Measuring Transformer Coupling Coefficient

Process for measuring transformer coupling coefficient, k, using SimSmith, for a FT114-61 Ferrite Toroid core with 10T #22, close spaced, on opposite ends of the core.

Measuring coil inductance using AIM-4170D

AIM-4170D bench setup for measuring coil inductance. Also pictured are the OSL devices used to calibrate to the SO-239.

Set up VNA such that the measurement is taken close to Xs = 50 Ohms.
Ls = 9.9738 uH

Measure coefficient of coupling using SimSmith

A trial and error step was performed to find a capacitor value which matches the leakage inductance of the device. The selected load is a 47 pF capacitor in series with a 49.9 Ohm load resistor. This step is required to keep the measurements within range of the VNA.

Using a "coupled" SimSmith transformer block, adjust k for best match to measurement.
k = 0.6

Example Secondary opposing measurement

Measure coefficient of coupling using Secondary Open Short Method

Formula for the secondary open-short method:

k = SQRT(1 - Lshort / Lopen)
An approximation which assumes the wire resistance is zero.

AIM-4170D Measurements
Value	L uH	Measurement KHz	Zmag
Lopen (L1 with L2 Open)	10.0047	804	50
Lshort (L1 with L2 Short)	6.1366	1315	50

k solution

k = SQRT(1 - 6.1366 / 10.0047) = 0.62

Measure coefficient of coupling using Series-adding Series-opposing Method

Formulas for Series-adding Series-opposing method:

M = (Ladd - Lopp) / 4
k = M / SQRT(L1 * L2)

AIM-4170D Measurements
Value	L uH	Measurement KHz	Zmag
L1 L2	10.0047	804	50
Ladd (L1 add L2)	32.679	246	50
Lopp (L1 oppose L2)	8.6192	939	50
L1 L2	10.0124	2000	126
Ladd (L1 add L2)	32.427	2000	407
Lopp (L1 oppose L2)	8.562	2000	108