Current Sense Transformers: Ferrite vs Nanocrystalline Cores for Accurate Current Measurement

Current sense transformers are widely used to measure AC currents in power electronics, providing galvanic isolation and high bandwidth with minimal insertion loss. In precision applications, the choice of core material—ferrite or nanocrystalline—strongly influences accuracy, frequency response, and error mechanisms.

This article consolidates a two‑part video riddle by prof. Sam Ben-Yaakov and its solution into a direct engineerng white paper, focusing on how core permeability and transformer magnetizing inductance affect current measurement performance.

Principle of operation and basic model

A current sense transformer can be modeled as a single‑turn primary conductor passing through a toroidal core and a multi‑turn secondary winding loaded by a resistor $R_T$​. The primary current $I_\text{in}$​ induces a magnetic flux $\Phi$ in the core, which generates a secondary voltage and current according to Faraday’s law.

For an ideal current transformer with a one‑turn primary:

• The turns ratio defines the ideal secondary current: $I_\text{sec, ideal} = \frac{I_\text{in}}{N_S}$​​, where $N_S$​ is the number of secondary turns.
• The load resistor $R_T$​ converts the secondary current into a measurable voltage $V_\text{out} = I_\text{sec} \cdot R_T$.
• The magnetic flux density in the core is $B = \frac{\Phi}{A_E}$​, where $A_E$​ is the effective cross‑section area of the toroid.

In practice, a magnetizing inductance appears in parallel with the ideal secondary, representing the current needed to establish the flux in the core. This magnetizing current does not flow through the load and thus introduces a measurement error if it becomes comparable to the ideal secondary current.

In the equivalent circuit, this magnetizing inductance is modeled as a branch in parallel with the ideal secondary winding, and the parallel combination is then in series with the burden resistor R_T.

Number of secondary turns: does core material matter?

The first question posed in the riddle is whether the number of turns on the secondary must differ between a ferrite and a nanocrystalline core, assuming:

• Same toroidal physical dimensions.
• Same primary current waveform.
• Same secondary output voltage $V_\text{out}$.
• Sinusoidal operation at 100 kHz.
• Same peak flux density $B = 200 \,\text{mT}$.

Starting from Faraday’s law, the induced secondary voltage can be written as:

• $V_\text{out} = N_S \cdot \frac{d\Phi}{dt} = N_S \cdot A_E \cdot \frac{dB}{dt}$​.

Assuming a sinusoidal output voltage $V_\text{out}(t) = \hat{V}_\text{out} \cos(\omega t)$, the flux density is:

• $B(t) = \frac{\hat{V}_\text{out}}{N_S A_E \omega} \sin(\omega t)$, giving $\hat{B} = \frac{\hat{V}_\text{out}}{N_S A_E \omega}$​​.

Solving for the required number of turns:

• $N_S = \frac{\hat{V}_\text{out}}{\hat{B} \cdot A_E \cdot f \cdot 2\pi}$

Because $\hat{V}_\text{out}$​, $\hat{B}$, $A_E$​, and the frequency $f$ are stated to be identical for both transformers, $N_S$​ is necessarily identical as well. The turns count is set by flux density, geometry, frequency, and output voltage, not by the core material’s permeability.

Key takeaway: For a given geometry, operating frequency, target V_out, and allowed peak B_max, the required secondary turns are the same for ferrite and nanocrystalline cores. The core material affects magnetizing inductance and losses, but not the turns count in this constrained scenario.

Magnetizing inductance and permeability

The second and more important question is whether there is any performance advantage to using a nanocrystalline core instead of ferrite, ignoring cost. The answer hinges on how relative permeability influences magnetizing inductance.

The inductance of an inductor or transformer winding is:

• $L = \frac{N^2 \mu A_E}{l_m}$​​, where:
  • $N$ is the number of turns.
  • $\mu = \mu_0 \mu_r$​ is the absolute permeability.
  • $A_E$​ is the core cross‑section.
  • $l_m$ is the magnetic path length.

Typical relative permeability values for widely used power and current-sensing materials are as follows:

• MnZn ferrite: the relative permeability, μ_r, usually falls somewhere between about 1,000 and 10,000 at room temperature, with the exact value varying by material grade and operating frequency.
• Nanocrystalline (CT/EMI tape-wound ungapped cores): μ_r can typically be adjusted over a broad range, from roughly 1,000 to 80,000 or higher, while specially processed alloys with optimized heat treatment can exceed 100,000.

With the same core dimensions and the same number of turns, a significantly higher μ_r results in a substantially greater magnetizing inductance in the secondary winding. In the equivalent circuit of a current sense transformer, this inductance is represented as a branch connected in parallel with the load resistor on the secondary side.

Impact on measurement accuracy

In an ideal transformer, all secondary current would flow through $R_T$, providing $I_\text{sec, ideal} = \frac{I_\text{in}}{N_S}$​​. In reality, the secondary current splits:

• One branch is the magnetizing current flowing into the magnetizing inductance.
• The other branch is the useful output current through $R_T$

The output current is governed by a current divider:

• The fraction of current flowing into the load is determined by the ratio of the load impedance to the parallel combination of load impedance and magnetizing impedance.

To keep the measurement close to ideal, the magnetizing impedance $|Z_M|$ must be much larger than $R_T$:

• If $|Z_M| \gg R_T$​, nearly all current flows through the load.
• If $|Z_M|$ drops (for example at lower frequencies), the magnetizing branch steals current, causing measurement error.

Because nanocrystalline cores can have much higher permeability, their magnetizing inductance and thus $|Z_M|$ are significantly larger for the same turns and geometry. This reduces the magnetizing current and improves accuracy over a broad frequency range.

Key advantage: a nanocrystalline core with high permeability yields a larger magnetizing inductance, leading to smaller magnetizing current and more accurate current transformation in the given example.

Frequency response and low‑frequency behavior

The magnetizing inductance contributes an impedance that increases with frequency:

• $|Z_M| = 2\pi f L_M$​, where $L_M$ is the magnetizing inductance.

At lower frequencies, $|Z_M|$ decreases. If it becomes comparable to $R_T$​, significant current flows into the magnetizing branch instead of the load, degrading accuracy. For a given secondary turns count:

• Higher $L_M$​ (via higher permeability) pushes the low‑frequency cutoff down, maintaining $|Z_M| \gg R_T$​ across a wider frequency range.
• This makes the current sense transformer less sensitive to frequency variations, such as operating below the nominal 100 kHz.

In the scenario described in the video, using a nanocrystalline core improves accuracy not just at the nominal frequency, but also helps maintain acceptable performance if the frequency drops, as the magnetizing impedance remains significantly larger than the load impedance.

Core material comparison: ferrite vs nanocrystalline

The following table summarizes the characteristics relevant to current sense transformers in the context of the example:

Parameter / aspect	Ferrite core	Nanocrystalline core
Typical relative permeability	Approximately 1,000–10,000 for MnZn power grades	Approximately 1,000–80,000+, up to >100,000 for CT/EMI grades
Magnetizing inductance (same N, geometry)	Lower LM, lower	ZM
Magnetizing current magnitude	Higher; more current diverted away from the load	Lower; less current diverted away from the load
Measurement accuracy (given example)	Lower accuracy due to larger magnetizing current	Higher accuracy, closer to ideal turns‑ratio behavior
Sensitivity to frequency drop	More sensitive;	ZM
Cost (not considered in performance comparison)	Lower material cost	Higher than ferrite but often lower than permalloy for CTs

These entries reflect typical qualitative ranges and relationships from core manufacturer datasheets and the referenced videos, not guaranteed values for any specific part number; designers must always verify exact figures against the chosen core’s datasheet.

Design‑in notes for engineers

Selecting turns and output resistor

Because the number of secondary turns is dictated by $B_\text{max}$​, geometry, frequency, and target output voltage, the designer should first choose:

• A safe peak flux density $B_\text{max}$​ according to the core datasheet.
• Operating frequency range and target $V_\text{out}$.
• The toroidal size and $A_E$.

Then apply:

• $N_S = \frac{\hat{V}_\text{out}}{\hat{B} \cdot A_E \cdot f \cdot 2\pi}$

Once $N_S$​ is fixed, $R_T$​ can be chosen such that:

• $V_\text{out} = \frac{I_\text{in}}{N_S} R_T$​ stays within the input range of the measurement circuitry.
• The power dissipation $P_{R_T} = I_\text{sec}^2 R_T$​ remains manageable.

In this procedure, the core material does not change the turns count in the constrained case where $B_\text{max}$​, geometry, frequency, and $V_\text{out}$​ are fixed.

Ensuring high magnetizing impedance

To minimize measurement error:

• Use a core material with high relative permeability to maximize $L_M$.
• Keep $|Z_M| = 2\pi f L_M$​ much larger than $R_T$​ across the intended frequency range.
• Avoid unnecessarily large $R_T$​, which would make the magnetizing branch more competitive in the current divider.

A nanocrystalline core with very high permeability is beneficial in this respect, as it keeps magnetizing current small relative to the useful secondary current.

Practical accuracy considerations

Even with high‑permeability cores, some non‑idealities remain:

• Core loss and hysteresis: cause phase shifts and minor errors between current and voltage, which must be assessed from manufacturer data.
• Saturation behavior: limits the maximum measurable current before linearity breaks down; specific limits should always be taken from the datasheet for the chosen core material and geometry.
• Frequency‑dependent losses: influence bandwidth and accuracy in applications with wide‑band current waveforms.

For critical measurements (e.g., protection or regulatory compliance), the exact flux density and saturation margin should be verified against core datasheet specifications rather than assumed.

Typical applications

Current sense transformers with ferrite or nanocrystalline cores are found in:

• Primary or secondary side current measurement in switching power supplies and DC‑DC converters.
• Over‑current protection and control loops in converters operating around 100 kHz or higher.
• Differential current measurement in isolated gate driver supplies and high‑side current sensing.

In applications where accuracy over a wide frequency range and low error due to magnetizing current are important, nanocrystalline cores are attractive despite their higher cost. For less critical sensing or where bandwidth requirements are moderate, ferrite cores may be adequate and more economical.

Conclusion

What engineers should take away

For a current sense transformer built on toroidal cores of identical geometry, operating at a given frequency with specified peak flux density and output voltage, the required secondary turns are the same regardless of whether the core material is ferrite or nanocrystalline. The turns count is determined by Faraday’s law and geometric parameters, not the permeability.

The decisive performance difference lies in the magnetizing inductance: nanocrystalline cores with very high permeability provide a much larger magnetizing impedance, resulting in lower magnetizing current and more accurate current transformation. This advantage also makes the transformer less sensitive to frequency reductions, helping maintain $|Z_M| \gg R_T$​ and keeping the measurement close to the ideal turns ratio behavior.

Design engineers should therefore treat core selection for current sense transformers as a trade‑off: ferrite offers lower cost, while nanocrystalline offers higher permeability and better accuracy when the magnetizing current needs to be minimized. Specific saturation limits, loss behavior, and detailed performance must always be confirmed from the manufacturer datasheet for the chosen core material and core size.

Source

This article is based on the technical explanation and worked solution presented in the original YouTube riddle and its follow‑up answer on current sense transformers and core material choice, interpreted for design engineers and purchasing professionals.

FAQ:

References

1. Current sense transformer riddle
2. Answer to: Current sense transformer riddle