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Donovan Brocker, Ph.D. - Milwaukee School of Engineering. Milwaukee, WI, US

Donovan Brocker, Ph.D.

Associate Professor | Milwaukee School of Engineering


Dr. Donovan Brocker’s areas of expertise include applied electromagnetics, antennas, and frequency selective surfaces.

Education, Licensure and Certification (2)

Ph.D.: Electrical Engineering, Penn State University 2016

B.S.: Electrical Engineering, University of Wisconsin-Milwaukee 2010

Minor in Physics


Dr. Donovan Brocker joined the MSOE faculty in 2019. He teaches courses in linear circuits, analog electronics, and electromagnetics. He previously was an assistant research professor at the Pennsylvania State University.

Areas of Expertise (3)


Frequency Selective Surfaces



Selected Publications (12)

Integration of a Generalized Ratio of Polynomials


Brandsema, M. J., Brocker, D. E.

2021 This paper provides a closed-form solution to the indefinite integral of a ratio of generalized polynomials where the denominator polynomial is raised to the general order r∈Z+. Such an integral arises in physics and engineering, the solution of which allows for closed-form analysis.

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Wideband Single-Layer FSS-Based Electromagnetic Absorber Using Complementary Susceptances

2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting

Brocker, D.E., Panaretos, A.H., Werner, D.H.,

2020 This paper investigates the circuit model of an electromagnetic absorber based on a single-layer frequency-selective surface exhibiting a thin profile and broadband absorption. The circuit model is decomposed into series and parallel susceptances, which are then made complementary near ω0 in an effort to maximize bandwidth. As a result, a versatile design strategy is developed with only three input dependencies: mean absorption frequency ω0, desired absorption magnitude, and desired absorber thickness t. The required circuit values can be directly defined in terms of these three design specifications.

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Circuit model for single-layer single-resonant ultra-thin FSS absorbers with wide bandwidth

IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting

Brocker, D.E., Panaretos, A.H., Werner, D.H.

2017 Electromagnetic absorbers based on frequency-selective surfaces have been explored for many applications. It is often useful to represent these devices using a circuit equivalence, which provides a physical insight into underlying performance capabilities and limitations. Yet, absorbers tend to deviate from their ideal circuit representations for ultra-thin implementations where coupling between layers becomes significant. To date, there has been little investigation into the corrective measures required to compensate for parasitic coupling associated with ultra-thin absorbers. In the paper, a circuit model is proposed for a broadband absorber comprised of a single-resonance FSS cascaded with a PEC-backed substrate. The thin nature of the absorber is shown to introduce undesirable coupling between the FSS and PEC layers, resulting in non-ideal performance. Two corrective measures are outlined with the goal of retuning the absorber for maximum bandwidth.

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Miniaturized Dual-Band Folded Patch Antenna With Independent Band Control Utilizing an Interdigitated Slot Loading

IEEE Transactions on Antennas and Propagation

Brocker, D.E., Jiang, Z.H., Gregory, M.D., Werner, D.H.

2016 A compact linearly polarized dual-band patch antenna with low cross-polarization and independent band control is presented. Miniaturization was achieved through a combination of shorting, subsequently folding, and by replacing the standard slot loading with a slot that is featured by a meander line. By replacing the standard straight slot with an interdigitated slot loading, the resonance condition was shifted to the lower operating band, facilitating significant antenna miniaturization and resulting in an element size equal to or smaller than 0.1λ 0 in all three dimensions. The antenna design procedure is outlined and a prototype for WiFi applications was fabricated and measured for impedance matching, radiation pattern, and broadside gain. A simulated parametric analysis was performed on the interdigitated slot geometry to determine how the antenna performance is controlled. Then, based on the parametric analysis, it was further demonstrated that the two operational bands of the antenna element could be independently controlled by changing only the geometrical dimensions of the interdigitated slot, leaving the base of the antenna entirely unaltered. As a result, the lower operating band could be fixed while the upper operating band could be shifted by up to 10%. Lastly, the effect of utilizing a small ground plane, in an effort to achieve a small antenna footprint, is discussed.

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Transformation optics-inspired dispersion-corrected gradient-index lens design

IEEE International Symposium on Antennas and Propagation (APSURSI)

Brocker, D.E., Campbell, S.D., Nagar, J., Werner, D.H.

2016 Transformation optics is applied to interpret the dispersive nature of materials via changes in geometry, providing an alternative methodology for dispersion correction. An example is proposed and analyzed to demonstrate the effectiveness of the proposed technique.

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A new GRIN lens design paradigm based on wavefront matching

IEEE International Symposium on Antennas and Propagation (APSURSI)

Nagar, J., Campbell, S.D., Brocker, D.E., Easum, J.A., Werner, D.H.

2016 GRadient INdex (GRIN) optics has revolutionized the field of lens design by providing an unparalleled amount of design freedom, resulting in high-performance optical systems. Unfortunately, this design freedom leads to a large number of parameters in multi-element systems, since the GRIN distributions need to be described in addition to the lens geometries. This can lead to slow convergence and stagnation for even the most robust numerical optimizers. This paper proposes a modular, black-box design paradigm which allows for the optimization of each element in the system independently. This leads to an efficient strategy to design all-GRIN systems from scratch, or to replace existing homogeneous doublets and triplets in a system with GRIN singlets.

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SWaP tradeoffs in the solution space of a hybrid radial-axial achromatic GRIN singlet

IEEE International Symposium on Antennas and Propagation (APSURSI)

Campbell, S.D., Brocker, D.E., Nagar, J., Werner, D.H.

2016 A radial-axial hybrid GRIN theory is developed in order to explore the solution space of an achromatic GRIN singlet. With the achromatic hybrid GRIN theory in hand, the tradeoffs between thickness, curvature, and GRIN type can be directly studied in the context of SWaP (size, weight, and power) reduction. Finally, the achromatic solution space of a Silicon-Germanium based material system is explored.

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Efficient modeling of the coupling from a small circular loop to a multi-conductor transmission line above a lossy ground Publisher

IEEE International Symposium on Antennas and Propagation (APSURSI)

Qin, Y., Brocker, D.E., Werner, P.L., Werner, D.H., Zhou, C.

2016 A low-frequency coupling model consisting of a multi-conductor transmission line (TL) system and a small circular loop antenna is presented. The TL system is composed of N perfect electrical conductor (PEC) wires above a lossy ground. An approximate and computationally efficient analytical method is proposed to predict the current distribution on each wire. The total electromagnetic (EM) fields produced by the small circular loop antenna above the lossy half-space are calculated by employing a discrete complex image method (DCIM). The resulting induced current distributions are subsequently calculated and validated with a commercially available moment method code.

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An analytical design methodology for dispersion-corrected metamaterial lenses

IEEE International Symposium on Antennas and Propagation (APSURSI)

Brocker, D.E., Campbell, S.D., Werner, D.H., Werner, P.L.

2016 An analytical method based on paraxial ray-tracing equations is proposed for designing gradient-index (GRIN) metamaterial lenses with dispersion-correction. An instructive example is considered to demonstrate the effectiveness.

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Efficient modeling of a small circular loop coupling to multi-conductor transmission lines above a PEC ground

IEEE International Symposium on Antennas and Propagation (APSURSI)

Qin, Y., Brocker, D.E., Werner, P.L., Werner, D.H., Zhou, C.

2016 A low-frequency coupling model from a small circular loop antenna to a multi-conductor transmission line (TL) system composed of N perfect electric conductor (PEC) wires above a PEC ground is presented. The telegrapher's equations for the model are presented, and a computationally efficient analytical solution for the induced current distributions is formulated for each wire. An example is constructed in FEKO and the induced currents are compared with the proposed method, showing excellent agreement.

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Simulation and Measurement of Medium-Frequency Signals Coupling From a Line to a Loop Antenna

IEEE Transactions on Industry Applications

Damiano, N.W., Li, J., Zhou, C., Brocker, D.E., Qin, Y., Werner, D.H., Werner, P.L.

2016 The underground-mining environment can affect radio-signal propagation in various ways. Understanding these effects is especially critical in evaluating communications systems used during normal mining operations and during mine emergencies. One of these types of communications systems relies on medium-frequency (MF) radio frequencies. This paper presents the simulation and measurement results of recent National Institute for Occupational Safety and Health (NIOSH) research aimed at investigating MF coupling between a transmission line (TL) and a loop antenna in an underground coal mine. Two different types of measurements were completed: 1) line-current distribution and 2) line-to-antenna coupling. Measurements were taken underground in an experimental coal mine and on a specially designed surface test area. The results of these tests are characterized by current along a TL and voltage induced in the loop from a line. This paper concludes with a discussion of issues for MF TLs. These include electromagnetic fields at the ends of the TL, connection of the ends of the TL, the effect of other conductors underground, and the proximity of coal or earth. These results could help operators by providing examples of these challenges that may be experienced underground and a method by which to measure voltage induced by a line.

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Three-dimensional gradient-index optics via injketaided additive manufacturing techniques

IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting

Campbell, S.D., Brocker, D.E., Werner, D.H., Dupuy, C., Park, S.K., Harmon, P.

2015 The ability to correct for monochromatic aberrations without the need for complex geometry has made gradient-index optics an attractive area of research, but manufacturing challenges have limited their application to a select few areas. In this study, a novel method for fabricating gradient-index lenses using inkjet solid free form three-dimensional printed optical polymers is proposed. A flat gradient-index lens based on the fabrication constraints is optimized using a powerful customized design synthesis tool. Cross-sectional views of its continuous index profile and a representative binary pixel-map are shown.

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