Originally posted by sebenste
Question: would replacing the RG-6 quad shielded length of cable with
RG-11 get me any improvement, or does the 7777 adjust the power
so that you do get an effective 26 dB gain out of the back end no
matter what? I can't move the antenna.
I know folks get that glazed over look when I break out the math, but it's
the only way to precisely answer this question.
The noise temperature Tn of two amplifiers in cascade is the noise
temperature of the first plus the noise temperature of the second
divided by the gain of the first:
Tn = T1 + T2/G1.
To convert Noise Figure(f) to noise temperature (Tn):
Tn = 290(10^(f/10) - 1)
So a 2.0 dB preamp has a noise temperature of 169.6K
Let's say that the Noise Figure of your receiver is 10 dB and your RG6 cable
loss is 5.0 dB for a total Noise Figure of 15.0 dB. The receiver noise
temperature is 8880K.
Then the system noise temperature is 169.6 + 8880/400 (26 dB) = 191.8K
To convert from noise temperature back to Noise Figure:
NF = 10 log(1 + Tn/290)
So the system Noise Figure is 2.2 dB. The gain of the preamp "washes out"
the noise of the receiver and connecting coax.
Now let's plug in a different value of coax loss. Your rich uncle buys you
some 7/8" Heliax ($6 a foot) and your coax loss goes down to 1.0 dB,
making your receiver noise figure 11.0 dB or 3361K.
169.6 + 3361/400 = 178K or 2.08 dB
Your rich uncle's $600 was the wrong place to put the money since it only
buys you an undetectable 0.12 dB of signal to noise ratio. You should have
spent it on a taller tower or mast, a bigger antenna or a better preamp
(in that order).
Now for something counter-intuitive. Let's say the gain of the preamp is
13 dB instead of 26 dB at the same 2.0 dB Noise Figure. Then the system
noise temperature (with the 5.0 dB loss RG-6) is 169.6 + 8880/20 (13 dB) =
613.6K or a system Noise Figure of 4.9 dB. In this case, 13 dB less preamp
gain only causes the loss of 2.7 dB of signal to noise ratio.