Part I: Finite Planar Array Model Design:

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1 In the name of Allah A two dimensional N x N y array based on Rectangular Waveguide Aperture Element In this example we tried to practice the modelling of two dimensional phased array configurations with finite array size in CST Microwave Studio. At the end of this exercise we also analyze an infinite 2D-dimensional array by using Floquet Excitation instead of waveport. I appreciate who adds any comment on this work by sending to: Smr.razavizadeh@ieee.org, or razavizadeh@yahoo.com Regards...Seyed Mohammadreza Part I: Finite Planar Array Model Design: Pick the waveguide end faces and then choose shell action for making a waveguide with thickness: We have a rectangular waveguide as our main array element. For the future and more analyze, we can define a material(here Vacuum) inside the waveguide as: 1

2 The last object is a Radom in front of the array element with epsilon:4 and loss free, this action can be perform by Extrude based on WG object, pick the front face of WG and then: Frequency Setting: Background Material: Setting the propagation region by Background, because the main radiation area is Z>0 in front of the Radom, we set a relative distance based on the largest dimension of the array element(here waveguide width of a, in 3*a), the back of the antenna element is not important for us because we normally are face with End-closed probe fed waveguide, later we will set at Boundary setting an PEC(Et=0) wall at Zmin based on equivalence principle for TE mode excitation : Excitation Definition: For waveguide the best choice is waveport and at Z=0, toward the positive direction of the Z-axis: 2

3 Boundary: As we said previously we have main radiation in Z>0 and no radiation in Z<0, so based on equivalence principle we can fill PEC material in Z<0 and the equivalent electric current of the tangential Ey field would be Ms. We have a 2-D array so we should set the boundary in x and y direction as periodic. Phase Setting: In planar antenna array we have two main parameters: progressive excitation phase of array elements of phase_x and phase_y, in x and y directions, respectively, and elements distances of d x and d y. A schematic view of a N N two dimensional Array A beam former block diagram of a 2 2 array In CST MWS we can set the phase parameters by phase shift/scan angle : As shown, our example has a progressive phase shift only in x-direction as phase_x and 0 all the elements are equal-phases in y-directions. If you put tick Scan Angle, the phase_x is the propagation phase constant of the surface wave on the array surface in x- direction and is useful for periodic metal, dielectric structure like EBG, Metamaterial and..., for studying the dispersion behaviour of them. The Theta and Phi is the incident plane wave direction when w use the unit cell and floquet excitation instead of period boundary and wave port.

4 Postprocessing: The elements distances of d x and d y could be set via postprocessing as following: Choose Advanced Tab, many features are available as below in Farfield setup: *Plot Mode: lin/log scale Result Type: Dir/G/... Polarization: **Array Setup: Special: Angular Width is the same 3dB-HPBW *For better viewing the main beam direction the linear scale is better than Log scale. **As shown in the Array setup window, the important array input data should be defined in this place. 4

5 Field Monitor: For far field, the field monitor should set at Far field/rcs. Frequency solver: For only field result, we just set the frequency solver at single sample frequency. Parametric Sweep: Far field and template based results: 5

6 Set what curves which you want to show: click on None tab and then: Click on Apply and ok: > 6

7 Part II: Infinite Planar Array(Floquet Sources) Another periodicity can be made by unit cell option in boundary setup. In this case we should eliminate the excitation and we use the floquet excitation which is based on two default mode based waveport excitations of Zmin and Zmax. In this excitation method the antenna acts in receiving mode by exposing by an incident plane wave source placed on planes of Zmin and Zmax(the results is based on superposition law for studying the reciprocal peroperties of the system). Boundary set up of Unit cell in x and y directions: Floquet Ports: Click on floquet tab and set mode number of ports which are placed at Zmin and Zmax(for example 2 is ok, because more mode number can alert you low memory space error!). Because of setting the Et=0 at Zmin the Zmin source cannot be defined. Next step is defining the planewave incident direction as inward, and at (θ=0, ϕ=0) directions which is equivalent to -z axis direction. Unit cell setup: We can define any desirable periodic structure like inclined and not right structure with various distances like below, by correspondent setup: Standard: if you tick the box result is the same. 7

8 Diagonal Inclined: Frequency setup: we can choose a list of port and desired modes. Results: Now we want to change the plane wave direction from (θ=0, ϕ=0) to (θ=45, ϕ=0). 8

9 New Results based on inclined propagation direction: it s clear that the main back scattered beam is (θ 330, ϕ=0) or (θ 45, ϕ=180). 9