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*Subject*: [amsat-bb] Re: Sensitivity and noise floor (theory question)*From*: "Chris Hill" <chris.hill@xxxxxxxxxxxxxxxx>*Date*: Sun, 14 Sep 2003 17:02:42 +0800

Hi David, There's a pretty good introduction to sensitivity, noise figure, noise temperature etc in the ARRL Handbook; the 1990 edition has this material on pages 12-1 to 12-3. Whether a pre-amp with a noise figure of 1.5dB would improve receive performance or not, depends on a number of parameters, including the gain of the pre-amp, the gain of the downconverter, and (quite importantly) any losses in the coax between the antenna and the downconverter's input. As a "rule of thumb", I'd venture that at 2.4GHz, you will achieve better improvements from dropping the noise temperature of your antenna system (ie minimise sidelobes receiving noise from the hot earth), and from decreasing coax losses (put the downconverter right at the feed). You can find some calculations on this in Appendix A of the following document: http://vhf.worldsbest.com.au/Downlink_Antenna_VK6KCH.pdf (approx 800kB in size). You asked about converting a .18uV SINAD (I assume FM mode), to a noise figure. This is also covered in Appendix A of the above document, as follows: dBW = 10 * Log((V^2)/50R) = 10 * Log((0.00000018^2V)/50R) = -151.88dBW The formula for working out the equivalent noise temperature of the receiver is: T = (C/(kB)) / (C/N) However, we can't just plug in "12dB SINAD" for the C/N, as the SINAD versus C/N curve of an FM receiver is definitely not linear! From a graph in "Modern Electronic Communications", p171 (Miller, Gary M., 3rd Ed., Prentice Hall International, NJ. 1988), I assume that a C/N of 8dB into a narrowband FM receiver is required in order to achieve a SINAD of 12dB. k is Boltzmann’ s constant, and B is bandwidth (let's use 16kHz, the usual figure for a "25kHz channel spaced" system). 16kHz = 10 * Log (16000Hz) = 42.04dBHz It's easier to do this calculation in dB instead of linear, so the formula is represented as: [T] = [C] - [k] - [B] - [C/N] [T] = -151.88dBW -(-228.6dBJ/K) - 42.04dBHz - 8dB = 26.68dBK The noise temperature of your receiver is therefore 10^(26.68/10) = 10^2.668 = 465.59K Or, expressed as a Noise Figure: NF = 10 * Log ((465.59K/290K) + 1) = 10 * Log (2.6054) = 4.16dB So finally, the answer: your .18uV sensitivity receiver has a noise figure of 4.16dB. I hope some of this is useful. 73 Chris vk6kch >This is a general radio theory question. > >My AO-40 downconverter has a NF of 1.7db. What exactly does that mean? >My 2m rig has a sensitivity of .18 micro Volts (12db SINAD). How is >this sensitivy related to the noise floor of the reciever in the rig? >Can I calculate the noise floor? Finally would I benefit from a 1.5 db >nf preamp in front of this reciever? > >Thanks for your knowledge here. Let me know if there are any good >sources to learn more about this... >-David Carr >KD5QGR > ---- Sent via amsat-bb@amsat.org. Opinions expressed are those of the author. Not an AMSAT member? Join now to support the amateur satellite program! To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

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