# How can I find mutual inductance and coupling coeffecient of coupled inductor knowing turns ratio, primary and seconday inductance?

Trying a simulation in PSIM I have turn ratios and primary and secondary inductances but don't know how to find mutual inductance and coupling coeffecient of coupled inductors

If you know the turns ratio and the primary inductance, you can predict the secondary inductance if the coupling was 100%: -

$$L_{secondary} = L_{primary}\cdot N^2$$

Where $$\N\$$ is the turns ratio from primary to secondary i.e. if Np is 1000 and Ns = 100 then $$\N^2\$$= 0.01.

Your calculated value of inductance for the secondary should be slightly bigger than your measured value if the transformer has decent coupling.

Be aware of parasitic capacitance if the inductance measurements were made using high frequencies. These can upset this type of prediction quite a lot.

So, the difference between predicted and measured secondary inductance is the leakage inductance. That leakage inductance is called the secondary referred leakage inductance.

That then allows you to calculate the coupling coefficient. For example if the secondary inductance is 10 uH and the predicted method suggested 20 uH then the coupling is 50%.

• Thankyou, sir actually I have both primary and secondary inductance already.I have L1=95uH, L2=1.5mH , Turn ratio=4, V_in=34.8V I want to find coupling coefficient and mutual inductance ? How can I find accurately? – Ammar Nov 19 '19 at 12:43
• OK then, what's 95 uH x 4 squared? – Andy aka Nov 19 '19 at 19:09
• 95uH x 4 = 1.5mH is secondary turns of coupled inductor – Ammar Nov 20 '19 at 12:42
• No, work it out properly and more exactly. – Andy aka Nov 20 '19 at 12:43
• Cmon, 16 x 95 uH doesn’t shouldn’t be a problem. – Andy aka Nov 20 '19 at 12:54