One problem with high frequency magnetic design is how to sort out the losses that contribute to a part's efficiency. With the exception of dc resistance, these losses are very difficult to separate and measure. Including the core when calculating these losses raises the inductance, adds core loss, and results in high Q. The problem with high Q is the difficulty in measuring it with good accuracy. By contrast, low Q is easier to measure accurately. High Q also makes measuring Rac difficult — and this is what we need to know.
Q=XL/Rac (1)
XL=2πfL (2)
Where:
XL=Inductive reactance
Rac=High frequency ac resistance
L=Inductance
f=Frequency
The major effects of measuring the coil without the core are dc resistance, proximity effect, and skin effect. Skin effect is relatively easy to calculate, and generally much lower than proximity effect, at normal operating frequencies of 25 KHz to 500 KHz. Many sources help to estimate the proximity effect with different wire sizes, number of turns, layers, and stranding. Even so, with complex coils, proximity effect becomes more and more difficult to calculate with good accuracy. The question is “how do you confirm you have reached an acceptable level of ac resistance and evaluate changes?” By measuring the Q of the coil at the operating frequency and beyond you can determine this value. Then you can plug it into the design analysis to ensure these losses are in a reasonable balance with other losses.
PFC Inductor Design
The PFC inductor design should have a low HF resistance (Rac). If achieving this without other trade-offs were possible, the design would be ideal; however, magnetic design is the management of trade-offs: A savings in one area can easily make things worse elsewhere with an overall loss increase. The curves of Rac vs. frequency show we can improve the HF loss component, yet calculations show a larger penalty in the LF component is a poor trade-off. We can accept higher HF loss for a much lower LF loss — a simpler part to build and a lower material cost.
Assuming a PFC inductor: 600W, 600μH, 150 KHz at 90Vrms in and 380Vdc out. Fig. 1 is a plot of Rac vs. frequency.
Rdc=0.050Ω
Rac/Rdc=28
IacLF=8Arms
IacHF=0.25Arms
HF=150 KHz
Here, the winding losses are:
IacLF2×Rdc=8 A2×0.050ΩW=3.2W
IacHF2×Rdc×Rac/Rdc=0.25 A2×0.050Ω×28=0.09W
Total Copper Loss=3.2W+0.09W=3.29W (No. 15) vs. 4.0W (7-strand No. 24AWG) and 6.4W (19-strand No. 31AWG)
It's an easy choice: No. 15AWG.
These are copper losses only, and they must balance with core losses to finalize the design. The example shows that for the PFC application, where there's a large LF component, the penalty is small — even when Rac is 28 times Rdc. This is because the Inductance selected keeps the ripple current low. This analysis didn't include the harmonics, which would likely increase the HF losses a little. The 7-strand No. 24AWG resulted in higher HF losses, even though the dc resistance was comparable.
PFC Output Transformer Design
In the switchmode transformer design working off the PFC output, Rac is everything. Many design alternatives are evaluated to minimize losses and control cost at the same time. The two selected to build for test are the single-strand 18AWG windings and the 7-strand 30AWG windings. In this application, the secondary is nearly the same, 360V, so the secondary is the same wire size as the primary. To make things worse, this application requires a push-pull primary at 380V input. To minimize leakage inductance, the design is wound with bifilar construction with the secondary sandwiched between one-half the primary windings. The voltage stress on the push-pull primary was controlled by winding with triple-insulated wire type TEX-E. The interleaving and extra insulation also helps reduce the HF resistance.
Assuming a PFC output transformer: 600W, 75 KHz with 380V in and 360Vout, Input at 90Vrms
IacHF=3.2A Rdc=0.1Ω
At 75 KHz, Rac/Rdc=1.3
The winding losses are:
IacHF2×Radc×Rac/Rdc=3.2A2× 0.1×1.3=1.3W
Secondary: IacHF=3.3A, Rdc= 0.09Ω
IacHF2×Rdc=3.3A2×0.09Ω=1W (7-strand No. 30AWG)
Total Copper loss=2.3W (7-strand No. 30AWG) or 3.6W (No. 18AWG)
Use the 7-strand No. 30AWG construction.
Running at 75 KHz, this design has about 40% less loss than the 18AWG coil, even though the dc resistance is more than twice as high. The curves in Fig. 2 show this, and above the fourth harmonic the 18AWG coil has lower loss. This is something to consider — but, not likely to be of significant benefit. Again, core losses must be added into the equation to complete the design, but the HF coil losses are definitely under control.
The measurements in this example also show less copper can result in lower losses at high frequencies. This is a very difficult concept; yet it's very clear in this example. The higher dc resistance winding has less HF resistance and, thus, lower loss in the application.
Two important concepts were reinforced by these measurements and calculations. First, stranding can make things worse before things get better. Second, less copper (higher dc resistance) can result in lower HF losses.
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