Matt,
I believe it is even more 'simple' than that.
When the ATU wattmeter is properly calibrated, it is then set to measure
an SWR of 1 at 50 ohms resistive load.
When a TUNE produces an SWR=1, the impedance at the input (coax inside
the K2) has been transformed to 50 ohms, so that is a known quantity.
The ATU L and C show the values used to arrive at that transformation,
and the NET parameter indicates whether the capacitor is on the input or
the output side. So the L network values and configuration are known.
It is then a task to solve the network equations for an L network having
series L and shunt C elements to arrive at the output impedance.
Yes, the transmission line impedance (at the BNC connector) will be the
conjugate of that impedance.
Nothing has been said about the SWR on the feedline nor the feedpoint
impedance at the antenna.
73,
Don W3FPR
On 7/31/2014 5:56 PM, Matt VK2RQ wrote:
I think I see where the confusion has arisen. Here we are talking about a K2 with
integrated KAT2 ATU. So, when I used the term "rig end of the feedline", I was
referring to where the feedline connects to the KAT2 BNC connector at the back of the K2,
which is the output or antenna side of the KAT2 ATU. In order to make the impedance where
the antenna connects to the KAT2 output look like 50+0j ohms, the KAT2 will use an LC
network to transform the impedance. The impedance of this LC network together with the
50ohms of the K2 final PA output will be equal to the complex conjugate of the impedance
you will see looking into the shack end of the feedline leading to your antenna.
For example, to keep the maths simple, let's consider a case where the impedance at the
end of the feedline in the shack works out to be 50+j100ohms. That is, the antenna is
slightly inductive. In order to transform this impedance to 50ohms, you could connect a
capacitor in series that has a reactance of 100ohms to cancel out the inductive reactance
of the antenna+feedline. If we look at the impedance of our matching network plus radio,
we see the capacitor in series with the 50ohm transmitter, so the impedance looking into
the "ATU" plus transmitter is 50-j100 ohms. This is the complex conjugate of
the impedance looking down the feedline towards the antenna, which we already see is
50+j100ohms.
In a more complicated scenario, the resistive component at the shack end of the
feedline may not be 50ohms, and our matching network will be more complicated,
and we will connect some reactance across the feedline and/or transmitter to
achieve the required impedance transformation. If you go through the maths, you
will again find the impedance looking into the ATU+transmitter is the complex
conjugate of the impedance looking into the feedline+antenna.
73,
Matt VK2RQ
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