**CALCULATING SYSTEM NOISE TEMPERATURE**

**IN
WEAK SIGNAL RECEIVING SYSTEMS**

Ralph Wallio, WØRPK WØRPK 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 WØRPK WØRPK 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.