A class of impedance transformers on coupled lines and multisection stepped-impedance transmission line are presented in this paper, which can achieve a wide operating band or passband. A direct synthesis approach is described and employed to design these transformers with Chebyshev frequency response. If the impedance transformation ratio, passband return loss (RL), and operating bandwidth are properly specified, all the required design parameters of these transformers can be explicitly determined. Moreover, a special region for realizable impedance transformation ratio and operating bandwidth with respect to the equal-ripple RL in the desired passband is extensively investigated. As such, various sets of design curves for synthesis design of our proposed impedance transformers are numerically derived. In final, the two prototype 50-25- Ω impedance transformers with the 62.5% fractional bandwidth and 20-dB passband RL are designed, fabricated, and measured to confirm the theoretical predictions in experiment.