Conductivity anisotropy and pseudogap in the microwave response of high-$T_c$ superconductors

Results of investigating the temperature dependences of the surface impedance $Z(T)=R(T)+\mathrm{i}X(T)$ and complex conductivity $\sigma(T)=\sigma'(T)-\mathrm{i}\sigma''(T)$ in the ab-planes and along the $c$-axis of high-$T_c$ superconductors (HTSCs) are reviewed and critically analyzed. An electrodynamic method is considered for extracting all components of $\hat\sigma(T)$ and $\hat Z(T)$ tensors from quantities measured in microwave experiments. The main attention is focused on the evolution of $\hat Z(T)$ and $\hat\sigma(T)$ dependences in a $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_{7-x}$ crystal with the oxygen content variation. Possible mechanisms of conductivity are discussed in the framework of models for normal, superconducting, and pseudogap states of HTSCs.