The article considers analytical expressions for electric field potentials that correspond to radio frequency funnels with quadratic, cubic and biquadratic profiles. The funnel electrodes are a sequence of diaphragms with a circular or multipole structure and apertures of variable size. The latter varies along the transport channel according to the desired law. The resulting expressions can be useful for fast, high-quality simulation of radiofrequency devices designed to convey ion beams with simultaneous focusing.