Ring diblock copolymers with different lengths of the A and B blocks have been investigated using theoretical and numerical simulation methods. The theoretical calculations are based on a first-order expansion in the parameter epsilon = 4 - d and extend to chains in a common Theta solvent, in a common good solvent, and in selective solvents, though only the first case is discussed in detail. The Monte Carlo calculations are performed for a common Theta solvent case with an off-lattice model of Gaussian units which interact through a Lennard-Jones potential. Averaged dimensions for each of the blocks and for the whole chain are obtained, and the theoretical and simulation results are analyzed and discussed. From the results, we have obtained general trends for all these different properties, and the most important differences and similarities with linear or homopolymer chains have been identified.