Wilkinson Power Divider
The Wilkinson divider splits an input signal into two output ports, or combines two inputs into one, while maintaining isolation between the output ports. It uses two λ/4 transmission line sections and one isolation resistor. Matched, isolated, and lossless (in the ideal case). Can be unequal-split for asymmetric power division.
Equations & Parameters ▸
\(Z_1=Z_0\!\sqrt{\tfrac{1+K^2}{K^3}},\quad Z_2=Z_0\!\sqrt{K(1+K^2)},\quad R_{iso}=Z_0\!\left(K+\tfrac{1}{K}\right)\)
| Z₀ | System characteristic impedance, typically 50 Ω. |
| K² | Power split ratio: output port 2 receives K² times more power than port 3. K=1 gives equal split (3 dB each). |
| f | Design frequency. The λ/4 sections are this length. |
| Z_arm1, Z_arm2 | λ/4 arm impedances. Equal split: both = Z₀√2. |
| R_iso | Isolation resistor between the two output ports. Equal split: R = 2Z₀. |
| εᵣ | Substrate dielectric for computing physical arm lengths. |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
Ω
1 = equal split (3dB/3dB)
for physical length. 1 = air/coax
Results
Transmission Line Arms
Z_arm1 (to port 2)—
Z_arm2 (to port 3)—
Physical arm length—
Split at port 2—
Split at port 3—
Isolation
Isolation resistor, R_iso—
Ideal isolation (>20 dB)—
Return loss at ports—
Diagram