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University of Oklahoma

1. Bhowmik, Lal Mohan. Applications of Floquet Analysis to Modern Phased Array Antennas.

Degree: PhD, 2019, University of Oklahoma

Next generation radar technology is based on phased array technology and provides remarkable scanning flexibility and spatial search capability for the multifunction weather and air surveillance radar systems. The future weather radar is comprised of thousands of antenna elements and requires strict polarization purity, grating lobe free system, low sidelobe levels, suppressed surface waves, low cross-polarization, with beam shape requirements. To address these demands is a serious challenge. Over the past few decades, phased array radar technology has been a tremendous advancement in search for future radar technology. With the blessing of modern computational electromagnetic tools, the theory behind the electromagnetic and circuit-level behavior of large-scale phased array system opened the door to analyze the wide variety of multi-layered, complex system of large arrays. However, numerous challenges still remained unsolved for large scale development. One such challenge in integrating a large phased array is the threat of grating lobes that are introduced by unavoidable disturbances to the periodic structure at the seams between mechanical sub-array modules. In particular, gaps in the ground plane may interrupt the natural currents between elements, leading to radiation from periodic sources that are spaced at regular distances that are typically many wavelengths apart. In order to quantify these grating lobe effects, an appropriate analysis framework and accurate model are of utmost importance. The model must capture all surface wave and mutual coupling between elements, and the analysis must have a clear formulation that allows for the calculation of worst-case grating lobe levels as well as differences in active reflection as a function of location within a sub-array. To accurately predict those effects, this dissertation work applied a modern method called Floquet framework, coupling with full wave solver to explore the grating lobe effects in infinite arrays of sub-arrays, with each physical sub-array potentially separated from the others by a gap or discontinuity in the ground plane. Calculations are then performed to extract active reflection coefficients and grating lobe levels from the resulting Floquet mode scattering parameters. Additionally, this Floquet framework is expanded from broadside to any scan angles in space. In the mathematical framework, the surface equivalence theorem based on Huygens’s equivalence principle is applied to authenticate its findings. From the simulation results, it is evident that the grating lobe amplitude level emerged to around 30 dB in the E-plane scan and E- plane grating lobes for a patch array. This is due to natural current disruption in between sub-arrays in the ground plane gap and it is very strong in the E-plane, leading to the potential for low-level grating lobe effects. The other planes and scan angles show less significant effects. It was found that the measurements qualitatively follow the simulated results. The Floquet-based method may therefore be used… Advisors/Committee Members: Fulton, Caleb (advisor), Remling, Christian (committee member), Bluestein, Howard (committee member), Goodman, Nathan (committee member), Sigmarsson, Hjalti (committee member), Ruyle, Jessica (committee member).

Subjects/Keywords: Scan blindness; Creeping waves; Cylindrical Electromagnetic Bandgap (EBG) structures; Floquet analysis; Grating lobe; MPAR; CPPAR; Phased array

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APA (6th Edition):

Bhowmik, L. M. (2019). Applications of Floquet Analysis to Modern Phased Array Antennas. (Doctoral Dissertation). University of Oklahoma. Retrieved from

Chicago Manual of Style (16th Edition):

Bhowmik, Lal Mohan. “Applications of Floquet Analysis to Modern Phased Array Antennas.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed February 27, 2021.

MLA Handbook (7th Edition):

Bhowmik, Lal Mohan. “Applications of Floquet Analysis to Modern Phased Array Antennas.” 2019. Web. 27 Feb 2021.


Bhowmik LM. Applications of Floquet Analysis to Modern Phased Array Antennas. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Feb 27]. Available from:

Council of Science Editors:

Bhowmik LM. Applications of Floquet Analysis to Modern Phased Array Antennas. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: