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In this paper, a low phase-noise planar oscillator employing an elliptic bandpass filter as a frequency stabilization element within its feedback loop is presented. The oscillator phase noise is significantly reduced by taking advantage of the group-delay peaks formed at the passband edges of the elliptic filter. A filter optimization technique for low phase-noise oscillator designs is introduced and applied to a four-pole bandpass elliptic filter. An X-band oscillator using the optimized filter in the feedback loop is designed and tested. At the oscillation frequency of 8.05 GHz, the measured phase noise is -143.5 dBc/Hz at 1-MHz offset frequency. The oscillator exhibits an output power of 3.5 dBm with an dc-RF efficiency of 10%. To the authors' best knowledge, this is the lowest phase noise performance for an X-band planar microwave oscillator.