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In this paper, we deal with the broadband constant beamwidth beamforming problem for circular arrays. The response vector of a circular array is expanded in the form of sum of an infinite series, whose core function is the first kind Bessel function. High order terms of this series are truncated so that the array response vectors at different frequency components can be transformed to be approximately equal to that at the reference frequency. Constant beamwidth beamforming vectors can be constructed by using the transforming procedure, so that beams at different frequencies are same as the reference beam. The effectiveness of this method is firstly verified by computer simulation. To further investigate the performance of the proposed method, lake-experiment was carried out for a 24-element uniform circular array with radius=1.5 m. Based on the data collected from the experiment, constant beamwidth beams were successfully formed at eight different frequencies covering one-octave frequency band. Although big amplitude difference among hydrophones was observed during the experiment, the constant beamwidth beams were still correctly formed except for some distortions at sidelobe region of the beampattern. From the experiment result, we can conclude that constant beamwidth beamforming approach proposed for circular array is applicable to practical systems and has good error tolerance.