ON THE NATURE OF CRITICAL-POINTS IN LEAKAGE REGIMES OF A CONDUCTOR-BACKED COPLANAR STRIP LINE

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or e quilibrium paints from catastrophe and bifurcation theories, in conjun ction with a full-wave integral equation solution. The existence of no ndegenerate or Morse critical points (MCP's) and degenerate or fold (t urning) critical points (FP's) in coupling and leakage regions are ass ociated with the occurrence of improper real and complex (leaky) solut ions. The locations and types of critical points determine the stabili ty and instability of the transmission line system with respect to sma ll changes in geometrical parameters, The dispersion behavior of impro per real and complex (leaky) solutions are efficiently reproduced in t he local neighborhood of MCP's and FP's using a Taylor series expansio n about those points, The qualitative and quantitative dynamic behavio r of the transmission line modes can be investigated by examining the evolution of nondegenerate and degenerate points versus some structura l parameter, such as strip width. The proposed analysis enables the pr ediction of bifurcation situations and the existence of improper real and complex solutions and gives a complete description of the system's structural behavior.