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This paper presents a novel automatic tuning mechanism that eliminates hand-tuning and is suitable for electronically-tunable microwave filters. The proposed method is based on a deep Q-learning approach using physics-based filter characteristic parameters like resonant frequency, bandwidth, insertion loss, and return loss. The whole tuning process is done automatically and does not require any pre-tuning or human expertise. Furthermore, unlike single-frequency post-production tuning techniques, the presented methodology is applicable to continuously-tunable filters covering a wide frequency range. This method is experimentally demonstrated on a 2-3.5 GHz evanescent-mode electronically-tunable bandpass filter. To the best of our knowledge, this is the first demonstration of such an automatic tuning mechanism where the user can specify any frequency of interest and the filter tunes automatically to that frequency within the entire operating range of the filter.