The Directional Coupler KU ITTC（定向耦合器KU ITTC）.pdfVIP

4/20/2010 The Directional Coupler.doc 1/11 The Directional Coupler A directional coupler is a 4-port network that is designed to divide and distribute power. Although this would seem to be a particularly mundane and simple task, these devices are both very important in microwave systems, and very difficult to design and construct. Two of the reasons for this difficulty are our desire for the device to be: 1. Matched B. Lossless Thus, we require a matched, lossless, and (to make it simple) reciprocal 4-port device! Recall that a matched, lossless, reciprocal, 4-port device was difficult to even mathematically determine, as the resulting scattering matrix must be (among other things) unitary. However, we were able to determine two possible mathematical solutions, which we called the symmetric solution: Jim Stiles The Univ. of Kansas Dept. of EECS 4/20/2010 The Directional Coupler.doc 2/11 ⎡ 0 α j β 0 ⎤ S ⎢⎢ α 0 0 j β ⎥⎥ ⎢j β 0 0 α ⎥ ⎢ ⎥ ⎣ 0 j β α 0 ⎦ And the asymmetric solution: ⎡0 α β 0 ⎤ ⎢α 0 0 −β ⎥ S ⎢ ⎥ ⎢β 0 0 α ⎥ ⎢ ⎥ ⎣0 −β α 0 ⎦ wherein for both cases, the relationship: 2 2 α + β =1 must be true in order for the device to be lossless (i.e., for S to be unitary). For most couplers we will find that α and β can (at least ideally) be represented by a real value c , known as the coupling coefficient.