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In this letter, the equivalent circuit method is employed to derive an upper bound for the bandwidth of ultrathin absorbers comprising high impedance surfaces. It is found that the maximum bandwidth is linearly determined by the thickness and the permeability of substrates. The proposed bound can be applied to ultrathin absorbers with frequency dispersive substrates. The mechanism of broadening bandwidth by the use of frequency dispersive substrates is discussed to provide guidelines for designing wideband ultrathin absorbers. Numerical examples are presented to illustrate the analytical results and show that the proposed upper bound can provide acceptable prediction of the maximum achievable bandwidth.