## Transformer Utilization Factor (TUF) of single phase half wave rectifier

Transformer Utilization Factor (TUF)While designing any power supply, it is necessary to determine the rating or the transformer. It can be done provided TUF is known. The value of TUF depends on the amount of power to be delivered to the load and the type of rectifier circuit to be used.

#### TUF = dc power delivered to the load /ac rating of transformer secondary

#### =P_{dc}/P_{ac.rated }

#### = P_{dc}/P_{in.rated}

At first sight it might appear as if the above ratio is the same as the conversion efficiency. Actually, it is not so because the rating of the transformer secondary is different from the actual power delivered by the secondary.

#### P_{dc }= V_{L(dc)}.I_{L(dc)}

#### = V_{LM}/π . VLM/R_{L}

#### = V_{LM}^{2} /πR_{L}

#### = V_{sm}^{2} /πR_{L - }if drop over R_{0 }is neglected

Now, the rated voltage of transformer secondary is V_{sm}/√2 but actual current flowing through the secondary is I_{L }= I_{LM}/2 (and not I_{LM} /√2) since it is a Half-Wave rectifier current.

#### P_{ac.rated }= V_{sm}/√2 .I_{LM}/2

#### = V_{sm}/√2 . V_{LM}/2R_{L}

#### = V_{sm}/2√2R_{L}

#### TUF = (V_{sm }^{2}/πR_{L})/(V_{sm}^{2}/2√2R_{L})

#### = 2√2/π

#### = 0.287

However, due to saturation effects produced by the flow of direct current through the transformer secondary, the value of TUF is further reduce to 0.2.

Obviously, dc power deliver to the load = ac transformer rating × TUF

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