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Experiments on acceleration of electrons and production of X-ray radiation with use of ceramic piezoelectric transformers installed in vacuum are described and analyzed. The piezoelectric transformer operates at resonance frequency. Electrons are accelerated from the high-voltage electrode of the ceramic piezoelectric transformer toward the grounded target, where they emit bremsstrahlung and characteristic X-ray radiation in the target material. The returning of the charge to the high-voltage electrode is provided due to electrons emitted from a filament installed in the vicinity of the target. It was found that the X-ray yield increases linearly at increasing of the pressure of the residual gas in the chamber within two orders of magnitude up to about 10 mTorr, when the gas discharge around of the piezoelectric transformer arises. Possibilities for application of piezoelectric transformers for production of accelerating voltage in small-size accelerators are discussed. [ABSTRACT FROM AUTHOR]