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Ambipolar devices have been reported in many technologies, including carbon nanotube field effect transistors (CNTFETs). The ambipolarity can be in-field controlled with a second gate, enabling the design of generalized logic gates with a high expressive power, i.e., the ability to implement more functions with fewer physical resources. Reported circuit design techniques using generalized logic gates show an improvement in terms of area and delay with respect to conventional CMOS circuits. In this paper, we characterize and study the power dissipation of generalized logic gates based on ambipolar CNTFETs. Our results show that the logic gates in the generalized CNTFET library dissipate 28% less power on average than a library of conventional CMOS gates. Further, we also perform logic synthesis and technology mapping, demonstrating that synthesized circuits mapped with the library of ambipolar logic gates dissipate 57% less power than CMOS circuits. By combining the benefits coming from the expressive power of generalized logic and from the CNTFET technology, we demonstrate that we can reduce the energy-delay-product by a factor of 20× using the ambipolar CNTFET technology.