# Transformer Utilization Factor (TUF)

Transformer Utilization Factor (TUF) is defined as the ratio of DC power output of a rectifier to the effective Transformer VA rating used in the same rectifier. Effective VA Rating of transformer is the average of primary and secondary VA rating of transformer.

The formula for TUF can be written as below.

Transformer utilization factor is a quantitative indication of the utilization of VA Rating of Transformer. The more the value of TUF, the more will be the utilization. In other words, the VA rating of required transformer will be less if TUF is more and vice versa.

Many times, transformer utilization factor is confused with efficiency of rectification. Basically, these are two different parameters. Mind that, rectification efficiency is the ratio of DC power output to the AC power input of the rectifier. But in TUF, instead of AC power input, VA rating of transformer secondary is used for calculation. VA rating of transformer is fixed and can be found on the name plate. It is independent of rectifier performance. But the performance of rectifier can of course be judged from the utilization of VA rating of transformer. This is the reason; TUF is a performance evaluation parameter of a rectifier.

Let us now calculate the value of transformer utilization factor for half wave; center tapped full wave and bridge rectifier one by one.

**Transformer Utilization Factor (TUF) of Half Wave Rectifier**

Half Wave Rectifier is the simplest rectifier circuit configuration employing only one diode to convert the AC input into DC. In this rectifier circuit, the output current flows only during the positive half cycle of the supply voltage. It does not flow during the negative half cycle as the diode is reversed biased during this halt time period.

To calculate the DC power output, we need to know DC output current and voltage of the half wave rectifier. Well, the average or DC output current is for half wave rectifier is equal to (I_{m}/π) where I_{m} is peak value of output current. Similarly, the average or dc voltage output is equal to (V_{m}/π).

DC Power Output, P_{dc} = Average Current x Average Voltage

= (I_{m}/π) (V_{m}/π)

= (I_{m} V_{m})/π^{2}

Now, we need to find the effective VA rating of Transformer. Since the voltage of source is sinusoidal, therefore its rms value will be equal to (V_{m}/√2). But the source current is not sinusoidal for half wave rectifier rather it is governed by the waveform of the load current. Why so? This is just because of transformer action. This means, the rms value of the source current will be equal to the rms value of the load current. As the rms value of load current for half wave rectifier is equal to (I_{m}/2), therefore the rms value of source current will also be equal to (I_{m}/2). One thing, I am repeatedly mentioning source, here source means transformer secondary.

Thus, the VA rating of Transformer = (V_{m}/√2)(I_{m}/2)

= (V_{m} I_{m}) /(2x√2)

Hence, transformer utilization factor of half wave rectifier can be calculated using the definition.

TUF = DC Power Output / VA Rating of Transformer

= [(I_{m} V_{m})/π^{2}] / [(V_{m} I_{m}) /(2x√2)]

= [(2x√2)/π^{2}]

= 0.2865

The transformer utilization factor of half wave rectifier is 0.2865. It means that the VA rating of transformer required for half wave rectifier is approximately 3.5 times (1/0.2865 = 3.5) of the DC power output. For example, the VA rating of required transformer for 100 watt load will be around 350 VA (0.35×100 = 350). This is quite poor utilization of transformer.

**Transformer Utilization Factor (TUF) of Center Tapped Full Wave Rectifier**

The method for finding transformer utilization factor of center tapped rectifier is a bit different than other type of rectifier. Here we need to individually find the VA rating of transformer primary and secondary and then take average of their values. This is done as current flows though one half of the winding for positive half cycle and through another half of the winding for negative half cycle.

The average or dc value of load current and voltage for center tapped full wave rectifier are (2I_{m}/π) and (2V_{m}/π) respectively. Therefore, the dc power output can be calculated as below.

DC Power Output, Pdc = (2I_{m}/π)(2V_{m}/π)

= (4I_{m}V_{m} )/π^{2}

Let us now find the VA rating of transformer. Since the voltage of each of the transformer secondary is sinusoidal, therefore its rms value will be equal to (V_{m}/√2). But the current in each of the transformer secondary only flows for half cycle, therefore its rms value will be (I_{m}/2).

VA rating of each of the Transformer Secondary

= (V_{m} I_{m} )/(2x√2)

Hence, total VA Rating of Transformer Secondary

= 2(V_{m} I_{m} )/(2x√2)

= (V_{m} I_{m} )/(√2)

= 0.707V_{m} I_{m}

Primary winding current of transformer is pure sinusoidal as current flows for both positive and negative half cycle irrespective of the fact that which diode conducts. Thus the rms value of transformer primary current is (I_{m}/√2).

VA Rating of Transformer Primary

= (V_{m} I_{m} )/2

= 0.5V_{m} I_{m}

Effective VA Ratio of Transformer

= (Primary VA + Secondary VA)/2

= (0.5V_{m} I_{m}+ 0.707V_{m} I_{m})/2

= 0.6035V_{m}I_{m}

TUF of Center Tapped Rectifier

= [(4I_{m}V_{m} )/π^{2}] / [0.6035V_{m}I_{m}]

= [(4×0.6035)/π^{2}]

= [(4×0.6035)/π^{2}]

= 0.672

Thus, the transformer utilization factor of center tapped rectifier is 0.672. This means, transformer VA rating required will be approximately 1.49 times (1/0.672 = 1.49) of the DC output. Hence the transformer VA required for 100 watt load for center tapped rectifier will be around 149 VA. This is quite good as compared to half wave rectifier. Isn’t it?

**Transformer Utilization Factor (TUF) of Bridge Rectifier**

The average value of load current and voltage for bridge rectifier is same as that for center tapped type. Therefore, the dc power output will also be same.

DC Power Output, Pdc = (2I_{m}/π)(2V_{m}/π)

= (4I_{m}V_{m} )/π^{2}

Let us now find the VA rating of transformer. Here we need not to find the VA rating of transformer primary and secondary separately. I hope you know why? This is because current is flowing in the entire secondary winding during positive and negative half cycle.

Since the voltage and current at transformer secondary terminal is sinusoidal, therefore their rms values will be (V_{m}/√2) and (I_{m}/√2) respectively.

VA Rating of Transformer

= rms Voltage x rms Current

= (V_{m}/√2) x (I_{m}/√2)

= V_{m}I_{m}/2

TUF of Bridge Rectifier

= [(4I_{m}V_{m} )/π^{2}] / [V_{m}I_{m}/2]

= 8/π^{2}

= 0.8106

Thus, the transformer utilization factor of bridge rectifier is 0.8106. This means, transformer VA rating required will be approximately 1.23 times (1/0.8106 = 1.23) of the DC output. Hence the transformer VA required for 100 watt load for center tapped rectifier will be around 123 VA. This is quite impressive figure as compared to half wave and center tapped rectifier.

Let us now compare the Transformer Utilization Factor (TUF) of the three types of rectifiers.

Sr. No. |
Rectifier Type |
TUF |
Required VA Rating of Transformer for 100 watt Load |

1) | Half Wave Rectifier | 0.2865 | 350 VA |

2) | Center Tapped Rectifier | 0.672 | 149 VA |

3) | Bridge Rectifier | 0.8106 | 123 VA |

Please write in comment box, which type of rectifier better utilizes the VA rating of transformer.

Bridge rectifier is the best in terms of transformer utilization factor.