We find low order approximations to the spherical nonreflecting boundary kernel for the wave equation in three dimensions. First we express the Laplace transform of the kernel as a rational function by solving for the zeros of a modified Bessel function. Then we formulate a linear time-invariant dynamical system whose transfer function is this rational function. Finally we use the Balanced Truncation method to generate loworder approximations.We compare our approach with a direct L2 minimization approach where a rational approximation is expressed as the ratio of two polynomials.