ToolsMicrostrip Patch Antenna CalculatorSubstrate ParametersDielectric Constant (ε r):Dielectric Height (h):Resonant Frequencyf r:GHzPhysical ParametersLength (L):Width (W):Input Impedance (Edge):OhmDescriptionThe microstrip patch antenna calculator determines the length (L) and width (W) of a rectangular microstrip patchantenna for a given resonant frequency or vice versa. The substrate parameters (ε r and h) are required. If theratio (L/W) is close to unity, the radiation pattern will be symmetric but may not provide a resonable input impedance. Therefore,this calculator also suggests a value for W. The radiation edge input impedance is also calculated and is based on W.SynthesizeEnter the desired resonant frequency (f r)to determine the physical length (L) and width (W) of themicrostrip line.
The input impedance at the radiation edge is also computed. Press Synthesize to see the results. AnalyzeEnter values for L and W for the microstrip patch to determine its f r. The input impedance at the radiation edge is also computed.Press Analyze to see the results.em: talk © 2006-2011 All Rights Reserved.
Patch antennas come in various shapes and sizes and consist of a patch of metal directly above a ground plane. Figure 5.27 shows an example of a patch antenna. The main disadvantage of these antennas is their relatively large size compared to other types of antennas. For example, some patch antennas are approximately half a wavelength on each side. The polarization can be either circular or linear depending on the design of the patch.
In a patch antenna, most of the propagation is above the ground plane and can have high directional gain. In a linear array of square patch antennas aligned along an axis of symmetry through the centers of all patches, one principal linear polarization is derived by connecting all probes aligned with the axis of symmetry; the other orthogonal polarization is derived by connecting another set of probes perpendicular to the axis of symmetry 116.
The cross-polarization fields of the array of patches in the V- and H-polarization are −27 and −30 dB, at ±0.15° with respect to the array boresight. The array is developed for the advanced SAR (ASAR) of the European Space Agency and has the following additional specifications:.Frequency of operation: 5.331 GHz.Bandwidth ±10 MHz: 3.75%.The maximum cross-polarization levels vary between −10 and 15 dB.Low cost and simplicity are the hallmarks of this approach. The patch antenna element developed for the PHased ARray SAR (PHARUS) operating at 5.3 GHz is an important variant of this approach 117. With reference to Figure 3.15, the two orthogonal polarizations are connected to a ratrace and the resulting co- and cross-polarization patterns are shown in Figure 3.15b. As can be seen, a broad minimum of the cross-polarization pattern is attained at the −25 dB level in the D-plane. The ratrace provides some 30 dB isolation between the two probes, accommodating the two polarizations.
The broad cross-polarization pattern and the high isolation between the two polarizations constitute a benchmark of performance for simple patch antennas. Comparable results are reported over a 5% (VSWR of 2) bandwidth at 2.4 GHz when the coupling mechanism from the patch consists of slots 118. The derivation of the two orthogonal linear polarization when a square patch is used.
(a) The derivation of the vertical and horizontal polarizations from the square patch. (b) Its co-and cross-polarization radiation patterns. (Courtesy TNO, Paquay et al.
117).The performance of four dual-polarized square patch antennas has been compared when the interconnections between patches vary 119. The optimum geometric arrangement of interconnections exhibited a cross-polarization level of −24 dB and an inter-polarization isolation of −33 dB.
The bandwidths attained by the four arrangements ranged between 3% and 8%. Huang 120 implemented a different interconnection scheme between the patches and reported an inter-polarization isolation figure of −40 dB and a cross-polarization level of −28 dB. Patch and loop antennas were designed with metamaterial dielectric substrates 10. The aim here was to significantly decrease the physical size at the operating frequency. A loop antenna with approximately one wavelength perimeter that resonated in air at 2.58 GHz was mounted over a stack of pc boards on which were etched groups of split ring resonators as shown in Fig. The resonant frequency with the metamaterial substrate was reduced by 23 percent, which indicates the size reduction. A greater decrease of resonant frequency was obtained when the split ring resonators were included in the same plane as the loop, both within the loop and outside it, resulting in a size reduction of 38 percent.
A dielectric substrate similar to that shown in Fig. 3.12 was used for a patch antenna, where a ground plane larger than the size of the patch was placed at the bottom side of the substrate. The resonant frequency of the antenna with the metamaterial substrate was reduced somewhat more than what would be expected from the natural pc board substrate alone. Reduction of size of the patch and the loop antennas was accompanied by decreased bandwidth.
In both cases, bandwidth was improved by adding nondriven antenna elements with slightly higher resonant frequencies on the opposite side of the dielectric from the driven element. Tatsuo Itoh, in, 2005 11.4.1 Microstrip Patch AntennaThe patch antenna has several desirable qualities, including a broadside radiation pattern that allows it to be integrated into two-dimensional arrays. The antenna is also low profile and low cost, has good conformability, and has ease of manufacturing. It is readily integrated with microstrip or coaxial probe feeding. Multilayer schemes have been used for other types of feeding, including CPW and strip line. With microstrip feeding, it is also a relatively simple task to implement either linear or circular polarization excitation of the antenna.
The patch antenna, shown in Figure 11.14 with microstrip feeding, is one of the most widely used planar antennas. Feeding is extremely important with the patch antenna, and it contributes to bandwidth, crosspolarization levels, and ripple. Microstrip-fed patches have very narrow bandwidths, almost invariably less than 5%. Other feed mechanisms have been used to increased bandwidth, including proximity coupling and aperture coupling, both of which require multilayer fabrication. A review of this technology is discussed in Pozar (1992). Alternatively, matched bandwidth of the antenna can be increased by making the antenna substrate electrically thicker, effectively lowering the Q-factor of the antenna cavity for increased bandwidth. High levels of TM 0 surface waves, however, can result and therefore reduce the radiation efficiency as well as degrade the radiation pattern if the surface wave generates radiation (which can occur at the edge of finite ground antennas).
The problem of electrically thick substrate is also a common one for high-frequency antennas on high-permittivity substrates, and high amounts of TM surface waves can result. FIGURE 11.14. Top View of Microstrip-Fed Patch AntennaReturning to Figure 11.14, the microstrip feed is inset into the antenna a distance x to obtain an input match.
The dimension b is chosen so that the cavity formed by the conductor on the top plane of the structure is resonant. This causes radiation at the two edges of the antenna, as shown by the fringing fields in the diagram. A simple and intuitive technique for modeling this antenna is the transmission line model. This model provides a reasonable estimate for the resonant frequency and a fairly accurate estimate of the input impedance close to resonance.
Due to the narrow bandwidth of the patch antenna, it is typically not accurate enough to guarantee first-pass design success. The bandwidth, however, does provide a useful starting point as well as useful insight into the operation of the antenna. A cross section of the patch antenna is shown in Figure 11.15. In this model, it is assumed that the patch antenna consists of a perfect magnetic conductor (PMC) walls on the sides of the patch antenna, giving rise to standing wave type modes inside the patch antenna cavity. The total length of the cavity is the length of the patch antenna (dimension b) and an effective length at each edge due to the microstrip open-end effect.
The fundamental resonance of the cavity formed by the microstrip patch antenna will occur at the frequency where the total effective length of the patch antenna, b + 2Δ l oc, is equal to one-half a guided wavelength in the microstrip cavity. The equation representing this concept is as follows. It is also desirable to have an estimate of the input impedance of the antenna. The simplest way for estimating this is the transmission line model for the patch antenna. In this case, the antenna is modeled as two radiating slots of width Δ l oc and length a separated by a microstrip transmission line with dimensions corresponding to the dimensions of the patch antenna.
Note that the feeding can be placed at one end of the antenna or at some point a distance x inside the patch, either by the use of an inset feed or a coaxial probe. The equivalent structure for interior feeding is shown in Figure 11.16. At resonance, the impedance of the radiating slot will be pure real.
To first-order for a ≪ λ 0 (which will be true on high-permittivity substrates), the radiation resistance of each slot may be approximated as. (11.37) R a = 90 λ 0 2 a 2.Equation 11.37 provides a reasonable first-order estimate of the input impedance of the patch antenna near resonance. Note that there are many other simple models that also provide a first-order estimate of the input impedance. Often, the designer must either fabricate and perform measurements or obtain a full-wave solution to the structure using an electromagnetic (EM) simulator to achieve accurate design data for the antenna. This simple model, however, provides a useful starting place for the design. Because the antenna's length determines the resonant frequency of the patch, higher antenna resonances will coincide with frequencies that are multiples of the fundamental resonance.
If active circuitry, which may generate harmonic frequencies, is integrated with the patch antenna, harmonic radiation leading to co-site interference may occur. A circular geometry patch antenna may be used to reduce this problem. In this case, higher resonances of the antenna will be determined by circular harmonics (Bessel functions) and can be designed to occur away from circuit harmonics. A plot of the input impedance of one particular type of circular geometry patch, the circular segment patch antenna, is shown in Figure 11.17 along with its geometry. By looking at the frequency scale of the plot, it is apparent that higher resonances do not correspond to harmonic frequency of active devices that may be integrated with the antenna.
Note that the input impedance was obtained by full-wave analysis. Measured radiation patterns of these types of antenna are comparable to that of a standard rectangular geometry patch antenna.
In addition, circular geometry patch antennas are often more compact than rectangular geometry patch antennas. Note that the antenna is fabricated on a standard RT/Duroid of permittivity 2.33 and a thickness of 31 mils. A 120° sector of the antenna has been removed for optimal impedance. A microstrip feed is placed 30° from the edge of the voided sector. The radius of the antenna is 740 mils. A patch antenna with the dimension of 10 × 8 cm 2 is printed on the four-layer magneto-dielectric materials with thicknesses of 2 cm and illustrated in Figure 10.36.
The size of the ground plane is 20 × 20 cm 2. The return loss and radiation patterns are shown in Figure 10.37(a) and (b), respectively. The resonant frequency of the fabricated antenna is about 277 MHz, and it provides a wide bandwidth of about BW = 3.2%. The size of the antenna is around with a miniaturization factor of 5.4.
The directivity of the antenna is D 0 = 2.9 dB, it has a front-to-back ratio of 1.3 dB with a ground plane size of 0.18 λ 0 × 0.18 λ 0, and the antenna efficiency is about e r = 67%. If a magneto-dielectric material with lower magnetic loss tangent of about 0.01 is used, the efficiency is increased to 82% while the bandwidth is decreased to BW = 2.8% ( Mosallaei & Sarabandi, 2004). Patch antenna over the engineered magneto-dielectric meta-substrate: (a) return loss and (b) radiation patterns. The magneto-dielectric substrate enhances the antenna bandwidth significantly (about 600%) ( Mosallaei & Sarabandi, 2004).It should be noted that to achieve the same miniaturization factor utilizing only a dielectric material ( μ r = 1), the relative permittivity would be 23.7. This reduces the bandwidth to about BW = 0.5%, which is shown in Figure 10.37(a).
The efficiency in this case for a dielectric loss tangent of 0.001 is about e r = 64%. Therefore, utilizing the magneto-dielectric meta-substrate, one can offer a miniaturized wideband planar antenna with high efficiency.
The antenna bandwidth for the proposed magneto-dielectric substrate is about six times higher than that of the dielectric substrate. A microstrip patch antenna is comprised of a radiating metallic patch situated on one side of a nonconducting substrate panel with a metallic ground plane placed on the other side of the panel. A patch antenna, depicted in Figure 1.39, can take many geometric shapes, with the rectangle, square, and circle being the most common.
The radiation of the patch is perpendicular to the board on which it is placed. The dimension L is slightly less than half the free-space wavelength divided by the square root of the effective dielectric constant of the board.
The feedline, in this case a microstrip line, is etched alongside the patch at the center of its width as shown in Figure 1.39 for the rectangular patch. The equivalent circuit for the microstrip line is shown in Figure 1.41. For a rectangular patch, the radiation is generated from the two edges with two equivalent slots as shown in Figure 1.39 8,9. The other two opposing edges that are W apart do not radiate so long as the feedline is at the center of the radiating edges. Thus, it can be concluded that a radiating patch can be modeled by two slots separated by a transmission line. Each slot can be represented by a parallel circuit of susceptance X and conductance G as shown by the equivalent circuit depicted in Figure 1.40. Note, however, that the circuit presented in Figure 1.40 does not model the mutual coupling present between the two radiating slots j nor does it account for the radiation due to the nonradiating edges of the patch.
Due to these limitations, this model becomes unsuitable to analyze nonrectangular shapes and hence it is very limited in its application 9. At this point it is important to elaborate on ε eff in Eqn (1.185).
A basic patch antenna is depicted in Figure 1.42. The distribution of the electric field of a rectangular patch when excited in its fundamental mode is also shown. The electric field is zero at the center of the patch and progresses to become maximum positive on one side and maximum negative on the opposite side. The polarization of the field interestingly enough depends on the instantaneous phase of the applied signal. Note, however, that the electric fields do not end immediately at the patch's edges but rather extend somewhat to the outer periphery of the patch.
These field extensions are known as fringing fields. The electric field radiates along the z axis, whereas the magnetic field is present in the x, y plane. It is because of these fringing fields that the patch looks electrically greater than its physical dimension. This increase in dimension of the patch along its path, and denoted by Δ L, is a function of the effective dielectric constant ε eff and the ratio W/ h as 10. (1.194) Y = G + j X G = W 120 λ ( 1 − 1 24 ( 2 π λ h ) 2 ), h λ. First, an embroidered textile patch antenna was fabricated on a polymer substrate ( ɛ r = 4.2 and tan δ = 0.01). Next, the antenna was measured on planar and cylindrical surfaces (see Figure 10.17).
As shown in Figure 10.17a, the measured resonance frequency of the planar textile patch antenna was 2.2 GHz, agreeing with that of its simulated copper counterpart. The measured realized gain was 5.6 dBi, which is only 0.3 dB lower than that of the copper patch antenna. The measured patterns were also in agreement with simulations.
We further note that this remarkable RF performance of the textile antenna does not degrade after repetitive flexing (more than 20 times). Figure 10.17. Textile patch antenna and its RF performances (a) on a planar surface and (b) mounted on a cylindrical surface. From Wang et al.
(2012b) Copyright © 2012 IEEE.To further evaluate the RF performance of the E-fiber antenna, the latter was mounted on a metallic cylinder (diameter = 80 mm). As shown in Figure 10.17b, the measured reflection coefficient and radiation patterns of the textile patch antenna were in good agreement with the simulations of the equivalent copper patch antenna. The realized gain was only 1 dB lower than simulation. Further, as compared to the flat configuration, the textile antenna had a lower resonance frequency of 2.06 GHz and a reduced gain of 3.0 dB. The frequency detuning is due to the 13% elongation of the patch dimension in the H-plane ( Wang et al., 2012b). However, the gain reduction is primarily because of the curvature and higher resistance of the textile’s surface.
The latter was due to the stretching of the E-fiber threads. Nevertheless, these results clearly demonstrate the remarkable RF and mechanical performance of the E-fiber antenna. Hertleer et al.
24 introduced a wearable patch antenna for operation in the 2.4, 2.4835 GHz band, made of a shock-absorbing, fire-retardant foam substrate and suitable for rescue worker applications. The antenna employs a simple topology, consisting of a truncated-corner rectangular patch (see Fig. 26.6), with coaxial feeding on the patch diagonal, allowing the excitation of two orthogonal modes that yield nearly circular polarization. The conductive parts of the antenna are composed of commercially available electrotextile materials, with very high conductivity, in particular “ShieldIt™” for the radiating patch and “Flectron ®” for the ground plane. The proposed antenna was first designed by means of an optimization performed by a full-wave EM solver, then prototyped and tested in different operating conditions. In particular, the authors showed, through both measurements and simulations, how the proximity of a human arm over which the antenna was bent affects its performance by producing a resonance frequency shift.
However, thanks to the design's relatively large −10 dB impedance bandwidth, the antenna still meets the design requirements when bent around a human arm. In 2008, using the same protective foam as a substrate, Vallozzi et al. 11 proposed a 2.45 GHz patch antenna with dual polarization, allowing to implement polarization diversity using a single, compact, wearable antenna. The antenna, shown in Fig. 26.7, employs a simple nearly square topology with a small slot in the center and with two coaxial feeds positioned symmetrically on the two patch diagonals. This allows the excitation of two orthogonal, linearly polarized waves that can simultaneously transmit/receive two independent radio waves for implementation of polarization diversity.
Antenna design and optimization were first performed with the aid of a full-wave EM solver, and then a prototype was constructed and its performance tested by measurements. In addition to a free-space situation, measurements were also performed on a human body in order to verify the antenna's resilience to the presence of a human body. In both cases, the measured reflection coefficients meet the design requirements ( S 11. Realized prototype of dual polarized patch antenna on foam substrate.To apply diversity in off-body communication, two such antennas can be integrated into a wearable textile system, worn on the front and back side of a human subject, realizing a fourth-order receive diversity communication link by combining both pattern and polarization diversity 25. By means of a realistic measurement campaign, it was shown that the proposed diversity system achieves a dramatic improvement in terms of received BERs in an off-body wireless communication link between a fixed transmitting base station and a receiving subject equipped with such an antenna system, moving into a typical indoor multipath environment.More recently, a novel and promising technology called substrate integrated waveguide (SIW), an already well-known fabrication technology for rigid printed circuit boards, was for the first time applied by Moro et al. To develop a wearable textile antenna for operation in the 2.45 GHz ISM band 26. Such a kind of patch antenna answers to important requirements in off-body communications, such as suppression of undesired surface waves and a high level of shielding from the human body, even with a very small ground plane, high directivity, and front-to-back ratio, as well as performance stability.
The structure consists of a cavity-backed slot antenna on a flexible protective foam substrate, with electrotextiles (Flectron) metallization on both sides. The top layer consists of a rectangular conductive layer with a dog-bone-shaped slot, representing the radiating element, while on the bottom layer a 50 Ω grounded coplanar waveguide represents the feeding line. A rectangular cavity is formed inside the antenna substrate, by using eyelets as metallized holes, with an appropriate spacing distance between each other. All geometrical parameters were optimized by means of a commercial full-wave EM solver, and after that the antenna was prototyped by a low-cost production technique. An experimental verification of the antenna performance in free space showed that the antenna exhibits a reflection coefficient lower than −10 dB in a bandwidth of 165 MHz, including the complete 2.45 GHz ISM band, a maximum gain of 3.21 dBi at 2.45 GHz, and a radiation efficiency of 68%.
Experiments were repeated with the antenna integrated on the back side of a body-worn firefighter jacket, showing that the performance deviates only slightly from the free-space state, with the maximum gain increasing to 4.9 dBi, owing to reflections by the human body. Effects of bending were also verified by simulations, resulting in a very small increase of resonance frequency for a bending radius of 10 cm, which does not compromise the overall performance in the operation band.
Later, the SIW cavity-backed slot antenna was used by Lemey et al. 27 as a starting point for the development of a novel energy-harvesting platform, obtained by solar cells and dedicated flexible circuitry, compactly integrated on the top and back surface of the SIW antenna structure, as depicted in Fig. 26.8. More specifically, two a-Si:H-solar cells were applied on the top side of the SIW antenna, while the necessary circuitry for the management of the output DC power from the solar harvesters was integrated on the back side and connected to the solar cells by means of wires routed through the eyelet holes. SIW cavity-backed slot antenna with integrated energy-harvesting platform.
(a) Front and (b) back.The integrated circuits were composed of a central power management system (CPMS) and a low power system (LPS), deployed on a flexible polyimide substrate on a ground plane, glued on the back side of the SIW. More details of the implementation are described in Ref. 27.Two other interesting compact structures for the implementation of wearable textile patch antennas operating at 2.45 GHz were proposed and studied by Liu et al. These antennas both reduced the size of a conventional structure by half, using electrical or magnetic symmetries.
In particular, the first antenna, called the quarter-wave patch, is built up by using half of a rectangular patch, by placing a shorting wall providing electrical symmetry. The second antenna, the half-mode cavity, originates from a half-mode substrate-integrated cavity, where an open aperture placed on the substrate's symmetry plane enables to only use one-half of the entire cavity. The authors first developed an analytical analysis of both structures.
Next, they built accurate EM simulation models, reproducing the features of their real textile implementation. Both antennas are made out of a low-loss nonabsorbent microwave radome foam PF-4 (thickness h = 3.2 mm and Ɛ r = 1.06), with a ground plane with size 10 × 10 cm, and a half-square top conducting layer consisting of silver-coated fabric NCS95R-CR. The shorting sides (one on the symmetry plane for the quarter-wave antenna, and three on the peripheral sides for the half-mode) are realized by linear embroidery with a conductive thread, consisting of stitches with 1-mm spacing and a total of 5 passes. Through simulations, it was found that seam compression caused by stitching produces a resonance frequency shift with respect to the ideal planar case. Hence, such an effect needs to be included in the model to correctly predict resonance frequency and performance. Real prototypes of the two antennas were built and their performance was experimentally assessed obtaining operational bandwidths of 300 and 130 MHz, and maximum gains of 5.3 and 5.1 dBi, for the quarter-wave patch and half-mode cavity, respectively.
Moreover, the effects of human body proximity on the performance parameters appeared to be indistinguishable, proving the good isolation properties of the ground plane. A novel type of resonant structure for RTD oscillators with a patch antenna can realize higher efficiencies ( Sekiguchi et al., 2010). The device structures of InGaAs/InAlAs RTD oscillators with a patch antenna are shown in Fig. 14.5. An RTD post, buried within a dielectric, is sandwiched between the patch and the ground plane on InP substrates. The oscillation frequency is decided by the resonant length L of the patch. The resonant length L is determined by a value of λ/2√ε r ( Kraus and Marhefka, 2001), where λ is the oscillation wavelength in a vacuum and ε, is the relative permittivity of the dielectric.
The input resistance of the patch can be tuned, by shifting the RTD post over a distance x away from the center of the patch, proportionally to sin2(πx/L) ( Kumar and Ray, 2003). Bias voltage on the RTD post is supplied at the center null point of the patch.
A parallel resistance is put between the bias supply lines in order to prevent parasitic oscillation due to return pass of the bias supply lines. Schematic structure of RTD oscillators integrated with patch antenna.The oscillation output of the RTD oscillators is maximized when the impedance of the antenna is matched to the RTDs. Although the patch antenna needs high gain RTDs due to its large load, the antenna that has several tens of ohms can satisfy the matching condition. The patch antenna of planar structures on substrates is easy to fabricate even for the array scheme. Since almost all fields emit toward the upper side of the substrate, dielectric lenses are not essential. As the oscillation output of the slot antenna fabricated by Suzuki et al.
(2010) emits mainly into the substrate, the lens on the opposite surface is required to avoid substrate modes.In the actual device, the RTD post of 2 to 4 μm-diameter on the InP substrate is formed by electron beam lithography and dry-etching techniques. An approximately 3 μm-thick layer of BCB is used to provide the magnitude of impedance of the patch antenna at about 50 Ω. Ti/Pd/Au metal in contact with the RTD post and Ti/Au metal in contact with the n-type InP substrate are adopted as the patch and the ground plane, respectively.InGaAs/InAlAs triple-barrier RTDs were used as a gain structure for THz frequency range ( Asada, 2001), which suppresses the broadening of sub-bands at quantum wells. Therefore, these types of RTDs enable resonant sharpness to be narrower compared with double-barrier RTDs ( Nakagawa et al, 1986). As a result, large negative differential conductance is expected against small peak current density. The triple-barrier RTD is designed to get negative differential conductance similar to double-barrier RTDs. The epitaxial layers consist of (from the top down), n +InGaAs (Si = 1 × 10 19 cm 3, 100 nm), n-InGaAs (Si = 2 × 10 18 cm 3, 50 nm), InGaAs spacer (undoped, 5 nm), AlAs barrier (undoped, 1.3 nm), InGaAs quantum well (undoped, 7.6 nm), InAlAs barrier (undoped, 2.6 nm), InGaAs quantum well (undoped, 5.6 nm), AlAs barrier (undoped, 1.3 nm), InGaAs spacer (undoped, 5 nm), n-InGaAs (Si = 2 × 10 18 cm 3, 50 nm), and n + InGaAs (Si = 1 × 10 19 cm 3, 3400 nm) on the n-type InP substrate.
The InGaAs and InAlAs layers are lattice-matched to InP substrates. One antenna type that may be fabricated from CNT sheet material is a patch antenna. This antenna geometry has proven to be quite effective for a variety of applications, including terrestrial and satellite communications systems and various radar electronic scanning arrays due to its low-profile, planar structure, reasonable bandwidth of typically 5–20%, and excellent gain of typically 7 dBi. The aperture-coupled patch antenna, shown in Fig. 26.13, provides an indirect feeding mechanism by which a microstrip feedline on the bottom surface of a lower substrate couples an applied signal up through an aperture located in a ground plane on the bottom surface of an upper substrate to a radiating patch located on the top surface.
Non Resonant Antenna
In order to construct this design, CNT sheet material is fabricated and transferred to a Kapton tape substrate, which provides both an adhesive bonding mechanism on one side and a lamination protective mechanism on the other. This Kapton-laminated CNT sheet is then affixed to the top surface of a dielectric board (62-mil-thick RT/Duroid 5870 in this example) and cut to the precise patch antenna dimensions using a circuit board router to form the patch layer. This layer is then combined with the lower substrate (20-mil-thick RT/Duroid 3010 in this example) which contains the microstrip feedline and ground-plane layers.
The patch is fabricated from copper for one prototype and from varying thicknesses of CNT sheet material for additional prototypes while the microstrip feedline and ground-plane layers are fabricated from copper for all prototypes. This facilitates the evaluation and comparison of the radiating properties of CNT sheet material vs that of the standard copper cladding.
Examples of fully fabricated copper and CNT sheet patch antenna prototypes are shown in Fig. The estimated thickness for the 0.5 oz copper cladding used on the RT/Duroid substrates in these prototypes is ∼17 μm. Electromagnetic simulations using a full-wave solver may be conducted to predict the antenna performance.
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A simulation model of this design is shown in Fig. The performance of a 0.5-μm-thick CNT sheet (∼10 layers of CNT sheet material) and a 5-μm-thick CNT sheet (∼100 layers of CNT sheet material) is evaluated through simulation. The CNT sheet patch is approximated as a finite conductivity boundary with the conductivity varied between simulations to evaluate its effect on the antenna performance. A starting value of ∼3e4 S/m has been applied based on reported conductivity measurements of CNT thread material.
The actual conductivity of the CNT sheet material may be significantly higher than that of the CNT thread and can likely be improved to at least 1e5–1e6 S/m with postprocessing techniques. The finite conductivity boundary has been placed in between two layers of 5-mil-thick Kapton film in order to represent the Kapton laminate/bonding layers on the actual prototype.
This film has an estimated permittivity of ε r = 3.5. The predicted effects of CNT sheet thickness and conductivity on patch antenna radiation performance are shown in Fig. Where ρ is the material resistivity, ω is the angular frequency, and μ is the material permeability. For an estimated conductivity of ∼3e4 S/m, frequency of 9 GHz and estimated permeability of 4πe-7 H/m, the skin depth for the CNT sheet material is estimated to be δ s ≈ 30 μm. This is higher than the 0.7 μm skin depth estimated for a copper sheet, because of its conductivity of ∼5.9e7 S/m. A significant improvement in the reflection coefficient occurs when the CNT sheet thickness is increased from 0.5 to 5 μm. An efficient patch antenna with S 11.
Figure 26.16. Measured reflection coefficient for CNT sheet and copper patch antenna prototypes. (For color version of this figure, the reader is referred to the online version of this book.)While the 0.5 μm CNT sheet patch antenna does resonate at ∼9 GHz, its reflection coefficient (−6 dB, or 25% power reflected back to RF source) is much higher than that of the standard copper antenna (−21 dB, or 0.8% power reflected back to RF source). The measured input impedance at 9 GHz is ∼44 + j8.8 Ω for the copper patch antenna and is ∼40.5 + j44 Ω for the 0.5 μm CNT sheet patch antenna. For these measurements, the real part represents the input resistance and the imaginary part represents the input reactance, with a positive value being inductive reactance and a negative value being capacitive reactance. A perfect match to the RF source would be a measurement of 50 + j0 Ω. Both resistance values are close to the desired 50 Ω, though the inductive reactance value for the CNT sheet patch is ∼5 times higher than that of the copper patch.A significant performance improvement is observed for the 5 μm CNT sheet patch antenna, with a −10.5 dB reflection coefficient at resonance.
A minor resonant frequency shift of ∼100 MHz (∼1.5%) from 9 to 8.85 GHz can be seen, potentially due to increased reactance from the CNT sheet layers and/or from fabrication tolerance errors. The measured input impedance at resonance is ∼75 + j28 Ω. Thus, while increasing the CNT sheet thickness does lower the reactance component of the input impedance, the resistance component increases and the overall reflection coefficient remains well above that of the copper patch antenna. It should be noted that a 5 μm sheet thickness is still well below the skin depth of ∼30 μm for a 3e4 S/m conductor. A CNT sheet composed of ∼600 layers of CNT sheet material would be needed in order to surpass the skin depth. With improved CNT sheet conductivity, the skin depth will decrease and the required number of CNT sheet layers will also decrease. While the example simulation results in Fig.
Antenna Resonant Frequency Formula
26.15 indicate a ∼6.5–7% bandwidth (∼600 MHz) of S 11. When the CNT sheet material is fabricated by pulling CNTs from an MWNT forest along a Teflon belt, the CNTs within the sheet bind together and are oriented in approximate alignment with the direction that the CNTs are pulled along the belt. Since electrons travel axially along the CNTs and rarely tunnel between neighboring nanotubes unless there is significant overlap, the RF performance of a CNT sheet patch antenna may be significantly impacted by the orientation of the CNTs within the sheet. For the prototype measured in Fig.
Microstrip Antenna
26.16, the CNTs within the sheet material are oriented parallel to the E-plane for the patch antenna (along the length of the patch, parallel to the microstrip feedline). It is possible to fabricate a CNT patch antenna with the CNTs oriented orthogonal to the antenna E-plane. This distinction is illustrated in Fig. The effect of CNT orientation on the patch antenna reflection coefficient is shown in Fig.
The reflection coefficient indicates that the orthogonal orientation of the CNT sheet to the E-plane of the antenna results in significant detuning at the expected resonance of ∼8.8–9 GHz and a potential resonant frequency shift down to ∼8.4 GHz (4–5% shift). The measured input impedance at this shifted resonance is ∼68 + j91 Ω. While the resistance component becomes closer to the desired 50 Ω, the inductive reactance component significantly increases when compared to the CNT sheet aligned with the E-plane. The measured radiation pattern and gain data for each of the prototypes for this example design is shown in Figs 26.19–26.21. The baseline copper patch antenna and the CNT patch antennas with the CNTs aligned with the E-plane of the patch all display a typical patch antenna radiation pattern, with a half-power beamwidth (HPBW) of ∼75–80° for both the E-plane and H-plane. Minor perturbations in some of the patterns are due to measurement error and/or radiation from the feedline and SubMiniature version A (SMA) connector feedpoint. The “orthogonal” CNT sheet patch antenna radiation pattern was not consistent between the E and H-planes and displays poor performance, as was expected from its poor measured reflection coefficient data.
Figure 26.21. Measured realized gain for CNT sheet and copper patch antenna prototypes. (For color version of this figure, the reader is referred to the online version of this book.)The copper patch antenna displays a realized gain of ∼5.6 dBi, just a little under the theoretical 7 dBi of an ideal patch antenna. The 5 μm “aligned” CNT sheet patch antenna exhibits a realized gain of 2.05 dBi, indicating an ∼3.5 dB tradeoff in radiated power for using 5 μm CNT sheet material in place of standard copper for the patch. A −3.5 dBi realized gain is observed when the CNT sheet thickness is reduced to 0.5 μm, indicating that the reduction in thickness results in a gain reduction of ∼9.1 dB from the standard copper patch and ∼5.5 dB from the 5 μm CNT sheet patch antenna. The impact that the CNT sheet orientation has on the radiation performance of the patch antenna is clearly seen with the 5 μm “orthogonal” CNT sheet patch antenna, which exhibits a realized gain of −6.1 dBi.
This is an ∼8.2 dB difference in realized gain between prototypes constructed with the exact same design and from the exact same batch of CNT sheet material, but with varied CNT orientation. This indicates significant polarization selectivity for the CNT sheet patch antennas depending on whether the CNTs within the sheet material were generally aligned with the E-plane of the antenna. This behavior may have significant applications to polarization-specific antennas and may be useful for improving isolation between neighboring antennas on a shared platform.