In the last chat, Magnetics Design Chat: Part 1, Optimal Design of Magnetics Components, our goal was to maximize transfer-power density in a magnetic component so that for a given maximum power, the component is as small as possible. The basic formula for transfer of power through a magnetic core was expressed by the simple relationship:

The two basic limitations on cores are:

This basic conclusion is so important, it bears repeating in another way:

**Optimal Turns**

The magnetic (core) and electric (winding) designs are connected through the choice of number of turns, *N* of winding, a central magnetic design parameter. Maximum core transfer-power density, or core *utilization*, determines turns limits. The turns minimum is *N _{λ}*:

Δ*φ*(*p̄ _{c}*) = Δ

The current referred to or “seen” by the core field is *Nī* = *N⋅ī *, where *ī* is the average current; *Nī* = *H̄⋅l*. It sets the magnetic op-pt and the extent of saturation through *k _{sat}*.

- Maximum turns that fit winding window,
*N*, is another turns limitation → allowable current density_{w}

The range of *N* is bounded by power-loss and saturation limits, and maximum window turns:

With adequate window area for turns, the design range of *N* is bracketed by core power-loss (*N _{λ}*) and saturation (

where circuit flux, Δ*λ* = *V _{p}⋅t_{on}*,

Solve for the primary-winding on-time power amplitude for the circuit,

where *V _{p}* and

and core volume,

Then

Then relating to on-time circuit power,

Average power transferred = on-time power, *P _{p}*, times the fraction of its duration,

We have maximized *P̄ _{p}* by equating the turns limits:

In the next chat, we will look at the circuit-design consequences of these new-found criteria for magnetics design.

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