Measuring magnetics

Intent

• Measure a wound part’s inductance, leakage, turns ratio and dc resistance, and know what limits each reading.
• Find the current at which a core saturates with a voltage pulse.
• Recognize readings distorted by self-resonance, by the test leads, and by the missing dc current.

Theory

What an impedance meter reads

An LCR meter applies a small sinusoidal signal at its test frequency and reports the part’s effective value there, its parasitics included [Keysight Technologies, Impedance Measurement Handbook]. A winding’s turns have capacitance between them, in parallel with its inductance (self-resonant frequency), and the reading rises as the test frequency approaches the self-resonance:

$$L_\mathrm{app} = \frac{L}{1 - \left(\frac{f}{f_\mathrm{srf}}\right)^{2}}$$

$L_\mathrm{app}$

inductance the meter reads

$L$

inductance

$f$

frequency

$f_\mathrm{srf}$

self-resonant frequency

Inductance a meter reads below self-resonance✓ verified by 8 tests

Assumptions, convention and source

Assumptions

• undamped L-C resonance
• sinusoidal steady state (phasor analysis)

Notes

the winding's capacitance in parallel makes the reading rise with the test frequency: 1 % high at a tenth of $f_\mathrm{srf}$, twice the inductance at 0.71 $f_\mathrm{srf}$; above $f_\mathrm{srf}$ the part is capacitive

Source

Alexander & Sadiku 2017, Ch. 9 (Sinusoids and Phasors: impedances in parallel); derived here

Derivation

step-by-step sympy derivation

Equation id

meas.L_app · equations.yaml entry

A test frequency well below the self-resonance reads the inductance; at a tenth of it the reading is 1 % high.

DC resistance

A two-wire ohmmeter reads the winding together with its test leads and their contacts. The four-wire (Kelvin) method passes the current through one pair of leads and senses the voltage with another, so the leads’ resistance stays out of the reading [Keithley Instruments 2014]. A winding of a few turns can have a resistance well below that of the leads.

Leakage, coupling and turns ratio

With the other winding shorted, a winding’s inductance is its leakage (short-circuit inductance); with it open, its full inductance (see leakage inductance). The test frequency has a window. It must stay well below the self-resonance, as for any inductance, and be high enough that the short takes the current: the magnetizing inductance’s reactance must be much larger than the shorted winding’s resistance referred to the measured side, or part of the current flows through the magnetizing inductance and the reading rises towards the open-circuit inductance (derived from the transformer model [Erickson & Maksimović 2020, Ch. 10]). The leakage’s reactance can be smaller than the windings’ resistance at a low test frequency: read it as a series inductance, the model for an inductor of low reactance [Keysight Technologies, Impedance Measurement Handbook].

The ratio of the open-circuit voltages is close to the turns ratio (ideal transformer) but slightly below it: the primary’s leakage and the magnetizing inductance divide the applied voltage (derived here):

$$V_2/V_1 = \frac{n L_M}{L_{\ell 1} + L_M}$$

$V_2/V_1$

open-circuit voltage ratio

$L_M$

magnetizing inductance (primary)

$L_{\ell 1}$

primary leakage inductance

$n$

turns ratio, secondary/primary

Open-circuit voltage ratio of a transformer✓ verified by 8 tests

Assumptions, convention and source

Assumptions

• two linearly coupled windings without resistance
• transformer modelled by its magnetizing inductance and one leakage inductance per winding (T model), referred to the primary

Notes

the primary's leakage and the magnetizing inductance divide the applied voltage, so the ratio reads below the turns ratio by about $L_{\ell 1}/L_M$ (1 % for a leakage of 1 % of $L_M$). Driven from the secondary, $V_1/V_2$ reads below $1/n$ by about the secondary's leakage over $L_M$, both referred to the primary. A driven winding whose resistance is not small against its reactance lowers the ratio further

Source

Erickson & Maksimović 2020, Ch. 10 (Basic Magnetics Theory: the transformer model with magnetizing and leakage inductances); derived here

Derivation

step-by-step sympy derivation

Equation id

xfmr.V_oc · equations.yaml entry

For the coupled windings example, the ratio reads 0.2475 for a turns ratio of 0.25. A test frequency so low that the driven winding’s resistance is not small against its reactance lowers the ratio further.

Saturation

An impedance meter’s small signal and zero dc current do not show saturation. A voltage step across the winding makes its current ramp at the voltage over the inductance (inductor current). Past the saturation flux density the core’s permeability collapses and the inductance falls sharply [Erickson & Maksimović 2020, Ch. 10] (see magnetic materials and the B-H curve), so the ramp steepens: the current where the slope starts to rise is the saturation current.

The B-H loop

With two windings on an ungapped core, Ampère’s law gives the field intensity from the primary’s current (Ampère's law), and Faraday’s law the flux density from the integral of the open secondary’s voltage (Faraday's law) [Erickson & Maksimović 2020, Ch. 10]. Plotted against each other, the two trace the core’s B-H loop.

Worked example

An example winding read at two test frequencies:

Winding self-resonance example

Symbol	Value	How it is obtained
$L$ inductance	1 mH	given
$C_p$ parasitic winding capacitance	20 pF	given
${f}_{\mathrm{lo}}$ frequency	100 kHz	given
${f}_{\mathrm{hi}}$ frequency	1 MHz	given
$f_\mathrm{srf}$ self-resonant frequency	1.13 MHz	Self-resonant frequency of an inductance with parallel parasitic capacitance
${L_\mathrm{app}}_{\mathrm{lo}}$ inductance the meter reads	1.01 mH	Inductance a meter reads below self-resonance
${L_\mathrm{app}}_{\mathrm{hi}}$ inductance the meter reads	4.75 mH	Inductance a meter reads below self-resonance

The winding resonates at 1.13 MHz. At 100 kHz the meter reads 1.008 mH, close to the 1 mH of the winding. At 1 MHz, close to the self-resonance, it reads 4.75 mH.

Try it

▶ Open in the equation explorer: Inductance a meter reads below self-resonance
Preset from the example lcr-srf

Sweep the test frequency: the reading is flat at low frequency and rises steeply towards the self-resonance. Raise $f_\mathrm{srf}$, as a winding with less capacitance would have, and compare.

Bench exercise

Measure a winding with many turns, such as a flyback primary, at each test frequency of an LCR meter, and find its self-resonance with an impedance analyzer or a frequency sweep. Estimate its capacitance from the self-resonance (self-resonant frequency), and compare the readings with the apparent-inductance equation. Then measure its dc resistance with two wires and with four: the difference is the leads and their contacts.

Gotchas

• Test frequency against self-resonance. A winding with many turns resonates low. The meter reads the effective value at its test frequency, parasitics included [Keysight Technologies, Impedance Measurement Handbook]: close to the self-resonance, that is well above the inductance (apparent inductance).
• Two-wire resistance includes the leads. Use four wires for a winding’s dc resistance [Keithley Instruments 2014].
• No dc current, no saturation. A meter’s reading holds at the peak current only if the core does not saturate there: check that with a current pulse at the design’s peak current.
• The open-circuit ratio is not quite the turns ratio. It reads low by about the driven winding’s leakage over the magnetizing inductance (open-circuit voltage ratio), and lower still where the winding’s resistance takes a share of the voltage.

Go deeper

• Application note Impedance Measurement Handbook (5950-3000) — Keysight Technologies · retrieved 2026-09-24
  How LCR meters and impedance analyzers measure, why a component's measured value depends on the test frequency and signal, and how to connect and compensate the test fixture.
• Application note Low Level Measurements Handbook, 7th edition — Keithley Instruments (Tektronix) · retrieved 2026-09-24
  Precision dc measurements, among them low resistances with the four-wire (Kelvin) method, which keeps the test leads' resistance out of the reading.
• Book chapter Basic Magnetics Theory (Ch. 10) — R. W. Erickson, D. Maksimović · retrieved 2026-09-23
  Magnetic circuits, the transformer model with magnetizing and leakage inductance, and core and winding loss mechanisms.

Quiz

1. A winding resonates at 1 MHz. At what test frequency does an LCR meter read its inductance within about 1 %?

   1. 100 kHz or lower
   2. 500 kHz
   3. 1 MHz
   4. At any frequency
   Answer and explanation

   Correct answer: A At a tenth of the self-resonance the reading is 1 % high; closer to it, much more.

2. At 0.71 of the self-resonant frequency, what does the meter read?

   1. About half the inductance
   2. The inductance
   3. About twice the inductance
   4. About ten times the inductance
   Answer and explanation

   Correct answer: C One over one minus 0.71 squared is 2.

3. Why measure a winding's dc resistance with four wires?

   1. It removes the winding's inductance
   2. It gives the ac resistance
   3. It heats the winding less
   4. The resistance of the leads and their contacts stays out of the reading
   Answer and explanation

   Correct answer: D One pair carries the current, the other senses the voltage and carries almost none, so the leads drop no voltage in the reading.

4. How does a voltage pulse show that a core saturates?

   1. The current ramps faster once the core saturates
   2. The current stops rising
   3. The voltage across the winding rises
   4. The current falls
   Answer and explanation

   Correct answer: A The current ramps at the voltage over the inductance; when the core saturates the inductance collapses and the ramp steepens.

5. With the secondary shorted, what does the primary's inductance reading give?

   1. The magnetizing inductance
   2. The leakage inductance, referred to the primary
   3. The winding capacitance
   4. The turns ratio
   Answer and explanation

   Correct answer: B The short cancels the shared flux; what the primary still sees is the flux the windings do not share.

6. What does an LCR meter's reading, taken without dc current, not tell?

   1. The winding's inductance at low current
   2. Whether the core saturates at the operating current
   3. The series resistance at the test frequency
   4. The inductance at the test frequency
   Answer and explanation

   Correct answer: B Its small signal does not reach the flux density of the peak current: check saturation with a current pulse.

7. A transformer's primary leakage is 1 % of its magnetizing inductance, and its turns ratio n is 0.25. Driven from the primary, at a test frequency where the winding's resistance is negligible, what does the open-circuit voltage ratio read?

   1. 0.2525
   2. 0.25
   3. 0.2475
   4. 0.2
   Answer and explanation

   Correct answer: C The primary's leakage and the magnetizing inductance divide the applied voltage, so the ratio is the turns ratio divided by 1.01: about 1 % low.