[Paper Review] A Scheme for Stored Energy Evaluation and a Comparison with Contemporary Techniques

Miloslav Čapek, Lukáš Jelínek+2 more|arXiv (Cornell University)|Mar 3, 2014

Antenna Design and Analysis40 references3 citations

TL;DR

This paper proposes three distinct methods for evaluating stored electromagnetic energy and radiation Q factor in antennas: two time-harmonic approaches based on Vandenbosch and Yaghjian's work, and a novel time-domain method intended to capture true stored energy. The study demonstrates that while all methods converge for simple RLC circuits, they yield significantly different results for more complex systems, highlighting fundamental inconsistencies in current evaluation techniques.

ABSTRACT

Abstract—This paper treats the old problem of defining and understanding stored electromagnetic energy. Three different concepts for evaluating the stored energy and the radiation Q factor of an antenna are introduced. The first two use time harmonic quantities and are based on the work of Vandenbosch and Yaghjian. The third concept is a time-domain method which aims to deliver the true stored energy. The concepts are discussed and compared on the basis of examples of varying complexity, including evaluation of Q factors for non-radiating lumped RLC circuits and a canonical dipole radiator. It is shown that all three concepts unite for special cases of parallel and series RLC circuits. For other (even very simple) circuits, the approaches yield significantly different results. Index Terms—Antenna theory, electromagnetic theory, electri-cally small antennas, Q factor. I.

Motivation & Objective

• To address the long-standing challenge of defining and quantifying stored electromagnetic energy in antennas.
• To evaluate and compare three distinct theoretical approaches—two time-harmonic and one time-domain—for computing stored energy and Q factor.
• To identify conditions under which these methods agree or diverge, particularly in non-radiating and radiating systems.
• To assess the validity and consistency of existing techniques, especially for electrically small antennas and complex circuits.

Proposed method

• The first two methods apply time-harmonic formulations based on the theoretical frameworks of Vandenbosch and Yaghjian to compute stored energy and Q factor.
• The third method introduces a time-domain approach designed to compute the true stored energy by analyzing energy storage over time.
• The methods are applied and compared across a range of systems, from simple series and parallel RLC circuits to a canonical dipole radiator.
• Energy and Q factor values are computed and contrasted across all three methods to assess consistency and divergence.
• Theoretical derivations and numerical examples are used to evaluate performance and convergence across different system complexities.
• The analysis focuses on identifying when the methods yield identical results and when they diverge, particularly in non-ideal or complex configurations.

Experimental results

Research questions

• RQ1 Under what conditions do the time-harmonic and time-domain methods for stored energy evaluation produce equivalent results?
• RQ2 How do the three methods compare in their computed Q factors for non-radiating lumped RLC circuits?
• RQ3 To what extent do the methods agree for canonical radiating structures like a dipole antenna?
• RQ4 Why do the methods yield significantly different results for certain complex circuits despite theoretical expectations of consistency?
• RQ5 What are the implications of methodological divergence for the design and analysis of electrically small antennas?

Key findings

• The three methods converge exactly for idealized series and parallel RLC circuits, confirming consistency in simple, non-radiating cases.
• For more complex or non-ideal circuits, the methods produce significantly different stored energy and Q factor values, indicating methodological inconsistencies.
• The time-domain method yields distinct results compared to the time-harmonic approaches, suggesting it may better represent true stored energy in dynamic systems.
• The divergence in results highlights fundamental ambiguities in defining stored electromagnetic energy, especially in radiating systems.
• The study reveals that current techniques for Q factor evaluation are not universally consistent, challenging assumptions in antenna theory and design.