Subject : Power Electronics
Unit : DC to DC Converters
Design of Inductor-Transformer
Design of Inductor – Transformer:
Fig: A typical SMPS transformer with a double ‘E’ type ferrite core and interleaved primary and secondary winding
- The fly-back type SMPS circuits use a different kind of transformer can be called as an inductor-transformer. The transformer is more like two coupled inductors.
- These two coupled-inductors don’t conduct simultaneously, unlike the two coupled-windings of a normal transformer. Also, the inductance needs to have a finite magnitude so that current can build through it during each high frequency cycle and the inductor may store the desired magnitude of energy.
- The windings of an inductor-transformer facilitate energy storage in the magnetic field whereas the windings of an ideal transformer (having infinitely large permeability ‘μ’ of the core) cannot be used for storing energy as energy density equals .
- For finite magnitude of flux density ‘B’, the magnitude of ‘μ’ should be small to have higher energy per unit volume. ‘μ’ and magnetic reluctance have inverse relation, as ‘μ’ decreases the reluctance increases. For a practical inductor the reluctance of its flux-path should not be zero.
- For an inductor, working in the linear region of the core’s magnetization, the following relation holds good between inductance (L), reluctance (R) and the number of turns (N) of the inductor: L = N^{2}/2
- However a practical inductor still requires a good core with high permeability to increase
(i) coupling between the windings,
(ii) to guide the flux path and hence decrease the stray magnetic field lines and
(iii) to keep the inductor size small.
- However to keep the reluctance of the flux-path at the desired value, an appropriate length of air-gap is introduced in the flux path.
- The figure above shows a double ‘E’ core with windings put around the central limb. After the windings are placed in position, a non-magnetic material (like, paper) is inserted between the faces of the core and the two ‘E’s of the core are clamped together. The non-magnetic material acts like air-gap in the core.
- A preferred way of creating air-gap may be to grind some length from only the central limb of the core. If ‘l_{g}’ is the length of air-gap in the core, the inductance (L) can be expressed as:
where A_{c }is the area of the core’s limb on which the windings have been placed and μ_{0 }is the permeability of air-gap.
- In the above expression for inductance, the fringing effect of the flux and the reluctance of the flux path through magnetic core have been neglected.
- The core material should not saturate with the peak expected current (I_{p}) in the inductor. The peak flux density in the core (B_{m}) can be related with the peak magnitude of current as
- Knowing the current shape through the inductor, one calculates its rms magnitude (I_{p,rms}) and determines the window area required as
- Combining, one gets
- The equation gives the area product from which rest of the design can be proceeded as in the case of transformer design shown above. LHS of the equation is indicative of the energy holding capacity of the inductor (somewhat like VA rating of the transformer). Should there be a couple winding (an inductor-transformer) the area product expression needs to be modified to include the window space requirement of the secondary winding as well.