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BEAM FORMING NETWORKS ( BFN’s ) EE 525 Antenna Engineering

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BFN’s constrained feeds space (optical) feeds transform feeds (constrained and/or optical)

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● Series feed ● Parallel feed ● True time delay feed ● Multiple beam matrix feed - Butler matrix - Blass matrix Types of Constrained Feed Systems

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Elements of Constrained Feed Systems ● Transmission lines ● Hybrids ● Magic T’s ● Directional couplers ● Coaxial lines ● Striplins

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Types of Constrained Feeds ● Series feed ● Parallel feed ● True time delay feed ● Multiple beam matrix feed - Butler matrix - Blass matrix

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Series Feed

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Parallel Feed

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True Time Delay Feed

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time delay from wavefront to input feed is the same for every pathtime delay from wavefront to input feed is the same for every path ● waves via all paths add in phase at the feed point for every frequency component in the pulse ● there is no reduction in the peak value of the received pulse ● time delay = ndsinθ/c ● not suitable frequency scanning ● suitable for wideband applications

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Butler Matrix Feed System ● is a passive feeding N x N network with beam steering capabilities ● consist of hybrid junctions (or directional couplers) and fixed phase shifters. ● (N/2) log 2 N hybrids and (N/2) log 2 (N – 1) fixed phase shifters are required to form the network. ● hybrids can be either 90° or 180° 3-dB hybrids

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Butler Matrix

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-distrubutes RF signals to -distrubutes RF signals to radiating elements radiating elements -providees orthogonal beamforming -providees orthogonal beamforming

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Butler Matrix ●multiple beamforming can be achieved by exciting two or more beam ports with RF signals at the same time. ●two adjacent beams cannot be formed simultaneously as they will add up to produce a single beam beam

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The Butler Matrix as a Fourier Transformer - the field amplitude at the n th output element due to unit excitation at the m th beam port -using superposition for an arbitrary input distribution f(m) will result in a superposition of discrete plane waves weighted by f(m), resulting in the Fourier Transform :

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Butler Matrix

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Advantages ● Simple network using few component types easily implemented in stripline or microstrip ● beams generated are of the Woodward-Lawson type with narrow beamwidth, high directivity and are orthogonal narrow beamwidth, high directivity and are orthogonal ● the ideal Butler matrix is the analog equivalent of the discrete Fourier Transform discrete Fourier Transform ● low-loss as minimum insertion loss in hybrids, phase shifters and transmission lines phase shifters and transmission lines ● Design of large matrices is easy

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Butler Matrix Disadvantages ● beam-width and beam angle vary with frequency; thus the Butler matrix forms phased-steered beams that squint with frequency ● has a complex interconnection scheme for large matrices

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Blass Matrix Feed Sysyem employs a set of N antenna array element transmission lines that intersect a set of M beam port lines (with directional couplers at each intersection) matrix is terminated with matched loads upper feedline radiates a broadside beam Feed line tilt angle and propagation constants determines beam position

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Blass Matrix

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Advantages ● The interconnection layout of the circuit is simple as no crossovers or multilayers are needed ● Time-delayed beams produced do not squint with frequency. ● Shaped beams can be produced by controlling the coupling ratios of the couplers

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Blass Matrix Disadvantages ● Each coupler on any given feed-line must have a different coupling value >> complicates design !! ● array configuration requires more couplers than the Butler matrix >> greater cost and weight !!

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Optical (Space) Feeds Transmission type Transmission type Reflection type Reflection type

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Space-Fed Arrays less expensive to construct compared to corporate-fed arrays less expensive to construct compared to corporate-fed arrays suffer from spillover and reflection losses and do not offer good pattern control for sidelobes suffer from spillover and reflection losses and do not offer good pattern control for sidelobes

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Optical Feeds - Principal Features free space exists between the feed(s) and the radiating aperture free space exists between the feed(s) and the radiating aperture aperture distribution is determined mainly by the pattern of the feed. aperture distribution is determined mainly by the pattern of the feed. The larger the FOV, the greater the complexity and the cost of the antenna system. The larger the FOV, the greater the complexity and the cost of the antenna system.

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Transmission Type array elements and phase shifters are connected to an array of pickup elements, illuminated by a feed at a given focal distance array elements and phase shifters are connected to an array of pickup elements, illuminated by a feed at a given focal distance Phase shifters are set to provide the required phase increments. Phase shifters are set to provide the required phase increments.

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Reflection Type The concept is the same with the transmission model, except the presence of short circuits behind the phase shifters The concept is the same with the transmission model, except the presence of short circuits behind the phase shifters amount of required phase shift at each element is half that of the transmission case amount of required phase shift at each element is half that of the transmission case

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Transmission & Reflection Types

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Phased Array With Paraboloid The reflectarray aperture is placed in the region forward of the focus.The reflectarray aperture is placed in the region forward of the focus. Picks up the converging field andphase-shifts it to refocus on the primary feed(s)Picks up the converging field andphase-shifts it to refocus on the primary feed(s)

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Optical Transform Feeds feed systems in which the input to the feed and the resulting aperture distribution of the array are related by one or more Fourier transforms. feed systems in which the input to the feed and the resulting aperture distribution of the array are related by one or more Fourier transforms.

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Optical Transform Feeds (large lens fed by a small lens)

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REFERENCES Lo Y.T., Lee S.W.,’Antenna Handbook’,Van Nostrand Reinhold,1988, Lo Y.T., Lee S.W.,’Antenna Handbook’,Van Nostrand Reinhold,1988, 113/thesis.pdf 113/thesis.pdf Jasic, H., Antenna Engineering Handbook Jasic, H., Antenna Engineering Handbook Johnson, R.C., Jasic H., Antenna Engineering Handbook Johnson, R.C., Jasic H., Antenna Engineering Handbook Ming H.C., Tsandoulas G.N., A dual-reflector optical feed for wide-band phased arrays, IEEE Transactions on Antennas and Propagation Ming H.C., Tsandoulas G.N., A dual-reflector optical feed for wide-band phased arrays, IEEE Transactions on Antennas and Propagation Mailloux, R.J., Phased Array Antanna Handbook Mailloux, R.J., Phased Array Antanna Handbook Hansen, R.C., Phased Array Antennas Hansen, R.C., Phased Array Antennas Mailloux, R.J., Space Fed Subarrays using a Displaced Feed, Internet Mailloux, R.J., Space Fed Subarrays using a Displaced Feed, Internet

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