Doubt regarding core loss calculation for forward converter

Hello Aneesh,

The core-loss equations and core-loss curves of the ferrite material datasheets use peak flux density, which is the zero-to-peak value, not the peak-to-peak value.  This is a consequence of traditionally using sinusoidal excitation for core loss measurements.  The ac flux passes from positive peak through zero to negative peak, and back again. For SMPS design, a forward-mode flux traversal usually goes from near zero (maybe some remnant flux) to the peak and back to near zero.  But this flux path can be considered as a peak-to-peak swing centered around a DC offset at 1/2 of the zero-to-peak flux density. 

Since the losses are based on the ac traversal around the B-H loop, and this loop is centered around the 1/2-point of the peak flux, only 1/2 of the peak flux density is used for the loss equations and curves.  This application note Magnetic Core Characteristics (2) slup124.pdf has some discussion on this topic, on page 2-5, that explains it better than I can.    

Regards,

Ulrich

Hi Aneesh, 

Yes, that is correct.  Use 0.1T for your loss calculation if your delta-B, based on turns, voltage, on-time, and core area, is 0.2T.  

Regards,

Ulrich

Hi Aneesh,

That is also correct.  The same flux density treatment applies to inductor core loss as in transformer core loss.  However, be aware that the delta-B is the result of a delta-H corresponding to a delta-I through the inductor.  It may be misleading to think of finding the flux density (B) which corresponds to 0.75A.  To be more precise, you are finding the delta-B which corresponds to the delta-I of 1.5A around a dc operating point of 5.0A, and using 1/2 of that delta-B for your core loss calculations.

I make all these precise distinction because, for a buck-PWM output inductor, the permeability may reduce as dc bias current increases, so the delta-B for delta-1.5A may be different at a 5-A bias than it is at a 2-A bias level, for example.  This is especially true when using powdered-iron type cores.  If you have a gapped-ferrite core for the output inductor, the inductor properties generally stay linear until the core saturates, where the properties will change rather suddenly.  With powdered-iron cores, the core will partially saturate with higher dc bias current and the delta-I will result in a wider delta-B than at low loads.  I suggest to review the design information provided by Magnetics, Inc. and Micrometals concerning their powder-core products for core loss and other considerations. 

But, assuming you have a gapped-ferrite inductor, its core loss treatment is very similar to that of a ferrite transformer.  More on this can be found in an application paper Indtr & Flyback Xfmr Design (5) slup127.pdf with an example on page 5-9.  This paper and the others I have mentioned previously are all found in TI's Magnetics Design Handbook which can be obtained here: https://www.ti.com/seclit/ml/slup132/slup132.pdf .  I find this handbook to be an invaluable source of guidance on basic and advanced magnetics design issues.

Regards,
Ulrich 

Hi Aneesh,

The issue of temperature rise for a magnetic component does not have a precise answer. There is a general formula that usually makes a good estimation of delta-T that has been quoted in several magnetics vendors' literature. It has yielded reasonable results, in my experience, and I believe that's why everyone keeps using it. The following section has been copied from the Magnetics, Inc. website from one of their help files:

"The observed temperature rise depends heavily on environmental factors such as ambient temperature, airflow, geometry, and the thermal conductivity of all the materials involved. A useful first cut equation relates the surface area of the magnetic with the total losses to yield an approximate temperature rise (from room temperature, in still air):

Rise (°C) = [Total Loss (mW) / Surf. Area (cm^2)] ^0.833

For example, assume a transformer with copper and core adding up to about 0.6 W, and having a surface area (top, sides and bottom of the wound device) around 15 cm^2. Then the approximate ΔT is [600/15]^0.833 = 22°C.
Other factors that should not be overlooked are skin and proximity effects in the copper conductors, and fringing effects. The fringing problem occurs with gapped cores, where flux at the gap can intersect with copper near the gap and generate eddy currents. It is possible for the losses due to those eddy currents to exceed the total core losses in the inductor."
(Excerpted from: https://www.mag-inc.com/design/design-guides/designing-with-magnetic-cores-at-high-temperatures )

It is important to use the correct units of mW and cm^2, and to make sure to include ALL of the losses, core + copper loss, in the total loss factor. Keep in mind that it is an estimation, although usually a good one, applicable to room temperature and still air. Moving air, higher ambient, nearby heat, and/or enclosed spaces will affect this estimate, but it is usually apparent how these different conditions can either decrease or increase the original estimate. Once your paper design is finished to your satisfaction, the prototype transformer or inductor should be constructed with a thermocouple embedded at the hot spot (usually under the inner most winding, or between bobbin and core) and operated at maximum conditions to verify your expectations.

Regards,
Ulrich

Hello Aneesh,

Both equations are correct, but the difference lies in the units that are applied to the variables.

The equation from the Magnetics, Inc. handbook is based on the CGS system of units (centimeter, gram, second), which is an older system used in the early days of magnetics design. In the past few decades many documents and companies have moved to the SI system (metric) of units, on which the second equation is based. TI’s application note “Introduction and Basic Magnetics” slup123.pdf discusses this topic.  This app-note is the first paper in the TI Magnetics Design Handbook that I mentioned  in an earlier reply.

Because of the differences in units, once you start a design in a particular system, you need to continue to use the same system throughout the design to avoid conflicting results. For example, a couple of the major differences between the two equations are core area in cm^2 or m^2, and flux density in Gauss or Teslas.  On the other hand, Volts, turns (N) and seconds are the same in both systems.

 Although it is good practice to choose one system and stick with it, a lot of very useful design guides and informational papers were and are written in either system, so be prepared to have to understand the concepts presented and translate between the two unit systems as necessary to get the most out of the information presented.   The concepts are the same even though many units and equations are different.

Incidentally, the Magnetics, Inc. equation, which includes a factor of "4", applies only to a square wave and the "B" is 1/2 of the total delta-B as shown in their Figure 1.  This "4" accounts for a factor of 2 to cover 1/2 of the switching period (because of the square wave) and another factor of 2 to cover the full delta-B.  My preference, and that of many other application papers, is to use: delta-B = (V*T*10^-8)/(Ae*N) where V is the dc voltage applied to the inductance, T is the time applied in seconds, Ae (same as Ac) is the effective core area (in cm^2 for this CGS equation) and N is the number of turns of the winding.  Then use 1/2 of this delta-B to determine core loss.   This Volt-second method is not strictly limited to square wave-shapes.  The product L*I can often substitute for V*T (based on V/L = dI/dt) when the inductance and peak-to-peak current are already known and V is a dc quantity.   

Regards,
Ulrich