Not quite, you can see the math method produced a smoother curve. And this is closer to reality, because energy in the main line goes mainly one way and exibits less reflection between ports, whereas with your other method there are reflections bouncing back between In and Out ports interacting with each other and that causes ripple. I still think nobody is doing directivity measurements this way.
Agree that measurement from different ports is more accuracy. But for me it was just to understand the qualitative characteristics, rather than to measure out with great accuracy. And by this reason I use long cables (1m) from SA, so I think is effected in resonance ripple on curve. And this method is not my invention. I see this one in several sources, first one I can remember is rf-explorer site.
Also, you cant measure devices well with a spectrum analyzer at high frequencies. You need a VNA for that to calibrate out the instrument ports mismatch.
I think you understand that phase response (that produce VNA) is not so important for understanding how good this coupler, frequency response is enough IMHO. Of course SA has TG normalization and I did it. BTW I have small VNA (Tiny), but it has not so good dynamical range (60..70dB). And I understand that VNA is better
As to your doubts on the coupler model , you can send a email to Minicircuits, attach a photo and ask them to confirm.
Yes... I already think about it
Anyway is somebody can tell me how good this coupler work in lower frequency (from 100 kHz)?