Unequal-split branchline coupler

New for February 2023.  This content was split from our main branchline coupler page and is currently being expanded.

By varying the impedances of the opposite arms in a branchline coupler, unequal power splits can be obtained, as shown in the figure below.

The equations for the line impedances Z_0A and Z_0B are given below, as functions of the power split PA/PB and the system impedance Z₀.

The plot below shows the characteristic impedances Z0A and Z0B, for a fifty ohm system, as a function of the coupling ratio PA/PB expressed in dB. Note that two very different topologies result when P_A is greater than P_B (Z_0A and Z_0B are higher impedance than in an equal-split branchline) and when P_A is less than P_B (Z_0A and Z_0B are lower impedance than in an equal-split branchline).

The chart above does not completely tell the story of the tradeoffs made when you select which port provides the most power. Check out the power split responses for PA/PB=0.25 and PA/PB=4.0 below. The bandwidth for PA/PB=4.0 is far superior.

Check out our unequal-split power divider calculator, it handles Wilkinsons, rat-races and branch-line couplers!