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*Subject*: RE: [amsat-bb] Question from a newcomer*From*: "Dr. Tom Clark" <tac@xxxxxxxxx>*Date*: Thu, 22 Nov 2001 12:28:29 -0500*In-Reply-To*: <01bd01c17356$727c1240$6501a8c0@netins.net>

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.] ---- Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

**Follow-Ups**:**R: Question from a newcomer***From:*i8cvs

**References**:**Re: Question from a newcomer***From:*hasan schiers

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