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 (LP) of 16.5 mH; a primary dc resistance (RP) of 14 Ù; a secondary dc resistance (RS) 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 RS), 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, LE, where RE = a2RS and LP is the primary inductance:
To calculate the equivalent (leakage) inductance at 1000 Hz:
ù = 2ðf = 6.28 * 103
XLP = ùLP = 104
RP = a2RS = 11.7
Substituting in the given equations gives: XO = 1.3; and LE = 207 µH.
This (LE) 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
XLP = ùLP = 1.63 * 103
RP = a2RS = 11.7
Substituting in the given equations results in: XO = 0.084, and LE = 0.85 µH. For all practical purposes, this (LE) 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 (LM1) for all tabulated transformers is within 20% of the calculation (LE1) when LL is subtracted.
A good rule of thumb when selecting the frequency for measuring leakage inductance is to be sure that the primary reactance (XLP) is at least 100 times the reflected secondary dc resistance (a2R).