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Generally,the dielectric properties and the conductivity are closely linked.In order to study the relation between the dielectric properties and the conductivity,we have performed systematically investigation on the dielectric properties and conductivity of double-perovskite Sr2CoNbO6 ceramic.Our results reveal that the Sr2CoNbO6 ceramic exhibited high dielectric permittivity,and three dielectric relaxations were observed.The dielectric properties for low-temperature are closely related to the nearly constant loss (NCL).The low-temperature relaxation may be the low-temperature Maxwell-Wager (M-W) relaxation caused by the frozen holes with the activated energy of 0.177 eV.The middle-temperature relaxation was related to the dipolar effect due to the hopping holes,and presents two Arrhenius segments with the activated energy of 0.143 eV and 0.218 eV for the low- and high- temperature segments,respectively.The high-temperature relaxation was M-W type relaxation contributions of depletion layers with the activated energy of 0.151 eV.Despite there have a variety of investigation for dielectric properties,few papers on low-temperature M-W relaxation and the NCL are reported.This is because the NCL regime dominates the ac conductivity at high frequency or low temperature and the low-temperature M-W relaxation also at high frequency or low temperature.It is been found that the NCL and the low-temperature M-W relaxation are closely linked.Moreover,the ac conductivity can be described by the “universal dielectric response” (UDR) at the same time a polaronic relaxation was been found.Besides,for ac conductivity when there are strong decreases at low frequencies caused by grain boundary or electrode contact,M-W relaxation resulting from interface been observed.