Bagley Power Divider | Qucs-S S-parameter Viewer Documentation

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# 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:

\[Zbr = \frac{2 × Z₀} {\sqrt{N}}\]

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

- RF Circuit Synthesis Tools