ELECTRONIC BEAM steering has long been commonplace in military systems such as direction-finding (DF) radars. It is also becoming practical for commercial communicationsespecially newer cellular systems incorporating adaptive antenna technologies such as multiple-input, multiple-output (MIMO) antenna arrays.

A mainstay of many beam-steering or beamforming networks is the Butler matrix. It is an N x N matrix, where N equals the number of input and output ports, such as a 4 x 4 or an 8 x 8 Butler matrix. A passive Butler matrix can be fabricated by a combination of components, including power dividers/combiners, hybrid couplers, and phase shifters. A quadrature hybrid, for example, will yield two outputs that are in phase and in quadrature (90-deg. offset) relative to the phase of an input signal. Hybrid couplers can provide a 180-deg. phase shift; this enables different components to be combined, achieving (to give one example) outputs with 0, 90, 180, and 270 deg. phase states relative to an input signal for beamforming.

Butler matrices for beamforming networks are characterized by key electrical parameters, including insertion loss, isolation between ports, amplitude balance, phase balance, and power-handling capabilityall specifications that are used to compare the performance of hybrid couplers and power dividers/combiners. Specifications such as amplitude and phase balance, which should be as low as possible to ensure predictable generation of signal amplitude and phase when delivered to an antenna element for beamforming, are characteristic of the quality of a Butler matrix design and manufacturing methods. Simply put, a reproducible design built by proven manufacturing methods yields minimal amplitude and phase variations.

As an example of an 8 x 8 Butler matrix constructed with passive components, model bm88701 from TRM Microwave, is designed for two different frequency bands within the range of 1025 to 1095 mHz (**Fig. 1**). it is constructed with a combination of 180-deg. hybrid couplers and coaxial cables with known electrical lengths. the unit achieves amplitude balance of 1 db or better between outputs and phase balance of 3 deg. or better for desired phase states. model bm88701, which can handle 8 W average power and as much as 400 W peak power, controls insertion loss to 1 db or less and provides at least 18 db isolation between ports. the input/output VSWr is typically 1.30:1. The 8 x 8 Butler matrix features a chemical conversion coating per mil-c-5541 class 3 requirements and optional paint finish.

An example of a smaller Butler matrix, a 4 x 4 unit developed by trm for airborne applications (**Fig. 2**), combines ferrite, coaxial, and microstrip technologies. Designed for 500 to 2000 mHz, it exhibits less than 1.5 db insertion loss and more than 25 db isolation over that range. Incorporating eight 0-deg. power dividers, four 0-deg. power combiners, four 180-deg. power combiners, and a 50-O delay line, the collection of components fits in a nickel- plated aluminum housing measuring just 2.5 x 6.0 x 0.6 in., excluding SMA connectors.

Since Butler matrices are almost universally custom designs, these two units can only serve as examples; each system integrator will have their own requirements for such parameters as number of input and output ports, frequency range, and other electrical and mechanical parameters. To learn more about Butler matrices, the firm is offering a free white paper; visit www.whitepapers.trmmicrowave.com for more information.

**TRM Microwave**, 280 South River Road, Bedford, NH 03110; (603) 627-6000.