Design and optimization of lumped-element LCM directional couplers

The well-known concept of image impedances is used to develop lumped-element mid-series and mid-shunt equivalents to the quarter-wave coupled-transmission-line directional coupler. These lumped-element equivalent circuits are symmetric about two axes, and are composed of one or more sections with equal phase delay per section. The crucial condition imposed in the design procedure is to force the propagation functions for the even- and odd-modes to be equal to each other. Three-section couplers are examined most closely, and the cascade and tandem connections are also explored.;Couplers designed using this technique are optimized in the frequency domain, and a marked improvement in isolation and input port reflection coefficient is observed. Furthermore, the individual element values in the designed and the corresponding element values in the optimized three-section couplers are found to be related by linear transformations.;Optimized three-section couplers are connected in cascade and tandem configurations, and the cascade connected couplers are optimized in their entirety, again resulting in a significant improvement in isolation and input port reflection coefficient.;An optimized 8.34 dB three-section lumped-element LCM directional coupler was built and tested and the laboratory measurements are found to be in close agreement with theoretical performance.;A VS FORTRAN compiler listing of the optimizer program is included.