Wilkinson Power Divider

Overview

The Wilkinson power divider is the most widely used RF power splitter topology. It provides matched ports, high isolation between outputs, and can be designed for equal or unequal power split ratios.

Topology

           ┌───[Zbr, λ/4]──── Output #1
           │               |
Input  ────┤              [R]
           │               |
           └───[Zbr, λ/4]──── Output #2

Key components:

  • Two λ/4 transmission line branches

  • One isolation resistor (R) between outputs. If the balance is perfect, no current flows through it.

Design Equations

Equal Power Split (K = 1, 0 dB ratio)

\[Z₂ = Z₃ = √2 × Z₀ ≈ 70.7 Ω (for Z₀ = 50Ω) R = 2 × Z₀ = 100 Ω\]

Power division:

\[P₂ = P₃ = Pin / 2 (3 dB to each output)\]

Unequal Power Split (K ≠ 1)

Power ratio: K = P₂/P₃ (linear), or K_dB = 10 × log₁₀(K)

Branch impedances:

\[Z₂ = Z₀ × √(2 × (1 + K) / K) Z₃ = Z₀ × √(2 × (1 + K))\]

Isolation resistor:

\[R₂ = Z₀ × K (series with Port 2) R₃ = Z₀ / K (series with Port 3) R = R₂ + R₃ = Z₀ × (K + 1/K)\]

Power division:

\[P₂ = Pin × K/(K + 1) P₃ = Pin × 1/(K + 1)\]

Example: Equal Split, Z₀ = 50 Ω, f₀ = 2 GHz

Design:

\[Z₂ = Z₃ = 50 × √2 = 70.7 Ω R = 2 × 50 = 100 Ω λ/4 = (3×10⁸) / (4 × 2×10⁹) = 37.5 mm\]

Advantages

  1. Matched ports: All ports matched to Z₀

  2. Good isolation: Typically 20–30 dB between outputs

  3. Good bandwidth: 20–40% fractional

  4. Scalable: Can cascade for N-way division (N = 2ⁿ)

  5. Well-established: Mature design, extensive literature

Limitations

  1. Resistor loss: Isolation resistor may dissipate power if the circuit is not perfectly balanced

  2. Physical size: λ/4 lines large at low frequency

  3. Unequal split limitations:

    • Wide Z₂/Z₃ ratios → fabrication challenges

    • Large K → very high/low impedances

Rule of thumb: Keep 30Ω < Z₂, Z₃ < 150Ω for practical fabrication

References

[1] Wilkinson, E. J. (1960). “An N-Way Hybrid Power Divider.” IRE Trans. Microwave Theory Tech., MTT-8, pp. 116-118.

[2] Pozar, D. M. (2012). Microwave Engineering (4th ed.), Section 7.3, pp. 336-340. Wiley.

See Also