Bagley Power Divider

Overview

N-way planar power divider suitable for splitting power to any odd number of outputs (>=3).

Topology

                                  Input
                                    │
                     ───────────────────────────────
                    │                               │  
                  [λ/4]                           [λ/4] 
                    │                               │  
                    │─────[λ/2]─────|─────[λ/2]─────│
                  Out #1          Out #2          Out #N     (odd)

Structure:

  • Input branches: Two λ/4 sections at Zbr connect to input

  • First output: Taken from left branch

  • Interconnections: λ/2 sections at Zbr connect remaining outputs

  • All lines: At impedance Zbr

Design Equations

For N Outputs (Equal Split)

Branch impedance:

\[Zbr = (2 × Z₀) / √N\]

All transmission lines:

  • Impedance: Zbr

  • Input vertical branches: λ/4 length

  • Horizontal interconnects: λ/2 length

Example

3-Way Divider, Z₀ = 50 Ω, f₀ = 2 GHz

Design:

Parameter

Value

Number of outputs

3

Zbr

(2 × 50) / √3 = 100 / 1.732 ≈ 57.7 Ω

λ₀

150 mm

λ/4

37.5 mm (vertical branches)

λ/2

75 mm (horizontal branches)

Physical Size

Total length (horizontal):

L_total ≈ (N - 1) × λ/2

N = 3: ~1.0λ
N = 4: ~1.5λ
N = 8: ~3.5λ

References

[1] Pozar, D. M. (2012). Microwave Engineering (4th ed.). Wiley.

See Also