This paper introduces a leakage model in the frequency domain to enhance the efficiency of side channel attacks of CMOS circuits. While usual techniques are focused on noise removal around clock harmonics, we show that the actual leakage is not necessary located in those expected bandwidths as experimentally observed by Mateos and Gebotys (A new correlation frequency analysis of the side channel, p 4, 2010). We start by building a theoretical modeling of power consumption and electromagnetic emanations before deriving from it a criterion to guide standard attacks. This criterion is then validated on real experiments, both on FPGA and ASIC, showing an impressive increase of the yield of SCA.