Can the Q of a loop antenna be changed?
If so what are some common techniques? (Formulae appreciated).
An RF tag system is designed to function in the near field of the antennas. The frequencies involved are in the 13 MHz range and the antennas used in these applications are defined as electrically short antennas (<0.1 $\lambda$).
The near field region of the reader antenna has reactive, evanescent currents that easily couple to nearby conducting materials. It is this phenomenon that the passive tag uses to easily harvest energy via its antenna in order to send its response. Any reduction of near field currents or near field distance will result in a shortened read range due to insufficient coupling in order to power the tag.
The OP specifically asked about altering the Q of the antenna system. This can be done by altering the physical aperture of the antenna or by the matching network.
It is important to understand that the Q of the antenna system determines its bandwidth. If the Q become too high, the narrower bandwidth may not allow proper reading of the tag. As the Q is lower through its matching network, the read range will be reduced.
You can alter the Q in an existing configuration by changing the value of the resistor in the matching network of the reader. This will also require adjustment of the other matching elements. As the resistance increases, the Q of the antenna system increases and vice versa. Removing the resistor entirely will maximize the Q for a given antenna. Since the resistor effectively dissipates power in order to lower the Q, the higher the value of the resistor, the greater the currents in the near field of the antenna and vice versa.
The mathematical approach to analyzing the matching network is an exercise in simple parallel/series reduction to determine the effect of the dissipative effect of the resistor. A blanket formula is not possible due to the various topologies of matching networks.