A Design Rule for Passive Reconfigurable Microwave Devices
Abstract
Every reconfigurable microwave device places a tuning element - a varactor, a diode, transistor, microelectromechanical or phase-change switch, a ferroelectric or liquid-crystal load - inside a fixed passive network. The network can make a small change of the element produce a large change of the response, and design practice often credits it with the device's tuning capability. This paper shows that a fixed, linear, passive network cannot add to that capability. Each tuning element carries a tuning budget, a dimensionless length computed from its own impedance trajectory, and a fixed passive network can transmit that budget or lose part of it, never enlarge it. The unit of the budget is the hyperbolic distance of the Smith chart: the distance from a match is the logarithm of the voltage standing-wave ratio, and the distance between two states sets their mutual mismatch and is the logarithm of their commutation quality factor. From one inequality we derive closed-form, ready-to-use limits for analog and digital phase shifters, true-time-delay lines, switches, attenuators, vector modulators, impedance tuners, tunable filters, reconfigurable antennas, metasurface cells and multiport networks; the two-state and attenuation limits are attained by explicit circuits, and the phase limit by a constant-loss trajectory. We introduce the Λ-chart, a Smith-chart companion on which budgets and requirements are read graphically, and apply it to four published microwave case studies.
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BibTeX
@misc{nadarloo2026design,
title = {{A Design Rule for Passive Reconfigurable Microwave Devices}},
author = {Ali Nadarloo and Mohammad Javad Hajiahmadi and Mohammad Soleimani},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06279},
eprint = {2611.06279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06279},
}
RIS
TY - UNPB
TI - A Design Rule for Passive Reconfigurable Microwave Devices
AU - Ali Nadarloo
AU - Mohammad Javad Hajiahmadi
AU - Mohammad Soleimani
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06279
UR - https://arxiv.org/abs/2611.06279
AB - Every reconfigurable microwave device places a tuning element - a varactor, a diode, transistor, microelectromechanical or phase-change switch, a ferroelectric or liquid-crystal load - inside a fixed passive network. The network can make a small change of the element produce a large change of the response, and design practice often credits it with the device's tuning capability. This paper shows that a fixed, linear, passive network cannot add to that capability. Each tuning element carries a tuning budget, a dimensionless length computed from its own impedance trajectory, and a fixed passive network can transmit that budget or lose part of it, never enlarge it. The unit of the budget is the hyperbolic distance of the Smith chart: the distance from a match is the logarithm of the voltage standing-wave ratio, and the distance between two states sets their mutual mismatch and is the logarithm of their commutation quality factor. From one inequality we derive closed-form, ready-to-use limits for analog and digital phase shifters, true-time-delay lines, switches, attenuators, vector modulators, impedance tuners, tunable filters, reconfigurable antennas, metasurface cells and multiport networks; the two-state and attenuation limits are attained by explicit circuits, and the phase limit by a constant-loss trajectory. We introduce the Λ-chart, a Smith-chart companion on which budgets and requirements are read graphically, and apply it to four published microwave case studies.
ER -