[amsat-bb] [Re: AMSAT-BB NF formula posting (amended)

[i8cvs]

Hi Ralph, W0RPK and All on the list.

Unfortunately in my previous message i have taped few mistake but hopefully the following calculation are actually correct.

I have rewrite the formula in another arithmetical form wich is easier to be used and not is corrupted or differently formatted sending it through BB

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 across the 50 ohm RX input
BW = Bandwidth in Hz (2400 Hz for SSB)
S/N = Signal to Noise ratio in power ratio 

The sensitivity for YAESU FT-726R of W0RPK in 2 meters is specified
for 10 dB of (S+N)/N  and not for 10 dB of S/N as required by the formula
so that we must convert first (S+N)/N into S/N as follow.

             S + N
S/N = ----------- - 1  =  (10-1)  =  9  in power ratio
                N                            

Calculation of NF for sensitivity of 2 meters SSB/CW  less than 0.15 uV for
10 dB (S+N)/N ........... we compute:


NF    =  ( 0.15 x 10^-6)^2 ) x 20 ) / ( 2400 x 9 ) ) log    ) x 10 ) + 174 =  7.18 dB
    dB                                                                              10

                      ____________________________________-
                             
The sensitivity for  YAESU FT-726 R of W0RPK in 70 cm is specified
for 12 dB of (S+N)/N  and not for 10 dB of S/N as required by the formula
so that we must convert first (S+N)/N into S/N as follow:

S/N =  ( S + N ) / N ) - 1  =  10^( 12/10) ) -1 = 15.84 - 1 = 14.84 in power ratio
                                            

Calculation of NF for sensitivity of 70 cm SSB/CW less than 0.15 uV for a
12 dB (S+N)/N  ratio.............. we compute:

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

 CONCLUSION:

2 meters: Noise Figure NF = 7.18 dB

70 cm:     Noise Figure NF = 5.01 dB 

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

Please note that the above formula is valid only for Vi = input signal in uV 
applied across the 50 ohm RX input.

Unfortunately the manufacturers do not specify if Vi of the sensitivity
specifications is the voltage that we read with the RF Signal Generator
connected to the receiver input or if Vi is the voltage that we read over
the Signal Generator with open output.

This can generate ambiguity in calculating NF because measurement 
are made with a Signal Generator with 50 ohm impedance output 
connected to the receiver input wich impedance is as well 50 ohm
so that the output voltage of the Signal Generator is divided in two
equal parts across both the internal 50 ohm impedances.

BTW many commercial receiver NF calculations are demonstrating
that the value of NF match very well with the input voltage Vi so that
we can assume that the manufacturers specifications are giving Vi
as the voltage applied across the 50 ohm receiver input. 

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 any one is interested to it.

I use this formula very often and this numbars are burned into my brain HI HI !

Please Ralph let me know if your calculations match with the actual one ?! 

 I hope this helps and if there is 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