I have found that I need to crank to volume all the way up on my iphone to be able to get an adequate signal for Merlin to pick it up.
This is interesting. Are you saying that even with a parabola attached to your phone, you need to adjust the recording level to full to get Merlin to work?
I did the Attwater Prairie Chicken Auto loop running Merlin on my IPhone 12 Pro without an external mic attached. The in-built mic was pretty good and picked up birds like Grasshopper Sparrow, Upland Sandpiper etc. even over the car engine noise.
I understand a mic generates an electrical current, which is then boosted by the pre-amp, followed by A-D conversion. This makes me think that perhaps IPhones are not designed to 'receive' the electrical input from a standard external mic via a Lightning to Mini-jack adapter - the received voltage would seem too low.
I am a bit confused when you mention self powered mics, but then say you have two Telinga dishes. Are you using the dishes with your own mics? The Telinga Pro-X (with mini-jack connector) is not self powered, but require 5V DC PiP - does an adapter provide PiP?
I think that if you have gone to the expense of purchasing a professional parabola, I would run it to a dedicated recorder. If real-time Merlin is a must, and the internal mic is not cutting it, I would suggest that you may want to run a line out of the recorder to the phone (as suggested by anormalbirder1). With recorders there should be a gain or pad on the line out that you can adjust to suit the receiving device and make sure the input is strong enough.
Birdmic is not only the parabola, we have designed an specific interface that amplifies and modulates the sound
I am not an electrical engineer or phone specialist, but I find that it is interesting that the signal needs to be amplified and modulated. I presume that as suggested above, most phones cannot take the electrical signal from an external mic and apply reasonable amplification.
Not meaning to be difficult, but how much of the difference in the Wryneck recording do you estimate to be low noise parabola gain, and how much is from the BirdMic amplifier you have designed?
An IPhone short shotgun I looked at seemed to offer better directional performance but not to increase the signal level - is it possible that the low level 'line-in' needs to be compensated by additional amplification, even to match the signal level of the in-built mic?