For round shaped heat source or heat sink, the annular thermoelectric couple (ATEC) with annular shaped legs instead of flat-plate thermoelectric couple (FTEC) is proposed to solve the performance deterioration caused by geometries mismatching. Based on one-dimensional steady model, the fundamental formulas of ATEC are derived. The impact of geometric feature of ATEC manifested by the annular shaped parameter S-r, on the dimensionless output power and efficiency of ATEC under different temperature ratios, external loads and dimensionless figure of merits is examined theoretically. Also, to enhance the practicability of ATEC, some suggestions or notes are provided. Results show that the forms of fundamental formulas about ATEC are the same as those about FTEC. Compared to temperature ratio and dimensionless figure of merit, the influence of Sr is affected by external load seriously. The extremums of dimensionless output power and efficiency are presented on condition that S-r = 1. As the closer S-r is to 1, the larger the dimensionless output power is. In view of this behavior, a new structure including an additive material with high thermal conductivity is designed for recovering cost-free energy resources with ATEC. (C) 2014 Elsevier Ltd. All rights reserved.