# [amsat-bb] Re: AMSAT-BB NF formula posting

i8cvs domenico.i8cvs at tin.it
Fri Oct 4 20:24:06 PDT 2013

```Hi Ralph, W0RPK

I will write the formula in another arithmetical form:

NF   =  ( Vi x 10^-6 )^2 ) x 20 ) / (BW x S/N ) ) log    ) x 10 )  + 174
dB                                                                      10

where:

Vi = input signal in uV applied over the 50 ohm RX input
BW = Band Wide in Hz (2400 Hz for SSB)
S/N = Signal to Noise ratio in power ratio = 10

Going to your YAESU FT-726 R the sensitivity is specified for 10 dB of (S+N)/N  and not for 10 dB of S/N so that we must convert first (S+N)/N into S/N with the following formula:

S + N
S/N = ----------- - 1  =  10 log     (10-1) = 9.54 in power ratio
N                            10

Calculating the sensitivity for 2 meters SSB/CW  less than 0.15 uV  for 10 dB (S+N)/N  we have:

NF =    ( 0.15 x 10^-6)^2 ) x 20 ) / ( 2400 x 9.54 ) ) log    ) x 10 ) + 174 =  6.9 dB
dB                                                                               10
____________________________________

Calculating the sensitivity for 70 cm SSB/CW  less than 0.15 uV  for 12 dB (S+N)/N  we have:

S + N
S/N = ----------- - 1  =  10 log     (15.84 -1) = 14.84 in power ratio
N                            10

NF  =   (0.15 x 10^-6 )^2 ) x 20 ) / ( 2400 x 14.84 ) ) log   ) x 10 ) + 174 = 5.01 dB
dB                                                                                10

CONCLUSION:

The sensitivity in 2 meters and 70 cm is the same 0.15 uV but in 70 cm 0.15 uV are specified for 12 dB (S+N)/N and not 10 dB (S+N)/N as in 2 meters and so it happen that the receiver is more sensitive in 70 cm

The formulas where published into an old issue of the Ham Radio Magazine early about 1973 and I have to find it in my many papers after that I will send a copy to you but I remember  it very often ant this numbars are burned into my brain HI HI !

I hope this helps and if you have any question please let me know.

73" de i8CVS Domenico

----- Original Message -----
From: Ralph Wallio, W0RPK
To: domenico.i8cvs at tin.it
Sent: Friday, October 04, 2013 4:48 PM
Subject: AMSAT-BB NF formula posting

Domenico --

Thanks for posting the NF formula.  Your results for the ICOM IC-R10 cause me to reconsider what I have been estimating
for my much older YAESU FT-726R.  Specifications from the Yaesu Operating Manual:

2m SSB/CW     Less than 0.15uV for 10dB (S+N)/N

70cm SSB/CW   Less than 0.15uV for 12dB (S+N)/N

I would like to make this calculation myself but I am having trouble duplicating your results probably due to uncertainties
resulting from how the formula is formatted by AMSAT-BB.

Perhaps you have a document source to suggest that will resolve these uncertainties.

TNX es 73 de Ralph W0RPK

```