Impedance matching is a canonical problem in electrical engineering -- design a matching network that transfers maximum power from a generator to a load. Although the loads in this report are restricted to compact antennas, the mathematical exposition applies to any lumped load. Finding a good matching network is a diffcult numerical optimization problem. Therefore, techniques that compute bounds on the matching provide valuable information. For example, the Fano bounds discussed in this report bound the matching performance as a function of the frequency band. Therefore, the circuit design can see the matching performance against the bandwidth to make design decisions without having to solve countless matching problems. Moreover, the Fano bounds provide an excellent benchmark to assess the performance of actual matching circuits getting close enough to the best bounds is good enough. The Fano bounds are computed by maximizing the matching performance under inequality constraints. The inequality constraints are determined by analytic expansions of the load. Because symbolic manipulators compute these expansions and the numerical packages can solve the inequality constraints, the Fano bounds may be amenable to a hands-free computation. However, the sticking point for the Fano bounds is the requirement that the load be given in the Darlington representation. Therefore, this Phase I effort shows that the Fano bounds can automate and defers the Darlington computation to Phase II.