From RF Circuit Design by Christopher Bowick (page 32 bottom of the page left column):
The loaded Q of a critically coupled two-resonator circuit is approximately equal to 0.707 times the loaded Q of one of its resonators.
This isn't clear to me. How can I prove to myself that this is true?
The circuit that describes a critically coupled two-resonator circuit is basically a signal generator with a source resistance Rs feeding a parallel LC filter which is then coupled to another parallel LC filter through a coupling capacitor. The first LC filter is made up of L1 and C1 and the second LC filter is made up of L2 and C2. There is a coupling capacitor C12 between the two LC filters. The output of this two-resonator circuit feeds a load resistor RL.
This is schematically shown as: