The emergence of "acoustic diode" (AD) capable of rectifying acoustic wave like electrical diodes do to electricity has been believed to be able to offer unconventional manipulation on sound, e.g., to isolate the wrong-way reflection, and therefore have great potential in various important scenarios such as medical ultrasound applications. However, the existing ADs have always been suffering from the problem that the transmitted wave must have either doubled frequency or deviated direction, lacking the most crucial features for achieving such expectations in practice. Here we design and experimentally demonstrate a broadband yet compact non-reciprocal device with hitherto inaccessible functionality of maintaining the original frequency and high forward transmission while virtually blocking the backscattered wave, which is close to what a perfect AD is expected to provide and is promising to play the essential role in realistic acoustic systems like electric diodes do in electrical circuits. Such an extreme ability comes from inherently distinct mechanism based on the exploration of the acoustic characteristics in complex domain, in comparison to the previous designs that only utilize the real part of acoustical parameters. Furthermore, our design enables improving the sensitivity and the robustness of device simultaneously by tailoring an individual structural parameter, which can be regarded as the unique advantage over its electrical or thermal counterparts. We envision our design will take a significant step towards the realization of applicable acoustic one-way devices with potential applications in many scenarios, and inspire the research of non-reciprocal wave manipulation in other fields like electromagnetics.