A partial concentrator with parameters n, m, and c, is an n (inputs) × m (outputs) bipartile graph such that any set of k inputs, k≤c, has a perfect matching to some set of k outputs. A partial concentrator is regular if each input has M edges and each output has edges. We study the problem of maximizing c for given m,n and M. For Kufta and Vacroux, and Richards and Hwang gave a similar construction of a partial concentrator and proved c≥M2+M−1. If, furthermore, is a prime, the construction given by Richards and Hwang has a cyclic property. In this paper we use this cyclic property to prove c≥M2+2M−2. This is the best result possible for M=3 since it coincides with an upper bound previously proved.