# R: System NF Calculations

• Subject: R: [amsat-bb] System NF Calculations
• From: "i8cvs" <domenico.i8cvs@xxxxxx>
• Date: Sun, 20 May 2001 05:23:01 +0200

```Hi  Scott,

Noise Figure,noise bandwidth and 10 dB sensitivity for SSB/CW are neatly
tied togheer by the following formula:

S = -174 + 9.54 + NF + 10 x log    (BW)
10

where:
S is the 10 dB sensitivity (dBm)
-174 is the available thermal noise power density (dBm in 1.0 Hz at room
temperature)
9,54 is the signal to noise ratio S/N in dB  corresponding to  (S+N)/N= 10
dB
NF is Noise Figure in dB
BW is noise power in to the bandwith (Hz) : 2500 Hz for SSB

If now i put your computed NF= 7.84 dB in the above formula  i get
S= -122.64 dBm and not -126 dBm

In order to get S = -126 dBm i have to put in the formula NF=4.48 dB that
seams to be the receiver Noise Figure but to get S in terms of voltage,use
the formula

(S/20)
E= 0.4472 x 10

where E is the OPEN -circuit voltage (called "hard" signal level ) from a 50
ohm signal generator (twice the reading indicated on generator's output
meter with the generator operating into a 50 ohm load and S in decibels
relative to a milliwatt (dBm)

If now i  apply for E using -126/20 for the exponent i get a voltage of
2,24 microvolt that is exatly two time
the 0,11 microvolts specified by the manufacturer for a sensitivity of
10 dB S/N ratio in SSB/CW mode.

But 0,11 microvolt applied to a 50 ohm resistor produces exactly a power
of  -126 dBm and so 0,11 microvolt is not the open circuit E voltage to wich
the -126 dBm sensitivity must be correlated to complay with the above
formula

Probably the manufacturer of receivers tends to use for sensitivity the
voltage applied  across the 50 ohm
antenna impedance and not the open circuit voltage E of the generator and
probably they do this for commercial purposes in order to demostrate that
their receiver is more sensitive or 0,11 microvolt is better than 0,22
microvolt.

Now, according with the formula,if i believe to 0,11 microvolts i have to
multiply it by two and get E=0,22 microvolt by wich S= -126 dBm and the
receiver  Noise Figure is 4,48 dB

Believe or not,all of this is well described by  William
E.Sabin,W0IYH
in his article "Measuring SSB/CW Receiver Sensitivity "published in QST
october 1992 pages 30-33

73 de i8CVS Domenico

----- Original Message -----
From: Scott Townley <nx7u@arrl.net>
To: Joe Leikhim <jleikhim@nettally.com>; <amsat-bb@AMSAT.Org>
Sent: Saturday, May 19, 2001 5:13 PM
Subject: Re: [amsat-bb] System NF Calculations

> I imagine that the spec is actually 0.11uV for 10dB (S+N)/N (which
> algebraically is S/N+1)
> So -126dBm @ 10log(9)=9.54dB S/N
> -135.54dBm @ 0dB S/N = FkTB (noise figure*Boltzman's
> constant*temperature*bandwidth)
> Take out the B (assume 2.5kHz) 10*log(2500)=34dB
> -135.54-34=-166.14dBm/Hz=FkT
> kT at room temperature -174dBm/Hz
> F=-166.14-174=7.84dB
>
> My FT-726R claims 0.15uV for 10dB (S+N)/N, which would be
> 20*log(.15/.11)=2.7dB worse (NF=7.84+2.7=10.54dB).
>
> But, if you have sufficient gain in front of the RX, then NF(RX) isn't too
> important.  One must work out the system noise figure calculation to
> determine "sufficient".
>
>
>
> At 11:35 PM 5/18/01 -0400, Joe Leikhim wrote:
> >What is a typical noise figure for a multi-mode radio?
> >The 15dB in the spreadsheet example sounds like pretty sorry
> >performance.
> >The ICOM radios are spec'd at about  0.11uv (-126 dBm) for 10dB S/N in
> >CW/SSB modes. How does that equate to NF and  MDS?
> >
> >--
> >Joe Leikhim K4SAT
> >Jleikhim@nettally.com
> >
> >
> Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA.
> To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org
>

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