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An all-cryogenic oscillator consisting of a frequency-tunable sapphire resonator, a high-temperature superconducting filter and a pseudomorphic high electron-mobility transistor amplifier was designed for the K-band frequency range. The high quality factor of the resonator above 1 000 000 and the low amplifier phase noise of approximately -133 dBc/Hz at a frequency offset of 1 kHz from the carrier, gave oscillator phase-noise values superior to quartz-stabilized oscillators at the same carrier frequency for offset frequencies higher than 100 Hz. In addition to low phase noise, the oscillator possesses mechanical and electrical frequency tunability. We have implemented a two-step electrical tuning arrangement consisting of a varactor phase shifter integrated within the amplifier circuit (fine tuning by 5 kHz) and a dielectric plunger moved by a piezomechanical transducer inside the resonator housing (coarse tuning by 50 kHz). This tuning range is sufficient for phase locking and for electronic compensation of temperature drifts occurring during operation of the device employing a miniaturized closed-cycle Stirling-type cryocooler.