Stealth technology has been intensively studied for military applications for many years. One figure out that with some special reflection coatings printed on an object the reflected electromagnetic wave can be further reduced; therefore, the radar system can’t allocate the object. With this motivation, we aimed at designing the artificial surface for Radar Cross Section (RCS) reduction.
The reflection phase of an incident plane wave on a perfect electric conductor (PEC) is 180 degree, but is zero degree for a perfect magnetic conductor (PMC). As revealed in [1], the Radar Cross Section (RCS) can be reduced by the chessboard-like structure consisting of PEC and Artificial Magnetic Conductor (AMC). Around the operational frequency of the AMC elements, the reflections of the AMC and PEC have opposite phase, so for the normal incident plane wave the reflections cancel out, thus reducing the RCS.
Regarding the AMC surface, a mushroom-type structure was designed and experimentally verified by Sievenpiper [2]. Such a structure is constructed using commonly used Printed Circuit Board (PCB) technology. It consists of rectangular patches array connecting to the ground plane through via holes. Notably, the dimensions of the rectangular patch are smaller than that of the operational wavelength. The unit cell of the structure resembles a cavity resonator. Around the resonance frequency, the input impedance looking into the cavity is larger than that of the free space intrinsic impedance, so it is named as a High Impedance Surface (HIS).
With this high impedance characteristic, the reflected wave is in-phase with the incident wave, exhibiting the reflection characteristic of a perfect magnetic conductor.
capacitance between the patches and the resonance frequency of each unit cell. In addition to electrically tuning mechanism, the mechanically tuning method was also demonstrated in [5]. The mechanically tunable impedance surface consists of a high impedance ground and a separate tuning layer. The tuning layer is moved across the stationary high-impedance surface to vary the capacitance between the overlapping plates and tune the resonance frequency of the structure.
Artificial magnetic conductors for various metal shapes printed on the top of the surface have been studied [6]-[8]. As revealed in [6], a novel wideband artificial magnetic conductor (AMC) structure can act as high impedance surface covering the entire Ku-band from 12GHz to 18GHz for both TE and TM polarizations with respect to the angle of incidence. In [7], four kinds of Artificial Magnetic Conductors with rectangular lattices such as mushroom type high impedance surface, UC-PBG HIS, square patch and square loop Frequency selective surface (FSS) are analyzed and compared. The simulation results show that the loop FSS with smaller period has least sensitivity to the incident angle. A novel planar artificial magnetic conductor based on a frequency-selective surface has demonstrated for the application of frequencies below 1GHz, as shown in [8]. Besides, a simultaneous multi beam reflect-array has designed and validated by the experiment result. The measurements for near-field and far-field method are also discussed in [10].
The organization of this thesis is given as follows. In the next section, the structure configuration and the incident condition will be described. Secondly, the unit cell approach for determining the reflected phase angle of the AMC surface will be introduced. Moreover, the full structure simulation using CST Microwave Studio will be employed to calculate the scattering pattern of the AMC surface incident by a plane wave. In addition to the full-wave simulation, the simple formula based on the array antenna theory was developed for serving as an engineering design criterion. In the
successive section, we have fabricated the AMC surfaces and measured their reflection characteristics including the mono-static and bi-static RCS.
Chapter 2 Structure Configuration
Reflection phase of a 2D periodic structure consisting of metal patches array
As mentioned previously, a PEC surface can reflects a 180-degree phase shift with respect to the incident plane wave, while a PMC surface can have an in-phase reflected wave. As was well known, so far, the nature PMC were not found.
Nevertheless, the artificial PMC (named as artificial magnetic conductor throughout this thesis) can be realized by printing periodic metallic patterns on a grounded substrate, as will become clear later on. In this section, the structure with the reflection characteristics of AMC in a certain bandwidth will be first introduced.
Moreover, the parametric studies on the reflected phase angle against the dimension of the metal patch will be carried out to provide us a design criterion for designing a beam-steerable reflection surface. Secondly, the AMC with the square-patch dimensions arranged in specific.
Fig.2-1 A gradient AMC surface consisting of square patches array.
A two-dimensional periodic structure consisting of square metal patches printed on a substrate backed with metal ground plane is depicted in Fig. 2-1. Here, the structure is assumed to be infinite in extent along the x and y directions. The periods (unit-cell size) along the x- and y- axis are the same (denoted as d) and much smaller than that of the operational wavelength. The dimension of the square metal patch in each unit cell is denoted as a. A uniform plane wave is normally incident on the structure with its electric field along the y-axis. Notably, since the period d is assumed to be much smaller than that of the operation wavelength, all the higher space harmonics excluding (0, 0) will become evanescent (non-propagation) waves. The reflection characteristics of the infinite structure can be obtained through the unit cell approach.
Due to the normal incidence and electric-field vector along the y-axis, the unit cell is a rectangular tube with the two PEC walls along the y-axis and two PMC walls along the x-axis, respectively, as demonstrated in Fig.2-2(a). Such a unit cell structure can be regarded as a waveguide filled with inhomogeneous medium and terminated by a metal plate at its bottom surface, such as in Fig. 2-2(b) (c) (d). Furthermore, due to the boundary conditions given in the unit cell, the fundamental waveguide mode is TEM wave with its electric and magnetic fields along the y and x axes, respectively.
By resolving the scattering analysis of the waveguide mode by the discontinuity containing inhomogeneous medium and metal patch, the reflection amplitude and phase angle can be determined. Since the dielectric medium is assumed to be lossless and the metal is PEC, the incident wave will be totally reflected to the input port and only the reflected phase was demonstrated in the numerical simulations.
Fig. 2-2
Fig. 2-3 shows the reflection phase angle versus frequency for various dimensions of the square patch. The vertical axis represents the reflection phase angle in degree and the horizontal is the operational frequency. The dielectric substrate employed is FR4 with relative dielectric constant 4.4 and thickness 0.8mm. The period is 5mm.
From this figure, it is obvious to see that the reflection phase is zero degree at 15GHz for the case with patch dimension a=3.77mm. At 15GHz, the reflection phase angle deviates 0 degree as the patch dimension is varying. Such a simulation result reveals that we could manipulate the reflection phase angle by detuning the patch size. Notice that the phase angle difference against the patch size difference is nonlinear. It will
saturate as the patch dimension is greater than 4.9 mm or smaller than 1.9 mm.
Fig. 2-3 Reflection phase for different patch dimensions
Additionally, Table 1 lists the reflection phase angle for five dimensions under the frequency ranging from 14.7 GHz to 15.3GHz with 0.1GHz step. From this table, we know that we could manipulate the reflected phase angle by adjusting the patch dimension. Significantly, as shown in this table, around 15GHz, they have the progressively phase delay angle about 70 degree.
Chapter 3 Numerical Simulation
3.1 Reflection characteristics of a gradient AMC surface
As was calculated in the previous section, the phase angle of the plane wave reflected by an AMC surface could be adjusted by varying the dimension of the square metal patch and was listed in Table 2. Therefore, we could alter the reflection phase angle distribution by adjusting the dimensions of the metal patches in the 2D array. For example, as shown in Fig.2-1, a square patches array was printed on a dielectric substrate backed with a metal ground plane. The periods along the x- and y- direction are the same and denoted as d. Notably, the size of the patch is varying along the x-axis; however, they maintain the same size along the y-direction. The dimensions of the square patches along the x-direction are respectively denoted as a1, a2, a3, a4, and a5. Such an AMC surface can provide a gradient phase angle distribution along the x-axis; that is, they have a progress phase advance along the x-axis, as shown in Fig.3-1.
Table 2 .Parameter Values of the Designed Structure
Parameters a1 a2 a3 a4 a5
Values 2.32 mm 3.51 mm 3.77 mm 3.96 mm 4.39 mm
phase@15GHz 140° 70° 0° -70° -140°
Width of period : 5 mm Length of period : 5 mm
°Phase differences between adjacent cells : -70°
To understand the reflection characteristics of the gradient AMC surface, the full-wave simulation based on time-domain finite integration method (CST microwave studio) was employed for calculating the far-field scattering pattern. As shown in Fig.3-2, the gradient AMC surface was placed inside a rectangular box
equipped with absorbing boundary condition. The excitation is performed by a normally incident plane wave with the electric- and magnetic field along the y- and x- axis, respectively.
Fig.3-1 Reflection phase for patch dimensions a1 to a5
Figure 3-3(a) depicts the far-field scattering pattern over the x-z plane. Obviously, the reflection main beam is steered away from the normal incident direction.
Additionally, some space left between the AMC surface and absorbing boundaries results in the existence of forward scattering. With the scattering pattern demonstrated above, it allows us to have an artificial surface able to redirect the incident wave to a desired direction. As will become clear later, the commonly used array antenna formula can be used to figure out the far-field scattering pattern.
(a) (b)
(b) (d)
Fig. 3-3 Far field scattering pattern over the x-z plane with (a) 1 period (b) 2 periods (c) 3 periods (d) 6 periods along x-axis.
Besides, a periodic structure composed of several unit cells each of which is the gradient AMC surface shown previously was employed to calculate its scattering pattern. From Fig.3-3(a), (b), (c) and (d), we could observe that the reflection main-beam angle maintains and the beam-width is getting narrower with the increase in the unit cell number. Besides, the grating lobes are apparent in the periodic gradient AMC surfaces. Notably, due to the square unit cell as well as patch, both the polarizations can excite the progressive phase shift in the linear array; however, the reflection electric fields of the two cases are orthogonal to each other.
In addition to the far-field scattering pattern, we have calculated the reflection phase angle distribution on the plane with a distance 0.5 mm above the gradient AMC surface. As depicted in Fig.3-4, the horizontal axis represents the position along the x-axis indicated in the figure, while the vertical axis is the reflection phase angle in degree. Apparently, the reflection phase angle changes locally over each square patch.
Significantly, the phase angles over the center position of each square patches respectively are -140, -70, 0, 70, 140. From the array antenna theory, an antenna array with the progressive phase delay angle could radiate its main beam angle toward a specific direction. This may explain the beam-steering characteristic of the reflection wave shown in Fig.3-3.
Fig.3-4 Electric field phase distribution along x-axis on gradient AMC surface
3.2 Array antenna factor
In the chapter 2, we have demonstrated the reflection phase angle versus frequency for various dimensions of square patch. Moreover, in the first section of chapter 3, the gradient AMC surface containing five dimensions of metal-patch array were organized to obtain the unique reflection characteristics shown previously. The full-wave simulation has been carried out for resolving the electromagnetic fields distribution. Specifically, the reflection phase distribution over the gradient AMC surface was obtained for proving that such a design can have the localized phase distribution. Consequently, a simple formula based on the array antenna factor is developed to provide a basic understanding for the steering of reflection waves.
Returning to the structure configuration shown in Fig.2-1, because of the uniformity in the electric field along the y-axis, we may consider it as a one-dimensional antenna array consisting of N elements with their j-th current
amplitude and phase separately denoted as Ij and j at the position x = xj. If the coupling among the elements was neglected, the array factor contributing by the N elements can be written below.
Figure 3-5 demonstrated the scattering pattern obtained by using full-wave analysis and the array factor formula given previously. It is interesting to observe that the array factor formula can predict the steering of the reflected wave. Notice that the array factor formula neglects the mutual coupling among antennas; therefore, the discrepancy between them can be observed.
Fig.3-5 Comparison between array factor calculation result and CST simulation result
With the same phase differences between adjacent unit cells, the following Fig.3-6
AF I
je
jje
jkoxjsincosj1
NFigure 3-6(a) Figure 3-6(b) Phase differences: 0° Phase differences: 30°
Reflection angle: 0° Reflection angle: 19°
Figure 3-6(c) Phase differences: 50°
Reflection angle: 33°
Chapter 4 Experimental Studies
In order to increase the overall size of the AMC structure for higher gain reception, we repeat the period of phased array structure, as the following figure below.
Fig. 4-1 Linearly graded reflection phase from -140° to +140° with a 70° step along the unit cell index at 15 GHz. By repeating the period of the phased array, we can obtain the larger structure with higher reflection gain.
In order to measure the far-field pattern for normal incident condition, we design a horn fixture by woods. By changing the distance between horn and the structure plate for 20 cm and 36 cm, we can figure out the field coverage issue in the following measurement. Our measurement frequency is about 14 GHz to 16 GHz, and the central frequency is at 15 GHz. By comparing the far-field pattern at different
Fig.4-2 Measurement set-up
4.1 Bistatic RCS Measurement
Fig.4-3 Bistatic RCS measurement schematic diagram
Fig.4-4 Bistatic RCS measurement environment in chamber.
In bistatic RCS measurement, the transmitter horn rotates together with the tested structure, and the receiver horn is placed behind the transmitter by 4 meters away.
After rotating around, the reflection pattern of the tested surface can be measured, as shown in figure 4-3 and 4-4.
4.2 Monostatic RCS Measurement
Fig.4-5 Bistatic RCS measurement schematic diagram
In monostatic RCS measurement, transmitter and receiver horn are all stationary away from the tested structure by 4 meters. When the structure rotates around, we can measure the far field reflection pattern not only for the specific face, but all around the structure. (Figure 4-5, 4-6)
Chapter 5 Numerical Results, Experimental Results and Discussion
5.1 Numerical Results
The resonance frequency and the slope of phase-to- frequency curve (Fig.3-1) relate to four parameters: patch size, thickness of the substrate, dielectric constant and the unit cell dimension. By CST simulation, we will clearly know their relation between resonance frequency and these four parameters.
Patch Size
Generally, the larger patch size results in lower resonance frequency. As we can see in Table 3, the largest patch with a =4.39 mm has the lowest resonance frequency at 5 12 GHz; the smallest patch with a =2.32 mm has the highest resonance frequency at 1 almost 24 GHz in CST simulation. In figure 3-1, the curve with higher resonance frequency have smaller slope which indicates that it has more bandwidth.
Table 3 .Resonance frequency for CST simulation results against patch dimension
Patch dimension Resonance Frequency
For simulation, we let a=3.77 mm, r=4.4, period size=5×5 mm^2.
AMC structure can be equivalent to a LC circuit for resonant structure. For the
Fig.5-1 .Reflection phase for different thickness of substrate, h =0.4, 0.8 and 1.6 mm.
Table 4 .Resonance frequency for CST simulation results against thickness
Thickness of Substrate Resonance Frequency
CST Simulation
h=0.4 mm 17.01 GHz
h=0.8 mm 15.00 GHz
h=1.6 mm 11.31 GHz
Dielectric Constant
We have known that the dielectric constant is proportional to the parallel plate capacitance. The Substrate with high dielectric constant leads to high Q in its equivalent resonance circuit, so the slope of curve in figure 5-2 becomes larger with smaller bandwidth, and vice versa.
Fig.5-2 Reflection phase for different dielectric constants of substrate,
r=1.0, 2.2, 3.5, 4.4, 7.0, 8.6 and 10.2.
Table 5 .Resonance frequency for CST simulation results against dielectric constant
Dielectric Constant Resonance Frequency
CST Simulation
r=1.0 26.35 GHz
r=2.2 20.03 GHz
r=3.5 16.55 GHz
r=4.4 15.00 GHz
r=7.0 12.13 GHz
r=8.6 11.02 GHz
r=10.2 10.17 GHz
Unit Cell Dimension
In figure 5-3, we figure out that with larger unit cell dimension, the resonance frequency shifts to the higher frequency. On the contrary, with unit cell dimension smaller as d=3.8 mm, the resonance frequency shifts to the lower frequency. But the bandwidth changes slightly for different unit cell dimensions.
Fig.5-3 .Variation of reflection phase angle against unit cell dimensions.
5.2 Field Coverage
Electric field which the horn excites is not uniform to the far-field. In CST
Microwave Studio, the port we set as plane wave has uniform electric field. In order to simulate the actual situation, we draw a horn with the same size in the overall simulation. With a wave port excited, we will know the electric field distribution at any distance from the horn.
Fig.5-4 Electric field distribution at (a) 36 cm (b) 20 cm from the horn.
For distance 36 cm away from the horn, the uniform field coverage area is bigger than the one for 20 cm away. So that’s why the beam width of main beam for 36 cm away is a little smaller than the one for 20 cm. The comparison results between array factor calculation considering non-uniform electric field and CST simulation can be seen in figure 3-6.
5.3 Experimental Results
RCS reduction applications
From the scattering characteristics depicted in chapter 3, we know that the gradient AMC surface can reflect the normally incident wave away from the incoming direction. Such a unique characteristic is promising for the application of RCS reduction. However, in the previous examples, the incident electric field is perpendicular to the surface gradient direction (defined as vertical polarization) as the symbol of arrow attached in the figure 5-5. To design a surface able to work properly for vertical- and horizontal- polarization, the orthogonal gradient surfaces were placed into the same structure as indicated in Fig. 5-5. Throughout this thesis, this structure will be named as supercell AMC surface.
Using the full-wave analysis, the scattering far-field pattern of the supercell structure illuminated by a normally incident plane wave (with electric field along the y-axis) was obtained and shown in Fig.5-6. When observing along the x-axis, the two major beams are contributed by the two head-to-head gradient surfaces located at the upper-left and lower-right ones. It is worthy of note that due to the square pattern in its unit cell the vertical polarization can also excite the two gradient surfaces at the upper-right and lower-left ones, generating the two major beams along the y-axis.
Fig.5-5 Supercell AMC surface
Fig.5-6 3D pattern of supercell AMC surface for CST simulation
In addition to the numerical calculation, we have also fabricated the supercell and measured its bistatic and monostatic reflections, respectively. The measurement was carried out in an electromagnetic chamber using the vector network analyzer and standard gain horn antennas. Before measuring the reflection characteristic of the supercell AMC surface, the scattering characteristic of the background (absorber reflectance) was first measured for identifying the scattering sources. Beside, the reflection characteristic of the equal size metal plate was measured as a reference to
In addition to the numerical calculation, we have also fabricated the supercell and measured its bistatic and monostatic reflections, respectively. The measurement was carried out in an electromagnetic chamber using the vector network analyzer and standard gain horn antennas. Before measuring the reflection characteristic of the supercell AMC surface, the scattering characteristic of the background (absorber reflectance) was first measured for identifying the scattering sources. Beside, the reflection characteristic of the equal size metal plate was measured as a reference to