Accurate Synthesis of Four-Line Interdigitated Coupler

We present an accurate synthesis method for the design of a four-line interdigitated coupler in this paper. With the derivation of an admittance matrix of four coupled transmission lines and the use of an interconnecting condition, only half of the original coupled-line structure should be considered with its symmetric plane replaced by a perfect electric wall and/or perfect magnetic wall. Subsequently, two new mode admittances are, respectively, calculated from the propagation constants and the line impedances of c- and pi-modes, which are extracted from full-wave simulation. In this way, a reference chart is generated that presents the relation between the two mode admittances and physical dimensions of the coupled lines. With any prescribed performance, the physical dimensions of a four-line interdigitated coupler can effectively be synthesized by looking up this reference chart. Two examples are given to demonstrate the accuracy and flexibility of our proposed scheme. One is a conventional 3-dB four-line Lange coupler fabricated by a miniature hybrid microwave integrated circuit process. The other is a composite microstrip coplanar waveguide coupler made by a standard printed circuit board process. For both couplers, simulated and measured results are in good agreement. The proposed method is useful for the accurate synthesis and design of four-line couplers having an interdigitated topology.