Notes on attenuation from responses to questions asked on SARA Mailing List 5 January 2025

My Question:

Hi,

Basic question- say I save 2dB here by changing coax and 2dB there by doing something else. Does that mean the total saving is 2+2=4dB or, as it logarithmic scale, doss it not work that way?

Andy

Answers from SARA Mailing List:

Yes, since log(a*b) = log(a) + log(b)

So, if 2 parts of system had 3db loss and 5db loss respectively then total loss would be 3 x 5 = 15db. Is that correct?

No. 8dB.

No, it is 8dB. Lets make a simple example of two cables which have 3dB loss each:

3dB means that only half to the power is received at the end and this is calculated in dB: 10*log(0.5) = -3

If you have two cables concatenated, you get 0.5*0.5 = 0.25 of the power.

This is then expressed in dB: 10*log(0.5*0.5) = -6 which is the same as 10*log(0.5) + 10*log(0.5) as per equation which I sent earlier.

The Significance of that  “loss”  relates to Where it occurs :

Before the gain of the first LNA : = the dB loss = the dB increase in the system Noise Figure  = Bad

After the LNA, its degradation is diminished by the gain of the amplification.  = Minimal change in system performance

i.e. after the 40 dB gain of a SAWBird,  no problem with several dB loss .

See Friis Equation.

Assuming reasonable Tsys (almost-entirely dependent on LNA noise), then you only need enough gain in the system to
  “light up” a suitable number of bits of the ADC in the SDR with the ambient sky noise.

The analogy in analog systems would be enough gain to cause the chart-recorder pen to move noticeably for sky background.

Tsys ( almost-entirely dependent on LNA noise +  cable & connector loss prior to the LNA  ).