A Tunable Spherical Cap Microfluidic Electrically Small Antenna
Article first published online: 18 APR 2013
Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Volume 9, Issue 19, pages 3230–3234, October 11, 2013
How to Cite
Jobs, M., Hjort, K., Rydberg, A. and Wu, Z. (2013), A Tunable Spherical Cap Microfluidic Electrically Small Antenna. Small, 9: 3230–3234. doi: 10.1002/smll.201300070
- Issue published online: 4 OCT 2013
- Article first published online: 18 APR 2013
- Manuscript Revised: 12 MAR 2013
- Manuscript Received: 8 JAN 2013
- elastic electronics;
- microfluidic electronics;
- electrically small antenna;
- tunable antenna
We present a novel microfluidic three-dimensional electrically small antenna (ESA). It is easy to construct simply by pneumatically inflating a planar stretchable liquid alloy microfluidic antenna into a spherical cap. Its center frequency is tuned when it is inflated; demonstrating combined high efficiency and a wide tunable frequency range around its hemispherical shape.
In recent decades wireless electronics has witnessed a rapid advance in performance as well as miniaturization and now benefits from much smaller components with higher performance, more compact size and lower energy consumption. This has put great pressure on the miniaturization of antennas as well. Hence, high efficiency ESAs are attracting great attention both from academia and industry.1, 2
However, ESAs generally suffer from low efficiency since the losses in the antenna dominate over the radiation resistance as well as exhibiting very narrow bandwidths.3–5 These may require resistive loading to achieve the required bandwidth that lowers the efficiency even further. The minimum bandwidth (BW) requirements of an antenna is ultimately limited by the data rate and modulation used. At the same time, high antenna efficiency is needed, for maximizing the transmitted and received power. In order to obtain high efficiency, all resistances apart from radiation resistance must be minimized. The radiation resistance is reduced as the physical size of the antenna decreases. Therefore, the antenna becomes inherently more narrow-banded if both the size is reduced and high efficiency is maintained. In conclusion, due to the narrow-banded nature of ESAs, their performance becomes very sensitive to detuning of the central working frequency.
At a given frequency, f, the BW has its inverse in the quality factor (Q, the ratio of energy stored to power lost):
By approximating an antenna as a single resistor-inductor-capacitor (RLC) circuit, and based on the work of Chu, McLean predicted the minimum possible quality factor for a given fixed spherical antenna volume and linear polarization3, 4 to be:
where k = 2πf/c (c is the speed of light) and a is the radius of the minimum sphere encapsulating the entire antenna volume. Hence, the BW sets the minimum radius a for the antenna volume.
A way to overcome the problem of narrow bandwidth and reduced efficiency is to efficiently make use of the volume that the antenna occupies within the Chu-sphere. By increasing the occupied volume within the Chu-sphere the unloaded antenna Q-value can be reduced (approx. loaded Q divided by efficiency, i.e. Q/η), which improves efficiency at a certain bandwidth. The surface of a spherical antenna covers the entire surface of the Chu-sphere and as such it provides a very efficient way of minimizing the Q-value of the antenna. Because of this, spherical antennas perform very well as ESAs.5 However, hemispherical helix antennas provide a better base for practical antenna designs since the presence of a ground plane makes the antennas less sensitive to nearby coupling structures when applied in a real-world environment. The efficiency of hemispherical antennas has been shown to be close to that of a spherical antenna of the same radius.6 It should be noted, however, that the mandatory presence of a ground plane for any hemispherical helix antennas carries surface currents below and around the helix structure, thus making the exact limit of the radiating structures harder to define, and implying that the actual Chu-radius is slightly larger than the radius of the helical coil. The difficulty of defining an exact value puts a small ambiguity in the calculated Chu-limit for the antenna structure and as such it is important to point out the definition of the estimated Chu-radius for the calculated theoretical minimum Q-values.7
Small hemispherical ESAs demand advanced microfabrication. Recent advances in microfabrication now allow for novel ways to fabricate hemispherical ESAs at sizes down to 13 mm of radius,8 being good examples of the constant evolution of hemispherical helix antennas. However, all these hemispherical ESAs can only work at a fixed frequency and suffer from their narrow BW. One solution is to provide a small spherical cap ESA that can mechanically tune its central working frequency. In this work, we demonstrate a horizontally aligned spherical cap helix antenna that is tunable over a wide range of frequency, Figure 1, combining pneumatic tuning with recently proposed microfluidic antenna technology.9 The antenna presents a perfect spherical cap that can be continuously shaped from a planar antenna to a hemispherical antenna, and beyond. With simple fabrication, we obtain a 3D ESA that can work with great efficiency over a wide frequency range around its optimal hemispherical shape.
In our design, a stretchable substrate with the proposed horizontal spherical helix antenna is mounted over a rigid planar ground plane with a microstrip coupled feed to both antenna arms, Figure 1(b). Having an electromagnetically (non-galvanic) coupled feed to the microfluidic antenna reduces the risk of fabrication defects in the soft tunable part due to excessive heating during soldering, and simplifies the fabrication process greatly. The tunable part, a silicone foil with the liquid alloy antenna inside it, is held in place by an FR4 ring with nylon screws (Figure S1), providing an airtight and solder-free antenna integration. The stretchable antenna structure is inflated from underneath to create a spherical cap, with the exact antenna shape determined by the antenna pattern and the air-pressure induced underneath the substrate. By varying the compartment pressure, the antenna geometry is shaped, providing a mechanically tunable ESA structure, Figure 1(b,c). The pneumatic control makes the device slow, with response times in the order of a second. In addition, the stretchable substrate is permeable, which implies continuous pneumatic control.
When designing the proposed antenna structure, its shape can be predicted based on the minimization of the surface area of an enclosed volume. This allows the antenna structure to be fabricated and projected onto a planar stretchable foil that, when inflated, compliantly achieves the desired spherical cap. The antenna is modeled both as a perfect (PEC) structure and with losses included; resonance frequency, radiation pattern and efficiency were simulated. For more details, see the Supplementary Information.
The Wheeler Cap method was used to measure the antenna efficiency. Using a conducting cap with a radius corresponding to the limit of the reactive near field region, the antenna radiation losses could be separated from the total loss and the efficiency (η) calculated, Table 1. As can be seen in Table 1, the maximum measured efficiency was for an inflation height of 24 mm, which corresponds to a slightly overinflated structure. The main reason for obtaining the highest efficiency for this inflation relates to the fact that a larger antenna structure will experience higher radiation resistance in comparison with the radiated power. At an inflation of 24 mm, the largest radiating structure is obtained and as such the corresponding efficiency is also maximized.
|Height [mm]||Freq. [MHz]||S11 [dB]||BW [MHz]||Corr. [dB]||FBW [MHz]||Q||η -Meas.||ka||QChu, est||Q/η|
The pneumatic tuning provides a tunable range of the central frequency of 116 MHz: The measured bandwidth within the tunable range goes from 8 to 19 MHz for 426 and 542 MHz and the reflection coefficient was −25.6 dB and −6.5 dB, respectively. However, the efficiency is only high when the antenna cap is close to hemispherical. A drastic reduction is seen already when it is inflated 15 mm with a central frequency at 493 MHz. Still, the five higher inflation points provide a high efficiency tunable bandwidth of 14.4% (12.4% tunable range and 2% bandwidth at the endpoints), as compared to the stationary bandwidth of 2.4%. The antenna is reversible, i.e. when its shape is inflated again after unloading we get the same frequency for a specified height. In a series of 500 repetitions with an inflation cycle between 5 and 20 mm, the variation was always below 1%, Figure S4. However, after unloading, the antenna cannot retrieve a perfect planar shape.
The measured reflection coefficient for the tunable antenna is shown in Figure 2, while radiation characteristics are summarized in Table 1. Both the theoretical Q-value based on Chu's work3 and the measured Q-value divided by the efficiency (Q/η) were tabulated. The latter was included to validate the measured results, using the efficiency of the antenna to calculate the unloaded Q-value that should approach the Chu-limit. The tabulated values of Q/η indicate that the proposed structure, when compensated for efficiency, approaches the Chu-limit for the hemispherical or nearly hemispherical cap. As was previously mentioned, the proximity of the ground plane makes the exact limit of the radius of the Chu-sphere difficult to define, which introduces a small ambiguity in the calculated Chu-values. Based on simulation results, the ground current distribution beneath the hemispherical structure was estimated to cover an area of 22 mm in radius. The calculated minimum Q-value based on the Chu-limit is based on a linear polarized antenna. If the manufactured antenna is not perfectly linearly polarized the measured Q-value could be lowered. The theoretical minimal Q-value for a dual polarized antenna is roughly half of the linear case.
The measured Q-values are much lower than the theoretical values from the perfect (PEC) antenna model, Figure 3, clearly indicating losses in the structure. The presence of material losses implies that the actual measured Q-values correspond to the loaded Q-values. As the Q-value describes the ratio between the average energy stored in the reactive nearfield of the antenna and the energy lost per unit of time it is important to emphasize the difference between the measured Q for a lossless and a lossy structure. The measured Q as seen in Table 1 includes structure losses and needs to be adjusted to include the efficiency before a comparison between the Q-value for a structure without losses given by Chu can be made. The adjusted Q can be seen in Table 1 as Q/η. The losses present in the structure are contributed to three parameters: conductor losses, dielectric losses and coupling mismatch between the feed-line and losses due to finite conductivity structure. As stated earlier, the radiation resistance is reduced as the physical size of the antenna decreases. This means that for a smaller antenna the losses and both dielectric and conductors become larger as compared to the radiation resistances, thus lowering the total efficiency. When using a liquid alloy the cross-section of the coil should be increased and a higher-grade dielectric material in the rigid carrier and elastomer should be chosen to further enhance the performance. When available, a higher conductivity material for the coil should be used. Finally, fine tuning of the vertical distance between the feed-line and the antenna structure is likely to somewhat improve coupling and hence the Q-value. When comparing ESA of different sizes and frequencies, the major metrics used are the efficiency, bandwidth and reflection coefficient for the given electrical size of the antenna. The electrical size can be described by the ka factor given in (2), which relates the physical size to the operating frequency, thus giving a metric electrical size of the device. This allows comparison of ESAs with varying physical size but with similar obtained ka factors. When comparing the proposed antenna design with previously published articles,6, 8 the obtained performance for the given ka factor can be considered good.
The radiation pattern of the measured microfluidic antenna can be seen in Figure 4, together with the simulated radiation pattern. The measured radiation pattern shows good correspondence with the simulated one, the major exception being a null at Phi = 280 ° when measuring the cross-polarization. The measured null location corresponds well with antenna feed and cables connecting to the Antenna Under Test (AUT) and given that the cables lies orthogonal to the x-y plane, this further strengthen the assumption that cable effects are responsible. In order to reduce cable effect, a large ground plane was used. However, the SubMiniature version A (SMA) connector from the back of the ground plane protruded slightly at the feed. The measured results indicate a strong co-polarization, corresponding well with simulations and that of a theoretical infinitesimal electric dipole directed along the z-axis. The measured radiation pattern of the antenna showed an average 10 dB difference between co- and cross-polarization, corresponding well with simulations and validating the assumption that the calculated minimum Q-value should be based on the linearly polarized case. This radiation pattern corresponds well with the results obtained by similar helix antenna designs by others.6
The radiation patterns show that the basic antenna structure of a coupled hemispherical helix antenna placed on a conducting ground plane is suitable for applications that require the antenna to be insensitive to the material on which the antenna is placed. This is a key parameter for an ESA since the narrow bandwidth makes any detuning due to coupling to nearby structures drastically decrease the total performance of the antenna.
In summary, we have demonstrated a highly efficient electrically small antenna that counters its small bandwidth by being pneumatically tunable over a large frequency range (12.4% of its center frequency). The microstrip fed coupling from the rigid plane carrier to the spherical cap microfluidic stretchable antenna provides solder-free mounting and provides robust and low-cost fabrication. Potential applications for this antenna involve systems that require small physical dimension with high efficiency and a wide frequency range.
Fabrication of the Microfluidic Tunable Antenna: In principle, the Ecoflex elastomer has higher stretchability than the commonly used PDMS (Wacker Elastosil RT601 or Dow Corning Sylgard 184). If it was only for the high stretchability, it would be better to use it by itself. However, due to poor adhesion it is difficult to bond Ecoflex foils together after they are cured. Hence, since the commonly used PDMS materials easily bond after plasma treatment a bilayer foil of the two elastomers was made to solve this issue. The fabrication of the bilayer foil was adapted from a previous protocol curing layers of PDMS9 with the highly stretchable silicone.10, 11 The helix design was transferred from an SU-8 master on a 4-inch wafer, giving an average microfluidic channel cross-section of 500 × 75 μm2. A 10:1 mixed common PDMS (Elastosil RT601A and B, Wacker Chemie, Munich, Germany) was spun onto the silicon master at 1000 rpm for 45 s and half-cured on a hotplate set as 65 °C for 2 minutes. Afterwards, twice a mixed siloxane (Ecoflex 00-30, Smooth-on, Easton PA) kit (mixed ratio 1:1) was spun on the master at 500 rpm 45 s and half-cured. The microstructured silicone bilayer foil was fully cured by leaving it on its master in the laboratory ambience for half a day, after which it had a final thickness of around 550 μm. Another silicone bilayer foil was prepared using the same protocol on a blank silicon wafer as master. The silicone replica with structures was peeled off from its master and punched with two holes (using a flat syringe needle, gauge 22) at the two ends of the helix. After cleaning, the two silicone foils were bonded together using a corona discharger (ETP BD50, Chicago, IL) and stabilized in a 70 °C oven for 10 min. Then the liquid alloy (Galinstan, Geratherm Medical AG, Germany) was injected into the microfluidic channel network in the silicone with a syringe. Dispensing a drop of mixed siloxane to seal the hole and curing in the oven for a quarter of an hour finished the fabrication process for the tunable part of the antenna.
The tunable structure was fitted on a 1 mm FR4 substrate incorporating a 35 μm thick copper ground plane and a microstrip feed-line, which had been machined by a PCB milling machine (LPKF, Garbsen, Germany). The structure was attached to the FR4 substrate by using an FR4 ring held in place by nylon screws (M3 × 16 mm). The ring fixture was designed with an inner radius of 21 mm. The antenna was inflated by compressed air through an inlet in the middle of the fixture, defining the internal pressure and thus the inflation of the antenna structure to be controlled dynamically. This allowed the antenna height to be tuned between 0 and slightly beyond a hemispherical shape by inflating the structure. The carrier had an SMA fed microstrip coupled line for driving the antenna
Antenna Measurements: The antenna height was measured by using a series of custom-made dielectric spacers with predefined sizes. The antenna efficiency was measured using the Wheeler Cap method, with the measured result presented in Table 1. The antenna height was measured before and after the efficiency measurements since the Wheeler Cap made simultaneous height measurements impossible. Several measurements were made to verify repeatability. For calculations of the fractional bandwidth (FBW) the upper and lower bands were defined using the standard definition of half accepted power relative to the power accepted at resonance frequency. In addition, a correction factor was used to compensate for broadband losses and to ensure that the RLC antenna model gives correct FBW. The tabulated Q-values were calculated using the FBW and measured reflection coefficient. For the calculated ka factor of the measured PDMS antenna, the radius of the circular holder was used for height below that of a hemispherical antenna. In the case of extended inflation over the hemispherical shape, in order to include currents on the ground plane, the total height was used as the radius for calculating the theoretical minimum Q-value.
The fabricated antennas’ reflection coefficient, tunable range and radiation pattern were measured. The antenna reflection coefficient was measured using an Agilent E8364B PNA. The PNA was set to sweep from 100 MHz to 3 GHz. The silicone antenna was measured for eight different inflation heights; 5, 10, 15, 17, 20, 22, 24 and 25 mm. The radiation pattern for the AUT was measured in an anechoic chamber using an Anritsu MG3694A signal generator and an Agilent E4440A spectrum analyzer. The antenna alignment is shown in Figure S1 and was defined using a standard spherical coordinate system. The antenna was placed on a mechanically steerable turntable and the turntable was set to an angular resolution of 5°. The results were compared those obtained using CST simulated structure. Antenna feed connections and cables were not included in the simulated results, however the presence of the antenna ground plane help to reduce a spurious effect caused by cables and connectors. A linearly polarized reference antenna was used during the measurements to provide both co- and cross-polarized measurements with the E-field directed along the z-axis.
Supporting Information is available from the Wiley Online Library or from the author.
This work is partly funded by the Swedish Governmental Agency for Innovation Systems, through Uppsala Vinnova Excellence Center for Wireless Sensor Networks. Z.G. Wu holds a junior researcher position funded by the Swedish Research Council (Contract No. 621–2010-5443).
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