Minimum turns before core saturation

How many primary turns does this core need before it saturates?

N = \frac{V}{4.44 \cdot f \cdot A \cdot B}

Method

1. Convert the core area from square centimetres to square metres (divide by 10,000) and the flux density from gauss to tesla (divide by 10,000). Datasheets of this era quote both in the older units, which is why the conversions are here rather than assumed.
2. Convert the frequency to hertz.
3. The constant 4.44 is 4 × 1.11, where 1.11 is the form factor relating the RMS of a sine to its average. It is specific to sinusoidal drive — a square wave uses 4.0 instead, which permits about ten per cent fewer turns.
4. Multiply 4.44 by the frequency, the core area and the saturation flux density, then divide the applied voltage by that product.
5. The result is the fewest turns that keeps the core below saturation. Wind more than this for margin; never fewer.

Assumptions

• Sinusoidal drive. The 4.44 constant assumes a sine wave; a square wave uses 4.0. A VIC driven with gated pulses is neither, and the peak flux depends on the pulse’s volt-seconds rather than on any form factor.
• The flux density quoted is the saturation figure at the working temperature. Ferrite saturates at a markedly lower flux when hot than the room-temperature datasheet number, and a transformer that works cold and fails warm is usually this.
• No DC component. Any net DC through the winding offsets the flux and eats the headroom asymmetrically, so half the cycle saturates first.
• The core is ungapped. A gap raises the current the core can take before saturating and lowers the inductance; both change this answer.
• This gives the minimum, not the right answer. The turns that actually get wound also have to satisfy the ratio required, the window area available, and the wire gauge the current needs.