CALCULATING SYSTEM NOISE TEMPERATURE
IN WEAK SIGNAL RECEIVING SYSTEMS
Ralph Wallio, WRPK WRPK at netINS.net

My thanks to Bob Atkins, KA1GT, for his New Frontier QST column and these topics:
Calculating System Noise Temperature, QST January1982 page 80
Noise Temperature, Antenna Temperature and Sun Noise, QST July 1984 page 69
My thanks also to Gene Hinkle, K5PA, who found and corrected a formula error in the original source.


Having been thoroughly sucked into the black hole of VHF and above weak signal reception, our intrepid Ham Heroes have the continuing goal of yet another 0.5dB of sensitivity. Whether they are improving reception via tropo paths, OSCAR or high altitude balloon downlinks or moon bounce, they are always thinking of higher gain antennas and preamplifiers and lower loss feedlines. One important consideration toward these laudable goals is System Noise Temperature. This discussion presents a method to cut-and-try alleged system improvements at the keyboard so that false leads end up in the bit bucket.

The overall noise temperature of a receiving system is determined by:
Antenna Noise Temperature
Feed Line Losses and Temperatures

Preamplifier Gains and Noise Figures
and Receiver Noise Figure



Given values for these factors, System Noise Temperature (SNT) can be calculated:

SNT=TA+T1(L1-1)+(N1L1)+T2(L1/G1)(L2-1)+N2((L1L2)/G1)+(L1L2(L3-1)T3)/(G1G2)+N3((L1L2L3)/(G1G2))
                                                                     
(Formula correction by K5PA.)

TA = Antenna noise temperature
L() = Loss as a ratio 10^(dB/10)
T() = Physical temperature in degrees Kelvin (20dC=293dK)
G() = Gain as a ratio 10^(dB/10)
N() = Noise temperature (dK) N=293(10^(NF/10)-1)

(An EXCEL spreadsheet template is available via email attachment from WRPK WRPK at netINS.net)
EXCEL template formula corrected by K5PA to agree with on-line calculator for cascade circuits: http://www.rfdh.com/rfdb/nf.htm

Given the EXCEL spreadsheet template we will now make alleged system improvements. We are attempting to receive a 1W 70cm ATV signal from a high altitude balloon payload 300 miles away. We already have a 70cm gain antenna pointed at the horizon in the right direction but with 50 feet of RG-58 coax for a feed line (12dB/100ft loss at 450MHz) and no preamplifier. With the antenna pointed at the horizon and outside temperature of 20dC, antenna noise temperature is 293dK. Our video receiver has a noise figure of 3.5dBnf (or whatever but it doesn't matter because we are looking for relative improvements). Values for both preamps and feedlines 2 and 3 are set to zero.



Now we have an approximation of our current system noise temperature and we proceed with improvements. Our first step is to replace the RG-58 coax with RG-8 foam dielectric (4dB/100ft loss at 450MHz).



An improvement of 3.4dBnf is definitely worth the effort and expense. What if we added a GaAsFET preamplifier in the shack with 17dB gain and 0.5dBnf?



An improvement of 2.1dBnf is also definitely worth the effort and expense. What if we spent a little more money and moved the same preamp up to the antenna:



An improvement of 1.0dBnf doesn't seem like much but, when working with weak signals, it is also worth the effort. This exercise could go further with another preamp in the shack or even at the antenna but we have seen predicted improvements so we will stop here. Look for another discussion in these web pages about link budget calculations and how system noise temperature fits in the larger picture.


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