1. הנדסת חשמל ומחשבים Decoupling Feeding Network for Antenna Arrays Student: Eli Rivkin Supervisor: Prof. Reuven Shavit הפקולטה למדעי ההנדסה Faculty of Engineering Sciences Motivation: Mutual coupling among array elements causes difficulties in designing a predefined radiation pattern and in matching the system. The suggested feeding network matches the antenna array always, independently of the mutual coupling. Geometry: x z d d d d d d (4,4) (4,3) (4,2) (3,4) (3,3) (3,2) (2,4) (2,3) (2,2) (1,4) (1,3) (1,2) (3,1) (2,1) (1,1) (4,1) PEC y (x,y,z) - distance between elements - height above the PEC E-plane: H-plane: Mutual Coupling: each element’s current depends on the voltages of all the others Input impedance at each port: In general case, each current distribution needs a different matching network. Radiation Pattern: EF (element factor) AF (array factor) Examples: 1) Without scanning: 2) With scanning: Eigenmode Theory: Return Loss: Without the decoupling and matching network (DMN) the return loss depends on the excitation: dipole [H] is Hermitian ([H] H =[H]) => it can be diagonalized by a unitary matrix: The columns of [Q] are the eigenmodes of the antenna array. They are orthonormal vectors. - eigenefficiencies (eigenvalues) [H] - radiation matrix If [Q] diagonalizes [H] then it also diagonalizes [S] via: - modal reflection coefficients (complex, ) => energy conservation Decoupling Concept: bsbs asas Antenna Array [S] Decoupling Network [S D ] b a [S S ] has to be diagonal from the theory: The decoupling network is described by: ([Q]- matrix of eigenmodes) It is reciprocal and lossless. Its input and output ports are matched and decoupled. Power is transferred according to the matrix of eigenmodes [Q]. Each input port excites a different eigenmode => every excitation is a superposition of the orthonormal eigenmodes. All the input ports are independent of each other, so now it is possible to match each port individually. Decoupling Network #16 #2 #1 #1 (X) #32 (X) Matching Network 1# Matching Network 2# Matching Network 16# #1 (M) #2 (M) #16 (M) #2 (X) #16 (X) #17 (X) #18 (X) #1 (D) #2 (D) #16 (D) Antenna Array........................ - transfer matrix of all the matching networks The relation between the currents on the antennas I and the input voltages V in is: choose a current distribution (I) according to the desired radiation pattern, and you can get the input voltages to achieve it. Software Implementation of the DMN: Software implementation requires connecting the antenna array to a computer which does all the matrix calculations from above (after translating the signal to baseband and sampling). Hardware Implementation of the DMN: Objective: implementation of with passive microwave elements. Special case: array of 2 antennas with, so that:. In this case, will diagonalize [S] and decouple the 2-element array. Directional Coupler (Magic-T Hybrid) Our case: symmetric rearrangement of the elements in [S] leads to: According to the special case, our [Q] can be written in block matrix notation: 8 Magic-T Hybrids #1 #2 #3 #4 z x 1234 5678 9101112 131415 16 original arrangement pairs: 1 & 9, 2 & 10… Each of these pairs should be connected by a coupler. After this step the system matrix will be: no coupling between the 2 groups! z x 1234 5678 9101112 13141516 symmetry plane symmetric rearrangement z x 1234 5678 9101112 13141516 z x 1265 3487 11121615 91014 13 symmetry plane next step: Same procedure as before  8 more Magic-T Hybrids (4 for each group of 4)  no coupling between the 4 groups of 4 #1 #2 #3 #4 #1 #2 #3 #4......... #1 #2 #3 #4 #1 #2 #3 #4...... #1 #9 #8 #16 #1’ #9’ #8’ #16’ #1’’ #5’’ #12’’ #16’’ #1 #5 #12 #16 next step: No more symmetry planes have left => it’s impossible to use the same method again. A different method will be used to decouple each of the 4 sub-arrays, which is based on diagonalizing the imaginary and the real parts separately. [S 1 ] -jx 1 -jx 2 -jx 3 -jx 4 [S A ] [S B ] the input impedance matrix is diagonal - decoupling accomplished! (Givens Rotations) Each one of [A i ] and [B i ] represents a directional coupler (an arbitrary one, not a Magic-T as before).  The 4 sub-arrays which were left after the first method require 48 couplers.  The whole implementation requires 64 couplers. Antenna Array [S] b a