Specifying frequencies for leakage inductance measurements

In modern high-frequency circuits, the leakage inductance of the magnetic components can be a very important design consideration. However, it’s also important not to hamper the transformer manufacturer with unrealistic testing requirements. A little time spent considering the test frequency can save time and frustration later.

The typical transformer shown has a primary inductance (L_P) of 16.5 mH; a primary dc resistance (R_P) of 14 Ù; a secondary dc resistance (R_S) of 52 mÙ; a primary-to-secondary ratio (a) of 15 (210/14); and a leakage inductance (LL) of approximately 150 mH (Fig. 1). To measure the leakage inductance, first short the secondary winding, (i.e., load the secondary with its dc resistance, or R_S), then measure the inductance on the primary. The equivalent circuit is shown in Figure 2.

To calculate the inductance of the equivalent circuit, less the leakage inductance, rationalize the impedance equation and solve for the new inductance, L_E, where R_E = a2RS and L_P is the primary inductance:

where:

To calculate the equivalent (leakage) inductance at 1000 Hz:

ù = 2ðf = 6.28 * 10³
XL_P = ùL_P = 104
R_P = a²RS = 11.7

Substituting in the given equations gives: X_O = 1.3; and L_E = 207 µH.

This (L_E) plus the actual leakage inductance is the measured leakage inductance. For this example, the leakage inductance measures 360 µH (207 µH + 150 µH).

Now, calculating the equivalent inductance at 15,750 Hz:

ù = 2ðf = 9.89 * 10⁴
XL_P = ùL_P = 1.63 * 10³
R_P = a²RS = 11.7

Substituting in the given equations results in: X_O = 0.084, and L_E = 0.85 µH. For all practical purposes, this (L_E) plus the actual leakage inductance is the measured leakage inductance!

The table provides a listing of various transformers with their equivalent leakage inductance calculations at different frequencies and the leakage inductance measurements at f₂. The measured inductance at f₁ (L_M1) for all tabulated transformers is within 20% of the calculation (L_E1) when L_L is subtracted.

A good rule of thumb when selecting the frequency for measuring leakage inductance is to be sure that the primary reactance (XL_P) is at least 100 times the reflected secondary dc resistance (a²R).