₐ − 1)L + (Fᵣ − 1)L/Gₐ ≈ 2.555030.
With the cable after the LNA, Fₜₒₜ = Fₐ + (L − 1)/Gₐ + (Fᵣ − 1)L/Gₐ ≈ 1.312021.
Apply 10 log₁₀ to each total to obtain the table. In this model, the pre-LNA cable adds its full 3 dB to the no-cable chain's NF. After the LNA, the cable is not harmless, but its effect is much smaller. The two 17 dB gain budgets conceal a noise-figure difference of about 2.895 dB.
This comparison isolates loss placement. It does not say that a real active antenna can be rearranged this way, or that moving an amplifier is an approved installation change.
What an extra amplifier can and cannot compensate
An amplifier added after a lossy path can restore signal level at the receiver input. It can also reduce the relative contribution of the receiver's own added noise. It cannot remove the noise penalty of everything ahead of it: even an ideal noiseless amplifier preserves the SNR at its input rather than improving it.
This is why first-stage NF and gain must be considered together. Low early NF is valuable, while enough early gain limits later contributions. Increasing gain indefinitely is not the objective. In Analog Devices AN-2622, Gain and Noise Figure, attenuation placement and noise performance are treated as separate design considerations. Its component advice is not a gain recommendation for a ResiNav product.
Also separate this small-signal noise calculation from compression, clipping and receiver dynamic range. A chain with an attractive calculated NF can still overload. Conversely, a measure that helps avoid overload can change the weak-signal noise budget. One number cannot establish both behaviors.
Applying the result to a GNSS installation
Start the conducted calculation at a defined connector or internal reference plane. Identify which losses occur before the first active stage, which occur after it, and what each published NF includes. An active-antenna specification may describe an assembly rather than an isolated LNA. Adding its internal losses again would double-count them.
Use frequency-specific values for the actual chain. Do not combine the best NF at one frequency with cable loss or gain from another band. Keep antenna reception pattern and polarization outside a scalar conducted-gain sum; those describe a different part of reception.
Then interpret the outcome at the right level. NF is a reference-condition description of added noise, not a direct prediction of a satellite's C/N₀ or position error. Actual input noise depends on the antenna and its environment. Steer's noise-temperature example explicitly distinguishes antenna noise temperature from the standard NF reference. The GNSS C/N₀ and SNR guide explains the signal-quality quantities separately.
For an integration review, carry the ordered noise model alongside the documented RF path, cable losses and connector boundaries. The gain budget tells you about levels. The cascade model tells you why an early loss can remain significant even after those levels are restored. Neither calculation, by itself, establishes anti-jamming performance or a positioning guarantee.
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