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Miniature all-fiber phase modulators with a radially symmetrical piezoelectric ZnO jacket have been characterized over a wide frequency range up to 1 GHz. Multiple radial resonances with phase shift values as high as 0.82 rad were observed in the frequency region between 20-400 MHz. A linear dependence of the phase shift on the square root of the driving power is observed up to 125 mW with a phase shift efficiency of 0.21 and 0.175 rad//spl radic/mW per centimeter fiber length at 196.5 and 399.5 MHz, respectively. The dependence of the phase shift efficiency on the modulation length is demonstrated.