## Transformer Utilization Factor (TUF) of single-phase center-tap full-wave rectifier

Determination of transformer rating becomes, necessary while designing a power supply. For this transformer utilization factor (TUF), which is defined as the ration of power delivered to the load and ac rating of the transformer secondary, should be known.

So **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}**

Its value is found by considering the primary and secondary winding of the transformer saperately. Its value is **0.693** (as compared to **0.287** for a half-wave rectifier). In such a rectifier, there is no problem due to dc saturation of flux in the core because the dc current in the two halves of the secondary flow in opposite directions.

**Related topic**

**Single-phase full-wave rectifier****Average and RMS value of center-tap full wave rectifier****Efficiency of single-phase center-tap full wave rectifier****Frequency Component of single-phase center-tap full wave rectifier****Ripple Factor of single-phase center-tap full-wave rectifier****Regulation of single-phase full-wave center-tap rectifier****Peak Inverse Voltage of single-phase center-tap full-wave rectifier****Peak Current of single-phase center-tap full-wave rectifier****Advantage of center-tap Full-wave rectifier**

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In the third equation.. Idc is taken as Vlm /Rl.. Shouldn’t it be Vdc /Rl which in turn is Vlm / (pi*Rl)