{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

asymmetric_junct - Ideal asymmetric junction elements Relax...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Ideal asymmetric junction elements Relax the symmetry assumption and examine the resulting junction structure. For simplicity, consider two-port junction elements. As before, assume instantaneous power transmission between the ports without storage or dissipation of energy. Characterize the power flow in and out of a two- port junction structure using four real-valued wave-scattering variables. Using vector notation: u = u 1 u 2 (A.1) v = v 1 v 2 (A.2) The input and output power flows are the square of the length of these vectors, their inner products. P in = i=1 2 u i 2 = u t u (A.3) P out = i=1 2 v i 2 = v t v (A.4) The constitutive equations of the junction structure may be written as follows. v = f ( u ) (A.5) Geometrically, the requirement that power in equal power out means that the length of the vector v must equal the length of the vector u , i.e. their tips must lie on the perimeter of a circle (see figure A.1). For any two particular values of u and v , the algebraic relation f ( . ) is equivalent to a rotation operator . v = S ( u ) u (A.6) where the square matrix S is known as a scattering matrix . Mod. Sim. Dyn. Sys. page 1 Neville Hogan
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon