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When a printed circuit board (PCB) is mounted to a metal chassis, the cavity formed between the circuit board ground and the chassis can resonate at certain frequencies resulting in unintended radiated emissions. The cavity resonances can be effectively suppressed by using conductive mounting posts and adding a resistance in series with the connection between one or more of these mounting posts and the PCB ground plane. This paper derives a simple closed-form expression for determining an optimal series resistance for damping these cavity resonances over a wide range of frequencies. This analysis was done for rectangular boards mounted on four posts located near the corners. A similar analysis could be done to determine the optimal resistance values for other board shapes and mounting post locations. For the four-post configuration, shorting one or more of the posts does not affect the optimum resistance value for the remaining posts.