We design and implement an efficient high-current radio-frequency (RF) circuit, enabling fast and coherent coupling between magnetic levels in cold alkali atomic samples. It is based on a compact shape-optimized coil that maximizes the RF field coupling with the atomic magnetic dipole, and on coaxial transmission-line transformers that step up the field-generating current flowing in the coil to about 8 A for 100 W of RF power. The system is robust and versatile, as it generates a large RF field without compromising on the available optical access, and its central resonant frequency can be adjusted in situ. Our approach provides a cost-effective, reliable solution, featuring a low level of interference with surrounding electronic equipment thanks to its symmetric layout. We test the circuit performance using a maximum RF power of 80 W at a frequency around 82 MHz, which corresponds to a measured Rabi frequency $Omega_R/2pi simeq 18.5$ kHz, i.e. a $pi$-pulse duration of about 27 $mu$s, between two of the lowest states of ${}^6$Li at an offset magnetic field of 770 G. Our solution can be readily adapted to other atomic species and vacuum chamber designs, in view of increasing modularity of ultracold atom experiments.
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