Modeling of a broadband receiving system based on a meander series of Josephson YBaCuO grain boundary junctions integrated into a log-periodic antenna was carried out. The electromagnetic properties of the system, namely amplitude–frequency characteristic, beam pattern, and fraction of the absorbed power in each Josephson junction were investigated. Based on the obtained results, a numerical simulation of one-dimensional arrays was carried out. The dc characteristics of the detector were calculated, that is, current–voltage characteristic, responsivity, noise, and noise-equivalent power (NEP) for a 250 GHz external signal. The optimal number of junctions to obtain the minimum NEP was found. The use of a series of junctions allows one to increase the responsivity by a factor of 2.5, the NEP value by a factor of 1.5, and the power dynamic range by a factor of 5. For typical YBaCuO Josephson junctions fabricated on a ZrYO bicrystal substrate by magnetron deposition, the following parameters were obtained at a temperature of 77 K: responsivity = 9 kV/W; NEP = 3·10−13 W/Hz(1/2); power dynamic range = 1·106.