Lim-Eom Power Divider

Overview

Wideband 4-port power divider with unequal power split capability and excellent bandwidth performance. Developed by Lim and Eom, this topology provides multi-octave operation while maintaining arbitrary power ratios between three output ports.

Topology

                           Output #1
                              |
                              |
Input     ────────[Z2, λ/4]────────[Z1, λ/4]──────── [R0]
           |                                  |
           |                                  |
      [Z1, λ/4]                          [Z2, λ/4]
           |                                  |
           |                                  |
           |─────────────[Z0, λ/2]────────────|
           |                                  |
           |                                  |
      [Z4, λ/4]                           [Z5, λ/4]
           |                                  |
           |                                  |
Output #2 ────────[Z5, λ/4]────────[Z4, λ/4]────────  Output #3
                              |
                             [R0]

Key features:

  • Four ports: 1 input, 3 outputs

  • Two grounded isolation resistors (R1, R2)

  • Center λ/2 section (Z3) connects upper and lower halves

  • Arbitrary power ratios M:N:K at outputs

Design Equations

Power Split Ratios

Define output power ratios:

M = P₂/P_total    (Port 2 power ratio)
N = P₃/P_total    (Port 3 power ratio)
K = P₄/P_total    (Port 4 power ratio)

where M + N + K = 1

Impedance Calculations

d₁ = M + N + K = 1
d₂ = N + K

Z₁ = Z₀ × √(d₁/d₂) = Z₀ × √(1/(N + K))
Z₂ = Z₀ × √(d₁/M) = Z₀ × √(1/M)
Z₃ = Z₀
Z₄ = Z₀ × √(d₂/N) = Z₀ × √((N + K)/N)
Z₅ = Z₀ × √(d₂/K) = Z₀ × √((N + K)/K)

R₁ = R₂ = Z₀

Line Lengths

Z₁, Z₂, Z₄, Z₅: λ/4 at f₀
Z₃: λ/2 at f₀ (impedance repeater)

Example 1: Equal 3-Way Split (M = N = K = 1/3)

Design:

M = N = K = 1/3
d₂ = 2/3

Z₁ = 50 × √(1/(2/3)) = 50 × √1.5 ≈ 61.2 Ω
Z₂ = 50 × √(1/(1/3)) = 50 × √3 ≈ 86.6 Ω
Z₃ = 50 Ω
Z₄ = 50 × √((2/3)/(1/3)) = 50 × √2 ≈ 70.7 Ω
Z₅ = 50 × √((2/3)/(1/3)) = 50 × √2 ≈ 70.7 Ω

R₁ = R₂ = 50 Ω

Example 2: Unequal Split (M = 1/2, N = 1/3, K = 1/6)

Power distribution:

Port 2: 50% (3 dB)
Port 3: 33% (4.8 dB)
Port 4: 17% (7.8 dB)

Design:

M = 0.5, N = 0.333, K = 0.167
d₂ = 0.5

Z₁ = 50 × √(1/0.5) = 50 × √2 ≈ 70.7 Ω
Z₂ = 50 × √(1/0.5) = 50 × √2 ≈ 70.7 Ω
Z₃ = 50 Ω
Z₄ = 50 × √(0.5/0.333) ≈ 61.2 Ω
Z₅ = 50 × √(0.5/0.167) ≈ 86.6 Ω

R₁ = R₂ = 50 Ω

Advantages

  1. Wideband operation:

    • Wider than standard Wilkinson

  2. Arbitrary power split: Any M:N:K ratio

    • Full design flexibility

  3. High isolation: >20 dB between all outputs

    • Good for amplifier combining

    • Three-way isolation maintained

  4. Grounded resistors:

    • Direct heat-sinking possible

    • Similar to Gysel topology -> Better thermal management

    • Higher power capability

  5. All ports matched: Good return loss

    • Input and all outputs matched to Z₀

    • Low VSWR

Limitations

  1. Complexity: More complex than standard Wilkinson

    • Five different impedances

    • λ/2 section adds length

  2. Size:

    • λ/2 center section

    • More PCB area required

  3. Limited to 3 outputs: Fixed 4-port design

    • Cannot extend to N-way easily

    • For N≠3, use tree or other topology

Comparison with Other 3-Way Dividers

Feature

Lim-Eom

3-Way Wilkinson

Tree (2× Wilkinson)

Outputs

3

3

3

Bandwidth

100-150%

20-40%

20-40%

Unequal split

Arbitrary

Difficult

Limited

Size

Medium

Small

Large (2 stages)

Complexity

High

Medium

Medium

Isolation

>20 dB

>20 dB

>20 dB

Resistors

2 (grounded)

3 (floating)

2 (floating)

Power handling

High

Moderate

Moderate

References

[1] J.-S. Lim and S.-Y. Eom.”A New 3-Way Power Divider with Various Output Power Ratios,” 1996 IEEE MTT-S Int. Microwave Symp. Dig., pp. 785-788.

[2] Andrei Grebennikov. “Power combiners, impedance transformers and directional couplers: part II”. High Frequency Electronics. 2008

See Also