Characteristics of Coupled Microstrip Transmission Lines-I: Coupled-Mode Formulation of Inhomogeneous Lines

Coupled microstrip comblines filters

“…These capacitances are related to self and mutual capacitances and inductances through the following equations [5] …”

“…The relationships between coupled combline and single coupled lines impedances and phase constants can be found using single coupled microstrip line theory [5] combined with (11) and (12). These definitions and relationships may be represented by the following equations: …”

“…According to coupled microstrip lines theory [5], the coupled microstrip lines can be modeled by an equivalent lumped circuit. For the proposed model, a new lumped finger capacitance (C fg ) is added in this circuit.…”

“…For coupled lines in TEM modes, coupled modes can be expressed in terms of even and odd modes capacitance (C e a , C o a ) for air dielectric structure and for the one with dielectric substrate C e (e r ), C o (e r ). These capacitances are related to self and mutual capacitances and inductances through the following equations [5]…”

Coupled mode theory approximation for arbitrary conventional/metamaterial contradirectional coupled-line couplers

“…The coupled-mode theory, introduced by Louisell in [6] and extended to inhomogeneous structures in [7], has been rarely used due to its relative complexity, but it is completely general, provides deep insight into propagation and coupling phenomena, and seems to be the best approach for complex coupled-line structures such as those involving for instance metamaterial/asymmetric transmission lines.…”