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
ValueL uHMeasurement
KHz
Zmag
Lopen (L1 with L2 Open)10.004780450
Lshort (L1 with L2 Short)6.1366131550

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
ValueL uHMeasurement
KHz
Zmag
L1 L210.004780450
Ladd (L1 add L2)32.67924650
Lopp (L1 oppose L2)8.619293950
L1 L210.01242000126
Ladd (L1 add L2)32.4272000407
Lopp (L1 oppose L2)8.5622000108

k solution at 50 Ohm Zmag
M = (32.679 - 8.6192) / 4 = 6.015
k = 6.015 / SQRT(10.0047 * 10.0047) = 0.602

k solution at 2 MHz
M = (32.427 - 8.562) / 4 = 5.9663
k = 6.015 / SQRT(10.0124 * 10.0124) = 0.596

FT114-43

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



Example Secondary opposing measurement

AIM-4170D Measurements
ValueL uHMeasurement
KHz
Zmag
L1 L251.630097
Ladd (L1 add L2)198300373
Lopp (L1 oppose L2)9.6330018

k solution
M = (198 - 9.63) / 4 = 47.1
k = 47.1 / SQRT(51.6 * 51.6) = 0.913

Measure coefficient of coupling using SimSmith