An impedance transformer employing two-section coupled lines is presented in this study, which can achieve a wide operating band or passband with three reflection zeros. A direct synthesis approach is proposed and applied to the design of this transformer with the prescribed Chebyshev-function frequency response. If the impedance-transformation ratio, passband return loss (RL), and operating bandwidth are properly specified, all the required design parameters of this transformer can be explicitly gained. Furthermore, a special region for realisable impedance-transformation ratio and operating bandwidth with respect to the passband equal-ripple RL is extensively investigated. As such, various sets of design curves are numerically derived and graphically demonstrated for synthesis design of authors' proposed impedance transformer. As an example, a 50-25 impedance transformer with the 50% fractional bandwidth and 20 dB passband RL is designed, fabricated, and measured to confirm the theoretical predictions in the experiment.