The theory and design of a Tchebycheff tapered balun transformer which will function over frequency bandwidths as great as 100:1 is presented. The balun is an impedance matching transition from coaxial line to a balanced, two-conductor line. The transition is accomplished by cutting open the outer wall of the coax so that a cross-sectional view shows a sector of the outer conductor removed. As one progresses along the balun from the coaxial end, the open sector varies from zero to almost 2Â¿, yielding the transition to a two-conductor line. The balun impedance is tapered so that the input reflection coefficient follows a Tchebycheff response in the pass band. To synthesize the impedance taper, the impedance of a slotted coaxial line was obtained by means of a variational solution which yielded upper and lower bounds to the exact impedance. Slotted line impedance was determined experimentally by painting the line cross section on resistance card using silver paint and measuring the dc resistance of the section. The measured VSWR of a test balun did not exceed 1.25:1 over a 50:1 bandwidth. Dissipative loss was less than 0.1 db over most of the range. Measurements show that the unbalanced current at the output terminals is negligible.