  In this work, we study the transmission properties of one dimensional finite
periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression
is obtained for the total transmittance from a lattice of N cells, that allows
us to describe the transmission minima (maxima) when the system is in the
$\mathcal{PT}$-unbroken (broken) phase. Utilizing this expression, we provide
the necessary conditions, \textit{independent} of the number of cells, for the
occurrence of a CPA-laser for any finite $\mathcal{PT}$-symmetric periodic
potential. Under this conditions, we provide a recipe for building finite
periodic structures with near perfect absorption and extremely large
amplification.
