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Core losses in power magnetic components are important factors in their design. These losses are influenced by factors including frequency, temperature, and flux density waveform. A common empirical model to predict these losses is the Steinmetz equation and its derivatives such as the modified Steinmetz equation and the generalized Steinmetz equation. In this paper, these three models are modified to address magnetic saturation and temperature dependence. The work focuses on manganese zinc ferrite samples for low to medium frequency operation. Experimental hardware verification is provided and results obtained demonstrate that the proposed model modifications significantly reduce model error.