4. Loss expressions
4.1 Loss angle tangent : tanδ
Loss angle tangent, tanδ, is defind as the formula below
Where δ : Loss angle = phase angle between B and H
The magnetic losses can be splitted into three component as below Fig.4
1. Hysteresis losses
2. Eddy Current losses
3. Residual losses
This gives the formula
tanδ = tanδh + tanδf + tanδr
Where tanδh = histeresis loss angle tangent
Where tanδf = eddy current loss angle tangent
Where tanδr = residual loss angle tangent
4-2 Relative loss factor, tanδ/μi
This factor is defined as the loss angle tangent divided by permeability,
Relative loss factor = tanδ/μi
The loss angle tangent, tanδ , is reduced by an air gap in proportion to the ratio of permeabilities before and after airgap
presence,
Where μi and tanδ : permeability and loss angle tangent without an air-gap
μe and tanδe : permeability and loss angle tangent with an air-gap
Therefore, the relative loss factor, tanδ/μi does not depend on air gap size, when the air-gap is small.
4.3 Quality factor, Q
The quality factor Q, is defined as the reciprocal of loss angle tangent.
where, ω = 2πf = angular velocity
R = loss resistance of coil with magnetic core
4.4 Hysteresis material constant, ηB
This constant is defined as the formula below,
Where, tanδh = hysteresis loss angle tangent = tanδB2 - tanδB1
Where tanδB1 = loss tangent when the magnetic induction is B1
tanδB2 = loss tangent when the magnetic induction is B2
ΔB = B2 - B1
According to IEC 60401 for μe value greater than 500, B1 = 1.5mT and B2 = 3mT, frequency of 10KHz and
temperature of 25℃
4.5 Power Loss
For high excitation application, such as power transformer design in Switching Mode Power Suoolies (SMPS), the energy
dissipation(losses) is expressed in terms of power loss. Power losses are function not only of ferrite material but also
Power loss can be dicided into three components.