An accurate equivalent circuit (EC) design approach for wideband nonmagnetic absorbers operating at the low microwave frequency (1-10 GHz) is presented. Following the impedance matching approach, this communication introduces an EC model based on the simulated data and synthetic asymptotes for single- and double-layer frequency-selective surface (FSS)-based nonmagnetic absorbers. Two simple and commonly used resistive FSSs, i.e., square patch and single square loop, are considered in this communication. Compared to the full-wave simulations, the proposed EC model shows more than 95% accuracy. By employing the proposed model and genetic algorithm-based optimization, several designs of broadband absorbers are demonstrated. The presented single- and double-layer FSSs show 126% and 161% fractional bandwidth, respectively, with the total thickness close to the Rozanov limit. The results confirm that the proposed method is a simple and efficient way of designing thin wideband absorbers using single- or double-layer FSS configurations.