Design Notes and Efficiencies
Information on this page is intended to assist engineers to take full advantage of toroidal efficiencies when specifying a custom toroidal power transformer.
Most applications for power toroidal transformers are in power supplies, which generally incorporate rectifier circuits. Listed and illustrated here are typical circuits, and simple formulae for relating the AC and DC data. This information is for reference only; consult design handbooks or PLITRON directly for further assistance.
DUAL COMPLEMENTARY RECTIFIER – Very efficient. Best choice for two balanced outputs with a common return. The output windings are Bifilar wound for precisely matched series resistance, coupling and capacitance.Dual Complimentary Rectifier fig. 6
FULL WAVE BRIDGE – Most efficient use of toroid technology and secondaries. Best for high voltage outputs.
Full wave bride and Dual Complementary share the same conversion factors –
VAC = 0.8 x (VDC + 2)
IAC = 1.8 x IDC
FULL WAVE CENTER TAP – While more efficient than the half wave rectifier circuit, the full wave does not make full use of secondaries, but is good for high current, low voltage applications as there is only one diode drop per positive half cycle.
Both Dual Complementary and Full Wave Center tap configurations have the same AC to DC conversion ratios.
VAC = 1.7 x (VDC + 1)
IAC = 1.2 x IDC
HALF WAVE RECTIFIER – Half wave rectifier circuits should be avoided, as they are inefficient use of toroidal technology. They cause the core to become polarized and to saturate in one direction.
Standard values for regulation are given for Standard power transformers in the Selection chart, and the Ratings Table. Regulation may be expressed as a percentage with the following equation:
% Regulation = (VNL – VFL) / VFL X 100
VNL = No load volts. VFL = full load volts
Load regulation can be adjusted to conform to most requirements. Regulation factor is inversely proportional to efficiency and physical size, and proportional to temperature rise. All of these factors must be taken into consideration when the final regulation specification is determined.
In some applications, it may be more economical to specify a wider regulation transformer, and consider the use of higher voltage rating filter capacitors, and other components.
The regulation factors shown as standard in this catalog are optimum values, and provide a convenient, proven, equilibrium of efficiency, size and temperature rise, with manufacturability and repeatability. Deviations from standard regulation figures printed in this catalog will have the effects listed in Figure 3 in varying proportions.
As long as the cross sectional area of the toroidal core is held constant, the height and diameter may be varied to meet the customer’s requirement.
The functional optimum diameter to height ratio is 2:1. For low profile equipment requirements, a 3:1 ratio may be used. In cases where a minimum footprint is required, a 1.5:1 ratio could be considered. Aspect ratios of between 1:1.5 to 1:4 can be achieved without performance degradation.
Following are some examples –
1) The customer wanted to replace a laminated transformer in the same physical space. A 1: 1 diameter to height ratio toroid was designed, at twice the output power, and with vastly improved noise specifications.
2) A custom 500 VA toroid engineered to fit into a single rack height package. The transformer is less than 38mm high, but still exhibits good electrical and magnetic efficiency. The only physical restrictions are the limitations of winding machinery. A minimum center hole must be maintained in order to permit the insertion of the winding shuttle, for application of wire and insulation.
Significant reductions in transformer size and weight may be realized in most cases where the transformer is loaded intermittently. In these cases, the load is on (A) for a small portion of the total period (B); see Figure 1.
The period is much shorter than the overall thermal time constant of the transformer. To calculate the nominal power rating (VA) of the transformer use the following equation:
PNOM = PLOAD (A / B)
High Toroidal Efficiency
Efficiency is a measure of the transformer’s ability to deliver the input power to the load. Efficiency is expressed by:
%n = (POUT / PIN) x 100
Where POUT is output power, PIN is input power, n is efficiency. Toroids are far more efficient than conventional laminated types. Figure 5 shows typical curves for efficiency as a function of output power in relation to output power for various nominal rated transformers.
Toroidal transformers can offer extremely high efficiency, and figures of 96% and better are achievable.
Thermal Distribution Considerations
The textbook approach to transformer design indicates that power losses should be evenly distributed between core losses and copper losses. However, with the advent of low loss grain oriented silicon steels, and their extremely high utilization in modern toroidal construction, this is seldom the case. Core losses in toroids are typically 10 – 20% of total power losses. The balance of losses are related to copper. The theory is to balance copper losses equitably throughout the transformer. The ideal design would allocate copper losses evenly between primary and secondary windings.
Temperature rise calculations are based on a number of variables, which are shown in the diagram at right.
Material considerations should include thermal resistance specifications. A properly designed thermal circuit should allow for a thermally conductive construction, with windings placed such that heat can reach the outer surface, for further dissipation.
Copper has a positive temperature coefficient, so its resistance increases with temperature. As the temperature of the coil rises, the DC resistance of the windings will also increase, and a self heating cycle is introduced.
It is incumbent of the transformer designer to precalculate the temperature rise per winding into the final calculations, and adjust the output to compensate for this effect.
For applications requiring either a simple step-up or step-down of voltage, and where there is no need for electrical isolation between windings, an autoformer can be used. Significant size and weight reductions can result over isolated transformers. The power rating of an autoformer is given by the expression:
VA rated = POUT x (V HI – V LOW) / V HI
SHORTED TURN CONDITION
The high remanence of grain oriented silicon steel, lack of air gaps, and the excellent magnetic properties of toroidal transformers can cause a high magnetizing current on turn on, limited only by the low impedance of the primary winding. However, the duration of the inrush current is rarely longer than a half a cycle. The effect of this inrush becomes greater with an increase in toroidal power. 8 VA to 300 VA transformers should not require any protection. For transformers 300 VA and up a slow-blow fuse, delayed action circuit breaker, or some form of soft start circuitry should be considered. See Specifying a Custom Power Toroidal Transformer