Thank you for that clear explanation.
And regarding the distance from ground-plane, I've seen two different
specs one 30.5mm and the other 18mm.
Thanks again, Mike

Let's start out by assuming that the biquads are each 50 ohms (which
is something you can ensure by placing them at the correct distance
from the reflecting ground-plane).

Each 50-ohm biquad is fed through a suitable length of 50-ohm
semi-rigid coaxial line. Since the antenna's impedance matches that of
the coax, there will be a 1:1 SWR on the coax, and the same 50-ohm
impedance will appear at the far end of the coax. In this particular
case, the semi-rigid coax will consist of the part which goes through
the reflector (supporting the biquad) plus the trimmed 80mm section
(which ends up being 77mm after stripping and soldering).

There are four such 77mm lengths, which come together as two pairs.
At this point, each pair is soldered together, placing two 50-ohm
loads in parallel. This creates a 25-ohm load.

Now, each 25-ohm connection is soldered to a further length of 50-ohm
cable, 58mm long plus a bit for making the connection. The two 58mm
sections come together, at the SMA connector.

These 58mm sections act as impedance transformers. One of the useful
characteristics of a coax which is 1/4 or 3/4 or 5/4 electrical
wavelength long, is that it transforms a resistive impedance at one
end, to a different resistive impedance at the other... and the
geometric mean of these two impedances is equal to the characteristic
impedance of the feedline.

In this case, if you have a 25-ohm impedance at one end, and the cable
has a 50-ohm impedance, then the impedance at the other end of the
cable will be 100 ohms.

This places two 100-ohm impedances in parallel where they're connected
to the SMA jack, resulting in a 50-ohm impedance.

In the case of this particular design, the impedance-matching sections
(58mm) aren't actually the 3/4 electrical wavelength that one might
expect. UT141 has a velocity factor of 0.7, and my slide-rule
calculation suggests that they'd be around 65mm long for a true 3/4
electrical wavelength at 2.4 GHz.

I would guess that the biquad antennas aren't exactly 50 ohms
resistive, and that this impedance is being transformed somewhat by
the 77mm sections, and that the length of the final impedance-matching
section has been hand-tweaked to 58mm to give the best practical match
to 50 ohms (and thus SWR) for the antenna and phasing system.

That being the case, I'd probably recommend trying to reproduce the
antenna design as-published. If you switch to a cable having a
different velocity factor, you may need to do some cutting-and-trying
to get the right impedance match.

--
Dave Platt AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
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