Total noise figure of low band receiving system, passive antenna elements

This page was originally done in 2018 in Excel format. I converted it to html and Java script in 2021.

On low bands, 160m-30m, separate receiving antennas are often used. As background noise level is quite high, efficiency of such a receiving antenna doesn't need to be good. But what efficiency is enough? Here is a way to check if our antenna and receiver or preamplifier are good enough, so that they do not add significantly noise into our receiving system.

Antenna efficiency is the same as average gain, negative dBi-value, less than 1 in absolute values. Average gain of an antenna can be calculated with Eznec or other modelling SW.

Radio spectrum noise figures in a quiet QTH according to ITU-R Recommendation P.372-10 are:

MHz	F1/dB
30	20
20	23
10	30
7	33
3.7	37
1.85	46

Those numbers set the limit to how weak signals we can receive.

Noise figure Fn of two cascaded devices is:

Fn = F1 + (F2-1) / G1 , where all are absolute numbers, not dB.

F1 = radio spectrum noise figure, see above
F2 = receiver noise figure at antenna output. Cable loss is added to the RX noise figure. If a high gain preamplifier is used, F2 is the noise figure of it.
G1 = antenna average gain, always less than 1, negative dB-value.

Total noise figure calculator

factor	symbol	value in dB	absolute	contribution
radio spectrum NF	F1
ant average gain	G1
RX noise figure	F2			↓
→ total noise figure	Fn		←
→ addition to F1	∆		-	-

Calculate

Example 1:

Our antenna is 2 λ long Beverage on 3.8MHz:
• Modelled average gain = -17.8dBi, [and max gain = -4.24dBi @ 24deg elevation. Directivity = 13.5dB.]
• Radio noise figure = 7dB. Cable and other loss from antenna to radio = 3dB.

How many dB's are we losing in our S/N, compared to an ideal case?
→The answer is:0.45dB

Example 2:

Flag antenna on 160m band:
• average gain = -35.3dBi, [and max gain = -27.5dBi @31deg, directivity = 7.8dB.]
• Preamplifier at the antenna feedpoint F2 = 3dB.

How many dB's are we losing in our S/N, compared to an ideal case?
→ Noise figure increase = Fn-F1= 0.35dB, is acceptable. We are getting all possible signal.

→ If preamplifier noise figure F2 were 10dB, we would lose 2.5dB in S/N, which is not acceptable any more.