The behavior of the wide-band transmission-line transformer for nonoptimum line impedance

The transmission-line transformer can perfectly match at a single frequency any resistance ratio greater than or equal to four. This requires an optimum choice for the impedance and length of the line. For short lines, the transformer behavior is insensitive to small variations from optimum of the line impedance. A simple easily applied theory predicts the transformer behavior as a function of line length, the ratio of resistances to be matched, and the departure of line impedance from the optimum value.