Aims. Bright ring-like structure emission of the CN molecule has been observed in protoplanetary disks. We investigate whether such structures are due to the morphology of the disk itself or if they are instead an intrinsic feature of CN emission. With the intention of using CN as a diagnostic, we also address to which physical and chemical parameters CN is most sensitive. Methods. A set of disk models were run for different stellar spectra, masses, and physical structures via the 2D thermochemical code DALI. An updated chemical network that accounts for the most relevant CN reactions was adopted. Results. Ring-shaped emission is found to be a common feature of all adopted models; the highest abundance is found in the upper outer regions of the disk, and the column density peaks at 30−100 AU for T Tauri stars with standard accretion rates. Higher mass disks generally show brighter CN. Higher UV fields, such as those appropriate for T Tauri stars with high accretion rates or for Herbig Ae stars or for higher disk flaring, generally result in brighter and larger rings. These trends are due to the main formation paths of CN, which all start with vibrationally excited H\hbox{$_2^*$} molecules, that are produced through far ultraviolet (FUV) pumping of H₂. The model results compare well with observed disk-integrated CN fluxes and the observed location of the CN ring for the TW Hya disk. Conclusions. CN rings are produced naturally in protoplanetary disks and do not require a specific underlying disk structure such as a dust cavity or gap. The strong link between FUV flux and CN emission can provide critical information regarding the vertical structure of the disk and the distribution of dust grains which affects the UV penetration, and could help to break some degeneracies in the SED fitting. In contrast with C₂H or c-C₃H₂, the CN flux is not very sensitive to carbon and oxygen depletion.