This paper proposes a technique which allows quadband impedance matching and impedance level shifting Doherty power amplifier (DPA) design. By using novel coupler networks with reactance and choosing appropriate complex load impedances, the quadband DPA can reach a power back-off range (OBO) of over 9 dB. In addition, the peak PA branch and the carrier PA branch use different coupler network parameters in order to satisfy different impedance requirements. To illustrate the design procedure a quadband DPA with 9 dB OBO operating in 0.5-0.7 GHz, 1.5-1.7 GHz, 2.5-2.7 GHz, and 3.5-3.7 GHz frequency ranges is designed, fabricated and tested. Measurements demonstrate that the DPA can deliver saturated output power between 43.1 dBm and 43.8 dBm in all four bands, with a drain efficiency ranging from 63.3% to 66.5%. Also, drain efficiency of from 42.2% to 52.3 % can be obtained at an OBO of 9 dB level. The DPA implemented here shows state-of-the-art performance for OBO under quad-band operation.