Articulo Fabry Pe or t

8/20/2019 Articulo Fabry Pe or t

1/17

See discussions, stats, and author profiles for this publication at:https://www.researchgate.net/publication/270794552

Planar Fabry-Perot directive

antenna: A simplified analysis by

equivalent circuit approach

ARTICLE in

JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS · JANUARY2015

Impact Factor: 0.73 · DOI: 10.1080/09205071.2014.997838

READS

54

2 AUTHORS:

Giuseppe Di Massa

Università della Calabria

310 PUBLICATIONS 1,067 CITATIONS

SEE PROFILE

Hugo Oswaldo Moreno Aviles

Escuela Superior Politécnica de C…

14 PUBLICATIONS 40 CITATIONS

SEE PROFILE

Available from: Giuseppe Di Massa

Retrieved on: 05 January 2016

https://www.researchgate.net/profile/Hugo_Moreno_Aviles?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_4https://www.researchgate.net/institution/Escuela_Superior_Politecnica_de_Chimborazo?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_6https://www.researchgate.net/profile/Giuseppe_Di_Massa?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_4https://www.researchgate.net/profile/Giuseppe_Di_Massa?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_4https://www.researchgate.net/institution/Universita_della_Calabria?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_6https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_1https://www.researchgate.net/profile/Hugo_Moreno_Aviles?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_7https://www.researchgate.net/institution/Escuela_Superior_Politecnica_de_Chimborazo?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_6https://www.researchgate.net/profile/Hugo_Moreno_Aviles?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_5https://www.researchgate.net/profile/Hugo_Moreno_Aviles?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_4https://www.researchgate.net/profile/Giuseppe_Di_Massa?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_7https://www.researchgate.net/institution/Universita_della_Calabria?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_6https://www.researchgate.net/profile/Giuseppe_Di_Massa?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_5https://www.researchgate.net/profile/Giuseppe_Di_Massa?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_1https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_3https://www.researchgate.net/publication/270794552_Planar_Fabry-Perot_directive_antenna_A_simplified_analysis_by_equivalent_circuit_approach?enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA%3D%3D&el=1_x_2


2/17

This article was downloaded by: [Univ Studi Della Calabria]On: 12 January 2015, At: 09:33Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Click for updates

Journal of Electromagnetic Waves and

ApplicationsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tewa20

Planar Fabry–Perot directive antenna: a

simplified analysis by equivalent circuit

approachG. Di Massaa, S. Costanzoa & H.O. Morenoba Dipartimento di Ingegneria Informatica, Modellistica, Elettronicae Sistemistica, UniversitÁ Della Calabria, Rende (Cs), 87036, Italy.b Facultad de Informatica y Electronica, Escuela SuperiorPolitecnica De Chimborazo, Riobamba, Ecuador.Published online: 08 Jan 2015.

To cite this article: G. Di Massa, S. Costanzo & H.O. Moreno (2015): Planar Fabry–Perot directiveantenna: a simplified analysis by equivalent circuit approach, Journal of Electromagnetic Wavesand Applications, DOI: 10.1080/09205071.2014.997838

To link to this article: http://dx.doi.org/10.1080/09205071.2014.997838

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the

“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

http://crossmark.crossref.org/dialog/?doi=10.1080/09205071.2014.997838&domain=pdf&date_stamp=2015-01-08http://www.tandfonline.com/loi/tewa20http://dx.doi.org/10.1080/09205071.2014.997838http://www.tandfonline.com/action/showCitFormats?doi=10.1080/09205071.2014.997838http://www.tandfonline.com/loi/tewa20http://crossmark.crossref.org/dialog/?doi=10.1080/09205071.2014.997838&domain=pdf&date_stamp=2015-01-08


3/17

Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditions


4/17

Journal of Electromagnetic Waves and Applications, 2015http://dx.doi.org/10.1080/09205071.2014.997838

Planar Fabry–Perot directive antenna: a simplified analysis byequivalent circuit approach

G. Di Massaa∗, S. Costanzoa and H.O. Morenob

a Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, UniversitÁ DellaCalabria, Rende (Cs) 87036, Italy; bFacultad de Informatica y Electronica, Escuela Superior

Politecnica De Chimborazo, Riobamba, Ecuador

( Received 3 June 2014; accepted 8 December 2014)

A new approach is proposed for the analysis and design of a planar Fabry–Perot antenna.The complete modal analysis of the field into the cavity leads to a simplified equivalentcircuit, able to provide a reliable description of the coupling with the feeding waveguide,as well as to compute theequivalent currents on theradiating apertures, thus obtaining theradiated far-field. The proposed approach is preliminary validated on a metallic Fabry–Perot antenna structure. Then, a modified configuration, based on a cavity partially-filledwith a dielectric substrate, is assumed to obtain a Fabry–Perot antenna with improvedbandwidth features. Experimental validations on array prototypes are successfully dis-cussed.

Keywords: Fabry–Perot cavity; antennas; millimeter waves

1. Introduction

Millimeter-wave frequencies are very attractive resources for telecommunications, as being

useful in many applications which include the realization of high data rate links in pico

cellular networks, local multipoint data services, automotive radars, inter-satellite commu-

nications, and so on.

Spherical or hemispherical Fabry–Perot [1] antennas [2,3] give a very interesting solu-

tion, as being able to provide a high agility in the design-synthesis process. In the existing

configurations, one or both reflecting mirrors are composed by metal strip gratings, and

the basic idea is that the gaussian field distribution on the mirrors could provide a far-field

in the absence or with very low sidelobes. This advantage is obtained at the expense of a

complicated mechanical structure.

In [4], an optimized partially reflecting surface, placed in front of a waveguide aperture

on a ground plane, is used to obtain a high gain antenna with a useful frequency bandwidth

equal to 100 MHz.

In [5], an empty planar metallic Fabry–Perot antenna is studied using a 3-D MoM

(method of moments) simulation code with a thin wire approximation. The ground plane is

taken into account by adopting the image theory, and the resonance condition is excited by a

patch antenna placed into the cavity in the proximity of the ground plane. The experimental

study shows a good agreement with the simulation results, but a very little bandwidth is

observed.

∗Corresponding author. Email: [email protected]

© 2015 Taylor & Francis

https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3356030_High_gain_planar_antenna_using_optimized_partially_reflective_surface?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3356030_High_gain_planar_antenna_using_optimized_partially_reflective_surface?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3356030_High_gain_planar_antenna_using_optimized_partially_reflective_surface?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3018428_A_Metallic_Fabry-Perot_Directive_Antenna?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3018428_A_Metallic_Fabry-Perot_Directive_Antenna?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3018428_A_Metallic_Fabry-Perot_Directive_Antenna?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3018428_A_Metallic_Fabry-Perot_Directive_Antenna?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3356030_High_gain_planar_antenna_using_optimized_partially_reflective_surface?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/3017372_A_New_Concept_of_Focusing_Antennas_Using_Plane-Parallel_Fabry-Perot_Cavities_with_Nonuniform_Mirrors?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==


5/17

2 G. Di Massa et al.

In [6], the directivity and bandwidth of Fabry–Perot resonator antennas made of two

different ground plates with a partially-reflecting surface, are theoretically studied. A sim-

plified model considering the plane waves propagation in the parallel plate waveguide is

adopted, and the directivity of Fabry–Perot resonator is shown to obtain its maximum when

the primary source is located at a specific position.

In [7], a Fabry–Perot cavity is used to design a 60 GHz single-feed directive antenna

given by a ground plane covered by a frequency selective surface, with the adoption of a

simple synthesis process based on a transmission line model.

In this paper, a Fabry–Perot antenna composed by an open resonator with plane mirrors is

considered. An equivalent circuit based on a modal analysis of the open resonator is adopted

for the characterization of the proposed structure, in order to optimize the coupling between

the feeding rectangular waveguide and the planar open cavity. Preliminary results on the

metallic Fabry–Perot antenna are discussed as predicted by the adopted equivalent circuit.

Then, a modified Fabry–Perot configuration based on the insertion of a dielectric substrate,

is proposed to significantly improve the operation bandwidth of the original metallic Fabry–

Perot structure. Experimental results on a K u -band partially-filled 8 × 8 elements array aresuccessfully reported to demonstrate a radiation bandwidth improvement of about 48%.

The paper is organized as follows. First, in Section 2, the theoretical background of

the proposed method for an open resonator composed by metallic rectangular mirrors

is presented. In Section 3, the feeding-waveguide-to-cavity and the cavity-to-free space

couplings are analyzed for the case of metallic Fabry–Perot antenna. In Section 4, the

problem of antenna bandwidth improvement is addressed by introducing the partially-filled

antenna configuration and the relative experimental results assessing the proposed approach

are presented. Finally, conclusions and future works are outlined in Section 5.

2. Open resonator composed by rectangular mirrors

2.1. Outline of open resonator theory

Let us consider an open resonator composed by two parallel metallic rectangular mirrors,

as illustrated in Figure 1.

In order to give a modal analysis for the assumed structure, let us consider the wave

equation for a rectangular field component:

∇ 2u + k 2u = 0 (1)

with the boundary condition u = 0 on the mirrors.

2l

2a

2b

z

x

y

Figure 1. Rectangular open resonator.

https://www.researchgate.net/publication/224439489_Design_of_a_single-feed_60_GHz_planar_metallic_Fabry-Perot_cavity_antenna_with_20_dB_gain?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/224439489_Design_of_a_single-feed_60_GHz_planar_metallic_Fabry-Perot_cavity_antenna_with_20_dB_gain?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/224439489_Design_of_a_single-feed_60_GHz_planar_metallic_Fabry-Perot_cavity_antenna_with_20_dB_gain?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==https://www.researchgate.net/publication/224439489_Design_of_a_single-feed_60_GHz_planar_metallic_Fabry-Perot_cavity_antenna_with_20_dB_gain?el=1_x_8&enrichId=rgreq-6ee6e1b7-a7de-491a-8065-44b79bd2a34f&enrichSource=Y292ZXJQYWdlOzI3MDc5NDU1MjtBUzoxODUxMTE1MjU5OTQ0OTZAMTQyMTE0NTQzNTAzOA==


6/17

Journal of Electromagnetic Waves and Applications 3

The solution of Equation (1), assuming a e jωt time dependence, can be written as:

u = v( x, y, z)e− jkz − (−1)q v( x, y, − z)e jkz (2)where q is the longitudinal mode number. Assuming that function v has a very slow variation

with respect to variable z , so that its second derivative could be neglected with respect tothe term

k ∂v∂ z , it is easy to obtain the well-known parabolic approximation to the waveequation:

∂ 2v

∂ x 2 + ∂

2v

∂ y2 − 2 jk ∂v

∂ z = 0 (3)

with the boundary conditions:v( x, y, −l) = 0, for | x| > a or | y| > b;v( x, y, −l) = e j (2kl−πq)v( x, y, l), for | x|


7/17


The value of quality factor Q due to the only radiation loss is given by:

Q = q4 p"

(13)

with

p" π γ m22 M 2a

+ π γ n22 M 2b

(14)

Let us introduce the dimensionless coordinates:

ξ =

k

2l x, η =

k

2l y, ζ = z

2l (15)

In the above coordinate system, the variables ξ, η, at the end of the mirror x = ±a, y = ±b,assume the values:

ξ e

= ±

M a

2

ηe

= ±

M b

2

(16)

where the parameter M a,b is related to the Fresnel number N [8]:

M =√

8π N (17)

In the (ξ , η , ζ ) coordinates, we have:

u (ξ , η , ζ ) = 2e− jπ pva (ξ ) vb (η) cos (πqζ ) , (q odd) (18)u (ξ , η , ζ ) = 2e− jπ pva (ξ ) vb (η) sin (πqζ ) , (q even) (19)

where

va (ξ ) = cos π mξ ( M a + γ + jγ )

, (m = 1, 3 . . . )

va (ξ ) = sinπ mξ

( M a + γ + jγ ), (m = 2, 4 . . . )

vb (η) = cosπnη

( M b + γ + jγ ), (n = 1, 3 . . . )

vb (η) = sinπ nη

( M b + γ + j γ ), (n = 2, 4 . . . ) (20)

2.2. Electromagnetic field into the cavity

The electromagnetic field into the cavity can be expressed in terms of (quasi)-transverse

electromagnetic modes as follows:

E =mn

V mn emn (21)

H =mn

I mn hmn (22)

The relation between function u = u( x, y, z) and the electromagnetic field can be estab-lished with the aid of Hertz vector e by the following relationships:

e = ∇∇ · e + k 2e (23)h = j k

Z w∇ × e (24)


8/17


where k = ω√ εµ and Z w =

µε .

Let us set:

e x = u; e y = e z = 0 (25)into Equations (23) and (24). Neglecting the losses and considering the (1 1 1) mode, we

obtain the modal solution for the y component of the magnetic field as:

H y = − j k

Z w

π

l e− jπ p

cos

π ξ

M a + γ

cos

π η

M b + γ

sin

π z2l

(26)

and the x component of the electric field as:

E x =

k 2 − k 2l

π 2

( M a + γ )2

2e− jπ p

cos π ξ M a + γ cos π η M b + γ cosπ z2l (27)Finally, from Equations (26) and (27) we obtain the equivalent surface impedance at the zabscissa, given as:

Z T = j Z w2l

π

k − 1

2l

π 2

( M a + γ )2

cotπ

2l z (28)

3. Metallic Fabry–Perot antenna

The antenna is a parallelepipedal flat structure with a square flat metallic base that is coupledby a slot to a rectangular waveguide, and a radiating face composed by a metallic sheet were

the radiating slots are cut (Figure 2).

Figure 2. Metallic Fabry–Perot antenna.


9/17


Figure 3. Equivalent circuit of metallic cavity.

3.1. Rectangular waveguide-to-cavity coupling

Following what developed in [9–11], the coupling between the field inside the cavity,

Equations (23) and (24), and the field into a rectangular metallic waveguide, assumed

as cavity feed, is matched on the coupling aperture, thus allowing an equivalent circuit

representation where only one cavity resonant mode is taken into account, while all T E n0modes of the exciting waveguide are considered. Under the above hypotheses, the equivalentcircuit modeling both the cavity behavior and the cavity-to-waveguide coupling is derived

(Figure 3).

In Figure 3, parameters L 0 and C give the inductance and the capacity of the equivalentcavity, respectively; the term R is the resistance due to the losses on the metallic sheet,parameter L gives the inductance representing the length increase due to non perfectconducting sheets, β01 is the cavity-waveguide coupling factor, Le is the inductance dueto higher non propagating modes in the waveguide, and Z 0 represents the characteristicimpedance of the feeding waveguide. In the Appendix 1 a more detailed description is

reported.

When the second metallic sheet in Figure 2 is replaced with a partially reflecting

surface,[12] an equivalent impedance is inserted into the circuit of Figure 4. The value

of Z S is obtained following the approach given in [13]

1

Z S = 1

j X L− 1

j X C + 1

Z W (29)

where with reference to Figure 2,

X L Z W

= d yλ

ln csc

π

2

d y − W d y

(30)

X C Z W

= −4 d xλ

ln cscπ

2

Ld x

−1(31)

and Z W = 120π is the free space impedance.The reported circuit leads to optimize the transition and to compute the field, inside the

cavity, which impinges on the radiating sheet, thus allowing the radiated field computation

from the equivalent currents on the radiating apertures.

3.2. Cavity-to-free space coupling

In order to compute the radiated field from the slots cut into one wall of the resonator, the

electromagnetic field in the resonator (26) is used to obtain the incident field on the slots

and subsequently derive from it the equivalent magnetic current.


10/17


L’

C

Le

Lo

R’

ZS

Zg

1: 01

Figure 4. Equivalent circuit of radiating cavity.

In the Bethe’s original theory,[14] the incident field is considered in the absence of the

aperture. The magnetic dipole moment is related to the incident field as follows:

M = −αmHt (32)where Ht is the tangential magnetic field at the center of the aperture, and the magnetic

polarizability, for small rectangular aperture, is given by [15]:

αm = 0.132

lg

1 + 0.66W LW 3 (33)

W and L being the aperture dimensions, with L W .In the presence of a slot grid, the array factor can be expressed as:

F (θ, φ) = M g=1

N h=1

I g,he jk (r ·−→r gh ) (34)

where I g,h is the amplitude for each point-source (g, h), which is equal to the magneticdipole moment M evaluated at the point:

( x, y) =

g − M + 12

d x ,

h − N + 1

2

d y (35)

while

r = x sin θ cos φ + y sin θ sin φ + z cos θ (36)−→r gh = g − M + 12

d x x +h − N + 1

2

d y y (37)

M and N being the number of elements along x and y directions.

3.3. Numerical results

Following the reasoning of previous paragraphs, the antenna configuration in Figure 2 is

considered. An array of 8 × 8 elements is assumed, with dimensions 2l = 10 mm, d x =12.5 mm, d y

=12.5mm, W

=6.35 mm, and L

=2 mm. A WR62 feeding waveguide, in

the K u band, with dimensions W a = 15.8mm, W b1 = 7.9 mm is considered.The analysis of the coupling between a rectangular cavity feeding waveguide and the

planar open cavity is performed by taking into account the results of previous paragraphs. In


11/17


0 1 2 3 4 5 6 7−20

−15

−10

−5

0

b [mm]

S 1 1

[ d B ]

Proposed approachHFSS simulation

Figure 5. Return loss versus waveguide height.

14.5 14.6 14.7 14.8 14.9 15 15.1 15.2

−35

−30

−25

−20

−15

−10

−5

Frequency (GHz)

S 1 1 ( d B )

HFSS simulation

Proposed approach

Figure 6. Return loss versus frequency.

particular, for the considered cavity of Figure 2, the result reported in Figure 5 is obtained

for a frequency of 14.85 GHz. The resonant frequency established from (8) is used to

compute the circuit elements under Table A1. Results obtained with the equivalent circuit

are compared with a full wave simulation. It is exploited to maximize the coupling between

the waveguide and the cavity, thus terminating the feeding section into an aperture of size

W a =

15.8 mm, W b=

1.3 mm.

In Figure 6, the return loss of the cavity as function of the frequency, computed by the

proposed equivalent circuit, is reported.

Afirst preliminary result of the radiation diagram using the simplifiedanalysis, compared

with full wave simulation, of the proposed antenna is reported in Figure 7 where, due to

the tapering of the exciting field of the slots, a substantial reduction of the sidelobes can be

observed.

4. Fabry–Perot antenna with improved bandwidth

In order to improve the operation bandwidth of the Fabry–Perot antenna configuration in

Figure 2, a modified structure partially-filled with a dielectric substrate is considered, as

illustrated in Figure 8. The gain and half-power fractional bandwidth are primarily deter-

mined by the cover reflection coefficient.[16–18] The method for bandwidth enlargement


12/17


−100 −80 −60 −40 −20 0 20 40 60 80 100−35

−30

−25

−20

−15

−10

−5

0

Angle (deg)

N o r m a l i z e d p a t t e r n ( d B )

Proposed approach

HFSS simulation

Figure 7. Radiated field of metallic Fabry–Perot antenna.

Figure 8. Partially-filled Fabry–Perot antenna.

focuses on the design of the cover. By adjusting the phase of the reflection coefficient, the

resonance condition of the cavity can be satisfied in a wider range of frequencies. Such an

optimized reflection response can be realized by introducing a dielectric layer.

In the following paragraphs, the expression of the electromagnetic field into the partially-

filled cavity are derived, and experimental results on a K u-band prototype are reported toshow a significant bandwidth improvement with respect to the case of metallic Fabry–Perot

structure of Figure 2.


13/17


Figure 9. Photograph of partially-filled Fabry–Perot antenna.

4.1. Electromagnetic field into the partially-filled cavity

When assuming a partially-filled cavity, the quasi-transverse electromagnetic field in the

dielectric, for h1 − l ≤ z ≤ h1 + h2 − l, is given as:

H 2 y = − j Aεk

Z w

π

l e− jπ p

cos

π ξ

M a + γ

cos

π η

M b + γ

sin

π z

2l2

(38)

14.4 14.5 14.6 14.7 14.8 14.9 15 15.10

2

4

6

8

10

12

14

16

18

20

Frequency [GHz]

[ d B ]

Empty Cavity (Simulation)

Partially Filled Cavity (Simulation)

Partially Filled Cavity (Measurement)

Frequency [GHz]

Figure 10. Boresight gain versus frequency: comparison between metallic and partially-filled Fabry–Perot antenna.


14/17


Figure 11. Radiation patterns of partially filled Fabry–Perot antenna (comparison betweenmeasurements and proposed analysis method): (a) f = 14.6 GHz, (b) f = 14.85 GHz.

E 2 x = B εk 2 − √ εk 2l

π 2

( M a + γ )2 2e− jπ p

cos

π ξ

M a + γ

cos

π η

M b + γ

cos

π z

2l2

= Z T 2 H 2 y (39)

where l2 = h1 + h2 − l.For z = h1 − l, the field into the empty part (Equations (26) and (27)), and the field in

the dielectric-filled part must be equal, thus applying the continuity of tangential fields at

the air-dielectric interface, it is easy to derive the expressions for the terms A and B :

A = 1ε

sin π2l (h1 − l)

sin

π2l2

(h1 − l) (40)


15/17


B = Z T 2 Z T

A (41)

where Z S 2 and Z S are derived from (28) and (39) for z = h1 − l.

4.2. Experimental results

In order to assess the analysis method outlined in the previous paragraphs, a partially-filled

Fabry–Perot antenna composed by an array of 8 × 8 elements, with inter-element spacingsd x = d y = 12.5 mm and slot dimensions W = 6.35 mm L = 2 mm, is realized andexperimentally tested. Referring to Figure 8, a plane distance l = h1 + h2 = 9.662 mmis considered, which is given by the sum of an empty space h1 = 8.9 mm and a dielectric(r = 2.33) with thickness h2 = 0.762 mm. The optimal coupling is obtained for a feedingwaveguide with dimensions W a = 18.8 mm, W b = 2 mm, at a frequency f = 14.85 GHz.The partially-filled Fabry–Perot antenna is realized and tested into the Microwave Labora-

tory at University of Calabria (Figure 9).

The enhanced bandwidth behavior of the partially-filled Fabry–Perot antenna can beeasily observed from the boresight gain results illustrated in Figure 10, where an improve-

ment of about 48% is obtained with the insertion of the dielectric substrate, and a good

agreement between simulations and measurements is demonstrated in the case of partially-

filled antenna configuration.

The wideband feature of the proposed antenna structure is further proved by the very

similar behavior of the radiation patterns (obtained from near-field to far-field transforma-

tion) at different frequencies, as illustrated in Figure 11, where the successful agreement

between results obtained from measurements and those derived from the proposed analysis

method can be also observed.

5. Conclusions and future work

An open planar cavity antenna has been presented in this work, by providing an equivalent

simplified circuit and obtaining both input characteristics and radiation diagrams of the

antenna. In particular, a modified configuration based on a cavity partially-filled with a

dielectric substrate is proposed to significantly improve the antenna radiation bandwidth.

For future developments, the following comments are in order:

• the development of a synthesis procedure using the positions and the dimensions of the radiating slots will be considered. In particular, a change in the slots dimension

will modify the amplitude of the magnetic current, thus leading to control the shapeof the radiation pattern;

• several types of radiating elements and feeding structures will be analyzed in futuredevelopments.

References

[1] Fabry C, Perot A. Theorie et Applications d’une Nouvélle Method de Spectroscopie

Interférentielle [Theory and applications for a new method of spectroscopy interferential]. Ann.

Chim. Phys. 1899;16:115.

[2] Di Massa G, Boccia L,Amendola G. Gaussian beam antennas based on open resonator structures.In: 28th ESA Antenna Workshop on Space Antenna Systems and Technologies; Olanda; 2005.

[3] Sauleau R, Coquet P, Matsui T, Daniel J.A new concept of focusing antennas using plane-parallel

Fabry–Perot cavities with nonuniform mirrors. IEEE Trans. Ant. Propag. 2003;51:3171–3175.


16/17


[4] Feresidis AP, Vardaxoglou JC. High gain planar antenna using optimised partially reflective

surface. IEE Proc. Microw. Ant. Propag. 2001;148:345–350.

[5] Guérin N, Enoch S, Tayeb G, Sabouroux P, Vincent P, Legacy H.A metallic Fabry–Perot Directive

Antenna. IEEE Trans. Ant. Propag. 2006;54:220–224.

[6] Liu Z-G. Effect of primary source location on Fabry–Perot resonator antenna. In: Asia Pacific

Microwave Conference, APMC; Singapore; 2009. p. 1809–1812.[7] Hosseini SA, Capolino F, De Flaviis F. Design of a single-feed 60 GHz planar metallic Fabry–

Perotcavity antenna with 20 dB gain. In: IEEE International Workshop on Antenna Technology,

iWAT; Santa Monica, CA; 2009.

[8] Fox AG, Li T. Resonant modes in a maser interferometer. BeIl Sys. Tech. J. 1961;40:453–488.

[9] Bucci O, Di Massa G. Open resonator powered by rectangular waveguide. IEE Proc.-H.

1992;139:323–329.

[10] Di Massa G, Costanzo S, Moreno OH. Open resonator system for reflectarray elements

characterization. Int. J. Ant. Propag; 2012:7 p. Article ID: 912809. doi:10.1155/2012/912809.

[11] Di Massa G, Costanzo S, Moreno OH. Accurate circuit model of open resonator system for

dielectric material characterization. J. Electromagn. Waves Appl. 2012;26:783–794.

[12] Von Trentini G. Partially reflecting sheet arrays. IRE Trans. Ant. Propag. 1956;4:666–671.[13] Whitbourn LB, Compton RC. Equivalent-circuit formulas for metal grid reflectors at dielectri

boundary. Appl. Opt. 1985;24:217–220.

[14] Bethe HA. Theory of diffraction from small holes. Phys. Rev. 1944;66:163–182.

[15] McDonald NA. Simple approximations for the longitudinal magnetic polarizabilities of some

small apertures. IEEE Trans. Microw. Tech. 1988;MTT36:1141–1144.

[16] Feresidis AP, Vardaxoglou JC. High gain planar antenna using optimised partially reflective

surfaces. IEE Proc-Microiv. Ant. Propag. 2001;148:345–350.

[17] Costa F, Genovesi S, Monorchio A. On the bandwidth of high-impedance frequency selective

surfaces. IEEE Ant. Wireless Propag. Lett. 2009;8:1341–1344.

[18] Wang N, Zhang C, Zeng Q, Wang N, Xu J. New dielectric 1-D EBG structure for the design of

wideband resonator antennas. Prog. Electromagn. Res. 2013;141:233–248.[19] Di Massa G. Microwave open resonator techniques – part I: theory. In: Costanzo S, editor.

Microwave materials characterization; Rijeka (HRV); InTech Web; 2012.

Appendix 1. Equivalent circuit

The details of the following derivation are given in [19], which is the reference for the meaning of the symbols.

Let us consider our system under the assumption of negligible intercoupling between cavitymodes, i.e.:

αnm

=

1

2 M h∗n

·hm d S

=0 i f n

=m (A1)

The coupling factor between the waveguide and cavity modes,

βnm =

Ae

gm × h∗n · n̂d S = −

A

h∗n · hgmd S . (A2)

Considering, with reference to Figure 2, the waveguide y component magnetic field for oddmodes,

H y = j K z

K 2t

mπ

W asin

mπ

W a

y − W a

2

(A3)

and the magnetic field of the cavity (26) considered constant on the coupling aperture,

H y = j k Z W

π

l e− jπ p (A4)

http://dx.doi.org/10.1155/2012/912809http://dx.doi.org/10.1155/2012/912809http://dx.doi.org/10.1155/2012/912809http://dx.doi.org/10.1155/2012/912809


17/17


Table A1. Expressions for the circuit elements of Figure 3.

L0 µ0l ( H ) C εl/(k 0l)2 (F)

L’ µ0δ ( H ) R 2/σ δ ()

we can express the coupling factor (A2) as:

β0m = K zk

K t Z W

1

l e jπ p

2W a W bm

(A5)

with p = j p at resonant frequency of cavity.By enforcing the continuity of magnetic field tangential component over the coupling aperture,

we get for the equivalent terminal impedance relative to the fundamental mode [ 19]:

Z =

ζ 0

ζ 1

1 + 1 − = −

ζ 0

β201 F 0 +ζ

0 k =1β0k

β012

ζ k

(A6)

Hence, for the sum at the right hand side of (A6), we have:

ζ 0

k =3,5,··

β0k

β01

2ζ k = j ζ 0

∞k =0

1

(2k + 3)21

2k +32W a

λ2 − 1

j ζ 0

2W aλ

∞k =0

1

(2k + 3)3 = j ωµW a 1

π

1 − 1

8

ζ (3) − 1

= j ω Le

(A7)

wherein ζ (·) denotes the Rieman zeta function. From Equation (A7), we have the value of L e: Le = 16.5 10−3µ0 a [henry] (A8)

The explicit expression for the elements of equivalent circuit reported under Figure 3 are collectedunder Table A1.

In Table A1 k 0 = ω0√ 0µ0 with ω0 resonant frequency of cavity.

Documents

Articulo Fabry Pe or t