Low-Cost Unattended Design of Miniaturized 4 × 4 Butler Matrices with Nonstandard Phase Differences

Abstract

Design of Butler matrices dedicated to Internet of Things and 5th generation (5G) mobile systems—where small size and high performance are of primary concern—is a challenging task that often exceeds capabilities of conventional techniques. Lack of appropriate, unified design approaches is a serious bottleneck for the development of Butler structures for contemporary applications. In this work, a low-cost bottom-up procedure for rigorous and unattended design of miniaturized 4 × 4 Butler matrices is proposed. The presented approach exploits numerical algorithms (governed by a set of suitable objective functions) to control synthesis, implementation, optimization, and fine-tuning of the structure and its individual building blocks. The framework is demonstrated using two miniaturized matrices with nonstandard output-port phase differences. Numerical results indicate that the computational cost of the design process using the presented framework is over 80% lower compared to the conventional approach. The footprints of optimized matrices are only 696 and 767 mm2, respectively. Small size and operation frequency of around 2.6 GHz make the circuits of potential use for mobile devices dedicated to work within a sub-6 GHz 5G spectrum. Both structures have been benchmarked against the state-of-the-art designs from the literature in terms of performance and size. Measurements of the fabricated Butler matrix prototype are also provided.

Insertion Loss and Phase Compensation Using a Circular Slot Via-Hole in a Compact 5G Millimeter Wave (mmWave) Butler Matrix at 28 GHz

“…Due to beamforming, there will be an increase in signal energy to the intended user and a decrease in the interference. The co-integration of the elements in the Butler matrix (BM) would not have been such a critical issue in a much lower GHz frequency band, as confirmed in [6,7]. As compared to the mmWave, it should be critically designed by controlling the inter-connection and inter-coupling among the BM elements, since, in the mmWave, the high path loss arises quadratically with the frequency (path loss ∝ f 2 ) as defined by Friis' law [8].…”

“…The field strength is parallel to the via, where the field reduces when the distance increases from the via. The current flowing along the via provides a partial inductance, L. The via behaves as a parasitic series inductance as in (6),…”

“…The size of the structure is 2.17 λ0 × 2.69 λ0 at the center frequency of 28 GHz. The internal structure of the BM and the new structure with extension strip line, ΔL, with input ports (1-4) and output ports (5)(6)(7)(8) is illustrated in Figure 20. The final design of BM that includes the additional strip line has a new dimension of 100 mm × 82.5 mm, equivalent to 9.34 λ0 × 7.7 λ0 at the center frequency of 28 GHz.…”

Design and Implementation of C-Band Large-Power Planar Butler Matrix in SRS

“…The machining parameter error of 0.4 mm is out of the range of machining accuracy and causes a phase error of about 2°. Figure 23 shows the experimental [29][30][31] setup of the multipactor measurement [18], which includes the data acquisition and processing system. A portion of the incident power applied to the device under test is extracted, fed into a coupling circuit, and nulled against a part of the extracted reflected power.…”

Multi-Beam 5G Antenna With Miniaturized Butler Matrix Using Stacked LTCC

“…This is particularly important in contemporary, space-limited applications such as IoT devices, mobile devices, and sensor networks. [21], [22].…”