Powder Cores can be well suited for the inductors designed in DC/DC Converters. Although the requirements for the inductors vary depending on the design of the DC/DC Converter, general inductor requirements include:
Whether the DC/DC Converter topology is a Buck Converter, a Boost Converter, or other type of converter, the general design requirements are:
Other parameters that can be specified include:
ILavg = 7.75Adc
L = 45µH
VON = 36V
VOFF = 12V
f = 85kHz
Given ILavg and L, one can calculate the energy storage of the inductor via the formula:
Energy Storage (µJ) = 0.5 * L(µH) * (ILavg(A))2 = 0.5 * 45µH * (7.75A)2 = 1351µJ
One can then refer to the energy storage curve for a desired part. Below is a plot of the Ampere‐Turns versus Energy Storage for Part Number MS‐106060‐2, which can be found on the data sheet for the part.
One can then see that for 1351µJ, Approximately 208 Ampere-Turns are required, and for a current of 7.75A, approximately 27 turns are required. One can also calculate the inductance at I=0A by multiplying the turns squared times the AL value of the core, found on the data sheet, as shown here:
L(0A) = 75nH/N2 * (27 turns)2 = 54,675nH = 54.7µH
If a Single Layer winding is selected, then a wire size of smaller diameter the 16‐AWG (1.25mm) is required to fit.
If 16‐AWG (1.25mm) wire is selected, in which case there may be a slight overlap of a turn, then the Rdc can be calculated by:
27 turns * (15.3 milliohms at 26 turns) / 26 turns = 15.9 milliohms
The Copper Loss can then be calculated as follows:
Copper Loss (W) = 0.0159 ohms * (7.75A)2 = 0.955W
To Calculate Core Loss, one first needs to know the flux density. Flux Density can be calculated by knowing the core, and either the ripple current, or the "ON" or "OFF" time of the switch. In either case, VON * tON must equal VOFF * tOFF, which must also equal L * Ipp. To calculate tON:
tON = (1/f)/(VON/VOFF+1) = (1/85,000Hz)/(36V/12V+1) = 2.941µs
tOFF = (1/f)/(VOFF/VON +1) = (1/f) – tON = (1/85,000Hz) – 2.941&mciro;s = 8.824&mciro;s
Similarly, the ripple current is:
Ipp(A) = VON(V) * tON(&mciro;s) / L(&mciro;H) = VOFF(V) * tOFF(&mciro;s) / L(&mciro;H) = 2.353App
Flux Density (Bpk) can then be calculated by:
Bpk(G) = VON(V) * tON(s) * 108 / (2 * Ae(cm2) * N) = L(H) * Ipp(A) * 108 / (2 * Ae(cm2) * N)
=36V * 2.941 * 10‐6 s / (2 * 0.654cm2 * 27 turns) = 300G
From the frequency and the Flux Density, the Core Loss can be interpolated from the following graph, also found on the data sheet:
At 300G and 85kHz, the core loss is approximately 53mW/cm3. Since the core volume is 4.15cm3, the total loss is:
53mW/cm3 * 4.15cm3 = 220mW = 0.220W
Therefore the total loss is the sum of the conductor loss and the core loss. In this example, the total loss is 1.215W.
If no forced air is cooling the inductor, the temperature rise can be estimated via:
Temperature Rise (C°) = (Total Power Dissipation (mW)/Surface Area (cm2))0.833 = (1215mW/28.8cm2)0.833 = 22.6C°.
DC‐DC Converter designs can be simulated with the DC Bias design module of our Inductor Design Software. The design inputs are supplied as shown:
Any other design constraints can be entered through use of the "Parameters" menu bar, and the screen shown here:
Results are can then be viewed, as in the following screenshot:
The part, , can be found on the Micrometals website.
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