Equivalent Circuit Model and Experimental Analysis of an ... - URSI
Equivalent Circuit Model and Experimental Analysis of an Ultrawideband Hybrid EBG/Ferrite Ground Plane Jodie M. Bell* and Magdy F. Iskander Hawaii Center for Advanced Communications, Honolulu, HI E-mail: {jodieb; magdy}@hawaii.edu Abstract This paper presents the development of an equivalent circuit model as well as the experimental analysis of the ultrawideband and low-profile hybrid electromagnetic band-gap (EBG)/ferrite ground plane presented in [1, 2]. With the development of the equivalent circuit model a better understanding of the operation of the hybrid ground plane in relation to the hybrid structure geometry as well as the hybrid structure material properties is obtained. Experimental measurements were performed in a transverse electromagnetic (TEM) cell. As it will be shown, experimental results of the reflectivity and phase analyses of the hybrid ground plane show good correlation with the simulated results. 1. Introduction The design and analysis of a novel ultrawideband hybrid electromagnetic band-gap (EBG)/ferrite structure that implements a combination of the mushroom type EBG structure with ferrite absorbing material were presented in [1, 2]. This design provides for a low-profile and conformal ultrawideband ground plane that is needed for backing ultrawideband antennas with minimal impact on the achievable bandwidth. As was reported in [2], the hybrid design offers a bandwidth exceeding 40:1 ranging from 120MHz to 4.86GHz. An equivalent circuit model of the hybrid ground plane was developed to provide a better understanding of the operation of the hybrid ground plane in relation to the hybrid structure geometry as well as the hybrid structure material properties. The development of the equivalent circuit model along with the knowledge gained from the equivalent circuit model can lead to a more efficient and straight forward design strategy for subsequent hybrid ground plane variations. A transverse electromagnetic (TEM) cell which consists of a flared square coaxial transmission line was implemented to experimentally verify the performance of the hybrid ground plane. To ensure accurate experimental results IEEE Standard 1128-1998 [3] was used to perform the experimental measurements on the hybrid ground plane. 2. Hybrid EBG/Ferrite Ground Plane The hybrid ground plane, shown in Fig. 1, that incorporates the implementation of the mushroom EBG structure and ETS-Lindgren’s ferrite tile absorber is described in [1, 2]. The design consists of an EBG structure with a slab of ferrite absorber resting on the ground plane of the EBG structure. A small portion of the ferrite slab is removed around each of the vias of the EBG structure to allow the structure to behave as desired. The hybrid ground plane provides the desired performance characteristics with minimal limitations over an ultrawideband by using the ferrite absorber component to absorb the antennas backward radiation in the lower frequency band while the EBG structure component of the design is used to provide a desirable phase for the reflected backward radiation in the frequency band above the operational region of the ferrite absorber. The ferrite absorber region of operation is defined where less than -14dB of reflected radiation is seen from the hybrid ground plane while the EBG region of operation is defined where the phase of the reflected radiation is between ±90° regardless of the magnitude of the reflected radiation. 3. Equivalent Circuit Model The equivalent circuit model of the hybrid ground plane was developed through close observation of the geometry of the hybrid structure as well as the material properties of the hybrid
structure. Through this observation the relevant circuit components that could describe the operation of the hybrid structure were implemented in the circuit model as shown in Fig. 2. In the equivalent circuit model C represents the capacitances created between the surface patches by the buildup of charges on the edges of the patches, L represents the inductances created by the currents traveling the paths along the patches, vias, and the EBG ground plane which are greatly affected by the frequency dependent permeability properties of the ferrite absorber, and R represents the resistances created by the effect of the inclusion of the ferrite absorber on the aforementioned currents. When determining the optimal component values for the equivalent circuit model it is important to have an accurate manner of predicting the component values to be able to provide the necessary restrictions for the optimizer engine. Therefore, the methods described in [4], seen in Eq. 1 and 2, for predicting the values of the capacitance and inductance for the mushroom type EBG structure were also used to predict the capacitance and inductance values for the hybrid ground plane. In addition, Eq. 3 was used to predict the resistance values for the hybrid ground plane.
C=
wP (ε sub + ε 0 )
π
′ tS L = µ sub ′′ t S R = −2πfµ sub
⎛ wE cosh −1 ⎜⎜ ⎝ wE − wP
⎞ ⎟⎟ ⎠
(1) (2) (3)
In Eq. 1, 2, and 3 wP is the patch width, wE is the element width, and tS is the structure thickness while εsub and µsub are the effective permittivity and effective permeability of the air/ferrite substrate supporting the hybrid structure. To determine the optimal values of each of the circuit components the surface impedance of the hybrid ground pane was first calculated from the reflectivity and phase analyses results determined using Ansoft’s HFSS. Then using the global optimization software package provided by Tomlab as an add-on for Matlab [5] with starting values for the circuit components equal to the analytically predicted component values, the optimal values for each component were determined to provide the previously calculated surface impedance of the hybrid ground plane. As Fig. 3 depicts, the predicted component values show good correlation with the optimal component values. Therefore, it can be concluded that the equivalent circuit model depicted in Fig. 2 accurately represents the hybrid structure and that Eq. 1, 2, and 3 provide accurate predictions for the equivalent circuit model components. 4. Experimental Measurement Procedure To implement a free space measurement method it is suggested that the surface under test (SUT) be at least 10λ x 10λ at the lowest frequency of interest [3]. To cover the desired low frequency limit of 100MHz measurements would require the fabrication of a hybrid ground plane that is at least 30m x 30m which is too large for practical purposes. Therefore, a TEM cell was designed and fabricated to experimentally verify the performance of the hybrid ground plane. To ensure accurate experimental results IEEE Standard 1128-1998 [3] was used to perform the experimental measurements. The experimental setup is shown in Fig. 4. To start the experimental measurements a full one-port S11 calibration is performed on the network analyzer at the cable connector that connects to the excitation port of the TEM cell. The TEM cell is then terminated with a metallic shorting plate as the SUT. Time gating is then used to discriminate the reflection from the SUT from other undesired reflections. The time gated reflection coefficient measurements for the metallic plate are stored as the reference for subsequent results calculations. The metallic shorting plate is then replaced with the hybrid ground plane as the SUT. As with the metallic shorting plate, time gating is used to discriminate the reflection from the SUT from other undesired reflections. The ratio of the magnitude of the reflection coefficient of the hybrid ground plane to the magnitude of the reflection coefficient of the metallic shorting plate is calculated to provide the reflectivity of the hybrid ground plane. To determine the phase offset at the surface of the hybrid ground plane twice the electrical distance to the surface of the hybrid ground plane
(taking into account for the round trip to and from the SUT) for each frequency point is subtracted from the phase of the measured reflection coefficient for the hybrid ground plane. The physical distance to the surface of the hybrid ground plane is determined by subtracting the thickness of the hybrid ground plane from the physical distance to the reference metallic plate which is determined from the time domain reflection coefficient results for the reference metallic plate. Since the TEM cell is air filled the calculation of the electrical distance from the physical distance for each frequency point is straightforward as shown in Eq. 4.
D E = 360 o *
DP
λ
(4)
Where DP is the physical distance to the surface of the hybrid ground plane and λ is the wavelength. 5. Experimental Analysis Results Results of the experimental reflectivity and phase analyses for the hybrid ground plane are shown in Fig. 5. This includes the simulation results, which consist of both a simulated infinite array of the hybrid ground plane and a simulated experimental test setup including the TEM cell, as well as the measured data. The phase analysis comparison, seen in Fig. 5a, shows good agreement between the measured and simulated data while the reflectivity analysis comparison, seen in Fig. 5b, shows good agreement between the measured and simulated data at the lower frequencies with a trend to diverge at the higher frequencies. Because of the low field intensities, the reflectivity is less than -12dB, very little noise can cause noticeable measurement errors. The discrepancy in the reflectivity is believed to be due to the higher-order modes in the TEM cell. The higher-order mode with the greatest field strength begins to propagate in the TEM cell at approximately 475MHz which correlates well with the point at which the measured and simulated data begin to diverge. This as well as other observations regarding the measured characteristics of the hybrid ground plane will be discussed in the presentation. References [1] J. M. Bell, M. F. Iskander, and J. J. Lee, Ultrawideband Hybrid EBG/Ferrite Ground Plane for Low-Profile Array Antennas, IEEE Transactions on Antennas and Propagation, vol. 55, pp. 412, January 2007. [2] J. M. Bell and M. F. Iskander, Effective Propagation Properties of an Enhanced Hybrid EBG/Ferrite Ground Plane, IEEE Antennas and Wireless Propagation Letters, accepted for publication December 2007. [3] IEEE Standard 1128-1998, IEEE Recommended Practice for Radio-Frequency (RF) Absorber Evaluation in the Range of 30MHz to 5GHz, April 1998. [4] D. Sievenpiper, High-Impedance Electromagnetic Surfaces, Ph.D. Dissertation, University of California, Los Angeles, 1999. [5] Tomlab Optimization Inc., TOMLAB Optimization Environment [Online], Available: http://tomopt.com/tomlab. [6] R. Diaz, Magnetic Loading of Artificial Magnetic Conductors for Bandwidth Enhancement, IEEE Antennas and Propagation Society International Symposium, vol. 2, pp. 431-434, June 2003. [7] B. A. Kramer, S. Koulouridis, C.-C. Chen, and J. L. Volakis, A Novel Reflective Surface for an UHF Spiral Antenna, IEEE Antennas and Wireless Propagation Letters, vol. 5, pp. 32-34, December 2006. [8] J. M. Bell and M. F. Iskander, A Low-Profile Archimedean Spiral Antenna using an EBG Ground Plane, IEEE Antennas and Wireless Propagation Letters, vol. 3, pp. 223-226, 2004.
(a) Fig. 1. Fabricated hybrid EBG/ferrite ground plane.
C
L
R
Fig. 2. Equivalent circuit model of the hybrid EBG/ferrite ground plane.
(b) Fig. 4. Experimental test setup for measuring the performance of the hybrid ground plane.
(a)
(a)
(b)
(b) Fig. 5. Experimental analysis results for the hybrid ground plane: (a) phase and (b) reflectivity.
(c) Fig. 3. Comparative analysis of equivalent circuit model component values: (a) C, (b) L, and (c) R.
structure. Through this observation the relevant circuit components that could describe the operation of the hybrid structure were implemented in the circuit model as shown in Fig. 2. In the equivalent circuit model C represents the capacitances created between the surface patches by the buildup of charges on the edges of the patches, L represents the inductances created by the currents traveling the paths along the patches, vias, and the EBG ground plane which are greatly affected by the frequency dependent permeability properties of the ferrite absorber, and R represents the resistances created by the effect of the inclusion of the ferrite absorber on the aforementioned currents. When determining the optimal component values for the equivalent circuit model it is important to have an accurate manner of predicting the component values to be able to provide the necessary restrictions for the optimizer engine. Therefore, the methods described in [4], seen in Eq. 1 and 2, for predicting the values of the capacitance and inductance for the mushroom type EBG structure were also used to predict the capacitance and inductance values for the hybrid ground plane. In addition, Eq. 3 was used to predict the resistance values for the hybrid ground plane.
C=
wP (ε sub + ε 0 )
π
′ tS L = µ sub ′′ t S R = −2πfµ sub
⎛ wE cosh −1 ⎜⎜ ⎝ wE − wP
⎞ ⎟⎟ ⎠
(1) (2) (3)
In Eq. 1, 2, and 3 wP is the patch width, wE is the element width, and tS is the structure thickness while εsub and µsub are the effective permittivity and effective permeability of the air/ferrite substrate supporting the hybrid structure. To determine the optimal values of each of the circuit components the surface impedance of the hybrid ground pane was first calculated from the reflectivity and phase analyses results determined using Ansoft’s HFSS. Then using the global optimization software package provided by Tomlab as an add-on for Matlab [5] with starting values for the circuit components equal to the analytically predicted component values, the optimal values for each component were determined to provide the previously calculated surface impedance of the hybrid ground plane. As Fig. 3 depicts, the predicted component values show good correlation with the optimal component values. Therefore, it can be concluded that the equivalent circuit model depicted in Fig. 2 accurately represents the hybrid structure and that Eq. 1, 2, and 3 provide accurate predictions for the equivalent circuit model components. 4. Experimental Measurement Procedure To implement a free space measurement method it is suggested that the surface under test (SUT) be at least 10λ x 10λ at the lowest frequency of interest [3]. To cover the desired low frequency limit of 100MHz measurements would require the fabrication of a hybrid ground plane that is at least 30m x 30m which is too large for practical purposes. Therefore, a TEM cell was designed and fabricated to experimentally verify the performance of the hybrid ground plane. To ensure accurate experimental results IEEE Standard 1128-1998 [3] was used to perform the experimental measurements. The experimental setup is shown in Fig. 4. To start the experimental measurements a full one-port S11 calibration is performed on the network analyzer at the cable connector that connects to the excitation port of the TEM cell. The TEM cell is then terminated with a metallic shorting plate as the SUT. Time gating is then used to discriminate the reflection from the SUT from other undesired reflections. The time gated reflection coefficient measurements for the metallic plate are stored as the reference for subsequent results calculations. The metallic shorting plate is then replaced with the hybrid ground plane as the SUT. As with the metallic shorting plate, time gating is used to discriminate the reflection from the SUT from other undesired reflections. The ratio of the magnitude of the reflection coefficient of the hybrid ground plane to the magnitude of the reflection coefficient of the metallic shorting plate is calculated to provide the reflectivity of the hybrid ground plane. To determine the phase offset at the surface of the hybrid ground plane twice the electrical distance to the surface of the hybrid ground plane
(taking into account for the round trip to and from the SUT) for each frequency point is subtracted from the phase of the measured reflection coefficient for the hybrid ground plane. The physical distance to the surface of the hybrid ground plane is determined by subtracting the thickness of the hybrid ground plane from the physical distance to the reference metallic plate which is determined from the time domain reflection coefficient results for the reference metallic plate. Since the TEM cell is air filled the calculation of the electrical distance from the physical distance for each frequency point is straightforward as shown in Eq. 4.
D E = 360 o *
DP
λ
(4)
Where DP is the physical distance to the surface of the hybrid ground plane and λ is the wavelength. 5. Experimental Analysis Results Results of the experimental reflectivity and phase analyses for the hybrid ground plane are shown in Fig. 5. This includes the simulation results, which consist of both a simulated infinite array of the hybrid ground plane and a simulated experimental test setup including the TEM cell, as well as the measured data. The phase analysis comparison, seen in Fig. 5a, shows good agreement between the measured and simulated data while the reflectivity analysis comparison, seen in Fig. 5b, shows good agreement between the measured and simulated data at the lower frequencies with a trend to diverge at the higher frequencies. Because of the low field intensities, the reflectivity is less than -12dB, very little noise can cause noticeable measurement errors. The discrepancy in the reflectivity is believed to be due to the higher-order modes in the TEM cell. The higher-order mode with the greatest field strength begins to propagate in the TEM cell at approximately 475MHz which correlates well with the point at which the measured and simulated data begin to diverge. This as well as other observations regarding the measured characteristics of the hybrid ground plane will be discussed in the presentation. References [1] J. M. Bell, M. F. Iskander, and J. J. Lee, Ultrawideband Hybrid EBG/Ferrite Ground Plane for Low-Profile Array Antennas, IEEE Transactions on Antennas and Propagation, vol. 55, pp. 412, January 2007. [2] J. M. Bell and M. F. Iskander, Effective Propagation Properties of an Enhanced Hybrid EBG/Ferrite Ground Plane, IEEE Antennas and Wireless Propagation Letters, accepted for publication December 2007. [3] IEEE Standard 1128-1998, IEEE Recommended Practice for Radio-Frequency (RF) Absorber Evaluation in the Range of 30MHz to 5GHz, April 1998. [4] D. Sievenpiper, High-Impedance Electromagnetic Surfaces, Ph.D. Dissertation, University of California, Los Angeles, 1999. [5] Tomlab Optimization Inc., TOMLAB Optimization Environment [Online], Available: http://tomopt.com/tomlab. [6] R. Diaz, Magnetic Loading of Artificial Magnetic Conductors for Bandwidth Enhancement, IEEE Antennas and Propagation Society International Symposium, vol. 2, pp. 431-434, June 2003. [7] B. A. Kramer, S. Koulouridis, C.-C. Chen, and J. L. Volakis, A Novel Reflective Surface for an UHF Spiral Antenna, IEEE Antennas and Wireless Propagation Letters, vol. 5, pp. 32-34, December 2006. [8] J. M. Bell and M. F. Iskander, A Low-Profile Archimedean Spiral Antenna using an EBG Ground Plane, IEEE Antennas and Wireless Propagation Letters, vol. 3, pp. 223-226, 2004.
(a) Fig. 1. Fabricated hybrid EBG/ferrite ground plane.
C
L
R
Fig. 2. Equivalent circuit model of the hybrid EBG/ferrite ground plane.
(b) Fig. 4. Experimental test setup for measuring the performance of the hybrid ground plane.
(a)
(a)
(b)
(b) Fig. 5. Experimental analysis results for the hybrid ground plane: (a) phase and (b) reflectivity.
(c) Fig. 3. Comparative analysis of equivalent circuit model component values: (a) C, (b) L, and (c) R.
