System noise

Last Updated on April 18, 2026 by John Berry

Radio amateurs are interested in the signal to noise ratio of received signals. In professional digital systems the interest is in E_b/N₀, the energy per bit over noise in a 1Hz bandwidth. Radio amateurs often use noise in the the 2.4kHz SSB channel as reference. To include electrical noise (from the various system components) we need to be able to calculate the threshold degradation and use that modified threshold in performance calculations.

We need to consider the electrical noise in a receiver system. Our aim in optimising our system is simple: to add as much gain as possible in the signal path (to overcome losses without overloading the receiver) while introducing as little noise as possible (to avoid degrading the receiver threshold). The system in my example comprises an array of four antennas, combiner, low noise amplifier, feeder, and receiver in the rig.

There are two steps needed.

Antenna noise contribution

First, calculate the noise figure of the antenna in its environment and have this available for use in a subsequent cascade calculation.

To calculate this, we need to revert to noise temperatures and look up the antenna noise temperature on the manufacturer’s website.

The formulas concerned are:

t_s=200(f_s-1)

Where t_s is the antenna noise temperature, f_s is the corresponding noise factor.

F_s=10log₁₀f_s

Where F_s is the noise figure, f_s is the corresponding noise factor from above.

A handy converter is available on the Microwaves 101 site.

In my case, the noise temperature of my 14-element 70cm Yagis is about 257°K (from manufacturer data). This gives a noise figure of about 2.8dB.

Antenna

There are four antennas in the array, and hence in principle, the four noise temperatures must add. However, each antenna will be directional. It’s likely that the array will have a significantly narrower beamwidth than a single antenna of the same type. With a narrower beamwidth, the array will capture less noise. Hence the noise temperature of the array will be lower than that for the single antenna.

To complicate things further, the optimised four-stack array may have significantly fewer responses off the main beam when compared to a single antenna. This is another argument for improved noise performance from the array.

So, it’s complicated. It might be that the noise is increased, and it might be that it is reduced. Modelling would be needed to conclude this definitively.

To consider the antenna array in the noise calculation, I have assumed that a four-stack has the same noise temperature as a single antenna.

System noise contribution

Second, calculate the cascaded noise figure for all receiver elements to enable the threshold degradation from system noise to be deduced. The approach uses the Friis formulas for noise.

This is done using the cascade formula below:

Where f_s is the system noise factor and the various f_n and g_n are the noise factors and gains of the system stages. You can then see the system noise figure F_s in dB given by the formula below.

F_s=10log₁₀f_s

You can find a calculator and good discussion on this by Everything RF. The authors there have not obeyed the convention that linear variables are in lower case notation while (logarithmic) decibel values are in upper case.

Practical calculation

I assume a five-stage system comprising receiver, feeder and low noise amplifier, combiner and antenna array as shown below.

In my case, the LNA has a noise figure of 0.6dB and a gain of 20dB. I’ve assumed a manufacturer’s insertion loss figure for the antenna combiner of 0.5dB. I estimate the main feeder (and all connectors and pass-through losses) at 3dB, with the corresponding gain at -3dB. But I don’t have an accurate noise figure for the rig receiver, so I’ve estimated that at 3dB and assumed the gain of the first receiver stage at 20dB.

The system noise figure from above is 3.5dB.

Affect on system sensitivity

The rig receiver threshold sensitivity (for 0dB signal to noise for an SSB signal in a 2.4kHz channel) is -159dBW for a rig noise figure of 3dB. I calculated that there’s system noise figure from the cascade (including that receiver) of 3.5dB. The system sensitivity is now therefore -158.5dBW. That’s just half a dB worse than the receiver alone – half a dB threshold degradation. So, we’ve managed to add something like 40dB in the signal path (about 20dB antenna gain plus the gains and losses down to the receiver) while only adding 0.5dB to the noise.

The big advantage of the LNA is that we avoid adding around 3.5dB of losses in the signal path to the system noise figure. If I didn’t have the LNA in the example, I’d have a horrid 6.5dB effective noise figure with associated large threshold degradation.

The receiver sensitivity here is from the manufacturer’s equipment specification.

Just as a side exercise, it’s well worth using the cascade calculator to see where the system noise sensitivities are. Try reducing the LNA noise figure – the effect is big, justifying its use. Then try increasing the feeder loss (simulating poor quality feeder). Its effect is small, so paying good money for good feeder is a waste (considering the RX side in isolation). And see why using a low noise antenna (with narrow beamwidth and suppressed side lobes) is key. Its noise adds dB for dB. The formula above shows why it is the primary contributor of noise.

My threshold degradation is therefore 0.5dB for a huge benefit, and I’ve used the system sensitivity of -158.5dBW elsewhere in calculating the path budget.

Final note

I’ve used a rig noise figure of 3dB. This is poor (and may even be worse in practice) because rigs must meet reasonable intermodulation rejection and adjacent channel rejection. The additional circuitry that this necessarily adds to the rig degrades what might otherwise be a good noise figure. Adding a low noise amplifier often simply degrades receiver performance, making the system susceptible to interference. You will then need to add high-quality filtering to stop radar, cellular and other emitters undoing the benefits discussed here.