[TowerTalk] Noise figure in cascaded networks

[Ian White, G3SEK]

alsopb wrote:
>
>Guys,
>
>There is a lot of misinformation being stated here about noise figure
>in
>cascaded systems.
>
>According to Skolnik "Introduction to Radar Systems" the total noise
>figure in a cascaded system of two components (read antenna preamp and
>coax if you want) is:
>
>F = F1 + (F2-1)/G1
>
>Where F1 is the first component's noise figure,  F2 is the second
>components noise figure and G1 is the gain of the first component.
>

These F values are pure ratios, often called noise factors to
distinguish them from noise figures in dB. Otherwise, OK...

>Looking at this equation he states:
>"The contribution of the second network to the over-all noise figure
>may be made negligible if the gain of the first network is large."
>
>In otherwords, putting a high gain, low noise pre-amp at the antenna
>can  mitigate the loss of the coax (receive only) in total noise
>figure. This is contrary to what some people are trying to state here.
>
>This shouldn't be a suprise to anybody who has a mast mounted TV
>preamp or VHF mast mounted ham pre-amp.  They really work.
>
>There is a more general expression involving cascaded multi-network
>systems (e.g. preamp, coax, each of the receiver stages).  I refer you
>to the formula for this.  However, one can see from it that the loss
>in the coax will introduce additional noise into any cascaded system.
>Coax loss does introduce additional "noise" which affects the S/N
>ratio.  Again, this contrary to what some people are stating here.
>

On its own, the noise figure of your receiver will not tell you what the
noise level will be when you plug in an antenna - because you don't know
the antenna noise temperature.

The antenna noise temperature is a measure of how much noise it picks
up. A 50 ohm resistor (in a 50 ohm system) has a noise temperature very
close to its physical temperature (typically 290 K). HF antennas
typically produce noise levels equivalent to a noise temperature of many
thousands, or hundreds of thousands, of K.

The *system* noise temperature is what determines your signal/noise
ratio. This is partly due to the RX but also partly due to the antenna.
If you convert the RX noise figure into noise temperature, you can then
say simply:

T_system = T_rx + T_antenna.

If T_rx is the same as T_antenna, your signal/noise ratio will be 3dB
worse than with an ideal noiseless receiver.

It's not difficult to make the RX noise temperature extremely low, on
any band. But below a certain level, the improvement in s/n is not worth
having because strong-signal performance has to be severely compromised.

Generally a good design compromise is to make the RX noise temperature
somewhere close to the minimum antenna noise temperature you'd ever hear
on that band, at the quietest possible site.

These days, a lot of the RX noise problem has gone away because many
transceivers offer the choice between the barefoot RX, one or two
different preamps, and also different levels of attenuation. We can set
it up how we like.

>Now who want's to vote on the correct answer?  It isn't a matter of
>opinion.
>
Darn right it isnt!

This is all interesting stuff, but it really isn't any kind of "tower
talk", it isn't "amps", and it isn't pure contesting either. Time for a
new "DX technical" reflector, maybe?

73 from Ian G3SEK          Editor, 'The VHF/UHF DX Book'
                          'In Practice' columnist for RadCom (RSGB)
                           http://www.ifwtech.com/g3sek

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