The famous Popov criterion is used for absolute stability analysis of uncertain nonlinear systems. Uncertainty is assumed to exist in the linear subsystem in terms of coefficient perturbations in complex plane discs. Existing results, which are based on strict positive realness (SPR) conditions, are generalized so as to cover a wider spectrum of systems. All the results are then restated using circular arithmetic which is proposed as an alternative to SPR conditions. The use of circular arithmetic leads to non-conservative results at the expense of more computational effort. This is in contrast with the conservative results yielded by the computationally more efficient approach based on SPR conditions.