DC/DC Converter

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:

- High Saturation Magnetization to maintain inductance under high biasing currents
- Low Core Loss to prevent excessive heating in response to ripple current
- Sufficient Energy Storage capability for the application requirement

Whether the DC/DC Converter topology is a Buck Converter, a Boost Converter, or other type of converter, the general design requirements are:

- Average or DC Inductor Current (I
_{Lavg}) - Required Inductance at Average Inductor Current (L)
- Voltage across the inductor during the switches "ON" and "OFF" times, or the ripple current. (V
_{ON}and V_{OFF}or I_{pp}) - Time of the "ON" and "OFF" voltages, or the frequency. (t
_{ON}and t_{OFF}or f)

Other parameters that can be specified include:

- Maximum inductance swing from I=0 to I=I
_{Lavg} - Maximum Temperature Rise
- Single or Multiple Layer Winding on Toroids
- Amount of Winding Fill for Multiple Layers on Toroids
- Temperature Rise Factor, for simulating Cooling or Lack thereof

**Requirements:**

I_{Lavg} = 7.75Adc

L = 45µH

V_{ON} = 36V

V_{OFF} = 12V

f = 85kHz

Given I_{Lavg} and L, one can calculate the energy storage of the inductor via the formula:

Energy Storage (µJ) = 0.5 * L(µH) * (I_{Lavg}(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/N^{2} * (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 R_{dc} 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, V_{ON} * t_{ON} must equal V_{OFF} * t_{OFF}, which must also equal L * I_{pp}. To calculate t_{ON}:

t_{ON} = (1/f)/(V_{ON}/V_{OFF}+1) = (1/85,000Hz)/(36V/12V+1) = 2.941µs

and

t_{OFF} = (1/f)/(V_{OFF}/V_{ON} +1) = (1/f) – t_{ON} = (1/85,000Hz) – 2.941&mciro;s = 8.824&mciro;s

Similarly, the ripple current is:

Ipp(A) = V_{ON}(V) * t_{ON}(&mciro;s) / L(&mciro;H) = V_{OFF}(V) * t_{OFF}(&mciro;s) / L(&mciro;H) = 2.353A_{pp}

Flux Density (Bpk) can then be calculated by:

Bpk(G) = V_{ON}(V) * t_{ON}(s) * 10^{8} / (2 * Ae(cm^{2}) * N) = L(H) * I_{pp}(A) * 10^{8} / (2 * Ae(cm^{2}) * N)

=36V * 2.941 * 10^{‐6} s / (2 * 0.654cm^{2} * 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/cm^{3}. Since the core volume is 4.15cm^{3}, the total loss is:

53mW/cm^{3} * 4.15cm^{3} = 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 (cm^{2}))^{0.833} = (1215mW/28.8cm^{2})^{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: