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Transformers and Inductors for Electronics Applications

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Variable Definitions:

Amplitude - The peak current of a sinusoidal waveform, i.e. half of the peak-to-peak current.

Assume Layered Windings - "Layered windings" assumes that the windings fill the bobbin window and stack radially (as pictured). The windings take up the full breadth of the bobbin, and the heights of the windings are set such that they are proportional to the current integrated over the cycle and the number of turns of wire. The equation is: Hti = [Ni*Irmsi / ∑(N Irms)] window-ht . The turn lengths are calculated by determining the radial coordinate of each winding, and multiplying by 2π. By selecting this option, the user does not need to specify turn lengths or any winding cross section information. However, the core, winding window heights (only otherwise needed for 2-D mode), and center post diameter must be specified.

Average Length of a Turn - The average length of wire per turn for each winding (mm). This could be the total length of wire used divided by the number of turns. An estimate can be calculated based on the bobbin and winding geometry; for the case of a cylindrical winding, an approximation would be the radial coordinate from the center axis multiplied by 2π.

AWG Size Range - The range of American Wire Gauge (AWG) sizes to be considered in the optimization. If you wish to consider a custom range, select "other" in the drop-down menu, and enter a list in the text box that appears. For example: "40 41 43" or "40,41,43". The formula y = 0.0050*(92)^((36-x)/39) is used to convert AWG (x) to inches diameter (y).

Breadth of Bobbin Window - Required for all simulation modes. The breadth of the bobbin (in millimeters); the dimension parallel to the center leg as shown in Figure 1.

Breadth of Core Window - Required for all simulation modes. This dimension is taken in the direction parallel to the center leg, as shown in Figure 1.


Figure 1: Bobbin and Core Window Dimensions

Center of Winding - X Coordinate - The location of the center of each winding cross section in the winding window relative to the edge of the core as drawn below in Figure 2. The coordinate should be specified as the radial distance from the center post (edge of the core window) as drawn.

Center of Winding - Y Coordinate - The location of the center of each winding cross section in the winding window relative to the edge of the core as drawn below in Figure 2. The coordinate should be specified as the axial distance to the left edge of the core window as drawn.


Figure 2: Locating the coordinates, (X, Y), of the center of each winding. X1 refers to the X coordinate of the first winding, and X2 refers to the X coordinate of the second winding and so on. These dimensions are only needed when you specify the winding geometry of your magnetic component.

Center post diameter - The diameter in millimeters of the center post in the magnetic core. For a square centerpost, use diameter = perimeter/pi. The centerpost diameter and the radial location of the center are used to calculate the average turn length of each winding.

Current at time t - Current in the winding at the point in time between by the time segment durations. Current is specified at the beginning of the each time segment.

Duration of each time segment - Time span in microseconds for the piecewise linear time segment for piecewise linear current waveform specification.

Frequency - The operating frequency of the inductor in hertz. The same for all windings.

Gap Length - The length in millimeters of the air gap in the magnetic core. If "No legs gapped" is selected for the gapping configuration, this value will be ignored, and the gap length will be set to zero.

Gap Location - The location of any air gaps in magnetic core. Select gapping configuration from the images shown. If "No legs gapped" is selected, the gap length parameter, if specified, will be ignored (and the gap length will be set to zero).

Height of Bobbin Window - The available winding height, calculated as the distance from the inner radius of the bobbin to the inner edge of the core, as shown in Figure 1. This dimension is required for the two dimensional analysis or for all modes with the layered windings assumption.

Height of Core Window - It is taken in the direction perpendicular to the center leg, as shown in Figure 1. This dimension is required for the two dimensional analysis or for all modes with the layered windings assumption.

Horizontal divisions in each winding - Number of horizontal divisions of each winding for finite element calculation (20 divisions is the default).

Magnetic field integrals - Enter the result from your own finite element software or other calculation method. Simulate the inductor with 1 amp flowing in each winding and take the integral of the square of the magnetic field over the area of each of the windings and enter the values. Then repeat the field integrals with 1 amp simulated in all unique combinations of pairs of windings (e.g.: 1 and 2, 1 and 3, 2 and 3). The input form will provide the specific prompts automatically depending on the number of windings. For more information, see "Using Your Own FEM Software".

Number of images of the Winding Window Geometry to be computed in the x-direction - Number of images of the Winding Window Geometry to be computed in the x (vertical in figures above) direction for finite element simulation. Five images is the default, typically sufficient for 0.05% accuracy (J. Pollock, T. Abdallah, C. R. Sullivan, "Easy-To-Use CAD Tools for Litz-Wire Winding Optimization" Feb. 2003). For a detailed explanation of the method of images, see P.J. Lawrenson K.J. Binns and C.W. Trowbridge, The Analytical and Numerical Solution of Electric and Magnetic Fields, J. Wiley, 1992.

Number of images of the Winding Window Geometry to be computed in the y-direction - Number of images of the Winding Window Geometry to be computed in the y (horizontal in figures above) direction for finite element simulation. Five images is the default, typically sufficient for 0.05% accuracy (J. Pollock, T. Abdallah, C. R. Sullivan, "Easy-To-Use CAD Tools for Litz-Wire Winding Optimization" Feb. 2003). For a detailed explanation of the method of images, see P.J. Lawrenson K.J. Binns and C.W. Trowbridge, The Analytical and Numerical Solution of Electric and Magnetic Fields, J. Wiley, 1992.

Number of strands - The number of parallel strands of wire in each of the windings.

Number of Time Segments - The number of time segments to be used to specify the piecewise linear approximation of the current waveform, if in piecewise linear current specification mode. The current in each winding must be specified at the beginning of each time segment.

Number of Turns - The number of turns of wire in each winding.

Number of Windings - This is the total number of windings in the magnetic component being optimized. For example, a simple inductor has one winding. A simple transformer has two windings: a primary and a secondary. More complex components can have larger numbers of windings.

Maximum Achievable Packing Factor - Maximum achievable packing factor describes the ratio of the cross sectional area occupied by the wire cross section versus open space for the winding expressed relative to "perfect square packing". Thus the packing factor takes into account both the packing of individual litz wire bundles and the packing of whole bundles on each other into a winding cross section. Perfect square packing occupies π/4 of the area. So, for example, a winding with packing factor of 0.5 would have wire cross section occupying π/8 of the window cross sectional area. A typical number for litz wire is Fp = 0.35, resulting in 28% of winding area occupied by copper.

Phase Angle - Any shift in a windings sinusoidal excitation waveform relative to the sine wave entered for the reference winding, entered in degrees.

Simulation Mode - Litzopt can simulate one- or two- dimensional field geometry internally. For 3-D field simulation, an external finite element modeling software can be used to obtain the magnetic field integrals. These can be input directly in "External mode". See the individual descriptions on the "Start Optimization" page and "Easy-To-Use CAD Tools for Litz-Wire Winding Optimization" for more details.

Temperature - Required to determine the resistivity of copper for calculation. The temperature entered should be the operating temperature of the magnetic component in degrees centigrade. The electrical resistivity of copper is 1.7241 x 10 -8 Ωm at 20 C. We use the following linear approximation to adjust for the temperature:ρ(T) = ρ0[1+α(T-T0)] where the temperature coefficient α = 0.0039 K-1 and ρ0 is the input temperature.

Vertical divisions in each winding - Number of vertical divisions of each winding for finite element calculation (20 divisions is the default).

Volume of each winding - Volume of each winding in cubic millimeters. The magnetic field integrals (below) are divided by the volume of the corresponding winding to get an equivalent average squared magnetic field.

Winding Cross Section Height - The radial dimension of the winding cross section, as shown in Figure 3. This input is required unless "Assume layered windings" is checked.

Winding Cross Section Width - Axial (horizontal as drawn) dimension of the winding cross section, as shown in Figure 3. This input is required for the 2-D simulation unless "Assume layered windings" is checked.


Figure 3: The dimensions needed to determine the cross sectional area of each winding

Winding Wire Insulation Build - The insulation build on the wire used for the windings in magnetic component. The thickness of the insulation layer on the wire affects the outer diameter used in calculations and determines what designs will fit in the bobbin window. The formula used is dt = dr*alpha * (dc/dr)^beta where dt is the outer diameter including insulation, dr is the diameter (m) of AWG 40, and dc is the diameter (m) of of the wire used. The constants alpha and beta are 1.12 and 0.97 for single build and 1.24 and 0.94 for heavy build respectively. The formula y = 0.0050*(92)^((36-x)/39) is used to convert AWG (x) to inches diameter (y).

Wire gauge - AWG (American Wire Gauge) size for each winding. The formula y = 0.0050 * 92^((36-x)/39) is used to convert AWG x, to inches diameter, y.