Power Transport Theorem Based Decoupling Mode Theory for Wave-Port-Fed Transmitting Antennas

Employing the work-energy principle based physical interpretation for characteristic mode theories (CMTs), it is exposed that: strictly speaking, the existing CMTs are the modal analysis theories for incident-field-driven scattering objects and lumped-port-driven transmitting antennas, but not for wave-port-fed transmitting antennas, so they cannot provide an exact modal analysis to wave-port-fed antennas. This paper focuses on establishing an effective modal analysis theory for wave-port-fed antennas. Power transport theorem (PTT), which governs the transport process of the power-flow passing through wave-port-fed antenna, is derived. It is found out that the input power contained in PTT is the source to sustain a stationary power transport. Under PTT framework, a novel modal analysis theory — decoupling mode theory (DMT) — is established for the antenna. By orthogonalizing input power operator (IPO), the PTT-based DMT can construct a set of energy-decoupled modes (DMs) for the antenna. A novel concept of "electric-magnetic energy-decoupling factor" / "electric-magnetic phase-mismatching factor" is introduced for quantifying the coupling/matching degree between modal electric field and modal magnetic field. A field-based definition for modal input impedance and admittance is proposed as an alternative for the conventional circuit-based definition. Three somewhat different but not contradictory physical meanings of modal significance (MS) are summarized.

Power Transport Theorem Based Decoupling Mode Theory for Wave-Port-Fed Transmitting Antennas

Employing the work-energy principle based physical interpretation for characteristic mode theories (CMTs), it is exposed that: strictly speaking, the existing CMTs are the modal analysis theories for incident-field-driven scattering objects and lumped-port-driven transmitting antennas, but not for wave-port-fed transmitting antennas, so they cannot provide an exact modal analysis to wave-port-fed antennas. This paper focuses on establishing an effective modal analysis theory for wave-port-fed antennas. Power transport theorem (PTT), which governs the transport process of the power-flow passing through wave-port-fed antenna, is derived. It is found out that the input power contained in PTT is the source to sustain a stationary power transport. Under PTT framework, a novel modal analysis theory — decoupling mode theory (DMT) — is established for the antenna. By orthogonalizing input power operator (IPO), the PTT-based DMT can construct a set of energy-decoupled modes (DMs) for the antenna. A novel concept of "electric-magnetic energy-decoupling factor" / "electric-magnetic phase-mismatching factor" is introduced for quantifying the coupling/matching degree between modal electric field and modal magnetic field. A field-based definition for modal input impedance and admittance is proposed as an alternative for the conventional circuit-based definition. Three somewhat different but not contradictory physical meanings of modal significance (MS) are summarized.

Power Transport Theorem Based Decoupling Mode Theory for Wave-guiding Structures

Power transport theorem (PTT) governing the transport process of the power-flow passing through waveguide is derived. The input power as the source term in PTT is found to be the one for sustaining a stationary power transport, and the corresponding input power operator (IPO) is formulated. The travelling-wave condition satisfied by the travelling-wave modes one-directionally propagating along the waveguide is introduced as a counterpart of the famous Sommerfeld's radiation condition satisfied by the radiative fields distributing in far zone. Employing the travelling-wave condition and some other necessary conditions, the dependent currents in IPO are effectively eliminated. Under PTT framework, the recently developed decoupling mode theory (DMT) for wave-port-fed antennas is further generalized to waveguides. The PTT-based DMT (PTT-DMT) focuses on constructing a set of energy-decoupled modes (DMs) for any pre-selected objective waveguide by orthogonalizing the IPO with only independent current, and any two different DMs don't have net energy exchange in an integral period. The PTT-DMT is an effective alternative for classical eigen-mode theory. The alternative realizes an effective unification for waveguide-oriented modal analysis theory and antenna-oriented modal analysis theory, such that the theories can be easily integrated into a single theory for whole waveguide-antenna combined system in the future.

Power Transport Theorem Based Decoupling Mode Theory for Wave-guiding Structures

Power transport theorem (PTT) governing the transport process of the power-flow passing through waveguide is derived. The input power as the source term in PTT is found to be the one for sustaining a stationary power transport, and the corresponding input power operator (IPO) is formulated. The travelling-wave condition satisfied by the travelling-wave modes one-directionally propagating along the waveguide is introduced as a counterpart of the famous Sommerfeld's radiation condition satisfied by the radiative fields distributing in far zone. Employing the travelling-wave condition and some other necessary conditions, the dependent currents in IPO are effectively eliminated. Under PTT framework, the recently developed decoupling mode theory (DMT) for wave-port-fed antennas is further generalized to waveguides. The PTT-based DMT (PTT-DMT) focuses on constructing a set of energy-decoupled modes (DMs) for any pre-selected objective waveguide by orthogonalizing the IPO with only independent current, and any two different DMs don't have net energy exchange in an integral period. The PTT-DMT is an effective alternative for classical eigen-mode theory. The alternative realizes an effective unification for waveguide-oriented modal analysis theory and antenna-oriented modal analysis theory, such that the theories can be easily integrated into a single theory for whole waveguide-antenna combined system in the future.

Basics of Fluid Dynamics

In this chapter, studies on basic properties of fluids are conducted. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. The Reynolds Transport theorem and its derivation is presented. The well-known Conservation laws, Conservation of Mass, Conservation of Momentum and Conservation of Energy, which are the foundation of almost all Engineering mechanics simulation are derived from Reynolds transport theorem and through intuition. The Navier–Stokes equation for incompressible flows are fully derived consequently. To help with the solution of the Navier–Stokes equation, the velocity and pressure terms Navier–Stokes equation are reduced into a vorticity stream function. Classification of basic types of Partial differential equations and their corresponding properties is discussed. Finally, classification of different types of flows and their corresponding characteristics in relation to their corresponding type of PDEs are discussed.

Transport Theorem for Spaces and Subspaces of Arbitrary Dimensions

Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, M ≤ N . The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived.