Bagley Polygon Divider
Understanding Bagley Polygon Dividers
The Bagley polygon divider was developed to overcome the fundamental bandwidth limitation of conventional quarter-wave power dividers. A standard Wilkinson divider achieves perfect match and isolation only at the design frequency and its odd harmonics, yielding roughly 1.5:1 usable bandwidth. The polygon topology solves this by creating a closed-loop structure where signals reach each output through two complementary paths (clockwise and counterclockwise around the ring). As frequency shifts, the changing electrical lengths of these paths maintain constructive interference at the output ports across a much wider band.
The polygon geometry naturally enforces amplitude and phase symmetry. For an N-way split, the polygon has N vertices with output ports and one input vertex. The total perimeter is approximately one wavelength at center frequency, and the segment impedance is set to Z0√N to satisfy the impedance matching conditions at each junction. Practical implementations in microstrip or stripline must account for junction discontinuities, substrate dispersion, and inter-segment coupling, particularly above 10 GHz where the polygon becomes electrically compact.
Design Equations
Zseg = Z0 × √N
3-way: Zseg = 50 × √3 = 86.6 Ω
4-way: Zseg = 50 × √4 = 100 Ω
Segment Electrical Length:
θseg = 360° / (N + 1) at center frequency
Ideal Split Loss:
Lsplit = 10 log10(N) dB
3-way: 4.77 dB; 4-way: 6.02 dB; 5-way: 6.99 dB
Bagley Polygon vs. Other N-Way Dividers
| Topology | Bandwidth | Amplitude Balance | Phase Balance | Complexity | Scalability |
|---|---|---|---|---|---|
| Bagley Polygon | 4:1+ | ±0.5 dB | ±3° | Moderate | Good (N ≤ 6) |
| Wilkinson (single) | 1.5:1 | ±0.2 dB | ±1° | Low | Binary only (2n) |
| Wilkinson (multi-section) | 3:1 | ±0.3 dB | ±2° | High | Binary only (2n) |
| Radial Divider | 10:1+ | ±0.5 dB | ±2° | High | Excellent (N ≤ 32) |
| Corporate (cascaded) | 2:1 | ±0.5 dB | ±5° | Moderate | Binary only (2n) |
Frequently Asked Questions
How does the Bagley polygon achieve wider bandwidth than Wilkinson dividers?
The closed-loop polygon creates multiple resonant paths between input and each output. At any frequency, signals reach outputs through clockwise and counterclockwise paths. As frequency changes, the electrical lengths shift, but the polygon symmetry maintains constructive interference across a 4:1 or wider band, compared to the single quarter-wave resonance of a Wilkinson (1.5:1 bandwidth).
What determines the segment impedance?
For an N-way divider in a Z0 system, each polygon segment must have impedance Zseg = Z0√N. A 3-way in 50 Ω: 86.6 Ω. A 4-way: 100 Ω. For high N, the segment impedance becomes impractically high for microstrip (5-way: 111.8 Ω), often requiring stripline or suspended substrate where higher impedances are achievable.
Where are Bagley polygon dividers used?
Primary applications include wideband phased array feed networks for EW and SIGINT (2-18 GHz), broadband test fixtures for multi-port characterization, corporate feeds for Vivaldi antenna arrays, and multi-channel receiver front ends needing equal-phase wideband splitting. The planar topology integrates naturally into PCB antenna systems.