Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensors Using Coupled Line Sections

Abstract

Highly sensitive permittivity sensors operating in reflection and exploiting phase variation are presented in this article. The sensors are one-port structures implemented by means of a pair of coupled lines, the sensitive region, with an appropriate termination. In particular, it is demonstrated that by either short-circuiting the crossed port to the input port of the device (opening the remaining two ports), or opening the crossed port to the input port (terminating the other two ports with a short-circuit), the sensitivity can be driven to very high values, controlled by the coupling factor. For that purpose, the electrical length of the pair of coupled lines must be set to 90 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> when such lines are loaded with the reference (REF) material. Thus, the sensitivity is optimized for dielectric constants (the input variable) in the vicinity of the dielectric constant of the REF material, where the indicated phase condition is fulfilled. The output variable is the phase of the reflection coefficient, an easily measurable quantity. For validation purposes, three prototype sensors are designed and fabricated. The achieved sensitivities in two of the fabricated sensors are as high as 659.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> and 736.0 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> , with figures of merit (FoMs), or ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared-wavelength, of FoM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 9401 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda^2$</tex-math> </inline-formula> and 12 690 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda$</tex-math> </inline-formula> , respectively, i.e., very competitive values. Moreover, the indicated high sensitivities and FoMs have been achieved without the need to add further circuit stages to the sensing region, contrarily to other highly sensitive phase-variation sensors, where sensitivity optimization is achieved at the expense of an increase in the overall sensor size.