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VK2ZRG > TECH 24.03.06 08:37l 99 Lines 4478 Bytes #999 (0) @ WW
BID : 2260_VK2ZRG
Read: DL1LCA GUEST OE7FMI
Subj: Understanding noise figure
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Sent: 060324/0341Z @:VK2WI.#SYD.NSW.AUS.OC #:9645 [SYDNEY] FBB7 $:2260_VK2ZRG
From: VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
To : TECH@WW
VK2ZRG/TPK 1.83d Msg #:2260 Date:24-03-06 Time:3:41Z
Understanding noise figure by VK2ZRG 24/3/2006
You may not republish this bulletin on packet radio.
Noise figure is a term used to rate the noise performance of an amplifier
or receiver in comparison to a perfect noise free amplifier or receiver.
Noise figure is the dB equivalent of noise factor which is a dimensionless
power ratio.
If you were to compare a perfect amplifier to a real world amplifier of the
same gain (at the same temperature), with input terminations at the same
temperature, then the ratio of the two output levels noise is the noise
factor.
You might imagine that the perfect amplifier would not have any output
noise. However any resistance, at a temperature above absolute zero, will
generate noise. So the noise at the output of the perfect amplifier is the
amplified noise from the input termination. There would only be zero noise
output from the perfect amplifier if its input termination had a temperature
of zero Kelvins or -237.15 degrees Celsius.
The input termination generates noise equal to KBT. Where K is Boltzmanns
constant of 1.38 * 1E-23, B is the band width in Hz and T is the temperature
in Kelvins. At 17 degrees Celsius, the noise power from any resistance is
-174 dBm or -204 dBw per Hz band width. dBm is a power level referenced to
one milliwatt. (dBw uses a one watt reference.)
The input termination for a receiver is the antenna. The equivalent
temperature of an antenna can be taken as the temperature of what the antenna
"looks" at. An antenna used for terrestrial communication will have an
effective noise temperature of 290 Kelvins or so, while a dish antenna
pointed at a satellite could have an equivalent temperature of under
30 Kelvins, depending on side lobes and spillover from its feed horn.
It is often more convenient to express the noise performance of a Low Noise
Amplifier (LNA) in terms of Kelvins. In this case, the noise in Kelvins is the
temperature of the input termination of a perfect amplifier that produces the
same noise as a real world amplifier with an input termination at a
temperature of zero Kelvins.
Kelvins add, so to get the "System noise" you just add the antenna noise
to the LNA noise where both values are in Kelvins. It is system noise that
you must consider when calculating the Minimum Discernable Signal (MSD) of
a receiver.
For frequencies below 30 MHz or so, man made noise, galactic noise and
atmospheric noise will generally be much greater than receiver noise.
Noise figure is generally independent of receiver or amplifier band width.
Increased receiver band width just increases the noise at the receiver output.
Noise figure of a wide band amplifier may deteriorate at the band limits.
Measuring noise figure with the full band width will give an average value in
this case. Using a lesser measuring band width allows the noise figure versus
frequency to be determined.
Here is an example of a 2 metre LNA using a BFG135 transistor that I
designed and built. The collector current was set to 92 mA to achieve a
high third order output intercept point of greater than +37 dBm.
Freq Noise Gain
MHz fig dB dB
135 2.20 21.61 Input VSWR is less than 1.1:1 for 144-148 MHz
136 2.16 21.71
138 2.10 21.85 Output VSWR is less than 1.2:1 for 144-148 MHz
140 2.08 21.98
142 2.06 22.06 Input/output isolation better than 25 dB
144 2.03 22.11
146 2.02 22.11
148 2.02 22.06
150 2.06 21.97
152 2.10 21.85
154 2.13 21.71
155 2.15 21.63
The three quantities of noise factor, noise figure and noise temperature
may be converted with these simple formulas. Base 10 logs are used.
(My DBCONV7 programme will do the maths for you.)
Noise figure = 10 * Log(Noise factor)
Noise factor = Antilog(Noise figure / 10)
Noise in Kelvins = 290 * 10^(noise figure/10 -1)
Noise figure = 10 * Log(1+(Kelvins/290))
Noise figure can be thought of as the reduction in the signal to noise
ratio, in dB, of a signal as it passes through an amplifier when the source
or antenna temperature is 290 Kelvins or 17 Celsius.
You may not republish this bulletin on packet radio.
Let me know if you found this bulletin informative.
73s from Ralph VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
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