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Re: Sensitivity and noise floor (theory question)



Hi David,

There's a pretty good introduction to sensitivity, noise figure, noise
temperature etc in the ARRL Handbook;  the 1990 edition has this material on
pages 12-1 to 12-3.

Whether a pre-amp with a noise figure of 1.5dB would improve receive
performance or not, depends on a number of parameters, including the gain of
the pre-amp, the gain of the downconverter, and (quite importantly) any
losses in the coax between the antenna and the downconverter's input.  As a
"rule of thumb", I'd venture that at 2.4GHz, you will achieve better
improvements from dropping the noise temperature of your antenna system (ie
minimise sidelobes receiving noise from the hot earth), and from decreasing
coax losses (put the downconverter right at the feed).

You can find some calculations on this in Appendix A of the following
document:
http://vhf.worldsbest.com.au/Downlink_Antenna_VK6KCH.pdf  (approx 800kB in
size).

You asked about converting a .18uV SINAD (I assume FM mode), to a noise
figure.   This is also covered in Appendix A of the above document, as
follows:

dBW = 10 * Log((V^2)/50R)
    = 10 * Log((0.00000018^2V)/50R)
    = -151.88dBW

The formula for working out the equivalent noise temperature of the receiver
is:

T = (C/(kB)) / (C/N)

However, we can't just plug in "12dB SINAD" for the C/N, as the SINAD versus
C/N curve of an FM receiver is definitely not linear!  From a graph in
"Modern Electronic Communications", p171 (Miller, Gary M., 3rd Ed., Prentice
Hall International, NJ. 1988), I assume that a C/N of 8dB into a narrowband
FM receiver is required in order to achieve a SINAD of 12dB.

k is Boltzmanní s constant, and B is bandwidth (let's use 16kHz, the usual
figure for a "25kHz channel spaced" system).  16kHz = 10 * Log (16000Hz) =
42.04dBHz

It's easier to do this calculation in dB instead of linear, so the formula
is represented as:

[T] = [C] - [k] - [B] - [C/N]

[T] = -151.88dBW -(-228.6dBJ/K) - 42.04dBHz - 8dB = 26.68dBK

The noise temperature of your receiver is therefore 10^(26.68/10) = 10^2.668
= 465.59K

Or, expressed as a Noise Figure:

NF = 10 * Log ((465.59K/290K) + 1)
   = 10 * Log (2.6054)
   = 4.16dB


So finally, the answer:  your .18uV sensitivity receiver has a noise figure
of 4.16dB.



I hope some of this is useful.


73 Chris vk6kch



>This is a general radio theory question.
>
>My AO-40 downconverter has a NF of 1.7db.  What exactly does that mean?
>My 2m rig has a sensitivity of .18 micro Volts (12db SINAD).  How is
>this sensitivy related to the noise floor of the reciever in the rig?
>Can I calculate the noise floor?  Finally would I benefit from a 1.5 db
>nf preamp in front of this reciever?
>
>Thanks for your knowledge here.  Let me know if there are any good
>sources to learn more about this...
>-David Carr
>KD5QGR
>


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