The instrumentation of a low-temperature three-mode gravitationa1 radiation antenna incorporating a low-noise dc SQUID provided by IBM is described. The feedback circuitry necessary to maintain the linearity and dynamic range of the SQUID was found to drive the resonant system due to high coupling between the input coil and the feedback coil of the SQUID. In order for this type of planar thin-film dc SQUID to be useful for gravitational radiation detectors and other applications requiring high Q input circuits, a solution to this feedback problem is needed. To this end, the nonlinear equations describing the dc SQUID with linear feedback are solved in terms of an isolated SQUID. The important feedback parameters for a high Q resonant system are found to be the slew rate of the electronics and the coupling constant ratio α2if/α2f, where α2if is the energy coupling efficiency between the feedback coil and input coil and α2f is the energy coupling efficiency between the feedback coil and the SQUID loop. Methods to reduce the effect of the feedback on the input circuit are also discussed.