Wilkinson
Understanding the Wilkinson Divider
The Wilkinson divider is elegant in its simplicity and performance. With just two quarter-wave lines and one resistor, it achieves matched input, matched outputs, and perfect isolation between outputs (at the design frequency). No other three-port device achieves this without loss.
Wilkinson Design
- Line impedance: Z_line = Z0 x sqrt(2) = 70.7 ohms (for equal split, 50-ohm system).
- Line length: lambda/4 at the design frequency.
- Isolation resistor: R = 2 x Z0 = 100 ohms (for 50-ohm system).
Wilkinson Properties
- Lossless for matched outputs: When both outputs are terminated in Z0, all power from the input reaches the outputs with zero theoretical loss (beyond the 3 dB split).
- Lossy for mismatched outputs: Reflected power from mismatched outputs is absorbed by the isolation resistor.
- Bandwidth: About 20% for single-section. Multi-section Wilkinson dividers extend bandwidth to octave or more.
Z_line = Z0 x sqrt(2) = 70.7 ohms
R_isolation = 2 x Z0 = 100 ohms
Line length = lambda/4
S-parameters at center frequency:
S11 = 0 (matched input)
S22 = S33 = 0 (matched outputs)
S23 = S32 = 0 (isolated outputs)
|S21| = |S31| = 1/sqrt(2) = -3.01 dB
Frequently Asked Questions
What is a Wilkinson divider?
A Wilkinson divider splits a signal into two equal parts with matched ports and isolation between outputs. It uses two 70.7-ohm quarter-wave lines and a 100-ohm bridging resistor (in a 50-ohm system). It is the standard power divider in microwave circuits.
Is the Wilkinson divider lossless?
When both output ports are matched, the Wilkinson is theoretically lossless beyond the inherent 3 dB splitting loss. The isolation resistor only dissipates power when the output ports are mismatched or receive signals of different amplitude/phase.
Can a Wilkinson divide unequally?
Yes. Unequal-split Wilkinson dividers use different line impedances for the two arms. The line impedances and isolation resistor values are calculated from the desired power ratio. Common unequal splits are 6 dB (75% / 25%) and 10 dB (90% / 10%).