4 × 4 BUTLER MATRIX SYNTHESIS

After determining the dimensions of the 90-degree hybrid couplers and the 45-degree phase shifters, the 4 × 4 Butler matrix (see Figure 9) was synthesized using the topology in Figure 1. A flexible layout method places components based on the spacing of adjacent couplers. With this approach, each component, including 90-degree hybrid couplers, 45-degree phase shifters and phase-compensation circuits, can be individually simulated and optimized. Also, the input and output ports of the Butler matrix can be flexibly placed.

Figure 7

Figure 7 Simulated transmission (a), phase (b) and reflection (c) characteristics of the 22.5-degree phase shifter.

Figure 8

Figure 8 Simulated transmission (a), phase (b) and reflection (c) characteristics of the 67.5-degree phase shifter.

Figure 9

Figure 9 Layout and dimensions of the 4 × 4 Butler matrix.

The phase shifters have phase differences with respect to a microstrip line of fixed length. Unfortunately, the lengths of the through lines in the non-phase-shifting paths between the corresponding connected two couplers are lengthy and dependent (see Line 0 in Figure 9). Therefore, to provide the needed phase shift, the extra microstrip lines, whose lengths are determined by the spacing of the connected couplers, must be compensated in the corresponding phase-shifting paths. Ideally, the phase-compensation circuits should be designed so as to not affect the overall layout. The 45-degree phase-shifting paths all have the same trace format of line 1 with the extended lines of length LC. Thus, when the spacing of adjacent couplers is determined, denoted by Sh and Sv in Figure 9, the length of line 0 is determined, and the value of LC is easily adjusted to guarantee a phase difference of 45 degrees between lines 1 and 0. Line 0 can be flexibly routed to maintain a certain line spacing within the same metal layer.

The prototype 4 × 4 Butler matrix was designed and simulated on a Rogers 4003C substrate. Each component, including the 90-degree hybrid coupler, 45-degree phase shifter and the phase-compensation circuit were individually simulated and optimized. Full-wave simulations and optimizations were performed using ANSYS software. Most of the physical parameters have been noted; the remaining physical parameters in Figure 9 are: LC=6.95, W50=1.15, Sh=45.6 and Sv=34.1 mm.

Figure 10

Figure 10 Layout and dimensions of the 8 × 8 Butler matrix

8 × 8 BUTLER MATRIX SYNTHESIS

In a similar fashion, the prototype 8 × 8 Butler matrix was designed and simulated, using Rogers 4003C substrate and each component individually simulated and optimized. The full-wave simulations and optimizations were performed, and the realizable physical parameters are shown in Figure 10. As with the 4 x 4 matrix, most of the physical parameters have been listed previously. The remaining are: L1=9.53, L2=6.35, L3=6.35, W50=1.15, Sh8=46.2 and Sv8=50.85 mm.

Figure 11

Figure 11 Fabricated 4 × 4 Butler matrix.

Figure 12

Figure 12 Fabricated 8 × 8 Butler matrix.

 

MEASURED RESULTS

The fabricated 4 × 4 and 8 × 8 matrices are shown in Figures 11 and 12, respectively. The sizes are approximately 89 × 54 mm for 4 × 4 Butler matrix and 212 × 118 mm for the 8 × 8 matrix.

Figure 13

Figure 13 Simulated (solid black) vs. measured (dotted red) characteristics of the 4 × 4 Butler matrix: transmission (a), reflection (b) and port 1 coupling (c).

Measurements with a Keysight vector network analyzer are in agreement with the simulations, as shown in Figures 13 and 14. As the 4 × 4 Butler matrix has a plane of reflection symmetry, shown in Figure 9, the simulated and measured results are only presented when port 1 is excited. The differential phases are shown with ports 1 and 2 excited. In Figure 13a, S51, S61, S71 and S81 are shown, indicated about 7 dB for the insertion loss with approximately 1 dB of amplitude imbalance. Figure 13b shows greater than 15 dB return loss at all input ports over the entire band from 2 to 6 GHz. Figure 13c shows the isolation characteristics of port 1 from the other three input ports: 15 dB for port 2, 20 dB for port 3 and 30 dB for port 4. The differential phases of beam 1L (with an ideal differential phase of 135 degrees) and 2L (with an ideal differential phase of 45 degrees) are plotted in Figures 14a and b, respectively, showing 5-degree phase imbalance for the 135-degree phase shift of beam 1L and 3-degree phase imbalance for the 45-degree phase shift of beam 2L. The 8 × 8 Butler matrix has similar characteristics (see Figure 15).

Figure 14

Figure 14 Simulated (solid black) vs. measured (dotted red) differential phase between adjacent antenna ports of the 4 × 4 Butler matrix: beam 1L with 135-degree differential phase (a) and beam 2L with 45-degree differential phase (b).

CONCLUSION

Slot-coupled technology was used to design 2 to 6 GHz 4 × 4 and 8 × 8 Butler matrices, and a three metal-layer structure avoided crossover circuits. Phase-compensation circuits were added based on the spacing of adjacent couplers, a helpful design approach. Measurement results agree with the simulations. A 100 percent fractional bandwidth was achieved, which is attractive for wideband beamforming systems.

Figure 15

Figure 15 Measured performance of the 8 × 8 Butler matrix: transmission (a), reflection (b) and differential phase (c) for each beam.

ACKNOWLEDGMENT

This work was supported in part by the National Natural Science Foundation of China under Grant 61671149, Grant 61861136002 and Grant 61701110.

References

  1. W. T. Fang and Y. S. Lin, “Highly Integrated Switched Beamformer Module for 2.4-GHz Wireless Transceiver Application,” IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 9, September 2016, pp. 2933–2942.
  2. K. Wincza and S. Gruszczynski, “Broadband Integrated 8×8 Butler Matrix Utilizing Quadrature Couplers and Schiffman Phase Shifters for Multibeam Antennas with Broadside Beam,” IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 8, August 2018, pp. 2596–2604.
  3. H. N. Chu and T. G. Ma, “An Extended 4×4 Butler Matrix with Enhanced Beam Controllability and Widened Spatial Coverage,” IEEE Transactions on Microwave Theory and Techniques, Vol. 66, No. 3, March 2018, pp. 1301–1311.
  4. S. Trinh-Van, J. M. Lee, Y. Yang, K. Y. Lee and K. Hwang, “A Sidelobe-Reduced Four-Beam Array Antenna Fed by a Modified 4×4 Butler Matrix for 5G Applications,” IEEE Transactions on Antennas and Propagation, Vol. 67, No. 7, July 2019, pp. 4528–4536.
  5. A. M. Abbosh and M. E. Bialkowski, “Design of Compact Directional Couplers for UWB Applications,” IEEE Transactions on Microwave Theory and Techniques, Vol. 55, No. 2, February 2007, pp. 189–194.
  6. A. M. Abbosh, “Ultra-Wideband Phase Shifters,” IEEE Transactions on Microwave Theory and Techniques, Vol. 55, No. 9, September 2007, pp. 1935–1941.
  7. S. Z. Ibrahim and M. E. Bialkowski, “Wideband 4×4 Butler Matrix Employing Microstrip-Slot Technique,” Microwave and Optical Technology Letters, Vol. 52, No. 12, December 2010, pp. 2632–2636.
  8. A. Moscoso-Mártir, I. Molina-Fernández and A. Ortega-Moñux, “Wideband Slot-Coupled Butler Matrix,” IEEE Microwave and Wireless Components Letters, Vol. 24, No. 12, December 2014, pp. 848–850.
  9. P. I. Bantavis, C. I. Kolitsidas, T. Empliouk, M. Le Roy, B. L. G. Jonsson and G. A. Kyriacou, “A Cost-Effective Wideband Switched Beam Antenna System for a Small Cell Base Station,” IEEE Transactions on Antennas and Propagation, Vol. 66, No. 12, December 2018, pp. 6851–6861.