Topband: Hi Z amplifiers for 160m (LONG)

[John Kaufmann]

To assess the impact of amplifier circuit noise in "active" receive arrays,
we only need to be concerned with the contribution of amplifier circuit
noise relative to atmospheric noise.   The details of how signals are phased
in any particular array do not matter.  The objective is to keep the total
contribution of amplifier noise far below the atmospheric noise so as not to
degrade the overall system noise floor in any significant way.  However, we
need to understand that the combiner circuit that phases up the signals in a
receive phased array responds very differently to amplifier noise and
atmospheric noise.  This makes it less obvious how to determine whether the
circuit noise of a particular amplifier is "low enough".  Fortunately, there
is a simple way to determine that using basic principles.

Let's start with a single amplified vertical antenna.  To simplify the
analysis, we just set the gain of the vertical to 0 dB.  In practice we can
do a NEC analysis to calculate absolute gain in dBi, factoring in real
losses but that is not necessary and does not change the conclusions.  The
antenna feedpoint amplifier adds its own noise to whatever signal plus
atmospheric noise is received by the vertical.  Let's set the circuit noise
power equal to one "circuit noise unit" and the atmospheric noise power to
one "atmospheric noise unit".  Of course we can put voltage (or power)
numbers on those units, based on properties of the amplifier, the
atmospheric noise, the actual antenna gain, and the measurement bandwidth.
However, that makes things unnecessarily complicated, so we won't do that.

Next we create an array of N amplified vertical antennas, each one identical
to the single vertical we started out with.  We feed the signals from all
the antenna amplifiers into an ideal combiner circuit that does not add its
own noise.  The combiner circuit phases up signals to create a directive
beam pattern.  Now we ask how much atmospheric noise appears in the phased
up sum compared to the amount of total amplifier circuit noise.  

The atmospheric noises received at the various verticals are all correlated.
The correlation comes about because the atmospheric noise is the same at
each vertical except for time delay differences caused by geometric path
length differences to each antenna element.  However, as I described in an
earlier e-mail, the amplifier circuit noises coming from each of the antenna
amplifiers are all uncorrelated.

For uncorrelated noises, the combiner simply adds the circuit noise powers
of the individual amplifiers as I described previously.  For N elements with
N amplifiers, the total circuit noise power out of the combiner is then N
times one "circuit noise unit" (ignoring any additional gain or throughput
loss imparted by the combiner circuit).

To determine the total atmospheric noise coming out of the combiner circuit,
let's assume the atmospheric noise has a completely uniform distribution in
3-dimensional space.  That is, the strength of the atmospheric noise is the
same in every direction.  This is an idealized assumption, but is often a
reasonable approximation to reality.  Under these assumptions, the total
atmospheric noise out of the combiner turns out to be just one "atmospheric
noise unit"!  In other words, it is exactly the same as the atmospheric
noise coming out of a single vertical.  This is because the total
atmospheric noise power picked up by the array is just the gain of the array
(relative to a single vertical) averaged over all of 3-dimensional space
times one "atmospheric noise unit" (the noise picked up by a single
vertical).  That average gain is exactly 0 dB, so the total atmospheric
noise doesn't change in our idealized system.  It doesn't matter what the
antenna pattern is; the average gain is always 0 dB, which is why we did not
need to be concerned with details of how signals are phased up to form a
beam pattern.  Of course, a different gain applies to actual signals that
are coming from a specific direction and are not uniformly distributed like
atmospheric noise, which is why we see a S/N improvement when the array is
aimed at a signal of interest.

So, we have demonstrated that in relative terms, the amplifier circuit noise
power in an array of N amplified antennas goes up by a factor N whereas the
atmospheric noise does not change.  That increase in the amplifier noise
contribution relative to atmospheric noise degrades the overall noise figure
of the system.  However, as long as we keep the amplifier noise contribution
small enough, the noise figure degradation can also be kept to a minimum.
That is why having more amplified elements makes it more important to design
the antenna amplifiers for low circuit noise.

73, John W1FV






-----Original Message-----
From: Topband
[mailto:topband-bounces+john.kaufmann=verizon.net at contesting.com] On Behalf
Of Michael Tope
Sent: Thursday, March 12, 2020 4:37 PM
To: topband at contesting.com
Subject: Re: Topband: Hi Z amplifiers for 160m

Hi Lee,

Yes, if you are combining coherent signals that are not in phase, then 
the each of the voltage vectors is weighted by cos(phi-i) where phi-i is 
the angle between the i-th voltage vector and the 1st vector. If phi=0, 
then you have the case I described previously. I can see how this can 
get tricky, however, with an electrically short baseline where you are 
striving for cancellation in the rearward looking direction. It's like 
you cancel in the rearward direction and almost cancel in the preferred 
direction :-). This degrades the SNR not because the noise is adding up, 
but because the signals are subtracting down.

73, Mike W4EF.............