This paper studies circular designs for interference models, where atreatment assigned to a plot also affects its neighboring plots within a block.For the purpose of estimating total effects, the circular neighbor balanceddesign was shown to be universally optimal among designs which do not allowtreatments to be neighbors of themselves. Our study shows that self-neighboringblock sequences are actually the main ingredient for an optimal design. Here,we adopt the approximate design framework and study optimal designs in thewhole design space. Our approach is flexible enough to accommodate all possibledesign parameters, that is the block size and the number of blocks andtreatments. This approach can be broken down into two main steps: theidentification of the minimal supporting set of block sequences and theoptimality condition built on it. The former is critical for reducing thecomputational time from almost infinity to seconds. Meanwhile, the task offinding the minimal set is normally achieved through numerical methods, whichcan only handle small block sizes. Our approach is of a hybrid nature in orderto deal with all design sizes. When block size is not large, we provideexplicit expressions of the minimal set instead of relying on numericalmethods. For larger block sizes when a typical numerical method would fail, wetheoretically derived a reasonable size intermediate set of sequences, fromwhich the minimal set can be quickly derived through a customized algorithm.Taking it further, the optimality conditions allow us to obtain both symmetricand asymmetric designs. Lastly, we also investigate the trade-off issue betweencircular and noncircular designs, and provide guidelines on the choices.