Equipment is non-crystal controlled and relies on capacitance compensation for frequency satiability.
Range wasn't an issue with the radios on board aircraft
It most certainly was an issue.
air control was maintained on the Gruppe/squadron level.
Exactly as they could not coordinate large interception efforts. The Luftwaffe had to push actual control down to lower levels which meant:
Master signal stations (Ground) used crystal / quartz sets and had plenty of range
Is also true. However they did not control anything. Mostly they broadcast a "running comentary" on the location of the bomber stream.
The Reichsjaegerwelle could not reach the length and breadth of the Operational area in order to communicate with all the fighters in the air over Germany, France, Holland, etc...
"Y" control was also very fickle with only roughly 50 percent of the S.E. fighters being equipped with it in the first place.
and powerful receivers to maintain control of the air.
No such thing. The best you can do to recieve is built a good antenna. However it is subject to the law of reciprocity.
The operation of antennas, and telescopes in general, are governed by electromagnetic theory and diffraction theory plays an important role. In order to understand this, one first needs to know the reciprocity theorem. This theorem states that the telescope operates the same way whether it is receiving or transmitting radiation.
http://web.haystack.mit.edu/urei/tut6.htmlSo it will work only as good as the poorest antenna in the system. So while you may be blowing his socks off transmitting with a high dB gain antenna and the poor antenna will hear a poorer signal but most likely readable in the case of the Luftwaffe. When the poor antenna transmits, the high dB gain antenna will hear nothing or very little.
An amplifier could help but the absence of signal means nothing to amplify. An unreadable transmission really loud is still an unreadable transmission. It is just louder static.
Additionally these radios used the VHF spectrum. This spectrum properties mean it primarily uses ground wave propogation and is a "Line of Sight" radio.
http://members.aol.com/svennord/radio.htmSo you are dealing with the curvature of the earth, antenna, power output, and the height of the aircraft to determine range.
All the best,
Crumpp