Microwave conductivity survey of YBa$_2$Cu$_3$O$_{6+x}$: from underdoped to overdoped

Recent experimental results and theoretical proposals suggest significant changes in the electronic structure of the high-$T_c$ cuprate superconductors as one approaches optimal doping, including Fermi surface reconstruction associated with proposed electronic ordering transitions. As sensitive probes of the low-energy electrodynamics, microwave surface resistance and penetration depth measurements - from which the real and imaginary parts of the microwave conductivity may be extracted - are well-suited for investigating such changes in the electronic structure of the cuprates across their phase diagram. Here we present preliminary results of a detailed and systematic doping dependence study of the microwave conductivity of the cuprate superconductor YBa$_2$Cu$_3$O$_{6+x}$ from the underdoped to the overdoped regime. The implications of these results for various proposed scenarios will be discussed.