Transformer designer

Fill in your specification on the left-hand side. You can also load some common core and geometry properties instead of typing them.

You can specify up to ten windings, with current defined as RMS current entering the core. You select a current or number of turns to be calculated automatically if your numbers do not balance. You also specify limits on the core magenetisation.

The transformer design process is as follows: —

  1. Fill in the specifications, including kCu as the maximum packing factor. Don't forget to press Design now.
  2. Identify the lowest power that fulfils your magnetisation limit. You may need to choose another core to produce reasonable values.
  3. Look up the recommended wire diameters for your kCu. Enter wire diamters you have available (similar values to the recommendations) and enter them in the specification. Press Design Now to update the design.
  4. Choose a number of primary turns which low losses and that is below your packing factor and magnetisation limit.
  5. Look up the number of turns for each winding.

This website helps design transformers by providing estimations of loss and magnetisation as explained below. The first step is to divide the available winding area between the windings. This is done to keep the current density roughly equal throughout. This leads to the following wire diameter suggestions (for each winding \(x\) of the \(n\) windings).

$$ D_x = 2\cdot\sqrt{\frac{A_\textrm w k_\textrm{Cu} |N_x I_x|}{\pi N_x \sum\limits_{i=1}^n{|N_i I_i|}}} $$

The number of turns needed depends partly on the magnetisation of the transformer. The magnetising inductance is found from

$$ L_\textrm{m} = \frac{N^2}{S} $$

where \(L_\textrm{m}\) is magnetising inductance, \(N\) is the number of turns and \(S\) is the reluctance of a core. For a transformer without an air-gap, \(S={A_\textrm L}^{-1}\), hence

$$ L_\textrm{m} = {N^2} A_\textrm L $$

The magnetising current is the current in this inductor. It is usually measured on the primary winding. The primary magnetising current is found from the primary voltage by

$$ I_\textrm m = \frac{V_1}{2\pi f L_\textrm{m}} $$

This allows us to impose limits on the design of either

$$ N \ge \frac{V_1}{2\pi f A_\textrm L I_\textrm {m(max})} $$


$$ N \ge \sqrt\frac{L_\textrm{m(min)}}{A_\textrm L} $$

There is also a limit from saturation of the core, although frequently losses are the main limitation (especially at high frequency). The saturaton limit is

$$ N \le \frac{V_1 \sqrt 2}{2\pi f B_\textrm{sat}A_\textrm e} $$

Power loses come from two sources: the core and the windings. Core loss can be estimated using the Steinmetz equation

$$ P_\textrm{core} = k\cdot f^\alpha \cdot B^\beta \cdot V_\textrm e = k\cdot f^\alpha \cdot \left( \frac{V_1 \sqrt 2}{2\pi f A_\textrm e N_1} \right)^\beta \cdot V_\textrm e$$

Winding loss (per winding) can be estimated either accounting for skin depth or not

$$ P_\textrm{winding(skinless)} = I^2 \cdot\frac{4 N\rho l_\textrm w}{\pi D^2}$$
$$ P_\textrm{winding(skin)} = \frac{I^2 N l_\textrm w}{D}\cdot\sqrt{\frac{f \mu_0}{\pi \rho}}\cdot\Re{\left(\left(1-j\right)\cdot\frac{J_0\left(D\left(1-j\right)\sqrt{\frac{\pi f \mu_0}{4\rho}}\right)}{J_1\left(D\left(1-j\right)\sqrt{\frac{\pi f \mu_0}{4\rho}}\right)}\right)}$$

Transformer design is a compromise between all of these constraints.