A Method for Determining Optimal EBG Reflection Phase for Low Profile Dipole Antennas

Transcription

1 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY A Method for Determining Optimal EBG Reflection Phase for Low Profile Dipole Antennas Ian T. McMichael, Member, IEEE, Amir I. Zaghloul, Life Fellow, IEEE, and Mark S. Mirotznik, Senior Member, IEEE Abstract An analytical method for determining the optimal reflection phase of an electromagnetic band gap (EBG) ground plane to match a low profile dipole antenna is introduced. Image theory is used to incorporate the near field coupling between a dipole antenna and the ground plane. The main contribution of this paper is to show that the optimal EBG reflection phase can be determined at discrete frequencies where a theoretically perfect return loss occurs. The optimal reflection phase is then obtained over a wider frequency band of interest and is related to the antenna s return loss for a given feed impedance and antenna height above the EBG. The resulting reflection phase can be used as a reference for designing an EBG ground plane that is well matched to the antenna without time consuming iterative full wave numerical simulations. Numerical modeling results are compared to the optimal return loss derived from the analytical method to validate the design process. It is also shown that, for certain antennas, vias are not always necessary in the construction of the EBG, which eases the manufacturing process. Finally, a dipole and EBG are constructed using the optimal design method and measurements are compared to the simulations. Index Terms Electromagnetic band gap (EBG), low profile antenna, reflection phase. I. INTRODUCTION E LECTROMAGNETIC band gap (EBG) structures have been widely investigated as ground planes for low profile antennas because of their characteristic surface wave band gaps and frequency dependent reflection phase [1], [2]. It has been shown that a reflection phase of zero degrees will cause a horizontal dipole placed close to an EBG to radiate more efficiently than the same dipole placed close to a perfect electrically conducting (PEC) ground plane. However, even greater improvements to radiation efficiency occur when the reflection phase is [3]. The reasoning for this improved efficiency was explained in [4] using the model of a dipole and its image, where the image dipole incorporates a near-field mutual impedance. The image theory concept is extended in this paper Manuscript received August 06, 2012; revised November 30, 2012; accepted January 22, Date of publication February 01, 2013; date of current version May 01, I. T. McMichael is with the University of Delaware, Newark, DE USA, and also with the U.S. Army CERDEC RDECOM NVESD, Ft. Belvoir, VA USA. A. I. Zaghloul is with the Army Research Laboratory, Adelphi, MD USA. M. S. Mirotznik is with the Electrical and Computer Engineering Department, University of Delaware, Newark, DE USA ( mirotzni@ece.udel. edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TAP Fig. 1. (a) A dipole and its image in the near field region and (b) the equivalent dipole above an EBG ground plane. to determine the optimal reflection phase for matching an EBG to a low profile dipole antenna at discrete frequencies where a theoretically perfect impedance match occurs. The optimal reflection phase profile and its corresponding optimal return loss can then be used as a reference for designing an EBG ground plane for the chosen antenna configuration. The analytical optimizationofanebgmatchedtoalowprofile dipole is validated using a finite element optimization process and an example design is shown. II. OPTIMAL EBG REFLECTION PHASE Low profile antennas are typically spaced close enough to a ground plane so that the ground plane is in the near field region of the antenna. These near fields will preclude the use of plane wave approximations for determining the optimal reflection phase. Image theory can be used to establish equivalence between a dipole coupled to its image and a dipole coupled to an EBG as shown in Fig. 1. The phase difference between the dipole and its image is equivalent to the reflection phase of the EBG. This model is strictly valid only if there are no surface waves on the ground plane and it is infinitely large. If surface waves do exist, an additional distributed image current must be introduced [5]. If the ground plane does not support surface waves, then the image theory provides a reasonable model for finite sized ground planes. The dipole as shown in Fig. 1(a) has a driving-point impedance [6] where is the dipole s self impedance, is the mutual impedance between the dipole and its image, and is the phase difference between the current on the dipole and its image. Aperfect impedance match is achieved when the antenna s driving point impedance equals the feedingtransmissionline impedance,. Rearranging (1) and enforcing the condition (1) X/$ IEEE

2 2412 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY 2013 that the driving point impedance equals the feed line impedance, we can write (2) which is clearly only valid if the magnitude of the quantity on the right hand side is unity. The magnitude of the right hand side of (2) can be plotted over frequency to determine the exact frequencies where it equals 1. These discrete impedance values can then be inserted into (3) to determine the phase values that produce a theoretically perfect impedance match. Since the phase term in (1) is equivalent to the reflection phase of an EBG a distance away from the antenna, a designer can create an EBG ground plane to exhibit this reflection phase using published analytical EBG impedance formulas [5]. In this manner, a very good return loss can be realized for a given feed impedance and antenna height by using a single numerical model to determine and of an antenna and its image. This is more computationally efficient than using iterative numerical modeling optimization of an antenna and an EBG, which can be very time consuming. Alternatively, one can use (1) to find the best possible phase term over a range of frequencies instead of finding a perfect impedance match condition at discrete frequencies. By inserting (1) into the expression for return loss, we can write Fig. 2. Self impedance and mutual impedance of a pair of 91-mm-long dipoles separated a distance of mm. TABLE I NUMERICALLY OPTIMIZED PATCH WIDTHS (4) A simple numerical script can be written to find the minimum return loss at each frequency of interest by calculating (4) over a phase range of. It should be noted that while (4) can be used to find an optimum value for the return loss over a range of frequencies, the optimized value is not necessarily very low at all frequencies. The dipole is still limited in its radiation capability away from resonance. III. NUMERICAL VALIDATION An ideal thin dipole with a lumped port was numerically modeled using the Ansoft HFSS finite element software package. The thin dipole was 91 mm long with a GHz resonant frequency in free space. A replica dipole was then modeled a distance away and the and values were computed over a range of frequencies. Fig. 2 shows the computed self impedance and mutual impedance of the two dipoles. The same dipole as described above was then modeled at a distance (or ) above a square patch mushroom-type EBG with a substrate height of 5 mm, substrate of 5.8, and patch gap width of 1 mm. The size of the EBG was 7 unit cells by 7 unit cells, where a unit cell size is defined as the patch width plus the patch gap width. The patch width was varied at several discrete frequencies while all other parameters were held constant to find the values Fig. 3. Magnitude of the impedance ratio on the right hand side of (2). The quantity crosses 1 at two discrete frequencies,1.5and1.74ghz,wherethe dipole s driving point impedance matches the feeding transmission line s impedance. that produced the best return loss at each frequency. The optimal EBG parameters were then used in a unit cell analysis to determine the corresponding reflection phase. The patch widths that were numerically determined to produce the best return loss at discrete frequencies are shown in Table I. Using a feed line impedance of 50, the analytical optimization method described in Section II produced two discrete frequencies corresponding to a perfect impedance match. Fig. 3 shows the magnitude of the impedance ratio on the right hand side of (2) as a function of frequency, which has a value of 1 at two distinct frequencies. Fig. 4(a) shows the analytically derived optimal reflection phase curve along with the numerically optimized reflection phase. Fig. 4(b) shows the analytically optimized S11 for the dipole compared to the numerically optimized S11. It can be seen that the analytically derived phase values are in good agreement with the numerically optimized values. The numerically derived S11 diverges from the optimal

3 MCMICHAEL et al.: METHOD FOR DETERMINING OPTIMAL EBG REFLECTION PHASE FOR LOW PROFILE DIPOLE ANTENNAS 2413 Fig. 5. Analytically derived optimal reflection phase for two different feed impedance values. Fig. 4. (a) Analytically derived optimal reflection phase and HFSS optimal reflection phase for a dipole above an EBG. (b) Analytically derived optimal S11 and HFSS optimal S11 for a dipole above an EBG. S11 at higher frequencies because these frequencies are outside of the TE surface wave band gap region. In the above example, the optimal return loss for the dipole at 1.5GHzoccursforanEBGreflection phase of approximately 100, which is in the expected range of according to [3]. However, since the optimal return loss is a function of, which is affected by the dipole height, and a function of,it can be shown that the optimal return loss is not necessarily in the range of for all dipole configurations. As an example case, the optimal S11 and reflection phase were computed for the same dipole pair as in the previous example but with a feed impedance of 150 instead of 50. The resulting reflection phase is shown in Fig. 5 and compared to the reflection phase for a50 feed impedance. The S11 for the 150 feed impedance is shown in Fig. 6 as compared to the S11 for the 50 feed. The optimal S11 for the 150 feed now occurs at 1.59 GHz where the reflection phase is approximately 0. Another result of increasing the feed impedance in this example is that the bandwidth for a good return loss increased significantly. However, TE surface waves are supported above 1.59 GHz. Therefore, even though increasing the feed impedance increases the theoretical bandwidth, surface waves over part of the band prevent the theoretically optimal return loss from being achieved over the entire band. Increasing the physical spacing between the dipole and its image, which represents the dipole being raised higher above the EBG, causes the two dips in the optimal return loss to come Fig. 6. Analytically derived optimal return loss for two different feed impedance values. together. Increasing the dipole spacing also causes the optimal reflection phase to increase. This trend is intuitively reasonable since, in the case where the dipole spacing is increased to a half wavelength, or equivalently one quarter wavelength above a ground plane, the dipole is expected to radiate well when the reflection phase is 180 like a PEC produces. IV. EBG DESIGN EXAMPLE In the previous section, it was shown that a theoretically perfect return loss can be achieved for a horizontal dipole over an EBG. Since the dipole is well matched at a frequency where TE surface waves are not supported, we now show that this implies vias are not necessary in the construction of the EBG for particular feed configurations. It is shown in [5] that a TE surface wave traveling in the plane of the EBG and decaying away from the EBG surface will have the form where is the direction in which the wave is traveling, is the direction away from the face of the EBG in which the wave is decaying, is the propagation constant, is the decay constant, and is an amplitude. The propagation constant for the TE mode can be expressed as (5) (6)

4 2414 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY 2013 Fig. 7. Reflection phase (dashed) and surface impedance (solid) of an EBG without vias computed from the L C approximation. TM surface waves are supported when the surface impedance is positive and TE surface waves are supported with the surface impedance is negative. and the TE decay constant is where is the surface impedance of the EBG. The expressions for the case of TM surface waves can be found in [5]. For a surface wave to propagate, must be real. Additionally, must be real and positive to ensure that the wave decays away from the EBG surface. For TE surface waves, these conditions require to be negative and imaginary. An approximate expression for the surface impedance of an EBG is where is the EBG inductance, is the EBG capacitance, and is the EBG resonant frequency, which is defined as A plot of the surface impedance of an EBG with and derived using (8) is shown in Fig. 7. The values of and were calculated using the equations for an EBG without vias shown in [8]. It can be seen that the surface impedance is positive below and negative above. With regard to (5) (7), this implies that when the surface impedance is positive, or inductive, only TM surface waves are supported. When the surface impedance is negative, or capacitive, only TE surface waves are supported. As we have shown in Fig. 4, the low profile horizontal dipole with a 50 feed above an EBG has a good impedance matchwhenthereflection phase is approximately 100.This frequency region is where the surface impedance is positive and TE surface waves are not supported. Since the horizontal dipole itself radiates only TE waves with respect to the EBG ground plane, no TM surface modes exist. In this case, vias are not (7) (8) (9) necessary in the construction of the EBG since the vias function to suppress TM surface waves and create a surface wave band gap. In general, it is not the case that vias are unnecessary in EBG designs since many antennas and feed configurations will excite TM modes with respect to the ground plane. For example, if a dipole is fed using a coaxial cable coming up through the bottom of the EBG ground plane to reach the dipole element up above and a balun is not properly implemented, TM modes can be excited by the feeding structure and surface waves will be created. An example of this type of surface wave antenna is shown in [7]. Another example is that of a patch antenna on top of an EBG. The patch antenna itself creates TM modes and causes TM surface waves. In these cases, vias can be introduced into the EBG to suppress the TM surface waves. An EBG without vias and a dipole were designed and simulated in HFSS using the method described in Section II. The dipole was 73 mm long with 1 mm wide traces on opposite sides of a 0.79-mm-thick slab of FR4. The dipole resonates at 1.58 GHz without the EBG ground plane. The dipole is fed by a tapered balun on the same sheet of FR4, which transitions an unbalanced microstrip transmission line with a 50 characteristic impedance to balanced parallel strips with a 70 impedance. First, the optimal reflection phase and return loss were derived from a set of these dipoles simulated 12 mm apart. In this case, only one frequency resulted in a near perfect return loss since the impedance ratio of (2) only passed through unity at one frequency as opposed to the simplified lumped port dipole without a supporting layer of FR4 in Section II, which exhibited two good return loss frequencies. The reflection phase that produced the best return loss was 80 at 1.5 GHz. The analytically derived optimal reflection phase is not realizable over the entire frequency band of interest with a single EBG design, so a set of EBG parameters was chosen to exhibit an 80 reflection phase at 1.5 GHz. The EBG parameters that were chosen to create the required reflection phase are as follows: 4.5 substrate permittivity, 6.35-mm substrate height, 24-mm patch width, and 1 mm patch gap width. Fig. 8 shows the optimal reflection phase and the optimal S11 derived from the coupled dipole pair using the method described in Section II compared with the S11 and reflection phase of the designed EBG. The difference in the S11 resonant frequency of the simulated dipole compared to the theoretically optimum value is likely due to the finite dimensions of the simulated EBG, which was chosen to be 7 7 unit cells for practical implementation. Next, the 73-mm-long dipole with a tapered balun was constructed. The dipole is shown in Fig. 9 and the measured S11 is shown in Fig. 10 as compared with the S11 of the simulated antenna. The EBG ground plane was constructed using a7 7 grid of patches without vias on a grounded slab of 6.35-mm-thick Rogers TMM-4, which has a permittivity of 4.5. The patch width was 24 mm, which was determined to provide the appropriate reflection phase given by the optimization process. The width of the gap between patches was 1 mm. A 6-mm layer of Rohacell, which has a relative permittivity near 1, was placed on top of the EBG ground plane and the dipole

5 MCMICHAEL et al.: METHOD FOR DETERMINING OPTIMAL EBG REFLECTION PHASE FOR LOW PROFILE DIPOLE ANTENNAS 2415 Fig. 10. Return loss of the dipole shown in Fig. 9 compared to the numerically simulated dipole. Fig. 8. (a) Theoretically optimum reflection phase for a 73-mm-long dipole on a thin sheet of FR4 compared to the reflection phase of the designed EBG and (b) the theoretically optimum S11 for the dipole compared to the S11 of the simulated dipole over the EBG. Fig. 11. (a) Patch type EBG ground plane designed to create an optimal resonance with the dipole shown in Fig. 9. (b) Dipole with a balun over the EBG ground plane with a 6-mm spacer of Rohacell between the antenna and the EBG. Fig mm-long dipole on a 0.79-mm-thick sheet of FR4. The dipole is fed by a tapered balun, which transitions a microstrip line to parallel strips. was placed on top of the Rohacell spacer. The 6-mm spacing between the dipole and the EBG ground plane is at 1.5 GHz. Fig. 11 shows the EBG structure and the dipole antenna over the EBG ground plane. The measured S11 is shown in Fig. 12 and is compared with the simulated S11 and the theoretically determined optimum S11. The best S11 for the simulated antenna occurred at 1.45 GHz and the best S11 for the measured antenna occurred at 1.48 GHz, which are both close to the theoretically optimum value of 1.5 GHz. The reason the simulated and constructed antennas have a slightly different resonance than the theoretically optimum resonance is likely because the simulated and constructed EBG ground planes are finite in size and do not completely suppress all surface waves. The periodic patches do largely suppress the TE surface waves, but analysis of the EBG

6 2416 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY 2013 Fig. 12. S11 of the dipole over the EBG shown in Fig. 11 compared to the numerically simulated dipole and EBG. an EBG ground plane. The best possible reflection phase values were then derived over a broad frequency range and the corresponding return loss was shown. This analytical design method using image theory was validated by comparing results to a full wave numerical optimization process for a dipole above an EBG. This analytical technique for determining the optimal EBG reflection phase for low profile dipole antennas can be a useful tool for ground plane designers to achieve an optimal return loss in an efficient manner. Furthermore, it was shown that vias are not necessary in the EBG design for the special case when no TM modes are excited by the antenna or feed structure and the optimal impedance match occurs where TE modes are not supported. Finally, a dipole and EBG were constructed using the proposed design method. Measurements were in good agreement with the numerical model and the optimal return loss derived from the image theory method. While the authors believe the image theory design method to be general and applicable to other antenna types, initial simulations with bowtie, loop, and spiral antennas showed inconsistent results. Future investigations of optimal EBG design using the image theory method for various antenna types will be conducted. Fig. 13. Copolarized and cross-polarized gain patterns for the simulated dipole at its resonant frequency over the EBG ground plane. surface current density in HFSS shows a very small amount of current at the edge of the EBG. The copolarized and cross-polarized gain patterns for the simulated dipole at its resonant frequency over the EBG are shown in Fig. 13. The peak gain is 6.7 db near broadside and the back lobe is 26.7 db down from the main lobe. The cross-polarized gain, that is the gain due to the fields in the orthogonal direction from the dipole, is significantly lower than the copolarized gain. The beam pattern is slightly asymmetric, with the peak gain 2 offofbroadside,duetothefeed structure approaching the antenna from the side. Since the return loss of the simulated antenna and the constructed antenna were very similar, it should be expected that the gain pattern for the simulated antenna would also approximate the gain pattern of the constructed antenna. V. CONCLUSION A method for analytically deriving the optimal EBG reflection phase for low profile dipole antennas has been presented. Reflection phase values at discrete frequencies were shown to produce a theoretically perfect impedance match of a dipole to REFERENCES [1] D. Sievenpiper, High impedance electromagnetic surfaces, Ph.D. dissertation, Elect. Eng. Dept., Univ. California, Los Angeles, CA, USA, [2] Z. Li and Y. Rahmat-Sammi, PBG, PMC and PEC surface for antenna applications: A comparative study, in IEEE APS Dig., 2000, pp [3] F. Yang and Y. Rahmat-Samii, Reflection phase characterization of the EBG ground plane for low profile wire antenna applications, IEEE Trans. Antennas Propag., vol. 51, no. 10, pp , Oct [4] M. Abedin and M. Ali, Effects of EBG reflection phase profiles on the input impedance and bandwidth of ultrathin directional dipoles, IEEE Trans. Antennas Propag., vol. 53, no. 11, pp , Nov [5] S. Tretyakov, Analytical Modeling in Applied Electromagnetics. Boston, MA, USA: Artech House, 2003, pp [6] C. Balanis, Antenna Theory: Analysis and Design, 3rd ed. Hoboken, NJ, USA: Wiley, 2005, pp [7] F. Yang and Y. Rahmat-Samii, Electromagnetic Band Gap Structures in Antenna Engineering, ser. The Cambridge RF and Microwave Engineering Series, S. Cripps, Ed. New York, NY, USA: Cambridge Univ. Press, [8] O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko,A.Räisänen,andS.Tretyakov, Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches, IEEE Trans. Antennas Propag., vol. 56, no. 6, pp , Jun Ian T. McMichael (M 05) received the B.S.E.E. degree from George Mason University, Fairfax, VA, USA, in 2001, the M.S.E.E. degree from George Washington University, Washington, DC, USA, in 2008, and is currently working toward the Ph.D. degree in electrical and computer engineering at the University of Delaware, Newark, DE, USA. Since 2002, he has been with the U.S. Army RDECOM CERDEC Night Vision and Electronic Sensors Directorate, Ft. Belvoir, VA, USA. His research interests include electromagnetic sensors for landmine detection, computational electromagnetics, antenna design, and electromagnetic band gap structures.

7 MCMICHAEL et al.: METHOD FOR DETERMINING OPTIMAL EBG REFLECTION PHASE FOR LOW PROFILE DIPOLE ANTENNAS 2417 Amir I. Zaghloul (M 73 SM 00 F 02 LF 11) received the Ph.D. and M.A.Sc. degrees from the University of Waterloo, Canada in 1973 and 1970, respectively, and the B.Sc. degree (Hons.) from Cairo University, Egypt in 1965, all in electrical engineering. In 2001, he joined Virginia Polytechnic Institute and State University (Virginia Tech) as Professor in the Bradley Department of Electrical and Computer Engineering. Prior to Virginia Tech, he was at COMSAT Laboratories for 24 years performing and directing R&D efforts on satellite communications and antennas, where he received several research and patent awards, including the Exceptional Patent Award. He held positions at the University of Waterloo, Canada ( ), University of Toronto, Canada ( ), Aalborg University, Denmark (1976) and Johns Hopkins University, Maryland ( ). Mr. Zaghloul is an Associate Fellow for The American Institute of Aeronautics and Astronautics (AIAA), and is a member of Commissions A&B of the International Union of Radio Science (URSI); the IEEE Committee on Communications and Information Policy (CCIP); the IEEE Publication Services and Products Board (PSPB); and of the Administrative Committee of the IEEE Antennas Propagation Society. He was the general chair of the IEEE International Symposium on Antennas and Propagation and USNC/URSI Meeting, Washington, DC, USA, July He is a recipient of the 1986 Wheeler Prize Award for Best Application Paper in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. Mark S. Mirotznik (S 87 M 92) received the B.S.E.E. degree from Bradley University, Peoria, IL, USA, in 1988, and the M.S.E.E. and Ph.D. degrees from the University of Pennsylvania, Philadelphia, PA, USA, in 1991 and 1992, respectively. From 1992 to 2009, he was a Faculty Member with the Department of Electrical Engineering, The Catholic University of America, Washington, DC, USA. Since 2009, he has been an Associate Professor and Director of Educational Outreach with the Department of Electrical and Computer Engineering, University of Delaware, Newark. In addition to his academic positions, he an associate editor of the Journal of Optical Engineering and is a Senior Research Engineer for the Naval Surface Warfare Center (NSWC), Carderock Division. His research interests include applied electromagnetics and photonics, computational electromagnetics and multifunctional engineered materials. Prof. Mirotznik was the recipient of the 2010 Wheeler Prize Award for Best Application Paper in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.