It is well known that interference of the human body affects the performance of the antennas in mobile phone handsets. In this contribution, we investigate the use of miniaturized metallodielectric electromagnetic band gap (MEBG) structures embedded in the case of a mobile handset as a means of decoupling the antenna from the user's hand. The closely coupled MEBG concept is employed to achieve miniaturization of the order of 15:1. Full wave dispersion relations for planar closely coupled MEBG arrays are presented and are validated experimentally. The performance of a prototype handset with an embedded conformal MEBG is assessed experimentally and is compared to a similar prototype without the MEBG. Reduction in the detuning of the antenna because of the human hand by virtue of the MEBG is demonstrated. Moreover, the efficiency of the handset when loaded with a human hand model is shown to improve when the MEBG is in place. The improvements are attributed to the decoupling of the antenna from the user's hand, which is achieved by means of suppressing the fields in the locality of the hand.
 Rapid expansion of cellular personal communications has been experienced in the last decade. Smaller, lighter and more efficient handsets are required by the market. At the same time there is concern about the biological implications of the radiation absorbed by the human body [Okoniewski and Stuchly, 1996]. It has been pointed in the literature that significant degradation of the antenna's performance occurs because of the interaction with the human body [Okoniewski and Stuchly, 1996; Jensen and Rahmat-Samii, 1995]. The degradation of the antenna's performance results in shorter battery life, which in turn affects the weight of the phone.
 Holding a terminal handset with a human hand affects the antenna performance in at least two ways, namely, antenna detuning and efficiency degradation. Because of the high permittivity of the human hand placed in close proximity to the antenna, the resonant frequency is typically reduced. Therefore increased total power is required in order to achieve the same level of transmitting power at a specific frequency. Furthermore, power is absorbed by the hand, which is characterized by a significant conductivity value (thermal losses). This results in reduced radiation efficiency.
 The coupling of the user's hand to the antenna, which causes the degradation of the antenna performance, occurs via the electromagnetic fields that the antenna excites at the spatial location of the user's hand. It is therefore expected that by suppressing the electromagnetic (EM) fields at the locality of the user's hand, the performance degradation of the handset can be reduced. Electromagnetic band gap (EBG) structures are topologies that do not accept possible real solutions to Maxwell equations and therefore suppress EM fields [Gonzalo et al., 1999]. Metallodielectric electromagnetic band gap (MEBG) structures is a class of EBG structures that can be readily assembled on thin flexible materials and integrated conformal to the case of a handset terminal [Lee et al., 2000; De Maagt et al., 2003]. However, their size is typically too big for integration in terminal handheld devices. Recently, a class of miniaturized, thin and flexible MEBG surfaces, the closely coupled MEBGs, or CCMEBGs, has been presented [Feresidis et al., 2004]. These surfaces allow significant size reduction and exhibit a wide stopband for oblique as well as surface incident waves. Therefore they have the potential to isolate a handset's antenna from objects in close proximity by reducing the direct as well as surface wave coupling effects.
 In this paper we study the performance of a handset with embedded conformal metallodielectric MEBG in the handset plastic case. Closely coupled MEBG (CCMEBG) surfaces are employed as miniaturized structures that are pertinent for integration in a practical handset. In this context, the dispersion diagram of planar CCMEBG arrays is presented for the first time and an equivalent circuit approach is used to derive design guidelines. A simple handset prototype with embedded CCMEBG is then fabricated and tested. The detuning of the handset antenna caused by a human hand is assessed for prototype handsets with and without integrated MEBG. For both configurations, the antenna efficiency is measured and compared, and the radiation patterns are presented.
2. Miniaturized MEBG Structures
 Miniaturization is essential for application of MEBG surfaces to terminal handheld devices. As MEBGs are typically arrays of resonant elements, the physical dimension of each element, and hence the unit cell, is about a half wavelength. For devices operating at 1 GHz, this corresponds to 150 mm. A miniaturization by a factor in the order of 10 is then required for integration in modern handheld terminals. In this section the concept of CCMEBG surfaces is employed as means to achieve miniaturization of MEBG arrays [Feresidis et al., 2004]. The CCMEBG design is based on a double-layer array configuration with the two layers positioned in close proximity and shifted with respect to each other in order to produce maximum element coupling. The small spacing and overlapping of the elements of the two layers increases the capacitance values in an equivalent circuit representation of the structure, which results in significant lowering of the band gap frequency. The plane wave response of CCMEBG surfaces composed of dipole or tripole elements has been presented in an earlier study [Feresidis et al., 2004]. The measured surface wave response of these structures has also been reported. Here we calculate the dispersion diagrams (or Brillouin diagrams) of tripole CCMEBG surfaces using full wave method of moment (MOM) analysis [Vardaxoglou, 1997] and we study further size reduction of the array unit cell. For ungrounded dielectric slabs transverse electric (TE) band gaps are produced and will be studied throughout the paper.
 Tripole arrays have been used as two-dimensional elements with good symmetry properties (Figure 1a). When a tripole array is arranged on a hexagonal lattice, the irreducible Brillouin zone of the reciprocal lattice is small (Figure 1b). The letters Γ, M, and X denote the edge points of the Brillouin contour. This suggests that similar band gap performance is achieved for any direction of surface wave propagation in the plane of the array. We have used a tripole array geometry with the following dimensions: L = 5 mm, W = 0.5 mm, and periodicity D = 12 mm (Figure 1c). The dispersion curve for this array (TE modes) is shown in Figure 2a, where the cutoff of the band gap emerges at 10 GHz.
 A CCMEBG array design has been implemented using two tripole arrays printed on either side of a 0.12 mm thin dielectric layer with dielectric constant 3 and supported on a dielectric slab of thickness Ssub = 1.13 mm and permittivity 2.2. The tripole CCMEBG configuration is shown in Figure 1a. The dispersion diagram showing the first few TE modes of the double-layer tripole CCMEBG is shown in Figure 2. The modeling results show a TE band gap of 2.3 GHz, starting from 3.7 GHz to 6 GHz. The next band gap starts at 10 GHz, extending to 17.4 GHz, similar to the single-layer array. The tripole CCMEBG surface has been fabricated and measured. Surface wave measurements have been obtained using a pair of wideband antipodal Vivaldi antennas positioned on either side of the array. The measured transmission response is shown in Figure 3. The measured surface wave response of the single-layer tripole array of same dimensions is also shown for comparison. A reduction of the resonant frequency from 10 GHz to less than 4 GHz has been achieved. This corresponds to a miniaturization factor of more than 2.5.
 In order to further reduce the cutoff frequency, we need to further increase the capacitance between the two layers. This can be achieved in two ways; one way is to reduce the separation distance between the two layers and another is to increase the area of the overlapping surfaces. The latter can be achieved by increasing the width of the tripole arms. In this case, however, the full wave calculation of the dispersion properties becomes cumbersome. For wide tripole arms, entire domain functions are no longer suitable to describe the current distribution on the conducting elements in MOM type of solutions. Subdomain functions should then be employed, but with increased computational cost. Furthermore, for small separation distance, FEM type solvers require very small mesh dimensions, which dramatically increase the computational requirements, making the simulations impractical. We have therefore adopted a fast equivalent circuit approach method for the design of the miniaturized CCMEBG required for integration into the handset.
 Using the quasi-static expression for the capacitance C formed between two parallel plates of area A at distance d, we can readily obtain an estimation of the capacitance between the overlapping areas of the CCMEBG array according to
where ɛo is the dielectric constant of vacuum. For the unit cell of the array of Figure 1 it is found that C = 0.41 pF. Assuming that the CCMEBG array is to a first approximation described by a series LC circuit, we can apply the transverse resonance technique in order to obtain the dispersion relation. The transverse resonant method is well documented elsewhere [Pozar, 1998]; therefore we only outline the basic relation here that has been used in our calculations. For simplicity, in these calculations we have assumed a free-standing array. The propagation constant kTE of the first TE mode as a function of frequency is given by the following equation:
where ηo is the free space wave impedance and ωo = 1/ is the resonant frequency of the series LC circuit representing the array. For C = 0.41 pF and L = 2 nH we derive the dispersion relation of the first TE mode for the ΓM direction as shown in Figure 4. Good agreement is observed between this result and the dispersion relation obtained with the full wave method (Figure 2).
 In order to further miniaturize this array, we now increase the capacitance and for simplicity assume no significant variation of the inductance. Figure 4 shows the TE band gap for an LC circuit with C = 13.2 8pF and L as above. The cutoff has now significantly dropped to less than 1 GHz. Physically, this value of the capacitance can be obtained from a CCMEBG array with dimensions L = 7.0 mm, W = 5.0 mm, and periodicity D = 14.0 mm, with separation distance d = 50 μm. The array has been fabricated and the band gap measured. The measured transmission coefficient of the array on the handset case dielectric is shown in Figure 5. The cutoff is slightly lower than calculated because of the presence of the dielectric and the miniaturization achieved with respect to the single-layer design is in the order of 15:1. A narrowband propagating mode also appears at 1 GHz, but the transmission levels are below −20 dB at frequencies over 1.1 GHz. Although approximate, the simple LC model has proved to be very efficient in the design of the CCMEBG array.
3. Performance of MEBG Handset: Antenna Detuning and Efficiency
 In this section we integrate the designed CCMEBG into a handset prototype and assess its performance when the handset is held by a human hand. Simulated results have already shown the improvement in terms of the antenna detuning [Goussetis et al., 2004]. Here we present experimental results for the detuning, antenna efficiency, and radiation patterns.
 A simple inverted F antenna operating at 1.15 GHz has been designed. The antenna has been fabricated on a grounded dielectric substrate of thickness 1.13 mm and permittivity ɛr = 2.2. The antenna is mounted in a model handset case with overall dimensions 90 cm × 70 cm × 30 cm. The thickness of the hollow case is 2 mm, and the permittivity is approximately 3. The performance of the handset loaded with a human hand is compared with the handset alone as a means to assess the performance.
3.1. Antenna Detuning
 The detuning effect of the hand on the performance of a handset antenna is initially demonstrated. Figure 6a shows the return loss of the prototype handset in the absence of the human hand and in the case where a real human hand holds the handset case at increasingly smaller distances s from the plane of the antenna. It is obvious that as the hand moves closer to the antenna, the resonant frequency drops. As previously discussed, the detuning arrives as a result of the coupling of a high permittivity object (user's hand) with the antenna.
 We now introduce the miniaturized tripole CCMEBG structure embedded in the case of the handset as a means of suppressing the fields on the plastic case. Upon introducing the MEBG, the antenna design has to be optimized in order to achieve good matching. Figure 6b shows the return loss for the MEBG handset held by the same human hand at the same distances from the antenna. The resonant frequency of the antenna is now shown to be constant with the position of the hand. This result demonstrates the benefit of embedding the MEBG in the handset's case in reducing the antenna detuning.
 In order to compensate for the uncertainty with regard to the exact positioning of the human hand, we have carried out a statistical analysis for the above measurements. We have therefore repeated the measurements of Figures 6a and 6b for s = 1 cm 10 times each. The average resonant frequency with the corresponding standard deviation for the handset with and without the MEBG is shown in Figure 7. As shown, the matching frequency drops from 1.183 GHz to 1.163 GHz for the handset without the MEBG. For the MEBG handset the matching frequency drops from 1.115 GHz to 1.112 GHz, corresponding to approximately 10 times smaller frequency shift. The increased standard deviation in the latter measurement is attributed to the fact that the position of the hand within the unit cell of the MEBG varies.
3.2. Radiation Efficiency and Patterns
 In order to measure the effect of the human hand on the efficiency of the prototype handset, we have employed a liquid load attached on the handset to model the human hand. The load consists of 150 ml of liquid, which at 1.15 GHz is characterized by permittivity ɛ = 38.63, loss tangent tanδ = 0.008, and conductivity s = 1.2 1S/m2. The handset with the load is then measured in a fully anechoic chamber, and the three-dimensional radiation pattern is obtained. The efficiency is readily estimated upon integrating the radiated power in all directions. The measurement is repeated for the handset with and without the MEBG. The radiation efficiency of the loaded handset without the MEBG was measured 33.58%. The loaded MEBG handset yielded a radiation efficiency of 41.31%. This corresponds to an efficiency improvement of approximately 8%. This improvement is attributed to the reduced EM fields in the spatial location of the load, and hence reduced thermal losses, achieved by virtue of the MEBG.
Figure 8 shows the measurement setup in the anechoic chamber. The handset rotates around its axis on the θ plane for ϕ = 0° (Figure 8a) and ϕ = 90° (Figure 8b) values as shown in the graph. Figure 8 shows the handset in both cases for θ = 0°. The receiver measures both copolar and cross-polar radiations. For ϕ = 0°, the Eθ component is the copolar, whereas for ϕ = 90° the copolar component is Eϕ. Figure 9a shows the radiation pattern in the two main planes (ϕ = 0° and ϕ = 90°) for the loaded handset without the MEBG. Figure 9b shows the same radiation patterns for the MEBG handset. As can be observed, both radiation patterns are in accordance with the performance of a typical inverted F antenna mounted on a mobile handset [Saraereh et al., 2004].
 The presence of the MEBG, however, affects the radiation pattern as shown in Figure 9. In particular, in the ϕ = 0° plane the presence of the MEBG reduces the backward radiation of the copolar component (θ = 180°) by about 8 dB. This is attributed to the suppression of currents on the ground plane and associated edge effects because of the MEBG. No significant difference is observed in the radiation pattern of the cross-polar component (Eϕ). In the ϕ = 90° plane, the copolar radiation toward the lower end of the handset (θ = −90°) reduces by about 10 dB and a new null appears. The reduction of power radiated toward the direction where the MEBG is placed is attributed to the fact that the MEBG is acting as a stopband filter in this direction. The cross-polar component (Eθ) changes only slightly.
 Miniaturized MEBG structures have been investigated and integrated into a simple compact mobile handset model. Dispersion diagrams for closely coupled metallodielectric band gap (CCMEBG) structures have been produced. A circuit approach has been adopted as a fast and efficient design tool, and miniaturization by a factor of 15 has been demonstrated experimentally. The employment of miniaturized CCMEBGs has been proposed as a means of reducing the coupling of the human hand to the antenna. By means of fabricated prototypes, reduction in the antenna detuning and increase in the radiating efficiency have been demonstrated for the CCMEBG handset when it is being held by the user's hand. Measurements of the fabricated prototypes in a fully anechoic chamber have shown that integration of the MEBG does not to significantly affect the radiation patterns.
 This work is supported by the UK EPSRC research grant GR/R42580/01.