We develop the theory for a broadband constant-beamwidth transducer (CBT) formed by a conformal circular-arc line array of dipole elements. Appropriate amplitude shading of the source distribution leads to a far-field radiation pattern that is constant above a cutoff frequency determined by the prescribed beam width and arc radius. We illustrate the theory with examples, including numerical simulations of magnitude responses, full-sphere radiation patterns and directivity index. Unlike a circular-arc array of monopole elements, a dipole CBT maintains directivity control at low frequency. We give an example of one such array that achieves just 1 dB variation in directivity index over all frequencies.