A new model of the thermal amplifier consisting of three electronic reservoirs connected by two energy filters and an electronic conductor with negligible resistance is proposed. The thermal amplifier may have two different connective methods and can be regarded as the equivalent system composed of an energy selective electron (ESE) heat engine and an ESE heat pump. With the help of the theory of the ESE devices operating between two electronic reservoirs, the coefficient of performance and rate of heat-pumping of the thermal amplifier are directly derived. The effects of the center energy levels and the half width (or the half width at the half maximum) of two energy filters on the performance of the thermal amplifier are discussed. The maximum coefficient of performance and rate of heat-pumping are calculated. The optimally operating regions of the thermal amplifier are determined. Moreover, the optimum performance characteristics of the thermal amplifier with two configurations of energy filters are compared. (C) 2017 Elsevier Ltd. All rights reserved.