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VK2ZRG > TECH 27.09.08 12:16l 100 Lines 4739 Bytes #999 (0) @ WW
BID : 2674_VK2ZRG
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Subj: Noise figure calculations
Path: IZ3LSV<IK2XDE<DB0RES<WA7V<VK7AX<VK2TGB<VK2IO<VK2WI
Sent: 080927/0922Z @:VK2WI.#SYD.NSW.AUS.OC #:2717 [Sydney] $:2674_VK2ZRG
From: VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
To : TECH@WW
VK2ZRG/TPK 1.83d Msg #:2674 Date:27-09-08 Time:9:19Z
Hello to technical minded amateurs
In a recent tech bull on RF Signal Calculations, John G6MNY wrote:-
>Noise figures of preamps & Rx are additive, but as long as the Rx noise is
>drowned by the preamp noise by 10dB or so, then take just the preamp noise
>figure as the system noise. Noise figures of just the preamp device itself can
>be very misleading as input socket, input tuned circuit & radiated/PCB losses
>can often add 1-2dB to this.
Surely you must have been thinking of something else John, when you wrote
that. You must know that the purpose of adding a low noise pre-amp is to reduce
the noise figure. The only things that add when doing noise calculations are
Kelvins or a loss in dB's in front of an amplifier to the noise figure in dB.
Why make a dubious assumption about noise figures when an exact result may
be calculated with simple arithmetic? In the formula below noise figure and
gains are reduced to noise factor (a dimensionless ratio) and the numeric
gain ratio. e.g. a 3 dB noise figure is a noise factor of 2 and a 23 dB gain
is a gain of 200. This is the formula for a two stage calculation:-
F total = F1 + (F2-1)/G1
For example, a pre-amp with a 1 dB noise figure and 23 dB gain in front of a
receiver of 8 dB noise figure, connected by a co-axial cable with a 3 dB loss.
The noise figure looking into the co-axial cable will be 11 dB or a power
ratio of 12.59 (F2). F1 for a 1 dB noise figure = 1.259 and G1 = 200 for 23 dB.
Solving we get F total = 1.259 + (11.59/200) = 1.259 + 0.058 = 1.317
Converting 1.317 back to dB we get a system noise figure of 1.196 dB
I'm not sure what exactly you mean by the term "drowned" in the quote above
John, maybe you mean pre-amp gain. If the pre-amp had only 10 dB gain then the
system noise figure will be quite a bit worse.
e.g. F total = 1.259 + (11.59/10) = 2.418 or a noise figure of 3.834 dB
Working in Kelvins is a bit easier. This formula converts noise figure to
Kelvins. ( * is multiply and ^ means to the power of)
Kelvins = 290 * (10^(Noise figure/10)-1)
So a 1 dB noise figure = 75.1 K and 11 dB noise figure = 3361 Kelvins
System temp of the two amplifiers = K1 + K2/G1 = 75.1 + 3361/200 (Kelvins)
(Pre-amp gain of 23 dB) = 75.1 + 16.8 = 91.9 Kelvins
Converting 91.9 K to noise figure we get 1.317 dB
The total system temperature should include the effective antenna temperature
plus the effective temperature of any loss between antenna and pre-amp. These
just add to the amplifier temperature.
The effective temperature of a lossy component is:-
Te = Ta * (L-1) Kelvins
Where Ta is the ambient temperature in Kelvins and L is the reciprocal of
the fractional gain. Ta is generally assumed to be 290 K.
e.g. For a 1 dB loss (or 0.7943 gain) Te = 290 * (1/0.7943-1) = 75.1 Kelvins
e.g. For a 3 dB loss (or 0.5 gain) Te = 290 * (1/0.5 - 1) = 290 Kelvins
Effective antenna temperature is assumed as 290 K for a terrestrial RF link
and can be as low as 10 K for a high grade dish used for space communications.
This means that for a terrestrial RF link, for every dB you reduce the noise
figure you get exactly 1 dB improvement in SNR (signal to noise ratio), so
there is not a lot to be gained by getting the noise figure much under 1 dB.
No so for space communications; here with a low antenna temperature, a 1 dB
reduction in noise figure will give more than a 1 dB improvement in SNR.
e.g. For an effective antenna temperature of 30 K, reducing overall noise
figure from 2 dB to 1 dB gives a 2.8 dB increase in SNR. And, if by some
magic you could get an overall noise figure of 0 dB, then the SNR would be
5.4 dB better than for a 1 dB noise figure.
If you are fazed by the arithmetic above then use my DBCONV7 or EMEPATH
programmes to do the sums for you.
Re John's comment on not getting misled by the noise figure of the pre-amp
device. I have designed and built UHF pre-amps on G10 fibreglass PCB with noise
temperatures, measured with a HP 8970 noise figure meter, of under 20 Kelvins.
Sure, any circuit losses will add to the device noise figure but not a lot if
you are careful with the design. Losses in connectors are often over rated.
The loss in a high quality "N" or "SMA" connectors is < 0.1 dB below 2 GHz or
so. As for PL259/SO239 connectors, why would anyone in their right mind use
these? These connectors got the misnomer of "UHF" connectors when any frequency
above 30 MHz was considered as UHF.
73's de Ralph VK2ZRG @ VK2WI
P.S. to G8MNY You may not use any part of this bulletin in your TECH bulls
without my permission.
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