Theorems of compensation and Tellegen in non-sinusoidal circuits via geometric algebra

Abstract

Presently, it is not possible to corroborate Tellegen's theorem or to articulate the compensation theorem in the frequency domain when considering all the harmonics simultaneously. The circuit analysis approach based on geometric algebra is used here to solve these two challenges. We show here the significance of representing harmonics by k-vectors and how k-vectors process the magnitude, the phase and the frequency of a sine wave. We take a tutorial approach and provide examples to demonstrate both, the simplicity of this approach and how a distinct representation of time-domain signals of different frequencies facilitates both, energy analysis and confirming the principle of superposition and Kirchhoff's circuits’ laws in non-sinusoidal conditions when considering all the harmonics simultaneously.

Keywords

• frequency-domain analysis
• network analysis
• compensation
• algebra
• time-domain analysis
• reactive power
• time-domain signals
• energy analysis
• Kirchhoff's circuits
• nonsinusoidal circuits
• geometric algebra
• Tellegen's theorem
• circuit analysis