On 6/29/2015 10:48 AM, Wayne wrote:
As a lead in, I use a 16 ft vertical on 20-10 meters, mounted on a flat
metal roof. The antenna is fed with about 25 feet of RG-8, and there is
a tuner at the transmit end.

While I'm pretty happy with the antenna, I'd like to simplify the matching.

Thus, the question: what is the purpose of a 1:4 unun on a 43 foot
vertical? ( I assume the "4" side is on the antenna side.)

I'd expect a better coax to antenna match when the antenna feedpoint is
a high Z (example, at 30 meters), but I'd also expect a worse coax to
antenna match when the feedpoint is a low Z (example, at 10 meters).

Is that the way it works, or is there other magic involved?

I think we strayed off the path to answering your original question.

The short answer is that you are correct and there is no magic involved.
A bit longer answer is:

A 43ft vertical will present a feed impedance of 1010 + J 269.2 ohms at
30 meters. Using a 1:4 transformer at the feed point will reduce that to
253 + J 67 ohms. That is a bit closer to your 50 ohm line.

At 10 meters, the antenna will present a 147 + J 133 ohms impedance. A
1:4 transformer will reduce that to 37 + J 33 ohms.

There are several disclaimers I could include, but I think you
understand that the answers cannot be exact with the info presented.

I hope this helps.