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Planar Microwave Sensors Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Coupled Planar Microwave Resonators and Transmission-Line Structures

Author : Enrique Bronchalo

Published in: Coupled Structures for Microwave Sensing

Publisher: Springer Nature Switzerland

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Abstract

This chapter presents the fundamental concepts on coupled microwave structures, including coupled resonators, coupled transmission lines and coupled-line structures. Although many concepts and results here presented have a general validity in the microwave field, the chapter focuses on planar coupled structures, which are the building blocks of the sensors described in the book. The chapter introduces the fundamentals of microwave resonators (lumped and distributed) and coupled planar transmission lines, with special emphasis on coupled identical microstrip lines. Coupled resonators are addressed from the field and circuit approaches, introducing the concepts of electric and magnetic coupling, and resonance-frequency splitting. The last section of the chapter presents the coupled-line directional couplers and two-port coupled-line networks.

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previous chapter Planar Microwave Sensors
next chapter Permittivity Sensors Based on Coupled Line Sections
Footnotes
1
This attenuation constant, with units of nepers/second, is not to be confused with the attenuation constant of a transmission line, with units of nepers/meter, that appears later in this chapter. Although we will employ the same symbol for both, they rarely appear in the same context.
 
2
Note that the two lines share a common ground, a feature of unbalanced or single-ended planar lines like microstrip or coplanar waveguide transmission lines.
 
3
The angular frequency ωu introduced in Sect. 3.1 refers to identical uncoupled resonators (isolated from each other), while ω0, is the resonance frequency of each coupled resonator when the other one is shorted to ground (see Fig. 22). Under weak-coupling conditions, the difference between ω0 and ωu is small.
 
4
In this expression, the permittivity is supposed to be real (lossless substrate). For the general case, the different energy terms are (εEi)*Ej instead of ε; Ei*Ej.
 
5
If the coupling strength is high, or if the line width changes in the coupled region respect to the uncoupled region, the current and voltage distributions in both regions are different, and fulfill continuity conditions in the frontiers.
 
6
Using inverters as coupling networks does not suppose a serious limitation, as any lossless reciprocal two-port network can be converted into an inverter simply by adding suitable line sections at its ports [82]. Therefore, the only implication in the S parameters is a phase-shift.
 
7
In the type of couplers called forward directional couplers, a portion of the power entering through port 1 couples to port 4, while port 3 remains isolated [3]. This type of coupler, although possible, is rarely based on quasi-TEM coupled lines, being commonly based on other kinds of coupled structures, like metallic or dielectric waveguides.
 
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Metadata
Title
Coupled Planar Microwave Resonators and Transmission-Line Structures
Author
Enrique Bronchalo
Copyright Year
2024
Book
Coupled Structures for Microwave Sensing

Print ISBN: 978-3-031-53860-5

Electronic ISBN: 978-3-031-53861-2

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-53861-2_2