In‑Circuit Inductor & Transformer Testing for Switch‑Mode Power Supplies

by Wilson Lee, Technical Marketing Manager at Tektronix.

Inductors and transformers are the backbone of switch‑mode power supplies (SMPS). To guarantee reliable operation, their performance must be verified in‑circuit under real operating conditions.

While component datasheets and simulation models guide the design, parasitic effects, temperature swings, and signal variations often shift the actual behavior. This article walks through the fundamentals and practical steps for measuring inductors and transformers directly in a running SMPS, using modern oscilloscopes, probes, and B‑H curve analysis.

Inductor Theory

Faraday’s and Lenz’s laws describe the relationship between the current through an inductor and the voltage across it:

Rearranging and integrating gives:

In practice, you can extract the inductance by recording the voltage and current waveforms with an oscilloscope that supports differential voltage probes, current probes, and X‑vs‑Y plotting. This time‑domain approach captures the true inductance under the actual signal shape, amplitude, and frequency present in the supply.

Real inductors exhibit a dependence on current, temperature, and frequency, so their value can drift during operation.

Figure 1. A basic inductor consists of a coil wound on a ferromagnetic core. The current I (A) flows through N turns, and the inductance describes how that current induces magnetic flux.

For example, the inductance of a toroid can be approximated by:

where µ is the core permeability (H/m), N the number of turns, r the core radius (cm), and A the cross‑sectional area (cm²). Because N² dominates, the number of turns is the biggest lever for inductance. Selecting a core with high µ allows a smaller physical size and lower loss.

Core material and geometry therefore dictate inductance across all operating points and the resulting power loss.

Inductance Measurements

Designers normally verify inductance with an LCR meter after manufacturing. LCR meters excite the component with a narrow‑band sinusoid, which is adequate for a quick sanity check but not predictive of in‑circuit performance. In a SMPS, the excitation is typically a high‑frequency, non‑sinusoidal pulse, so in‑circuit measurement is essential.

To measure inductance in‑circuit, connect a differential voltage probe across the winding and a current probe to the same winding. The oscilloscope’s power‑analysis software integrates the voltage over time and divides by the current change, automatically removing DC offsets and averaging over many cycles.

When measuring a transformer, avoid loading the secondary. Measure the primary inductance under no‑load to obtain the magnetizing inductance; loading the secondary will alter the effective inductance due to mutual coupling.

Figure 2. The average inductance (H) is obtained from the slope of current (CH2) versus the integrated voltage (CH1).

Figure 3. The I vs ∫V plot also reveals any DC bias that accumulates over cycles.

B‑H Curve Measurements

Magnetic components in a SMPS must operate in the linear region of their hysteresis loop to avoid saturation and excessive loss. However, operating conditions can vary with load changes, temperature, and startup transients, making design‑time prediction difficult.

B‑H curves, supplied by many core manufacturers, illustrate the relationship between magnetizing force H (A/m) and flux density B (T). They reveal key parameters:

• Permeability (µ) – the slope of the B‑H curve, indicating how efficiently the core converts H into B.
• Saturation flux density – the point where additional H no longer increases B.
• Hysteresis characteristics – the width of the loop, which correlates with core loss. Soft magnetic materials minimize remanence (Br) and coercive force (Hc).

Indicators of instability include a peak B approaching the saturation limit or a B‑H loop that shifts between cycles.

An oscilloscope can generate a B‑H plot by measuring the voltage across and current through the winding, then computing B and H from:

B = (1 / (µ₀·N·A)) · ∫V dt  H = I / (l)

where l is the magnetic path length. The scope’s analysis software automates this calculation.

Figure 4. Magnetic measurements on a transformer with multiple secondary windings. The orange waveform is the combined current when secondary windings are excited.

B‑H Curves for Transformers

When a transformer is loaded, part of the primary current feeds the secondary. To isolate the magnetizing current, model the transformer with an imaginary inductor, Lₘ, in parallel with the primary. Lₘ represents the core’s magnetic behavior and carries the magnetizing current only.

Figure 5. Equivalent circuit showing the magnetizing inductor Lₘ in parallel with the primary.

Loss Analysis

Magnetic losses dominate the efficiency budget of a SMPS. Core loss, comprising hysteresis and eddy‑current loss, depends on flux density and frequency, while copper loss arises from winding resistance.

The Steinmetz empirical formula estimates core loss:

where k, a, and b are material constants supplied by the core manufacturer. Datasheets often provide loss values for sinusoidal excitation, but in a SMPS the excitation is non‑sinusoidal, so on‑the‑fly measurement is preferable.

Figure 6. The scope’s power‑analysis feature averages the product v(t) × i(t) to yield the total magnetic loss, which includes both copper and core loss. Subtracting the manufacturer’s core loss yields the copper loss.

Scopes can perform this calculation for single‑winding inductors, multi‑winding inductors, or transformers. For a transformer, a differential probe on the primary and a current probe on the primary (and secondary if needed) feed the software, which then outputs the loss in watts.

In summary, inductors and transformers are critical to SMPS performance—filtering, isolation, energy storage, and timing. Accurate in‑circuit measurement using modern oscilloscopes and power‑analysis software ensures that these components meet their design specifications and operate reliably under all conditions.