Lumped Equivalent Models of Dual-Band Dual-Mode Transmission Lines and Their Application to Couplers

This brief presents four lumped-element units that are equivalent to dual-band, dual-mode transmission lines (TLs) ([
$Z_{L}$
,
$\theta _{L}$
]@
$f_{L}$
and [
$Z_{H}$
,
$\theta _{H}$
]@
$f_{H}$
), along with closed-form design equations. Couplers developed using these units exhibit a dual-band response, enabling independent configuration in each band. Within each individual band, the model permits the incorporation of arbitrary power division ratios, arbitrary phase differences ranging from 0° to 360°, and arbitrary port impedances. Facilitated by the use of lumped elements, it have a compact size and offering a big band ratio and high isolation between passbands. To validate the design approach, several design cases are demonstrated, and two coupler prototypes are fabricated.