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This paper presents a novel output filter approach for continuously frequency-tunable digital power amplifiers, suitable for future seamless and band-less applications in 5G, e.g. for cognitive radios (CR). The presented tunable output filter is based on a multi-bandstop lowpass response to regenerate the original microwave signal at the output of the digital amplifier stage by suppressing unwanted frequency components. Compared to conventional tunable bandpass solutions, it offers higher tunability, higher linearity, good power handling capability and moderate losses especially around the carrier frequency. A tunable power amplifier (PA) demonstrator consisting of a 4-stage digital GaN PA MMIC and the novel tunable filter, is designed and fabricated for a carrier frequency range from 1 GHz to 3 GHz. Tunability is achieved by using commercial barium strontium titanate (BST) varactors. Small signal measurements were performed to evaluate tunability and suppression capabilities of the novel filter structure, which reveal a frequency tunability of 67% with a suppression level of at least 13 dB for the undesired frequency components. The proposed filter structure exhibits a linearity over the tuning range with an OIP3 between 66 dBm to 70 dBm and high power handling capability. Finally, the performance analysis of the tunable PA demonstrator shows an peak efficiency of 70%. Due to frequency limitations of the used PA stage, the efficiency slowly degrades to 20% at the upper frequency band edge. Simultaneously, the output power varies between 27 dBm to 31 dBm.