Geometric algebra: a multivectorial proof of Tellegen's theorem in multiterminal networks

A generalised and multivectorial proof of Tellegen's theorem in multiterminal systems is presented using a new power multivector concept defined in the frequency domain. This approach permits in nonsinusoidal/linear and nonlinear situations formulating Tellegen's theorem in a novel complex-multivector representation, similar to Steinmetz's phasor model, based on complex numbers and limited to the purely sinusoidal case. In this sense, a suitable notation of voltage and current complex-vectors, associated to the elements and nodes of the network, is defined for easy development to Kirchhoff's laws in this environment. A numerical example illustrates the clear advantages of the suggested proof.