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Faraday's Law says a changing magnetic flux through a coil induces a voltage proportional to the number of turns and the rate of change of flux. For a sinusoidal supply, this reduces to the classic transformer EMF equation: V = 4.44·f·Bmax·Ac·N. The constant 4.44 comes from 2π/√2 (relating peak flux to the RMS voltage of a sine wave). This single equation is the foundation of every transformer, inductor and coil design.
| Quantity | Formula |
|---|---|
| Required turns | N = V / (4.44 × f × Bmax × Ac) |
| Voltage from turns | V = 4.44 × f × Bmax × Ac × N |
| Turns per volt | N/V = 1 / (4.44 × f × Bmax × Ac) |
| Turns ratio | Ns/Np = Vs/Vp |
Note the units: Bmax is in tesla (T) and Ac is converted from cm² to m² (÷10000) inside the formula. Higher frequency, higher flux density, or larger core area all mean fewer turns are needed for the same voltage — which is exactly why high-frequency SMPS transformers are so much smaller than 50/60 Hz mains transformers for the same power.
It is V = 4.44×f×Bmax×Ac×N, derived from Faraday's Law for a sinusoidal supply. It relates the RMS winding voltage to the frequency, peak core flux density, core area and number of turns.
It equals 2π/√2 ≈ 4.44, arising from converting the peak flux (from integrating a sinusoidal voltage) into the RMS voltage value. It is a fixed constant for any sinusoidal excitation.
Rearrange the EMF equation: N = V/(4.44×f×Bmax×Ac). Make sure Bmax is in tesla and Ac is in square metres (convert from cm² by dividing by 10,000).
It is the maximum magnetic flux density the core reaches during each cycle, in tesla. It is chosen below the core material's saturation flux density, with margin — typically 1.2–1.7 T for silicon steel, 0.2–0.4 T for ferrite.
The induced voltage per turn is proportional to frequency (more flux reversals per second), so at a higher frequency each turn contributes more volts, meaning fewer turns are needed for the same voltage — this is why SMPS transformers are so compact.
It is N/V = 1/(4.44×f×Bmax×Ac), a constant for a given core, frequency and flux density. Once known, you multiply it by any winding's target voltage to get that winding's turns — a common shortcut in transformer design.
Use the turns ratio: Ns = Np×(Vs/Vp), or independently calculate Ns from the EMF equation using the same core parameters and the secondary's target voltage.
Use the net (effective) core cross-sectional area, which accounts for the stacking factor of laminations (typically 90–97% of the gross geometric area) or the manufacturer's specified effective area for ferrite cores.
The core flux density rises above the design value and can saturate the core, causing a large increase in magnetising current, excessive heating, and audible buzzing (in mains transformers) or component failure (in SMPS).
The constant changes: for a square wave the equation becomes V = 4×f×Bmax×Ac×N (using 4 instead of 4.44), which is the standard form used for SMPS square-wave transformer design.
Pick a value comfortably below the core material's saturation flux density, leaving margin for supply overvoltage and temperature effects. Silicon steel mains cores commonly use 1.2–1.7 T; ferrite SMPS cores use 0.2–0.35 T to limit core loss.
The same Faraday's Law relationship applies to any coil on a magnetic core. For an inductor you would typically use it alongside the inductance formula (N²×AL or similar) rather than a fixed voltage target.
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