# How to estimate the magnetizing inductance in transformer?

I did a lab a month ago, one part just said that to set the signal generator to 5Vpp and connect it to primary coil in a transformer, and record the voltage at different frequency. Finally, estimate the magnetizing inductance. However, is it possible to measure the inductance in primary coil if we don't connect any load (such as an inductor) to the primary circuit? Or, the coil winded part in the transformer can be a kind of inductor?

• You are aware that a coil is an inductor and that the transformer primary is a coil, right? Mar 26, 2018 at 3:21

Here's a commonly used model of a real transformer:

Rp: Primary winding resistance

Lik: Primary leakage inductance

Rc: Core losses

Lm: Magnetizing inductance

According to the model above, measurements while secondary is open provide info about Lm.

Actually, the primary inductance measured with a LCR meter at a single frequency (generally 1kHz or 120Hz) while the secondary is open is an approximation of magnetizing inductance. However, Lm varies with core properties, temperature, frequency etc. So, measuring primary impedance for wide range of frequencies is the best practice to estimate the magnetizing inductance.

Procedure: First, you need to know the frequency that the transformer is designed for ($f_{tr}$). Then, apply an acceptable level of voltage with different frequencies (e.g. if ftr = 100kHz then the range can be [1kHz - 1MHz] with 50kHz or 100kHz steps) and measure the impedance ($Z_p$). If you put the values in a Z-f graph in logarithmic scale (both axis) then you'll get a linear view where you can fairly estimate Lm from $Z_p = 2 \pi \ f \ L_m$.

• By doing this, you will also measure the leakage inductance, isnt it ?
– Jess
Apr 21, 2020 at 9:37
• @Jess The result obtained with the procedure above "includes" the leakage (Since the purpose is to estimate the magnetizing inductance, we don't care much the effect of the leakage inductance). So it may not be possible to extract the leakage from the result directly. Since the leakage inductance does not contribute to the coupling between pri and sec, the best approach of measuring the leakage inductance could be shorting the secondary before applying a signal to the primary. Reference. Apr 21, 2020 at 16:06
• Thank you for your answer ! It is not possible to substract from the first measurement (the magnetizing inductance + the leakage inductance), the leakage inductance ? it adds one measurement to do in order to have the leakage inductance as you said by shorting the secondary output.
– Jess
Apr 21, 2020 at 17:20
1. Use DC power to measure resistance R.
2. Measure current by applying 110/220V Ac in primary coil while secondary coil is open-circuit.
3. Find total impedance Z from step 2 using Vrms and I rms. 4.Find inductive reactance Xl by substracting R from Z. Z^2=R^2+Xl^2
4. By finding Xl use below formula to find inductance L. Xl=2πfL
• I tried to build the circuit in this way, i.imgur.com/ltvatGB.png I only got the voltage reading in the primary circuit, so I need to get the current reading also so that I can estimate the magnetizing inductance? However, the lab manual just asked to find the primary circuit voltage, I am stuck... Dec 5, 2017 at 8:09
• Here is the instruction i.imgur.com/PsIpZzr.png Dec 5, 2017 at 8:10
• This also can be happend but primary coil has thin wire so every time you have to eliminate R from Z. I use 250VA transformer which hase R=75ohm. Dec 5, 2017 at 8:14
• I feel I am dying since I didn't measure the impedance...anyway, thank you bro! Dec 5, 2017 at 8:22
• Do you takling about ferrite transformers or iron core transformers? Dec 5, 2017 at 8:24

You can either measure current directly or use a small series resistor in line with one of the windings of the coil and measure the V drop.

At different frequencies the reactance in the coil changes and the current through the coil will change.

As has been stated by Rohat Kılıç xL (Reactive Resistance) = (2 x pi) x frequency(f) x inductance(l) However it is not as simple as that, as a transformer represents a tuned circuit as shown in the representative diagram Rohat Kılıç has shown.

At the highest absortion rate xl will reduce to its lowest point, at point which this would be considered to be the optimum magnetising inductance @ that frequency.