The Analysis of Broad-Band Microwave Ladder Networks

By expressing the transmission matrix in terms of the Pauli spin matrices it has been found possible to write formulas for symmetrical ladder networks that are practical for analysis, even in the presence of gross line effect or parameter variation. These formulas are particularly useful for broad-band microwave filters. General formulas are given for the combination of 2, 3, 4, and 5 elements. Detailed formulas are also given for elements that may be described as parallel resonant structures in shunt at the center of a length of line or waveguide. An example is given illustrating the "line effect" in a low-Q structure that otherwise would show a "Butterworth" or "semi-infinite slope" characteristic.