Unequal-Split Wilkinson Power Divider Calculator

A Wilkinson divider splits the input power between two outputs while keeping them isolated from each other. This tool sizes the unequal-split version for any power ratio: enter K and the characteristic impedance to get the impedances of five λ/4 lines and the isolation resistor R, with every port matched to Zo.

Any ratio K = Pb / PaFive λ/4 lines Z1–Z5Isolation resistor RAll ports matched to Zo

① Input parameters

Power ratio KPb / Pa Impedance ZoΩ

K = Pb / Pa. For Pa : Pb = 1 : 3, K = 3. K = 1 gives an equal (3 dB) Wilkinson split.

② Results

Line	Position	Impedance
Z1	Input λ/4 transformer	Ω
Z2	λ/4 branch toward Pa	Ω
Z3	λ/4 branch toward Pb	Ω
Z4	Pa output λ/4 transformer	Ω
Z5	Pb output λ/4 transformer	Ω
R	Isolation resistor between branches	Ω

Every line is λ/4 long (guided wavelength) at the center frequency. Convert impedance to trace width with the microstrip calculator.

Layout diagram

Blue blocks = λ/4 transmission lines (conductor), red = isolation resistor R. All three ports see Zo.

Power split

How to use

Enter the power ratio K = Pb / Pa (enter 2 if Pb should get twice the power of Pa).
Enter the system impedance Zo (normally 50 Ω).
Press Calculate to get Z1–Z5 and the isolation resistor R.
Make every line λ/4 long at the center frequency and convert impedances to widths with the microstrip calculator; place R as close as possible to the branch junctions.

Theory and formulas

Branch lines Z2 and Z3 set the unequal power split. Output lines Z4 and Z5 transform the internal branch impedances back to Zo, and input line Z1 transforms the parallel combination of the branches back to Zo. The isolation resistor R decouples the two outputs. With k = √K:

Z1 = Zo · ( k / (1 + K) )^1/4
Z2 = Zo · k^3/4 · (1 + K)^1/4
Z3 = Zo · (1 + K)^1/4 / k^5/4
Z4 = Zo · √k　　Z5 = Zo / √k
R = Zo · (1 + K) / k

Example with Zo = 50 Ω and K = 1: Z4 = Z5 = 50 Ω, R = 100 Ω, Z2 = Z3 ≈ 59.5 Ω and the input line Z1 ≈ 42.0 Ω. The ratio of the branch input impedances at the junction equals K, so the power divides by K.

Design tips

Large ratios push Z2 and Z3 apart and can give trace widths that are too narrow or too wide to build; on FR4 a practical range is roughly 20–120 Ω.
Compute λ/4 from the guided wavelength (λg = λ0 / √εeff); get εeff for microstrip from the microstrip calculator.
Use a small (0402/0603) chip resistor for R with the shortest possible connections so parasitics do not degrade isolation.
If you only need to sample a small amount of power, use a lumped directional coupler instead.

FAQ

How do I convert a dB difference to K?: K = 10^{(difference in dB / 10)}. If Pb should be 3 dB above Pa, K ≈ 2; for 6 dB, K ≈ 4.
Is a Wilkinson a coupler or a divider?: It is a power divider (and can be used in reverse as a combiner). Because its outputs are isolated it is often called a Wilkinson coupler, but it serves a different purpose than a sampling directional coupler.
How wide is the bandwidth?: A single-section Wilkinson is narrowband: matching and isolation are perfect only at the λ/4 center frequency and degrade away from it. This design cascades three λ/4 sections, so it is narrower than a single section. For wide bandwidth use a multi-section design and verify with EM simulation.

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