General model for loaded stub branch-line coupler

The work proposes a general model for the transmission line miniaturization equivalent. Solutions with different configurations can be readily found. The model is applied to the design of branch-line couplers, and design criteria are presented and analyzed. Previously reported approaches can be obtained by simply changing parameters using the general model. A 2GHz branch-line coupler is designed and fabricated to demonstrate the efficiency of the new method. A 900MHz branchline coupler from literature is re-designed and analyzed to show the differences between the proposed method and the previous work.