Wilkinson Divider Design
Understanding Wilkinson Divider Design
The Wilkinson divider is elegant: it achieves simultaneous matching at all three ports, equal power split, and isolation between output ports, all using only two quarter-wave lines and one resistor.
Wilkinson Design Equations
Z_quarter-wave = Z0 x sqrt(2) = 70.7 ohms
R_isolation = 2 x Z0 = 100 ohms
Length of each arm = lambda/4
Performance at center frequency:
S11 = 0 (perfect input match)
S22 = 0 (perfect output match)
S23 = 0 (perfect isolation)
S21 = S31 = -3 dB (equal split)
Bandwidth (S11 < -20 dB): ~40% for single section.
Multi-Section Wilkinson
Two-section Wilkinson uses two quarter-wave segments with different impedances and two resistors, extending bandwidth to 2:1 or greater.
Frequently Asked Questions
What is a Wilkinson divider?
A Wilkinson divider splits input power into two equal in-phase outputs using quarter-wave lines (70.7 ohms in 50-ohm systems) and a 100-ohm isolation resistor. It provides simultaneous matching, equal split, and port isolation.
How wide is the bandwidth?
Single-section: ~40% bandwidth for good match and isolation. Two-section: 2:1 bandwidth. Three-section: 3:1 bandwidth. Multi-section designs trade size for bandwidth.
Can Wilkinson divide unequally?
Yes. Unequal Wilkinson dividers use different arm impedances. For a K:1 power ratio, Z1 = Z0*sqrt(K*(1+K)) and Z2 = Z0*sqrt((1+K)/K). The isolation resistor also changes. Common for array feed networks.