Using a power transformer at a frequency it wasn't designed for
Powertransformer designs minimize weight and cost based on three assumptions: (1) the power source is a sine wave, (2) the frequency is fixed, and (3) the voltage will not exceed a specified maximum. Given this starting point, an efficient, costeffective design will set the peak value for magnetic flux density near the limit for the core material at maximum voltage, and the windings will use the least copper consistent with the power and efficiency requirements. Some margin is built in, but a power transformer is narrowly optimized for its application. This doesn't mean the transformer is picky about how it is applied, but it does mean that proper attention is required if the assumptions are changed.
When a load is present, total primary current is the vector sum of the excitation and load currents. Primary and secondary load currents circulate in opposite senses, causing their respective magnetic fields to cancel. Hence, only the excitation portion of the total current is responsible for the alternating magnetic field at the heart of transformer operation. Although the currents share the winding, they act as if they are separate. As for any other inductor, excitation current is proportional to driving voltage and inversely proportional to frequency, according to Ohm's Law for inductive reactance. The magnitude is expressed as follows:
If excitation current exceeds a critical value, the consequence is magnetic saturation of the core. This causes the instantaneous value of L to drop to the air core value of the winding, resulting in excessive current that can overheat and destroy the transformer. Therefore, if frequency is reduced, the driving voltage must be proportionately reduced to keep excitation current within the core limit.
For a power transformer designed for 115V_{RMS} at 400 Hz but used at 60 Hz, the input voltage must not exceed 115×60/400 = 17.25 V_{RMS}, but the transformer will work within this restriction. A transformer designed specifically for 240V at 60 Hz must not be driven with more than 240×50/60 = 200V at 50 Hz. Obviously, 50/60Hzrated transformers are designed for operation at 50 Hz and draw less excitation current at 60 Hz.
It is tempting to conclude that frequency and voltage can be scaled upward. From a magnetic flux viewpoint this is valid, but power dissipation is a second constraint. Notwithstanding that a welldesigned transformer can be 98%+ efficient, there are many loss terms. These include hysteresis loss, dielectric loss, magnetostriction, and copper loss from winding resistance, including skin and proximity effects.
The purpose of laminated construction is to divide the metal mass into thin, electrically insulated layers parallel to the magnetic field. This disrupts eddycurrent circulation, greatly reducing this contribution to power loss. Laminations used at 60 Hz are typically around 0.014in. thick. Higherfrequency designs benefit from thinner laminations but also need less core mass to handle the same amount of power. It is the weight savings possible with 400Hz power that drives use on aircraft.
Eddycurrent loss is described by a classic formula for power dissipation per unit volume of a laminated core (Reference 1). In simplified form, the contribution is expressed as
or more compactly,
where
P_{e} = eddy current power dissipation per unit volume
K_{p} = constant dependent on system of units
K_{e} = combination constant
f = frequency
B_{max} = magnetic flux density limit for chosen lamination alloy
a = thickness of lamination
σ = conductivity of lamination alloy
To apply the formula here, the internal parameter B_{max} must be related to driving voltage and frequency, since those are what the user controls. A suitable expression can be derived from
where
B_{max} = peak flux density
K_{b} = conversion constant dependent on units and construction
K_{B} = combined constant
Φ_{max} = peak induction field
L = primary inductance
I_{max} = peak excitation current
V_{RMS} = RMS voltage across winding
This result is independent of winding inductance. When inserted into the loss equation, the final result is, on a perunit volume basis, expressed as
This loss term is independent of frequency because B decreases by 1/f. The square law effect of V_{RMS} is general to other loss terms.
A naive calculation based solely on B_{MAX} shows that a 50Hz transformer driven at 400 Hz could handle up to eight times the rated voltage. However, the P_{e} equation shows a corresponding 64fold increase in eddycurrent loss. Perhaps the transformer could be driven this hard on a shortpulse, lowdutycycle basis, but that doesn't imply that the insulation could withstand the increased voltage. It just means that the transformer is being used at other than the design optimum. The bottom line is that for continuous operation, the rated voltage for a power transformer should be respected for frequencies at or above the design frequency. A 120Vac, 60Hz transformer pressed into service at 400 Hz is still a 120Vac transformer.
Finally, there is the question of wire gauge. For the same power level, lowerfrequency transformer windings tend to have more turns of finer wire, while higherfrequency designs generally use fewer turns of thicker wire. From the standpoint of transformer design, winding resistance scales as the inverse square of frequency. Simply put, a 50 or 60Hz transformer applied at 400 Hz will have disproportionately higher resistance than a purposebuilt 400Hz winding, resulting in degraded voltage regulation under varying loads. It is up to the circuit designer to factor this into the final result.
Note that these results are for power frequencies (Reference 2). The loss equations change if frequency is shifted high enough for parasitic components to affect performance. For example, highvoltage windings with many turns might have selfresonance low enough to affect operation. In general, it is not useful to push operating frequency beyond an order of magnitude in either direction. Performance should always be tested before commitment to an application.
These observations help us appreciate highperformance audio power transformers, which must handle a bandwidth of 20 Hz to 20 kHz with low losses and low distortion. Special winding techniques and highperformance magnetic materials are required to meet these specifications. Such transformers are of a different kind than linefrequency power transformers optimized for singlefrequency, fixedvoltage operation.
References 

Author information
Orin Laney is an independent consultant in signal integrity, EMC, RF instrumentation, and magnetics. He resides in Mountain View, CA.
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