Design the Wilkinson power divider that splits one RF/microwave signal into two (or combines two into one). Adjust the system impedance, operating frequency, substrate permittivity and split ratio to see the branch-line impedances, isolation resistor and quarter-wave line length update in real time.
Parameters
System impedance Z0
Ω
Reference impedance of the input/output ports. 50 Ω is standard
Operating frequency f
GHz
Centre frequency the divider is designed for
Substrate permittivity εr
Relative permittivity of the PCB dielectric (FR-4 ≈ 4.4)
Split ratio k (P2/P3)
Power ratio of output 2 to output 3. 1.0 = equal split
Results
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Branch Z (output 2) (Ω)
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Branch Z (output 3) (Ω)
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Isolation resistor R (Ω)
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λ/4 line length (mm)
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Output 2 split (dB)
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Effective permittivity εeff
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Wilkinson divider schematic — signal propagation animation
A signal travels from the input port through the quarter-wave lines and splits to the two output ports. A resistor R bridging the two outputs isolates the ports from each other.
General equations for an unequal split. K=√(P2/P3) is the voltage-ratio form of the split. Z02 and Z03 are the output-2 and output-3 branch lines, R the isolation resistor.
The physical length ℓ of a branch line is one quarter of the guided wavelength λg, found from the speed of light c, frequency f and effective permittivity εeff. For microstrip, εeff ≈ (εr+1)/2.
What is the Wilkinson Power Divider Simulator?
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A "Wilkinson power divider" splits a signal into two, right? So why not just fork the wire into two branches?
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Roughly that, yes — but at high frequency a "plain fork" causes trouble. If you split a 50 Ω line straight into two, the input now sees 25 Ω, so power reflects at the input port. Worse, whatever an antenna does on one output also disturbs the other output. The Wilkinson divider uses quarter-wave lines plus a single resistor to solve "input matching" and "output isolation" at the same time — it is a very clever little circuit.
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A quarter-wave line is a line one quarter wavelength long. Why does that specific length matter?
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A λ/4 transmission line acts as an impedance transformer. With a characteristic impedance Z0T, a load ZL at one end looks like Z0T²/ZL from the other end. In the equal-split Wilkinson, each output (50 Ω) connects to the input through a Z0·√2 ≈ 70.7 Ω quarter-wave line. The input then sees each line transformed to 100 Ω, and the two in parallel give exactly 50 Ω — a perfect match. Move the frequency slider on the left and you will see the quarter-wave length change in the chart below.
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Got it! So what does the resistor between the two outputs do? Are the quarter-wave lines not enough?
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Good question. The quarter-wave lines alone give input matching but do not isolate the output ports. If output 2's antenna reflects, that reflected wave finds its way to output 3. So you bridge a resistor R = 2Z0 (100 Ω for an equal split) between the two outputs. For the signal that arrives properly from the input, both ends of the resistor sit at the same potential, no current flows, and the resistor is "invisible". But for a reflected wave coming back from one output, the resistor sees a voltage difference across it and absorbs that wave cleanly. That is isolation — separating the outputs from each other.
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When I move the split ratio k slider, the two branch lines take different values. Is an unequal split also useful?
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It is. In an antenna array, for example, you may want to feed the centre element strongly and the edge elements weakly, so you deliberately split unequally. Set the ratio k = P2/P3 to 2 and output 2 gets twice the power of output 3. Then with K=√k the two branch lines become separate values Z02 and Z03, and the resistor changes to R = Z0(1+K²)/K. The default is the equal split (k=1) with the simple form Z02=Z03 and R=2Z0, but this tool also shows the line impedances for any unequal split.
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One last thing — splitting gives a −3 dB figure. Is that a loss?
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That is a "split", not a "loss". In an equal split the input power divides exactly in half between the two outputs. Half is a power ratio of 0.5, and in decibels 10·log10(0.5) ≈ −3.01 dB. So −3 dB is proof the circuit is working as it should. The real loss is the conductor and dielectric loss on top of that — about 0.1 to 0.5 dB in the 3 GHz band for a good design. So a measured −3.5 dB is healthy; if you see −5 dB, suspect the line or the soldering.
Frequently Asked Questions
For an equal split (ratio k=1), both branch lines are √2 times the system impedance Z0 — about 70.71 Ω quarter-wave lines for Z0=50 Ω. For an unequal split, set K=√k (k is the power ratio P2/P3) and use Z02 = Z0·√((1+K²)/K³) for the output-2 side and Z03 = Z0·√(K(1+K²)) for the output-3 side. Each line is exactly one quarter wavelength (λ/4) long.
A resistor R bridging the two output ports electrically isolates them from each other. For an equal split R = 2·Z0 (100 Ω for Z0=50 Ω); for an unequal split R = Z0·(1+K²)/K. A reflected wave generated at one output is absorbed by this resistor instead of leaking to the other output. Without the resistor the outputs interfere and the circuit is just a tee, not a divider.
Find the guided wavelength λg from the effective permittivity εeff, and the line length is one quarter of it: λg = c/(f·√εeff) (c is the speed of light, f the operating frequency), L = λg/4. For microstrip, εeff ≈ (εr+1)/2 gives a quick estimate. For an εr=4.4 substrate (FR-4 class) at 2.4 GHz, εeff ≈ 2.7, λg ≈ 76 mm, and the quarter-wave length is about 19 mm. The line gets shorter at higher frequency and higher εr.
In an ideal equal split the input power divides evenly between the two outputs, so each port receives −3.01 dB (exactly half). That is a fundamental split, not a loss. A real circuit adds conductor, dielectric and resistor losses, giving roughly 0.1 to 0.5 dB of extra insertion loss in the 3 GHz band. For an unequal split the stronger port sees less than −3 dB and the weaker port more.
Real-World Applications
Antenna-array feed networks: Phased arrays and patch-antenna arrays must distribute the power of one transmitter to many radiating elements. Wilkinson dividers are cascaded in a tree to build 4-way, 8-way and 16-way feed networks. To control the amplitude fed to each element — a tapered feed that drives the centre strongly and the edges weakly — unequal-split Wilkinson dividers are used.
Power-amplifier combining and dividing: High-power RF amplifiers combine the outputs of several transistors to reach large power. A Wilkinson divider splits the input equally among the amplifier stages, and the same circuit run in reverse combines the outputs. Because the output ports are isolated, the failure of one amplifier stage has limited impact on the others, raising overall system reliability.
Test and measurement setups: In the front ends of vector network analysers and spectrum analysers, and for splitting signal sources, Wilkinson dividers separate a reference signal from a measurement signal. The high isolation between output ports keeps one device under test from disturbing the other measurement path, enabling accurate measurements. Wideband and multi-section versions are also widely used in instrumentation.
Wireless equipment and base stations: Cellular base stations, Wi-Fi routers and satellite terminals embed Wilkinson dividers to split and combine transmit and receive signals. Because they can be printed directly on a PCB in microstrip or stripline, the only added component is a single isolation resistor — excellent for low cost, small size and mass production. Estimating the quarter-wave length with this tool gives a quick first approximation of the board layout.
Common Misconceptions and Pitfalls
A big misconception is that "a Wilkinson divider works over a wide frequency range". The basic Wilkinson uses quarter-wave lines, so it works correctly only at the design frequency. Once the line length departs from λ/4, the input matching, isolation and split balance all degrade. If you need a wide band beyond one octave, use a multi-section Wilkinson that cascades several quarter-wave lines. This tool targets the single-section basic form, so the values it gives are the design values at the centre frequency.
Next, the belief that "effective permittivity εeff = (εr+1)/2 is an exact value". This formula, which the tool uses, is only a simple microstrip approximation. The real εeff depends on the ratio of line width to substrate thickness, the conductor thickness and the surface roughness; for accuracy use the Hammerstad-Jensen equations or an electromagnetic simulator (method of moments, FEM). The simple formula carries an error of a few to over ten percent, and that error flows straight into λg and the line length. Always lock down the line dimensions with a detailed calculation or simulation before building a prototype.
Finally, the misconception that "the isolation resistor can be any ordinary resistor". This resistor must not only hold its design value but also have small parasitic inductance and capacitance at the operating frequency. Leaded resistors or large chip resistors carry too much inductance, which wrecks the isolation at high frequency. In the GHz range, use a small thin-film chip resistor and keep the mounting pads minimal. When the circuit is used as a combiner, the resistor dissipates power under unbalanced conditions, so allow margin in its power rating as well.
How to Use
Enter system characteristic impedance Z₀ (typically 50 Ω for RF/microwave systems)
Set operating frequency in GHz and substrate relative permittivity εᵣ (FR-4: 4.7, PTFE: 2.2)
Adjust coupling coefficient k (0 to 1) to control output isolation and power split symmetry
Click Calculate to compute λ/4 transmission line length, branch impedances, and isolation resistor value
Review output metrics: branch characteristic impedance (Z√2 for equal split), insertion loss in dB, and effective permittivity for PCB layout
Worked Example
Design a Wilkinson splitter for 2.4 GHz Wi-Fi application with Z₀=50 Ω on FR-4 substrate (εᵣ=4.7). System calculates: λ/4 line length ≈ 12.7 mm, branch impedance Z_branch = 70.7 Ω (50√2), isolation resistor R = 100 Ω, effective permittivity εeff ≈ 3.4. At equal power split, output 2 insertion loss = −3.0 dB per port with >15 dB isolation between outputs.
Practical Notes
For PCB microstrip implementation at 5 GHz, use εeff calculation to determine trace width; narrower traces increase branch impedance and require thinner substrates
Isolation resistor dissipates power when outputs are unbalanced; for 1 W input with 3 dB imbalance, resistor handles ~0.12 W—select adequate power rating
λ/4 length assumes homogeneous medium; account for fringing fields by measuring actual εeff from test coupons or electromagnetic simulation
Phase matching across branches critical above 10 GHz; manufacturing tolerances on line length cause >5° phase error and degrade isolation below 20 dB