One‑Pulse Characterization of Nonlinear Power Inductors

This article and presentation by Sam Ben-Yaakov describes one-pulse nonlinear-inductor measurement method that provides a compact way to extract nonlinear magnetic properties of power inductors, crucial for accurate design of high-density power converters.

Introduction

Nonlinear behavior of power inductors is a central design constraint in modern switched‑mode power supplies, resonant converters, and high‑current filters, yet it is still often characterized using small‑signal instruments that only capture a narrow operating region of the magnetic core. Accurate design of high‑density power converters requires knowledge of the inductance as a function of current, including the onset of saturation and the effective energy storage capability under realistic excitation conditions. The one‑pulse nonlinear‑inductor measurement method offers a compact and conceptually simple way to extract this information from a single current pulse, providing a direct link between the time‑domain response and the nonlinear magnetic properties of the inductor.

Conventional Inductance Measurement Approaches

LCR meters with DC bias

Traditional inductance measurement often uses LCR meters that superimpose a small AC excitation on a DC bias, reporting an effective inductance value at the chosen frequency. Under strong nonlinearity, this method effectively measures a small-signal incremental inductance around the operating point, which may differ from the large-signal behavior during converter switching.

The method assumes almost sinusoidal currents and voltages, which becomes questionable for strongly nonlinear cores where waveform distortion and higher harmonics are significant. As a result, LCR-based data often overestimates inductance under pulsed, high-current operation, leading to optimistic designs with underestimated ripple and saturation risk.

Line-frequency reactance techniques

Another conventional approach is to apply mains-frequency voltage to the inductor and compute inductance from measured RMS current and voltage using L=V/(2πfI)L = V/(2\pi f I). This method is simple but forces the inductor to operate at low frequency and often at flux excursions very different from those in high-frequency power electronics.

Because nonlinearity couples amplitude, frequency, and waveform shape, line-frequency results are of limited value for predicting behavior under high-frequency PWM waveforms. Moreover, the method provides only a single operating point rather than a complete inductance–current characteristic.

Pulse measurement with thyristors

Earlier pulse measurement systems discharged a capacitor through the inductor via a thyristor (SCR), creating a damped resonant current waveform.
From sampled voltage and current, incremental and secant inductance can be reconstructed, as well as core losses derived from the damping of the oscillation.

However, SCR-based systems suffer from limited control over pulse width and amplitude, since the thyristor cannot be turned off actively and the waveform is constrained by the resonant tank. These limitations reduce flexibility and make such methods less attractive compared to modern transistor-based pulse testers with fully programmable pulses.

Principle of the One‑Pulse Method

The core idea of the one‑pulse technique is to drive the inductor with a single, well‑defined voltage pulse, measure the resulting current waveform, and derive the inductance versus current characteristic from the relationship between applied voltage, current slope, and the magnetic core state. Because the excitation is time‑limited and unipolar, the method traces the magnetization along a controlled portion of the B–H curve, avoiding steady‑state heating and minimizing the influence of high‑frequency parasitics.

Voltage–Current Relationship in Inductors

For an ideal inductor with instantaneous inductance L, the terminal voltage–current relationship is given by the differential equation

v(t)=Ldi(t)dtv(t) = L \frac{di(t)}{dt}

which directly relates the slope of the current waveform to the applied voltage. In nonlinear magnetic components, the inductance becomes a function of current, L = L(i), so that the same applied voltage will generate different slopes as the core approaches saturation.

From One Pulse to L(i)

In the one‑pulse approach, a rectangular voltage pulse of amplitude V_p and duration T_p is applied across the inductor, and the current response is measured with sufficient temporal resolution. By differentiating the measured current and using the known applied voltage, the instantaneous inductance is computed as

L(i(t))=v(t)di(t)/dtL\big(i(t)\big) = \frac{v(t)}{di(t)/dt}

which yields an L–I curve from a single time‑domain experiment.

Test Bench Architecture

A practical one‑pulse measurement bench consists of a DC source, a fast power switch, the device under test (DUT) inductor, a current‑sensing element, and a control/measurement system (e.g., an oscilloscope or digital acquisition). The design must guarantee a well‑defined pulse shape, minimal parasitic ringing, and a measurement bandwidth high enough to faithfully reconstruct the current slope within the shortest relevant time intervals.

Key Hardware Components

The switch is typically implemented with a MOSFET or similar semiconductor device capable of fast turn‑on and turn‑off transitions, ensuring that the applied voltage is close to an ideal step for the duration of the pulse. Current measurement is commonly based on a low‑ohmic shunt resistor or a current probe; the shunt value must be chosen to minimize added series resistance while still providing a measurable voltage signal.

Component	Main requirement	Typical implementation
DC source	Stable output, sufficient voltage and current margin.	Laboratory DC supply or bulk DC bus.
Power switch	Fast transitions, low on‑resistance, appropriate voltage rating.	Power MOSFET with gate‑driver circuitry.
Inductor under test	Mounted with minimal loop inductance and parasitics.	Discrete power choke or custom wound core.
Current sensor	High bandwidth, low added series impedance.	Low‑ohmic shunt resistor or current probe.
Control and acquisition	Precise timing of pulse and high‑speed waveform capture.	Function generator plus digital oscilloscope or data acquisition card.

Role of Parasitic Elements

Parasitic resistance and stray capacitance in the test fixture can distort the apparent current slope, leading to errors in the inferred inductance. A small series resistor introduced for numerical stability in simulations, or the effective series resistance (ESR) of the inductor, must be accounted for when interpreting the measured waveforms.

Measurement Procedure

Executing a one‑pulse nonlinear‑inductor measurement requires careful planning of the pulse amplitude, duration, and repetition rate, along with a post‑processing workflow that maintains numerical robustness. Proper sequencing ensures that the inductor starts from a known magnetic state, the current remains within safe limits, and the derived L–I curve is physically consistent and useful for design.

Preparation and Initial Conditions

Before each measurement, the inductor should be demagnetized or driven to a defined initial bias point to control the effect of remanence and hysteresis on the measured response. Thermal stabilization is also important, as inductance in power components can significantly vary with temperature, which alters both the core permeability and copper resistance.

One‑Pulse Excitation and Acquisition

The test sequence begins by arming the acquisition system, then applying a single rectangular voltage pulse whose length is chosen to sweep the inductor current up to or slightly beyond the anticipated saturation level. During the pulse, the current waveform is recorded with high sampling rate; after the pulse, the system returns to a safe state and the captured data are processed to compute di/dt and, subsequently, the inductance.

Step	Action	Purpose
1	Set initial current and core state.	Control remanence and starting point on the B–H curve.
2	Configure pulse amplitude and duration.	Define target peak current and saturation region coverage.
3	Trigger and record the current waveform.	Capture data for L–I reconstruction from a single event.
4	Process data to compute \(di/dt\) and L(i).	Generate inductance versus current characteristic.
5	Repeat for different conditions if required.	Map temperature or bias‑dependent behavior.

Dealing with Remanence and Hysteresis

Remanent flux in the core can shift the effective operating point and cause asymmetry between rising and falling current segments, which must be considered when interpreting L–I curves. Demagnetizing cycles or symmetrical bipolar excitation sequences can be used between pulses when the objective is to characterize the average, rather than path‑dependent, inductance.

The switching device must support fast turn-on and turn-off with clean edges to ensure a well-defined voltage pulse across the inductor.
Current measurement can use a shunt resistor, Hall-effect sensor, or Rogowski coil, depending on the current range and required bandwidth.

Key component requirements

The DC supply must be capable of delivering the required pulse energy without excessive sag, or alternatively, an energy-storage capacitor can be charged between pulses. The switch must withstand both the peak current and the voltage overshoot due to circuit stray inductances and parasitic elements.

Measurement bandwidth should be sufficiently high to resolve the fastest current transitions, particularly at low currents where the inductance is highest and di/dt is smallest. Adequate galvanic isolation and shielding are required to prevent measurement corruption by high dv/dt and di/dt transients.

Example parameter ranges

Commercial pulse testers for power inductors can cover current ranges from approximately 0.1 A up to 10 kA, demonstrating the scalability of the method.
Pulse widths can be adjusted from microseconds to milliseconds, enabling characterization of both small signal chokes and large power magnetics.

The applied voltage can be chosen to match the intended converter bus voltage, providing a realistic test condition that mirrors actual operation.
Table below summarizes typical ranges and design considerations for a general-purpose one-pulse test rig.

Table: Typical design ranges

Parameter	Typical range	Design note
Test current range	0.1 A – 10 kA	Determines current sensor technology and switch rating.
Pulse width	1 µs – several ms	Short for low loss; long enough to reach target current.
Test voltage	Tens to several hundred volts	Prefer matching intended converter bus voltage.
Repetition rate	Up to a few Hz	Limited by thermal and core reset conditions.
Measurement bandwidth	Hundreds of kHz or higher	Needed to resolve rapid changes near saturation.

Data Processing and Inductance Extraction

The numerical extraction of nonlinear inductance from one‑pulse measurements hinges on robust differentiation of the measured current, compensation of parasitic effects, and mapping of the resulting L–I data into models suitable for circuit simulation. Care must be taken to avoid amplification of measurement noise, especially at low currents where the slope is small and the relative error can be high.

Numerical Differentiation and Smoothing

Because direct numerical differentiation of noisy data is ill‑conditioned, smoothing filters or curve‑fitting techniques are typically applied to the current waveform before evaluating di/dt. Polynomial fitting, spline interpolation, or low‑pass filtering can be used, with the trade‑off that excessive smoothing may blur sharp transitions near saturation, while insufficient smoothing leaves residual noise in the derived inductance.

Correction for Series Resistance

To isolate the inductive behavior, the voltage drop across series resistance components such as shunt resistors and inductor winding resistance must be subtracted from the applied voltage prior to computing L(i). This leads to the effective inductive voltage

which is then used in the inductance calculation.

Generating L–I Curves and Saturation Metrics

Once the instantaneous inductance has been calculated over the pulse duration, the data can be plotted as L(i) to visualize the inductor behavior from near‑zero current up to and beyond the saturation knee. Key metrics such as the saturation current, the small‑signal inductance at low current, and the energy‑handling capability can then be extracted for use in converter design and derating.

Comparison with Alternative Methods

Qualitative method comparison table

The following table contrasts key characteristics of several inductance measurement approaches beyond the one-pulse method. It highlights why single-pulse excitation is particularly suited to strongly nonlinear power magnetics.

Method	Excitation type	Nonlinear accuracy	Proximity to real converter operation
LCR meter with DC bias	Small-signal sinusoidal plus	Good for incremental values, limited for deep saturation.	Moderate; frequency and waveform differ from PWM.
Line-frequency reactance	Sinusoidal mains voltage	Poor in strongly nonlinear regime.	Low; very different from high-frequency switching.
SCR pulse discharge	Damped resonant pulse	Moderate; limited control over pulse shape.	Moderate; pulse waveform only approximates converter conditions.
One-pulse transistor-based	Single rectangular pulse	High; accurately captures saturation and hysteresis path.	High; can replicate actual converter pulse amplitude and width.

Advantages in frequency and waveform domain

Conventional frequency-domain measurements implicitly assume near-sinusoidal waveforms and linearity, which breaks down in the presence of sharp knees and hysteresis in the B–H curve. The one-pulse method works entirely in the time domain and makes no assumption about sinusoidality, allowing correct characterization even for highly distorted waveforms.

Because the test pulse can be matched to the converter’s actual gate signals and bus voltages, the measured inductance is directly relevant without complex extrapolation. This reduces the risk of discrepancies between laboratory datasheets and in-circuit behavior, especially for powder cores and gapped ferrites.

Applications in Power Electronics Design

One‑pulse nonlinear‑inductor measurements directly support the design of high‑performance converters by providing realistic inductance data under the same current levels and pulse durations encountered in actual operation. This enables more accurate prediction of current ripple, transient response, and core loss as compared to relying solely on small‑signal or catalog values.

Modeling for Circuit Simulation

The measured L–I characteristics can be translated into behavioral models or piecewise‑linear approximations for use in SPICE‑type simulators, allowing designers to explore the impact of saturation and nonlinearity on system dynamics. More advanced models can incorporate both the current‑dependent inductance and frequency‑dependent loss terms to capture core loss under realistic PWM excitation.

Component Selection and Derating

By comparing L–I curves from different inductors, designers can select components that maintain sufficient inductance over the expected current range, avoiding excessive ripple or early saturation. The method also supports the definition of derating rules, such as limiting operating current to a fraction of the measured saturation point to ensure acceptable efficiency and thermal performance.

Impact on core and winding selection

Knowing how inductance collapses with current enables accurate selection of core size, air gap, and number of turns to meet both ripple and saturation constraints. Underestimating nonlinearity often leads to thermal overstress, audible noise, and electromagnetic interference issues in practical hardware.

The one-pulse method also reveals differences between core materials such as ferrite, powdered iron, and high-flux alloys under identical pulsed conditions. Designers can therefore base material selection on directly comparable, application-relevant measurements rather than idealized catalog data.

Verification of newly designed magnetics

For custom magnetics, one-pulse testing provides rapid verification that the built inductor matches the expected inductance–current specification across the operating range. Deviations can indicate manufacturing variances such as incorrect gap, wrong number of turns, or unexpected material properties.

Pulse measurements can also be repeated after environmental stress, such as thermal cycling or aging, to monitor long-term stability of the magnetic characteristics. This contributes to more robust qualification of magnetics used in demanding applications like automotive and industrial drives.

Conclusion

Nonlinear behavior in magnetic cores fundamentally limits the accuracy of traditional sinusoidal and small-signal inductance measurements for power electronics design. The one-pulse nonlinear-inductor measurement method overcomes these limitations by directly exciting the inductor with application-relevant pulses and extracting incremental and secant inductance from the time-domain response.

By combining a simple, flexible test circuit with robust data processing, this approach yields high-fidelity inductance–current and energy characteristics suitable for both design and simulation workflows. As converter switching frequencies and power densities continue to rise, one-pulse characterization will remain a critical tool for engineers dealing with advanced core materials and tightly optimized inductors.

FAQ: One-Pulse Nonlinear Inductor Measurement