EI Laminated Transformer Design Calculator

The effective cross-sectional area is not the geometric area: there is an insulating coating between laminations, so the actual steel occupies only a fraction of the stack. This is the stacking factor, typically 95–97% depending on lamination thickness, and it must be applied before any other calculation.

Stack height is the only truly free geometric parameter: no standard fixes it, and with the same lamination size you can build a 5 VA or a 20 VA transformer depending on how many laminations are stacked. A square stack — stack height equal to the center-leg width — is the most common choice because it keeps the mean turn length short, but it is not a rule.

The area product summarizes the design: the core area determines how much flux can be carried, the window area determines how much copper fits, and obtainable power is proportional to their product. It is also the quantity used by Card 5 to select a core starting from the required VA.

Mean turn length is a geometric estimate, not a fixed datum: it depends on the bobbin, insulation thickness, and winding method. It is used to calculate winding resistance, so a 10% error here carries directly into the copper-loss estimate.

Turns per volt are the one transformer number worth remembering: multiply by voltage and you have the winding turns. They depend only on frequency, core area, and flux density, so they are a property of the core rather than of the external circuit.

Rounding matters more than it may appear. Turns must be integers, and removing one turn from the primary raises the flux density throughout the core: on a small core, where turns per volt are low, one turn less can mean an extra hundred gauss and a significant increase in losses. The card shows the B you actually obtain, not merely the value you requested.

The extra secondary turns compensate for the voltage drop under load: a few percent more turns are wound so that the full-load voltage falls to the desired value. The required allowance is indicated by the regulation calculated in Card 4, and the proper way to use these two cards is iteratively until the two values agree.

Primary current is not simply power divided by voltage: it also includes losses, so it depends on efficiency, which in turn depends on winding resistance, which depends on the wires selected from the current. This forms a loop, and the card solves it iteratively until the values converge.

Window fill is the constraint that rejects the most designs. Bare copper cannot occupy much more than about 40% of the window in a 50 Hz transformer: the rest is taken by enamel, bobbin, interlayer insulation, and the voids between round wires. If the limit is exceeded, there are three options — a taller stack, a larger lamination size, or a higher current density with increased heating.

Wire is selected with a cross-sectional area at least as large as the calculated requirement, so the actual current density shown is normally slightly lower than the requested value. For small diameters, the step between adjacent wire sizes is about 25% in cross-sectional area, which is clearly visible.

Copper losses depend on load and increase with the square of current; core losses do not, because they are present even at no load and depend on the selected flux density. This is why a transformer left energized without a load still consumes power and heats up: that is primarily the core loss.

I derive the specific core loss from the two points published in the electrical-steel datasheet — typically at 1.0 and 1.5 tesla — and interpolate using the exponent implied by those two points, usually around 2. This is an explicitly stated extrapolation, not a physical law: outside the range between the two points, and especially near saturation, the estimate becomes optimistic.

Voltage regulation is the quantity the end user notices: it is the drop from no-load to full-load voltage. In a small transformer it can easily be 10–15%, and most of it is resistive drop. If better regulation is required, the solution is not simply more turns but thicker wire, which usually means a larger core.

The design process starts from the area product: once frequency, flux density, current density, and window utilization are fixed, obtainable power is proportional to A_e·A_w, and the formula can be rearranged. The factor of two is present because the window must contain two windings, primary and secondary, each carrying its apparent power.

The table does not choose for you: for each lamination size it shows the required stack height. Rows highlighted in orange have a stack-to-leg ratio between 0.5 and 2.5, corresponding to practical constructions; below this range core material is underused, while above it the mean turn length grows enough for copper losses to erase much of the benefit.

Once a row has been selected, enter its size and stack in Card 1 and proceed through Cards 2, 3, and 4: they will show whether the copper fits and what the losses are. The real design process is this iteration, not a single calculated number.

The calculation assumes a two-winding transformer. With multiple secondaries, copper occupancy increases and the required area product rises, so treat this result as a lower bound.

Enamelled copper wire

Data sources

EI lamination dimensions: ASCO Components and Centersky catalogs, cross-checked against each other. The two sources agree on all common sizes, and the dimensions add up consistently to the overall width. Note: EI38.1 and EI85 do not exist under those names — the commercial sizes are EI38.4 and EI85.8.

Electrical-steel losses: thyssenkrupp powercore and POSCO datasheets for non-oriented grades (P1.0/50 and P1.5/50), and the CRGO M3–M6 technical data for grain-oriented grades (P1.5/50 and P1.7/50). The interpolation exponent is derived from the two points for each grade and is shown in the note below the global parameters.

Operating flux density: the sources genuinely differ here. One reference gives 1.2 T for 0.35 mm grain-oriented laminations, while McLyman’s handbook works through a design at 1.6 T using the same type of material. Neither is necessarily wrong: these are different design criteria, lower losses versus more aggressive use of the core. This is why the value is an input field rather than a fixed constant.

Current density and window fill: 2–3 A/mm² is the commonly used range; k_u ≈ 0.4 for 50 Hz transformers is McLyman’s value, accounting for wire insulation, packing, usable window area, and interwinding insulation.

Copper: resistivity 0.0172128 Ω·mm²/m at 20 °C and temperature coefficient 0.00393 per degree, from the NBS reference for 100% IACS annealed copper. Diameters are the current nominal series; cross-sectional area is calculated rather than tabulated.

What is not calculated: magnetizing current, because it would require the magnetic path length and the magnetization curve of the actual lamination grade, which are not published in a directly usable form. Temperature rise is also not calculated because it depends on ventilation, mounting, and impregnation: the tool provides total losses and loss density per square centimeter, while the thermal assessment remains a design decision.