# S/N degradation is related to external noise level and receive system internal noise

A question that arises from time to time is what is the minimum receiver noise figure for a given application.

This discussion considers the question applied to linear receivers, ie receivers with zero intermodulation distortion (IMD) and other non ideal characteristics, other than their internal noise which can be described by their Noise Figure (NF).

By definition, NF is the amount by which the component or system degrades the NF, so in dB it is the difference in the S/N in to S/N out. Implicit in that definition is that it is based on source internal noise of 290K equivalent.

## HF example

So for example lets say a receiver with quivalent noise bandwidth 2000Hz measures sensitivity of -125dBm for 10dB S/N out. We can calculate the noise in 2000Hz bandwidth from a 290K source to be -141dBm, and therefore the input S/N is -125 – -141 = 16dB. The ratio of the input S/N to output S/N is the difference in those in dB, 16-10=6dB. The NF is 6dB. We can also calculate an equivalent internal noise temperature of (10^(6/10)-1)*290=865K.

By convention, ambient noise (or external noise) is expressed in Kelvins, or dB wrt 290K. That does not imply that an antenna contributes exactly 290K.

So if Fam=13dB, Tam=10^(13/10)*290=5786K.

We can then say that if this receiver adds 865K of noise to the ambient 5786K, the total noise is now 6651K, an increase of 10*log(6651/5786)=0.6dB, so S/N has been degraded 0.6dB by the receiver in this scenario.

So, there are two factors that influence the extent of degradation, the ambient noise, and the receiver internal noise. The chart above shows the expected median ambient noise figure in Rural precincts from ITU-R P.372-13, and the calculated degradation in S/N ratio caused by internal noise of a receiver with NF 20dB (which is about what might be expected with the PREAMP OFF).

## UHF moon bounce example

Let's consider a receive system with NF=1.0dB (Teq=75.1K) at the antenna connector, and quiet radio sky of say 40K (we are pointing to the sky, this is not terrestrial noise). Though this might look like a pretty low noise receive system, you can see that total noise temperature is 75.1+40=115.1, so the degradation is 10*log(115.1/40)=4.6dB.

The situation would be very different for an antenna pointed horizontally as Tam would be a lot higher, and site dependent.

## Conclusions

We can calculate the degradation in S/N caused by receive system internal noise, and that should drive considerations about how good the receiver needs to be.

The discussion has assumed a linear receiver (zero IMD), and presence of IMD will add noise to the system, further degrading S/N. Measures to reduces susceptibility to IMD, even where they seem to reduce sensitivity, may result in improved S/N recovered.