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The paper presents an analysis of the single-phase saturated reactor using a mathematical model based on a 2-state switched linear circuit theory. It is shown that the observed incremental fundamental-frequency voltage/current characteristic is not an image of the B/H characteristic of the core, but when saturated corresponds to a reactance that is greater than the leakage reactance of the reactor. This increase is due to the inherent control action of the iron core and is influenced by the harmonic content of the terminal voltage of the saturated reactor. From the theory developed, the saturated reactor is seen to complete its full transient response in half a cycle. Experimental results using 100 VA models of both a saturated reactor and an equivalently controlled thyristor-switched reactor are given to confirm the theory.