The MRI rf coil known as the balanced high-pass-weighted hybrid birdcage is modified to obtain two homogeneous degenerate resonances, capable of generating circular polarization at widely separated frequencies, by including inductors in parallel with the ring (high-pass) tuning capacitors such that their isolated parallel resonant frequency is greater than the desired low-frequency (LF) homogeneous resonance and not greater than 10% more than the desired high-frequency (HF) homogeneous resonance. The coil is advantageous for the frequency-diameter product range of 10 to 60 MHz-m. The coil is preferably balanced at both frequencies such that the electric potentials vanish on the central axial plane at both the LF and HF homogeneous modes. Additional parasitic-mode-shifting reactive elements, either capacitors or inductors, may be added between adjacent rungs near their ends, and the rungs may each consist of two parallel bands shorted together at their ends, as in the Crozier birdcage. Note that a high-pass-weighted hybrid birdcage is defined as a hybrid birdcage in which the reactance of the rung series capacitors is significantly less than the reactance of the ring series capacitors.