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RE: Question from a newcomer



Alex, EA4BFK asked a question and N0AN gave the answer "don't worry, it's no
problem. Bet let me show how to make the calculation:

> How  can I calculate the NF for my receiver knowing that
> is as TM255 with the following specs:
>      Sensitivity 0.13 uV in SSB at 10 db (S+N/N)? Selectivity 2.1 KHz

1. Let's figure out how much power the spec means:

   Pspec = e^2/R = (0.13 x 10e-6 volts)^2/(50 ohms) = 3.38e-16 watts.

   which equates to -154.7 dBw (dB below 1 watt)
   or =124.7 dBm (dB below 1 milliwatt)

The spec says that the S/(S+N) noise floor is 10 dB below these numbers. A
little algebra (see comments at end) says that the Noise level is a factor
of 9 below these numbers, so the Noise Floor would then be a level of

   Pfloor = Pspec/9 = 3.76e-17 watts
   or  -164.25 dBw or -134.25 dBm in dB units

2. The physical temperature of a resistor is related to the power that the
resistor generates as white noise by

   Pnoise = kTB where T is the absolute temperature in Kelvin, B is the
       Bandwidth of the measurement in Hz, and k is Boltzmann's
       constant = 1.38e-23 watts/Hz/Kelvin.

every Hz of bandwidth has the same noise as every other Hz, so for the
spec's 2.1 kHz bandwidth, you have P/T = 1.38e-13 *2100 = 2.90e-20
watts/Kelvin of power.

3. Therefore the spec says that the noise floor is equivalent to a resistor
at a temperature of

      Tspec = Pfloor/(kB) = 3.76e-17/2.90e-20 = 1296K

4. Noise Figure and Noise Factor usually refer to room temperature of 290K,
so the spec corresponds to a Noise Factor F (which has no units) of

      F = (T+290)/290 = (1296/290)+1 = 5.47

The noise figure that is normally reported is related to the Noise Factor F
by

      NF = 10*log(F) which in your case is 7.4 dB

Hope this helped -- 73 de Tom, W3IWI


[An aside: Some may be surprised by the divide by 9 in step 1 and assert
that the value is 10.

Manufacturers have been known to share this confusion. The problem one of
definition -- Just how did the manufacturer measure what he calls S/S+N. If
he simply measured the noise signal that produces a 10 dB rise, then the
receiver has 9 units of added noise plus one original unit of noise. This is
commonly called a Y-factor of 10 and you will usually see Y-1 written in the
textbooks. This is what I assumed.

In some cases, manufacturers have chosen a different measurement strategy
(or incorrectly piece together other specs from data sheets) resulting in
the values that reflect actual S/N numbers, and then mis-label them as S/S+N
(which what is what users normally expect). If this is the case, then the
factor of 9 becomes 10.

If the factor = 10 and not 9, then the specs imply a 1166K noise
temperature, Noise Factor F=5.0 and NF=7.00. The NF=7.00 looks suspicious to
me. I always worry when "measured" spec sheet numbers "hit" exact numbers.
The agreement in this case under the =10 speculation is closer than the
chance agreements that PI=sqrt(10) and that there are PI*10e7 seconds in a
year.]


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