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[Technical article, rfforum Editorial Team]
The Wilkinson divider splits one input into two equal (or unequal) outputs with matched ports and, when the outputs are driven out of phase in the odd mode, dumps the difference power in a resistor. That isolation resistor is what separates it from a simple T-junction.
1. Equal-split 2-way
Two quarter-wave lines of impedance √2 · Z0 (≈ 70.7 Ω for 50 Ω) go from the input to each output. A resistor R = 2 · Z0 (100 Ω) sits between the two outputs. At the design frequency each output sees 50 Ω looking back, the input is matched, and isolation between outputs is ideally infinite for a lossless design.
2. Even/odd mode intuition
Even mode: both outputs driven in phase. No current flows in the resistor, so it disappears. Each branch looks like a 70.7 Ω quarter-wave transforming 100 Ω (the even-mode half-load arrangement) into 50 Ω at the input.
Odd mode: outputs driven differentially. The resistor mid-point is a virtual ground, each half sees 50 Ω, and the quarter-wave lines transform that so the input looks like a short at the junction for the odd mode — which is exactly what you want for isolation.
3. Bandwidth and multi-section
A single-section Wilkinson typically gives about 20–30 % fractional bandwidth for 20 dB isolation and good match. Cascading sections with tapered line impedances and multiple resistors widens the band, at the cost of size and resistor placement.
4. Practical layout issues
- The 100 Ω resistor must be small compared with a wavelength and sit right between the two output pads. A long loop between the resistor and the junction kills isolation.
- On microstrip the √2 · Z0 lines are wider than 50 Ω lines on the same stackup; watch the junction discontinuity.
- Power handling: in normal equal-split operation the resistor dissipates almost nothing. Under heavy output mismatch (one port open or short) it can take up to half the input power. Size the resistor for that fault case if your system can see it.
- Unequal-split Wilkinsons exist (different branch impedances and a resistor that is not 2 Z0). The algebra is messier but the even/odd idea is the same.
5. How much amplitude/phase imbalance matters
For combining two PAs, amplitude imbalance of 0.5 dB and phase imbalance of 10° already cost a visible fraction of a dB in combined power and degrade isolation. Measure both paths with a VNA (S21 and S31) before blaming the PAs.
Discussion: for a 2–6 GHz multi-section Wilkinson on your usual stackup, how many sections do you need before the resistor parasitics dominate the isolation floor?
— rfforum 编辑部 / Editorial Team
The Wilkinson divider splits one input into two equal (or unequal) outputs with matched ports and, when the outputs are driven out of phase in the odd mode, dumps the difference power in a resistor. That isolation resistor is what separates it from a simple T-junction.
1. Equal-split 2-way
Two quarter-wave lines of impedance √2 · Z0 (≈ 70.7 Ω for 50 Ω) go from the input to each output. A resistor R = 2 · Z0 (100 Ω) sits between the two outputs. At the design frequency each output sees 50 Ω looking back, the input is matched, and isolation between outputs is ideally infinite for a lossless design.
2. Even/odd mode intuition
Even mode: both outputs driven in phase. No current flows in the resistor, so it disappears. Each branch looks like a 70.7 Ω quarter-wave transforming 100 Ω (the even-mode half-load arrangement) into 50 Ω at the input.
Odd mode: outputs driven differentially. The resistor mid-point is a virtual ground, each half sees 50 Ω, and the quarter-wave lines transform that so the input looks like a short at the junction for the odd mode — which is exactly what you want for isolation.
3. Bandwidth and multi-section
A single-section Wilkinson typically gives about 20–30 % fractional bandwidth for 20 dB isolation and good match. Cascading sections with tapered line impedances and multiple resistors widens the band, at the cost of size and resistor placement.
4. Practical layout issues
- The 100 Ω resistor must be small compared with a wavelength and sit right between the two output pads. A long loop between the resistor and the junction kills isolation.
- On microstrip the √2 · Z0 lines are wider than 50 Ω lines on the same stackup; watch the junction discontinuity.
- Power handling: in normal equal-split operation the resistor dissipates almost nothing. Under heavy output mismatch (one port open or short) it can take up to half the input power. Size the resistor for that fault case if your system can see it.
- Unequal-split Wilkinsons exist (different branch impedances and a resistor that is not 2 Z0). The algebra is messier but the even/odd idea is the same.
5. How much amplitude/phase imbalance matters
For combining two PAs, amplitude imbalance of 0.5 dB and phase imbalance of 10° already cost a visible fraction of a dB in combined power and degrade isolation. Measure both paths with a VNA (S21 and S31) before blaming the PAs.
Discussion: for a 2–6 GHz multi-section Wilkinson on your usual stackup, how many sections do you need before the resistor parasitics dominate the isolation floor?
— rfforum 编辑部 / Editorial Team
