With reference to a conventional air planar inverted-F antenna this paper describes the miniaturization of the planar inverted-F antenna by dielectric loading of barium tetratitanate ceramics of very high permittivity (εr = 38, 80) at 1.8 GHz. It is found that a simple loading method can reduce the antenna size but at the cost of the antenna performance. For instance, the antenna gain becomes lower. Then a sophisticated loading approach based on a novel substrate-superstrate structure is developed to improve the antenna gain. The whole process of the gain enhancement is analyzed by using the finite difference time domain method. The simulations are excellently correlated with the experiments. They both show that the sophisticated loading technique can reduce the antenna size by four times and still maintains the comparable performance.
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 The demand for the miniaturization of portable communication equipment has been increasing along with the proliferation of personal communication systems (PCS) and this has, in turn, promoted considerable development of small antennas. It is seen that many novel designs of small antennas have been proposed in the past few years and most of them have been inspired from the configuration of a planar inverted-F antenna (PIFA). For examples: A PIFA with a full short circuit is investigated at 0.9 GHz band by Pedersen and Andersen . It is shown that the full short circuit PIFA has a lower absorption thereby reducing possible health hazards. Another PIFA with tuning diodes is explored also at 0.9 GHz band by Virga and Rahmat-Samii . It is illustrated that the diode-tunable PIFA has an enhanced bandwidth while maintaining a low-profile geometry. A third PIFA with an L slot is studied at 0.9 GHz and 1.8 GHz bands by Liu et al. . It is demonstrated that the dual-band PIFA has an isolation between bands of better than 17 dB still keeping almost the same size as a conventional PIFA at 0.9 GHz.
 PCS frequencies at 0.9 GHz, 1.8 GHz, and 2.4 GHz are in the lower range of microwave band, the conventional PIFA tends to be too large to be used with ever increasingly slimmer personal terminals, the reduction of the PIFA size thus becomes necessary and desirable. Some attempt to develop smaller planar inverted-F antennas through loading techniques has been made. A PIFA loaded with a rectangular metal prism is described at 0.9 GHz by Kagoshima et al. . The resonant frequency of the PIFA with load becomes lower than that of the PIFA without load indicating that the metal load can make the PIFA smaller. Another PIFA loaded with a capacitor is reported by Rowell and Murch . The PIFA designed at 1.8 GHz with a bandwidth of 178 MHz demonstrates that the capacitive load can reduce the resonance length of the PIFA from one fourth of wavelength to less than one eighth of wavelength. In this paper, we extend our early work and present a new PIFA loaded with temperature-stable and low-loss ceramics of very high permittivity at 1.8 GHz. It is shown that the simple use of a very high dielectric constant has the advantage of a reduction in size together with the disadvantages of a reduction in gain and bandwidth. Therefore, the sophisticated use of very high dielectric constants to overcome these deficiencies is proposed. Parameters of the PIFA, including input return loss, bandwidth, radiation pattern, and gain are presented. The performance enhancement of the dielectric loaded PIFA is modeled and simulated using the finite difference time domain (FDTD) method although it also can be analyzed by the moment method, the spatial network method, and the Wiener-Hopf method.
2. Antenna Geometry
 The geometry of the dielectric loaded PIFA is shown in Figure 1. The radiating element is printed on ceramic substrate of εr = 38 with thickness T1. The ceramic superstrate of εr = 80 and thickness T2 with a slab size of A × B = 49.5 × 49.5 mm2 is placed on the top of the radiating element. The thickness T1 is chosen based on the available thickness of the ceramic substrate and the thickness T2 is chosen to yield an optimized performance. The size of the radiating element is L1 × L2. The short circuit plate of width W is used to ground the radiating element and is located at the edge of the ceramic substrate so as to facilitate the fabrication process. The antenna is fed by a standard 50Ω coaxial cable probe located at (xo, yo).
Table 1 shows the dimensions of the dielectric loaded planar inverted-F antennas. Additionally, an unloaded conventional air planar inverted-F antenna is included for comparison purpose.
Table 1. Dimensions of Prototype 1.8 GHz Planar Inverted-F Antennas in Millimeters
3. FDTD Analysis
 In this paper, the FDTD method has been implemented to allow modeling and simulation of the dielectric loaded PIFA. The FDTD computation space was divided by a three-dimensional grid with cell size Δx, Δy, and Δz in the x, y, and z directions, respectively. It was truncated by the Liao et al.'s  second-order boundary condition to reduce reflection of the scattered fields. For the results that follow, cell sizes were Δz = 0.67 mm, Δx = Δy = 1.1 mm with the time increment Δt = 1.440 ps satisfying the Courant stability criteria.
 The object to be modeled here consists of a radiating plate element, a short circuit plate, a ground plate, a section of coaxial cable, a substrate slab, and a superstrate slab. The conducting plates were treated infinitely thin and modeled by setting the tangential electric fields to zero. The section of the feeding coaxial cable was modeled with a gap voltage introduced in the inner conductor following the approach of Jensen and Rahmat-Samii . The source function was a Gaussian pulse. The inner conductor and the probe were treated using the thin wire formulation developed by Taflove et al. .
 The far-field properties of the PIFA were computed using an improved time domain near-to-far field transformation scheme developed by T. K. Lo and Y. Hwang. The improved transformation scheme uses Love's equivalence principle that states either the magnetic or the electric current satisfying the corresponding boundary condition should be enough to compute the far-zone electromagnetic fields. This is different from the conventional near-to-far field transformation scheme, which uses both electric and magnetic currents on the equivalent surface that simultaneously satisfies two boundary conditions of continuation of tangential electric and magnetic fields, respectively. It was found that the improved transformation scheme could reduce the complexity of programming and memory used in the far-zone computation.
4. Measured and Calculated Results
 The reference and the simple loaded PIFAs have the lateral dimensions of 22.2 × 28.8 and 9.2 × 17.3 mm2, respectively. Their performance was measured and is represented by the solid and dashed curves, respectively in Figures 2 and 3. The measured return loss as a function of frequency is shown in Figure 2. Note that good matching has been achieved for both PIFAs at 1.8 GHz. The measured impedance bandwidths with the return loss ≤−10 dB criterion are 90 MHz and 19.5 MHz for the reference and the simple loaded PIFAs, respectively. Figures 3a and 3b show the measured radiation patterns of the two PIFAs in E and H planes, respectively. As shown, the simple loaded PIFA has an inferior reception. For example, the maximum received power in E plane is −39.3 dBm for the reference PIFA and is decreased to −47.7 dBm for the simple loaded PIFA. Figures 2 and 3 indicate that the simple loading of the PIFA with the substrate of high permittivity (εr = 38) ceramics reduces the impedance bandwidth from 5% to 1.08% and the reception gain at least by 8.4 dB although it has made the PIFA four times smaller.
Figure 4 displays the measured and calculated return loss for enhanced PIFA one with the feeding point (xo, yo) located at (3.3, 4.4). Agreement between the measured and calculated results is good. The return loss of more than 20 dB has been obtained at 1.8 GHz. The bandwidth is 16 MHz (0.9%) for both measured and calculated results. Figures 5a and 5b show the E-plane and H-plane radiation patterns, respectively. It is noted that the measured and calculated radiation pattern results are closely correlated. Figure 6 is the plot of the calculated far-zone electric field strength for enhanced PIFA one. It is seen that the peak electric field strength is −8.4 dBμV at 1.8 GHz. Figure 7 shows the calculated power recorded in the coaxial cable. The dash line represents the power of the Gaussian pulse source while the solid line stands for the input power to the antenna. Note that the input power is almost the same as that given by the Gaussian pulse source at 1.8 GHz. This shows again that enhanced PIFA one has been matched at 1.8 GHz. Both measured and calculated gain values for enhanced PIFA one are 6.9 dBi, which is comparable to that of the reference PIFA. In the gain enhancement process, it was observed that neither varying the substrate thickness T1 nor the width of the short circuit plate W but varying the superstrate thickness T2 had improved gain effectively. Figure 8 illustrates the gain improvement as a function of the superstrate thickness T2. The circles and crosses represent the measured and calculated gain results. They are in good agreement and both of them show that the gain of the PIFA increases with the superstrate thickness T2 in general and up to a maximum of 6.9 dBi at 4.69 mm. The superstrate thickness T2 = 4.69 mm is quite close to the quarter- wavelength of the guided wave in the superstrate (λg/4 = 4.65 mm), the resonance condition λg/4 has been satisfied, as a result, the maximum gain occurs at this thickness. This is consistent with the theory developed by Jackson and Alexopoulos . In the bandwidth enhancement process, it was identified that the substrate thickness T1 was the dominant factor to determine the impedance bandwidth. A double substrate thickness T1 has yielded a significant bandwidth enhancement. For example, enhanced PIFA two exhibits a bandwidth of 103 MHz (5.7%), which is 13 MHz wider than that of the reference PIFA. Table 2 summarizes the measured performance parameters of the enhanced PIFAs. The results show that the sophisticated loading of the PIFA with ceramics of very high permittivity in the novel substrate-superstrate structure the gain and the impedance bandwidth can be up to 7 dBi and 5.7%, respectively. The performance is comparable to those of the conventional air PIFA, however, more importantly a reduction of the lateral dimensions of four times has been achieved.
Table 2. Measured Performance Parameters of Enhanced PIFAs
 This paper has focused on the miniaturization of the planar inverted-F antenna by dielectric loading of barium tetratitanate ceramics of very high permittivity (εr = 38, 80). It has demonstrated that the simple loading method can reduce the antenna size but at the cost of the antenna performance. The sophisticated loading approach based on the novel substrate-superstrate structure has been developed to give the antenna at 1.8 GHz an improved performance with the gain up to 7 dBi and the impedance bandwidth 103 MHz (5.7%), which are comparable to those of the conventional air PIFA. The whole process of the gain and bandwidth enhancement has been analyzed by using the finite difference time domain method. The simulations are excellently correlated with the experiments. They both show that a reduction of the antenna size by four times has been achieved.
 The work was supported by the RGC Earmarked Grant, Hong Kong. The authors thank Prof. G. X. Zheng of Taiyuan University of Technology, China, for his contribution in the measurement of prototype antennas.