The rectifier circuit used in most electronic power supplies is a capacitive filtered single phase bridge rectifier, usually followed by a linear voltage regulator. The schematic of this rectifier is shown below: (Fig. 1):

Most of our transformers are used in rectifier circuits (Fig. 1), so we decided to devote this article to rectifier transformers and give some practical advice to power supply designers.

*"The alternating current supplied to the rectifier is always equal to the direct current drawn from the rectifier, when the leakage currents in the diodes are negligible."*

This is true if we compare the average currents (Im) on the AC and DC side of the rectifier. But alternating current is always measured as rms current (Irms) and direct current is always measured as average current (Im). The original statement is not correct if we compare Irms on the AC side with Im on the DC side of a rectifier.

The RMS current Irms is always greater than the average current Im due to the peak AC waveform. If we divide Irms by Im, we get the peak current value, which is called the form factor. (F = Irms / Im). The sharper the peaks, the higher the F value.

The heating effect of electric current in wiring, resistors, and transformer windings is proportional to the square of the rms current. The heating effect of the alternating current in the rectifier circuit is accordingly proportional to I_{S}^{2} = (F x Im) ^{2} = (F x I_{L}) ^{2}, or the square of the DC current times the form factor F squared. The temperature rise in a given rectifier transformer is thus highly dependent on the form factor (F) value, and the required rectifier transformer size cannot be determined until the actual form factor value is known.

In a rectifier of the type shown in Figure 1, F is anywhere between 1.11 and 5.0, depending on the relative impedances before and after the diode bridge. Once these impedances are known, F (and U_{C}) using graphical methods. But at this point, the power supply designer usually has a transformer prototype in his hand, so U_{C} and I_{S} can be determined quickly by bench tests. (Be careful when measuring I_{S} with a true rms current meter. Most AC meters measure Im, but are calibrated in I_{RMS}, assuming F = 1.11, which is true only for a sinusoid).

The following describes an accurate and simple method for determining Form Factor (F) from an oscilloscope using graphs.

Suppose we observe the current and voltage waveforms in different parts of the circuit shown in Figure 1 on a cathode ray tube oscilloscope so that we can compare the waveforms before and after the diode bridge. Diagrams I-III show waveforms for different capacitance values (C), assuming a transformer with negligible series inductance, for example **toroidal transformer.**

С = 0 Without regulator

C - worker (U_{r}/ U_{c}<10%) With regulator

The desired effect of the capacitor is to smooth the DC voltage, but at the same time it causes the AC current to flow in short pulses, which means a higher F and a higher RMS current in the transformer. The "angle of conductance" (α) of the rectifier can be measured directly from the waveform - just remember that the full half cycle is 180 °.

It is clear that the form factor (F) should depend on the conduction angle (α). We have calculated the exact relationship between F and α for toroidal transformers and the result is shown here in this graph. By measuring the conduction angle (α) on an oscilloscope, a very accurate form factor (F) value can be plotted on the graph. Variations in the DC load will change the conduction angle, and corresponding changes in the form factor can be easily identified.

The diagramming table provides additional information that can assist in evaluating power supply design options. In the comments to the diagrams, we determined the coefficient η = U_{DC} / ú_{o}, which relates the DC voltage to the peak no-load voltage of the secondary winding of the transformer. The flattening of the ac voltage waveform peaks is caused by the voltage drop in the total impedance ahead of the diode bridge, so it is reasonable to assume that η should vary with the conduction angle (α). We also calculated this ratio for toroidal transformers and the result is shown on the graph sheet as a dashed curve.

The graph can be used to determine the rectifier DC load regulation. DC load regulation δ_{UDC} / U_{DC} = (1-η) x 100%. Remember that the voltage drop across the diodes is included in the value of U_{DC}... Each voltage drop across the diode can be considered constant and equal to 1 V at all loads. Accordingly, net load regulation is slightly worse than 1-η, especially for low DC voltages.

It is important to note that better voltage conversion efficiency (measured by η) can only be obtained through a higher form factor, and conversely, a lower form factor can only be obtained through weaker DC load regulation.

The size of the transformer feeding the rectifier is proportional to the product of the open circuit voltage (U_{0}) and current capacity (I_{S}), which we call Po. The dotted line on the graph sheet represents the smallest Po value required for any value of α (any corresponding value of F or η) for a given DC power. (Po / P_{DC} = F / η√2).

The transformer has a minimum dimension (Po) of about 1.52 x P_{DC} (total DC power, including diode losses) for α = 75º, where η = 0.8 and F = 1.7. Unfortunately, it is not possible to always stay at a minimum, partly because better DC regulation is often required than the 20%, and partly because load regulation of transformers is highly dependent on the size of the transformer. DC load regulation and transformer load regulation are not proportional, but they tend to increase and decrease together, so very small transformers tend to operate above optimal values, and very large transformers operate at less than optimal α values.

Rectifier transformer design to meet specific U requirements_{C}, U_{L}, DC regulation, temperature rise, etc., requires accurate data for both form factor (F) and rectification efficiency (η). But F and η, in turn, are determined by the data of a not yet designed transformer, so the power supply designer falls into a trap. One way out is to take an old transformer, change it, and pray for the prototype to work.

Another way out is to let Elsta engineers start designing the transformer. Our application engineers have solid experience in the design of transformers and power supplies, and they have tools at their disposal to calculate and optimize transformers, so they can design not only the transformer that will work, but also the most economical transformer that will work efficiently.

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