In this paper, the analytical models for the electrothermal feedback of a ${mu}$-bolometer focal plane array(FPA) are proposed and applied to the conceptually designed FPA to investigate the electrothermal feedback effect on bolometer FPA signal. The temperature and resistance change of the ${mu}$-bolometer by the electrothermal feedback(ETF) model are increased upto 20 and 35.7 % of those of no feedback case, respectively, while those by the effective thermal conductance(ETC) model increased 8.5 and 15.1 %. The integration current and output voltage of a CTIA used as an column amplifier of FPA are also increased upto 41.6 and 32.4 % by the ETF model, while increased upto 17.2 and 13.5 % by the ETC model. The proposed models give more accurate temperature change, accordingly larger signal than no feedback considering case. Electrothermal feedback effect should be considered to design a high performance and high density ${mu}$-bolometer FPA. The proposed models are very useful to investigate the transient thermal analysis, also considered to be useful to predict the responsivity and dynamic range of ${mu}$-bolometer FPAs.