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This work discusses the design of a microstrip patch antenna and its use as an orientation-agnostic radiator in an origami-inspired folding antenna array. The antenna is based on a perturbed circular patch design that is impedance matched to reside in a radial feed network for a 2 × 2 array. This 2 × 2 array can be switched to provide sum and difference pattern behaviour. Both the feed network and the ground plane are modified to enable folding of the structure according to the Miura-ori pattern. The performance of a circularly polarised array is evaluated for a comprehensive range of fold angles to evaluate the impact of physical reconfiguration. Results for a simulated and fabricated circularly polarised array are provided for a 3 GHz design.

Design optimization of adaptive systems requires a robust analysis method that can accommodate various changes in design and boundary conditions. In this work, physics-informed neural networks (PINNs) are used to approximate solutions to differential equations across a range of problem parameter values. This mesh-free method simply requires residual evaluation at sampling points within the analysis domain and along boundaries, and the training process does not require any reference problem to be solved through conventional solution methods. The trained model can be used to predict the solution field, conduct parameter space analysis and design optimization. Using automatic differentiation, the design objective and their derivatives can be computed as a post process for a gradient-based design optimization. The method is demonstrated in a 1D heat transfer problem governed by the steady-state heat equation. Use of the PINN model for design optimization is illustrated in a problem of finding a material transition location to minimize temperature at a specified location. The PINN model that does not include problem parameters as input can be trained to within 0.05% error. PINN models that involve problem parameters as inputs are more difficult to train, especially when the input-to-output relationship is complex.

Origami, the art of paper folding, is a technologically transformative art with applications at many length scales from material microstructure design to space deployable structures. The transformation of a two-dimensional fold pattern to a three-dimensional structure makes origami a practical basis for deployability, light-weight materials, and self-actuation. In order to predict the complex motions of origami structures including path traversal of instabilities, accurate and efficient modeling techniques are required. While many approaches consider rigid facets and/or linear approximations to rotations, a truss and hinge finite element method is presented here within a global coordinate system framework to accurately capture the geometric nonlinearities while allowing for small to moderate facet deformation. Accurately capturing these modes of deformation is critical toward understanding the elastic energetic states required for design and analysis of multistable origami structures and mechanical metamaterials. Particular formulation developments that we address to solve origami mechanics problems include formulation of a continuous and differentiable fold angle, strategy for selecting fold path off the flat state, and integration of common numerical approaches important for origami (large rotation formulation, enforcement of periodic boundary conditions for tessellations, arc-length continuation method for solving highly nonlinear loading paths, and a perturbation strategy for handling bifurcations). After formulating this truss finite element method, we verify our modified finite element method on well-studied structures. The waterbomb fold pattern is studied, and the interplay of the stretching and folding energies are considered toward design of a bistable structure that exhibits a fold based snap-through instability. This study is followed by analysis of a cylindrical network of waterbombs (axial periodicity) that exhibits a stretch driven instability. Lastly, a tessellated square twist pattern, exhibiting multiple bifurcations off the flat state is presented that employs all aspects of our numerical method.

Filtering of electromagnetic signals is key for improved signal to noise ratios for a broad class of devices. However, maintaining filter performance in systems undergoing large changes in shape can be challenging, due to the interdependency between element geometry, orientation and lattice spacing. To address this challenge, an origami-based, reconfigurable spatial X-band filter with consistent frequency filtering is presented. Direct-write additive manufacturing is used to print metallic Archimedean spiral elements in a lattice on the substrate. Elements in the lattice couple to one another and this results in a frequency selective surface acting as a stop-band filter at a target frequency. The lattice is designed to maintain the filtered frequency through multiple fold angles. The combined design, modeling, fabrication, and experimental characterization results of this study provide a set of guidelines for future design of physically reconfigurable filters exhibiting sustained performance.

A machine learning algorithm that performs multifidelity domain decomposition is introduced. While the design of complex systems can be facilitated by numerical simulations, the determination of appropriate physics couplings and levels of model fidelity can be challenging. The proposed method automatically divides the computational domain into subregions and assigns required fidelity level, using a small number of high fidelity simulations to generate training data and low fidelity solutions as input data. Unsupervised and supervised machine learning algorithms are used to correlate features from low fidelity solutions to fidelity assignment. The effectiveness of the method is demonstrated in a problem of viscous fluid flow around a cylinder at Re ≈ 20. Ling et al. built physics-informed invariance and symmetry properties into machine learning models and demonstrated improved model generalizability. Along these lines, we avoid using problem dependent features such as coordinates of sample points, object geometry or flow conditions as explicit inputs to the machine learning model. Use of pointwise flow features generates large data sets from only one or two high fidelity simulations, and the fidelity predictor model achieved 99.5% accuracy at training points. The trained model was shown to be capable of predicting a fidelity map for a problem with an altered cylinder radius. A significant improvement in the prediction performance was seen when inputs are expanded to include multiscale features that incorporate neighborhood information.

Origami folding provides a novel method to transform two-dimensional (2D) sheets into complex functional structures. However, the enormity of the foldable design space necessitates development of algorithms to efficiently discover new origami fold patterns with specific performance objectives. To address this challenge, this work combines a recently developed efficient modified truss finite element model with a ground structure-based topology optimization framework. A nonlinear mechanics model is required to model the sequenced motion and large folding common in the actuation of origami structures. These highly nonlinear motions limit the ability to define convex objective functions, and parallelizable evolutionary optimization algorithms for traversing nonconvex origami design problems are developed and considered. The ability of this framework to discover fold topologies that maximize targeted actuation is verified for the well-known “Chomper” and “Square Twist” patterns. A simple twist-based design is also discovered using the verified framework. Through these case studies, the role of critical points and bifurcations emanating from sequenced deformation mechanisms (including interplay of folding, facet bending, and stretching) on design optimization is analyzed. In addition, the performance of both gradient and evolutionary optimization algorithms are explored, and genetic algorithms (GAs) consistently yield solutions with better performance given the apparent nonconvexity of the response-design space.

An origami design pattern is integrated to an active control system through camber morphing for vibration suppression and gust load alleviation in a typical wing section. Origami design parameters are optimized to have high sensitivity in chordwise fold angle and a maximum camber of 10% chord. A LQR controller is used to achieve the desired vibration suppression in a lightly damped aeroelastic system. The desired vibration suppression is achieved with change in camber of below 5% chord for an initial displacement condition induced vibration and less than 1% chord for gust excited vibration. Results also show that camber morphing is effective in suppressing vibration in both pitch and plunge degrees of freedom simultaneously.

Origami, as it moves from an art to a scientifically useful technology, enables a rich design space given the numerous bifurcations that exist off the flat state. In this work, we utilize origami as a platform for design of auxetic metamaterials and employ topology optimization for the automated robust discovery of these structures. In particular, the mechanical analysis is performed with an efficient and accurate nonlinear truss element model that captures the geometric nonlinearities associated with origami folding, and modal analysis off the flat state enables access to the many bifurcating branches of folding. Here, objective functions are explored that target a desired in-plane Poisson’s ratio. The Miura-ori fold pattern, a commonly studied flat-foldable pattern, is considered as a verification study for the framework presented.

This article introduces an origami-inspired passive morphing wing concept that is designed, analyzed and fabricated via a single analysis-oriented computational framework ensuring kinematic feasibility and path-uniqueness of a targeted motion. Supposing a notional in-plane wing morphing problem to provide perimeter boundary conditions, a fractal origami pattern that offers large in-plane strain while providing high out-of-plane stiffness is proposed as a supporting mechanism. To enable computational design and analysis of a complex origami pattern, a script-based multidisciplinary design and analysis computational tool, Computational Aircraft Prototype Synthesis (CAPS) is employed. A mathematical description of a fractal origami pattern is formulated to create the highly-symmetric, initial geometry. Then, a nonlinear structural analysis with a truss model is carried out to understand the evolving origami structure that promotes the desired wing shape change. CAPS is then employed to increase the geometric fidelity of the resultant shape by algorithmically converting the reconfigured origami structure from an infinitely-thin plate representation into a composite made of finitethickness plates and compliant hinges with multiple material assignments. A prototype of the final deformed design is fabricated in its maximally-compressed configuration using a multiple-material additive manufacturing technique, guaranteeing tensile loading over the operating domain, and thereby desired path uniqueness. The design, analysis and fabrication carried out in this work demonstrate the potential of using origami for morphing wings. More generally, the workflow developed for this study is demonstrated as a viable approach for multidisciplinary design and analysis of complex aircraft components.

Thermal management is a ubiquitous and critical engineering challenge for a broad range of applications, including combustion engines, high power electronics and chemical processing. However, conventional heat exchanger solutions are often static with limited ability to adaptively modulate heat transfer. Folding concepts from the ancient art form of origami could potentially address these challenges by providing large conducting surfaces that can also spatially reconfigure to regulate the flow and temperature field interactions with the heat transferring medium. In this study, trigonometric and nonlinear mechanical analysis techniques are applied to origami channel designs based on the “waterbomb” and Miura-ori unit cell to characterize the geometric properties of the structures as a function of folding. Both channels demonstrate a large range of flow control, with potentially enhanced mixing in the “waterbomb” channel, due to an axially varying cross-section. The results show promise for the use of origami-based heat exchanger designs for both improved passive and active control of heat transfer.

The ability of origami fold patterns to transform two-dimensional sheets into complex three-dimensional structures provides utility for design and development of multifunctional devices. Recently, a topology optimization framework has been developed to discover fold patterns that realize optimal performance including mechanical actuation. This work incorporates an efficient nonlinear mechanics model into the topology optimization framework that accurately captures the geometric non-linearities associated with large rotations of origami facets. A nonlinear truss model, with accommodation for fold stiffness and large rotations, is implemented in both gradient and non-gradient optimization algorithms in this study. The ability of this framework to discover fold topology maximizing actuation motion is verified for the well known “Chomper” and “Square Twist” patterns. In particular, the performance of various optimization algorithms is discussed, and genetic algorithms consistently yield solutions with better performance.

The physical reconfiguration and deployment of a 2×2 corporate-fed microstrip patch antenna array is investigated. The origami-inspired antenna array reconfigures structurally using a Miura-ori fold pattern to deploy to/from a compact folded state from/to a flat state. The impact of folding on the electromagnetic performance is evaluated across a range of physical states to study the impact of physical reconfiguration. In particular, the input impedance and beamforming capabilities are used to characterize the performance as a function of the primary folding parameter. These performance metrics are impacted by a feed network that extends across the folds and the beamforming capabilities that are impacted by the changing element spacing and orientation. Results from simulation and a fabricated structure are provided for a 2.4 GHz design.

Frequency tuning is investigated for a dipole-based frequency selective surface on a corrugated structure through origami folding. Three types of 1D folding patterns that alter the in-plane and out-of-plane element spacing at different rates are used to examine the frequency response in relation to spatial rearrangement. Folding decreases the in-plane spacing and leads to smaller Floquet periodicity lengths and a higher stop-band frequency. In some fold arrangements, folding increases the out-of-plane spacing and results in phase-shift and two distinct coupling modes.

A tunable miniaturized patch antenna is introduced. Miniaturization is achieved by placing a layer of complementary split-ring resonators horizontally between the radiating patch and the ground plane. Tuning is implemented by detouring the current flow on the additional layer through a lumped capacitor or varactor, thereby shifting the resonant frequency. The result is a miniaturized antenna that is compact, easily fabricated, and tunable across a useful band. A measured prototype demonstrates a tuning range of 2–2.45 GHz while maintaining an area no larger than 1/9 of a traditional patch antenna.

A technique for producing miniaturized tunable planar monopole antennas for wireless communication applications is introduced. Miniaturization is achieved by optimizing the geometry of a pixelated metallic patch surrounding the monopole antenna. Tuning of the antenna is implemented by varying the capacitance of a varactor diode loaded between the pixelated metallic patch and the ground plane. The result is an ultra-compact, dual band, folded monopole antenna that fits into a hemisphere of radius λ 0 /20 at 2.1 GHz. Varying the capacitance of the varactor diode enables the two resonance frequencies to be tuned simultaneously, covering multiple frequency bands for different wireless applications. A prototype antenna has been fabricated and measured, confirming the feasibility of the proposed design.

The efficient mapping between 2D and 3D spaces offered by origami facilitates the exploration of a vast design space of 3D reconfigurable devices. Many existing origami adaptations for engineering applications assume known folded geometries. However, “what to make” becomes a critical question for design problems where the intuition on the relationship between the geometry and function is limited. This article discusses a systematic design method for folding patterns used to tune electromagnetic performance. Radio frequency transmission characteristics of a frequency selective surface are investigated as an example. The fold stiffness distribution and the embedded actuator locations on a substrate are optimized using the sensitivity information obtained through the electromagnetic analysis in COMSOL. The optimal crease pattern and actuator distribution are used to fold a substrate hosting dipoles of known dimensions. Attaining a smooth optimization process proved to be challenging due to the high sensitivity of the FSS on the dipole orientations. A surrogate optimization problem is solved to achieve a resonant frequency tuning toward a target frequency.

Origami, the ancient art of paper folding, has recently garnered attention from the scientific community for its capacity for unique 2D – 3D shape change and programmable mechanical properties. Application areas of such properties include packaging, self-assembly, shock absorption and deployable structures. Recent studies have highlighted the role of the folded geometry to regulate the mechanical response of the origami structures, such as the increased compression stiffness of origami tubes or the tunable in-plane stiffness through select inversion of bi-stable fold vertices. In addition to geometric re-enforcement, the mechanical response of an origami structure can also be programmed through spatial patterning of the individual fold line stiffnesses. However, the coupling between the geometric and material stiffening design spaces for origami structures is poorly understood and design rules are needed to guide the use of material stiffening to enhance or mitigate a geometric stiffening effect. In this computational study, a modal analysis of a corrugated fold with varying degrees of pre-fold and different sets of fold stiffness distributions is evaluated to highlight the interaction between geometric and material stiffness mechanisms.

Origami devices have the ability to spatially reconfigure between 2D and 3D states through folding motions. The precise mapping of origami presents a novel method to spatially tune radio frequency (RF) devices, including adaptive antennas, sensors, reflectors, and frequency selective surfaces (FSSs). While conventional RF FSSs are designed based upon a planar distribution of conductive elements, this leaves the large design space of the out of plane dimension underutilized. We investigated this design regime through the computational study of four FSS origami tessellations with conductive dipoles. The dipole patterns showed increased resonance shift with decreased separation distances, with the separation in the direction orthogonal to the dipole orientations having a more significant effect. The coupling mechanisms between dipole neighbours were evaluated by comparing surface charge densities, which revealed the gain and loss of coupling as the dipoles moved in and out of alignment via folding. Collectively, these results provide a basis of origami FSS designs for experimental study and motivates the development of computational tools to systematically predict optimal fold patterns for targeted frequency response and directionality.

Reconfigurable structures based on origami design are useful for multifunctional applications, such as deployable shelters, solar array packaging, and tunable antennas. Origami provides a framework to decompose a complex 2D to 3D transformation into a series of folding operations about predetermined foldlines. Recent optimization toolsets have begun to enable a systematic search of the design space to optimize not only geometry but also mechanical performance criteria as well. However, selecting optimal fold patterns for large folding operations is challenging as geometric nonlinearity influences fold choice throughout the evolution. The present work investigates strategies for design optimization to incorporate the current and future configurations of the structure in the performance evaluation. An optimization method, combined with finite-element analysis, is used to distribute mechanical properties within an initially flat structure to determine optimal crease patterns to achieve desired motions. Out-of-plane and twist displacement objectives are used in three examples. The influence of load increment and geometric nonlinearity on the choice of crease patterns is studied, and appropriate optimization strategies are discussed.

A new design methodology for producing highly miniaturized patch antennas is introduced. The methodology uses complementary split-ring resonators placed horizontally between the patch and the ground plane. By optimizing the geometry of the split rings, sub-wavelength resonance of the patch antenna can be achieved with a good impedance match and radiation characteristics comparable to those of a traditional patch antenna on a finite ground plane. Construction of the optimized antenna is straightforward, requiring only the sandwiching of two etched circuit boards. High levels of miniaturization are demonstrated through simulations and experiments, with reductions of a factor of more than four in transverse dimension achieved for a circular patch resonant at 2.45 GHz. Although miniaturization is accompanied by a decrease in antenna radiation efficiency and a loss of fractional bandwidth, antenna performance remains acceptable even for a 1/16 reduction in patch area.

Fold-driven reconfigurable devices have a potential to expand functional spaces beyond traditional adaptive wave propagation strategies. In particular, designs inspired by the art of origami leverage the mathematics of origami to map designs defined on two-dimensional surfaces to complex three-dimensional shapes. The design space in this paradigm is vast, so a systematic method is needed to design a device that achieves its goal. In our initial effort, we surveyed electromagnetic wave propagation properties of foldable frequency selective surfaces (FSS) and foldable and deployable antennas based on various known origami designs to identify a number of working principles of functional tuning. We incorporated these findings in the implementation of a design method that finds an origami FSS pattern that achieves the desired frequency tuning. This method is adopted from density-based topology optimization, with a notion that anything functional could be described through a distribution of an effective density of the relevant material property. A substrate is “patterned” with foldable segments parameterized through torsional springs; electromagnetically relevant conductive patterns are described as predefined surfaces that remain unchanged. This talk will discuss the lessons learned from our investigations and remaining challenges of designing fold-driven reconfigurable devices for wave propagation control.

A topology optimization method is used to design two dimensional periodic structures with desirable transmission properties by distributing two materials of different permittivity over a rectangular representative cell. A plane wave expansion of the electric field at the input and output boundaries is used in the analysis. This allows non-homogeneous material distributions near the boundaries. Numerical examples are used to verify the robustness of the method and to investigate the importance of retaining higher modes in the expansions. It is found that the optimization problem typically admits possibly many local optima and the relevance of higher modes depends on the nature of the solution found. In some instances, higher modes play an important role and using only the dominant mode in the analysis is shown to result in errors in the evaluation of the performance of the design.

A new methodology for designing metamaterial-inspired antennas using an in situ optimization technique is introduced. Through this approach, an optimization tool such as a genetic algorithm is used to design a metamaterial pattern adjacent to an antenna to enhance the antenna's performance. As an example, the technique is used for miniaturization purposes where a loop antenna initially resonant at 2.45 GHz is made resonant at 960 MHz, providing a sevenfold reduction in antenna area over a conventional loop designed to operate at 960 MHz.

Aligned liquid crystal elastomers (LCEs) are capable of undergoing large reversible shape change in response to thermal stimuli and may act as actuators for many potential applications such as self-assembly and deployment of micro devices. Recent advances in LCE patterning tools have demonstrated sub-millimetre control of director orientation, enabling the preparation of materials with arbitrarily complex director fields. However, without design tools to connect the 2D director pattern with the activated 3D shape, LCE design relies on intuition and trial and error. Here we present a design methodology to generate reliable folding in monolithic LCEs designed with topology optimization. The distributions of order/disorder and director orientations are optimized so that the remotely actuated deformation closely matches a target deformation for origami folding. The optimal design exhibits a strategy to counteract the mechanical frustration that may lead to an undesirable deformation, such as anti-clastic bending. Multi-hinge networks were developed using insights from the optimal hinge designs and were demonstrated through the fabrication and reversible actuation of a self-folding box. Topology optimization provides an important step towards leveraging the opportunities afforded by LCE patterning into functional designs.

Reconfigurable structures based on origami design are useful for multi-functional applications, such as deployable shelters, solar array packaging, and tunable antennas. Origami provides a framework to decompose a complex 2D to 3D transformation into a series of folding operations about predetermined fold lines. Recent optimization toolsets have begun to enable a systematic search of the design space to not only optimize geometry, but mechanical performance criteria as well. However, selecting optimum fold patterns for large folding operations is challenging as geometric nonlinearity influences fold choice throughout the evolution. The present work investigates strategies for design optimization to incorporate the current and future configurations of the structure in the performance evaluation. An optimization method, combined with finite element analysis, is used to distribute mechanical properties within an initially flat structure to determine optimal crease patterns to achieve desired motions. Out-of-plane and twist displacement objectives are used in three examples. The influence of load increment and geometric nonlinearity on the choice of crease patterns is studied and appropriate optimization strategies are discussed.Copyright © 2015 by ASME

Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form of the structure and show potential for many engineering applications. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics place a severe limitation on design strategies based on intuition. The presented work proposes a systematic design method using topology optimization to distribute foldline properties within a reference crease pattern, adding or removing folds through optimization, for a mechanism design. Optimization techniques and mechanical analysis are co-utilized to identify an action origami building block and determine the optimal network connectivity between multiple actuators. Foldable structures are modeled as pin-joint truss structures with additional constraints on fold, or dihedral, angles. A continuous tuning of foldline stiffness leads to a rigid-to-compliant transformation of the local foldline property, the combination of which results in origami crease design optimization. The performance of a designed origami mechanism is evaluated in 3D by applying prescribed forces and finding displacements at set locations. A constraint on the number of foldlines is used to tune design complexity, highlighting the value-add of an optimization approach. Together, these results underscore that the optimization of function, in addition to shape, is a promising approach to origami design and motivates the further development of function-based origami design tools.

A foldable frequency selective surface (FSS) is introduced that may be tuned by changing the folding state. The FSS comprises periodic elements arranged in an origami-like fashion on a dielectric sheet. By folding and unfolding the FSS, the interaction with the incident field and the mutual interactions between the elements may be altered, resulting in a shift in resonance frequency. A sample design of a tunable FSS folded into a chevron pattern and decorated with cross-shaped copper prints allows a 19% shift of resonant frequency with a change in folding angle of 60°.

Liquid crystal polymer networks (LCNs) have unique advantages as potential constituents of origami-based smart materials due to their reversible actuations and availability of fabrication techniques to create complex strain fields. Although identifying functional designs is crucial in making use of this technology, conventional approaches have largely consisted of trial-and-error experimentation. We introduce an inverse design procedure based on a topology optimization method to map out an LCN pattern with a desired spontaneous strain field to achieve prescribed shapes. In this study, we focus on a target deformation of a film to create an improved hinge to be integrated into an origami structure. Our preliminary results indicate the potential of using computational tools to determine what designs yield desired functionalities and how to best pattern LCN films to achieve them.Copyright © 2014 by ASME

Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form of the structure and show potential for many engineering applications. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics place a severe limitation on design strategies based on intuition. The presented work proposes a systematic design method using topology optimization to distribute foldline properties within a reference crease pattern, adding or removing folds through optimization, for a mechanism design. Following the work of Schenk and Guest, foldable structures are modeled as pin-joint truss structures with additional constraints on fold, or dihedral, angles. The performance of a designed origami mechanism is evaluated in 3D by applying prescribed forces and finding displacements at set locations. The integration of the concept of origami in mechanism design thus allows for the description of designs in 2D and performance in 3D. Numerical examples indicate that origami mechanisms with desired deformations can be obtained using the proposed method. A constraint on the number of foldlines is used to simplify a design.Copyright © 2014 by ASME

The rapid growth of the market for wireless communication devices demands more flexibility in coordinating different wireless standards and devices while maintaining a small device profile. This has produced a need for compact antennas with frequency tunability across multiple operating bands. Many techniques have been developed to produce miniaturized antennas, including the use of slots and high-permittivity dielectrics. At the same time, techniques for producing tunable multi-band antennas have been devised. These include the loading of a multi-resonance structure, such as a multi-branch monopole or a planar inverted F antenna, with varactor diodes. However, such tuning techniques typically result in limited size reduction or increased manufacturing complexity.

An origami design method based on topology optimization is introduced. The design of a folding pattern is cast as a problem of assigning presence and type of fold to lines in a “ground structure,” using folding angles as design variables. A ground structure for origami design has lines drawn on a two dimensional domain, showing all line segments that may appear as crease lines in the folded geometry. For a given ground structure and folding angles, the 3D geometry of the folded sheet can be computed using the mathematics of origami. A topology optimization method is then used to find an optimal combination of folding angles, which results in a folding pattern with desired, target geometric properties.

Summary form only given. The recent rapidly growing markets of mobile handsets and computers demand packing more and more functionality into smaller devices. As a result, the need for compact antennas to cover multiple wireless communications frequency bands has increased dramatically. Typical solutions to miniaturize the size of an antenna require the use of slots or high-permittivity dielectrics, and methods of introducing extra circuits or special substrates to tune the resonance frequency have been commonly adopted. These techniques, however, suffer from limited size reduction, increased manufacturing complexity, and high overall cost. In this paper, a technique to create highly-miniaturized and tunable metamaterialinspired patch antennas is proposed. The miniaturization is achieved by loading a circular resonant disk parallel to the radiating patch (Ouedraogo et al., IEEE Trans. AP, vol.60, no.5, 2012). The structure on the resonant disk is optimized to form specific complimentary slots. Full wave simulations using HFSS have been conducted to assess the performance of the antenna and initial results have demonstrated that placing lumped components such as capacitors across a certain region on the complementary slot will alter the coupling between the slots and thus tune the resonance frequency of the circular patch. In light of this, it is proposed that the resonance frequency of the miniaturized antenna can be continuously tuned by replacing a properly chosen capacitor with a single varactor diode. This has been investigated in simulations, but it remains to be demonstrated in practice. A prototype circular patch antenna that contains both a resonant disk and a varactor diode is fabricated and measured to demonstrate the feasibility of the proposed design. By choosing a proper varactor diode and supplying an appropriate range of voltages, a patch antenna miniaturized to 1/16 its original surface area can be tuned from its initial operating frequency of 2.4GHz across a 50% tuning range. The radiation patterns and efficiency of the antenna will also be measured and compared with simulations and with the unloaded prototype.

A methodology based on combining topology optimization with a design in place procedure for metamaterial structures suitable for integrated antenna applications is presented. By optimizing the geometry of a pixelated area surrounding an antenna, it is shown that high levels of miniaturization of the antenna can be achieved while maintaining a high eciency. As an example, the methodology is used to design an ultra compact folded monopole antenna that ts into a hemisphere of radius 5.2 mm, or approximately one twentieth of a wavelength at 2.45 GHz, with an eciency above 80

The transmission characteristics of a folded surface decorated with a periodic arrangement of split-ring resonators is investigated. The folding pattern has one displacement degree of freedom, allowing motion that can be used to adjust the separation between the rings. When the geometry of the folded surface is varied by mechanical means, the change in spacing between the rings causes a shift in resonance frequency, making the surface mechanically tunable.