PCB Windings: Precision Planar Coils

Updated 14 July 2026

PCB windings are planar, lithographically defined inductive structures that replace traditional wire coils with precisely etched copper traces.
Their performance is driven by explicit geometric design, enabling advanced harmonic cancellation, high calibration repeatability, and improved sensitivity in various applications.
Applications span from high-precision rotating-coil probes and inductive position sensors to coreless transformers and micro axial-flux motors, each benefiting from optimized PCB layouts.

Searching arXiv for recent and foundational papers on PCB windings and closely related implementations. Printed-circuit-board (PCB) windings are coils, pickup loops, and related inductive structures implemented as planar etched traces on PCB layers rather than as hand-wound wire. Their defining technical feature is that conductor position, spacing, and relative geometry are set lithographically, which makes winding behavior strongly geometry-driven and, in many applications, analytically tractable. In the arXiv literature, PCB windings appear in magnetic-field-confining coils, rotating-coil probes for accelerator magnets, long curved search coils for rapid-cycling magnets, MHz inductive position sensors, coreless transformers, and micro-scale axial-flux motors. One early example reported a magnetic field confining coil “entirely made out of printed circuit boards (PCBs)” with sub- $10^{-3}$ field uniformity over a large fraction of the coil, measured with cesium magnetometers in a field range from $1$ to $10~\mu\mathrm{T}$ (Koss et al., 2017).

1. Fabrication concept and physical embodiments

The common construction principle is the replacement of mechanically placed turns by photolithographically defined copper traces. In rotating-coil field sensors, the windings are implemented as planar etched traces on PCB layers, with straight and parallel active segments extending along the magnet axis. The cited rotating PCB coil work states that wire placement precision on PCB is “at least an order of magnitude better than that of careful machining,” reports trace-width measurements around 50 μm with microscope repeatability of 1–2 μm, and notes that along long boards width may vary by about 5 μm on 50 μm traces. The same paper focuses on rigid multilayer PCB technology because it is commercially available and reliable for miniaturized boards, trace width ≈ 50 μm, trace thickness below 10 μm, trace-to-trace spacing ≈ 50 μm, and board lengths > 1 m (DiMarco et al., 2019).

Physical implementations vary by application. In the rotating-coil literature, one experimental probe used a 1.02 m long PCB, with 10 layers, and 9 turns per loop, mounted in a cylindrical rotating support. In accelerator search-coil work, a stationary curved flat-coil was assembled from 6 PCB segments, each 535 mm-long curved PCB, to form a 3.2 m probe; each segment carried 15 windings, each winding consisting of 1 pair of traces, with 3.5 mm width and 7.0 mm center spacing across a sampled aperture of 101.5 mm (DiMarco et al., 2019, DiMarco et al., 16 Sep 2025).

Other implementations show the same planar principle under very different electrical regimes. An inductive automotive position sensor used a 4-layer PCB, with the bottom two layers carrying the coil system and the top side carrying ASIC, passives, and connector; a demonstrated sample had two receiver coils, three windings each in series, and a periodicity of $p=5$ (Kuntz et al., 18 Mar 2025). A coreless PCB transformer for a 2 MHz active-clamp forward converter used a 2-layer arrangement with the primary winding on the top copper layer and the secondary on the bottom, both concentrically aligned, with $N_p/N_s = 23/23$ , inner radius 2 mm, outer radius 25 mm, trace width 0.635 mm, trace separation 0.47 mm, copper thickness 35 μm, and board thickness 1.6 mm (Ghaderloo et al., 2023). At smaller scale, a micro axial-flux permanent-magnet motor used a 48-layer stator formed from four 12-layer HDI modules, reported a 45% copper fill factor, and packaged the winding in a motor of 19 mm outer diameter (Wang et al., 28 Sep 2025).

2. Electromagnetic description and harmonic engineering

A recurring theme in the literature is that PCB winding performance is determined by explicit conductor geometry. For rotating coils, the harmonic sensitivity is written as a sum over wire coordinates,

$K_n = \sum_{j=1}^{\text{wires}} \frac{L}{R}\left(\frac{x_j+i y_j}{R}\right)^{n-1}(-1)^j,$

so harmonic cancellation becomes a layout problem: choose conductor positions and signs such that selected $K_n$ vanish. In this language, dipole bucking means $K_1=0$ , quadrupole bucking means $K_2=0$ , and sextupole bucking means $K_3=0$ (DiMarco, 2024).

For a simple radial loop of width $1$0, inner radius $1$1, and length $1$2, the dipole sensitivity is

$1$3

which is independent of radius, whereas higher-order sensitivities depend on radial placement. This is the basis of the dipole-bucked (DB) winding: place a second identical loop at a radial displacement $1$4, connect the two in opposition, and the dipole term cancels exactly while the quadrupole term remains. The same logic extends to dipole-quadrupole-bucked (DQB) windings and, in sextupole probes, to dipole-quadrupole-sextupole-bucked (DQSBuck) windings (DiMarco et al., 2019, DiMarco, 2024).

The sextupole rotating-coil paper by J. DiMarco makes this design rule explicit in compact grouped layouts. For grouped conductors with flanking widths $1$5, central width $1$6, and turn multiplicities $1$7 and $1$8, quadrupole bucking is obtained when

$1$9

The paper emphasizes that this condition is independent of lateral placement parameters, which permits compact and interleaved realizations. Two DQBuck circuits of opposite polarity can then be stacked or interleaved so that dipole, quadrupole, and sextupole responses are simultaneously suppressed on each layer (DiMarco, 2024).

In stationary flat-coil probes, the same geometry-to-signal relation appears in a different form. The Fermilab curved probe reconstructs $10~\mu\mathrm{T}$ 0 by fitting the simultaneous fluxes of 15 adjacent loops: $10~\mu\mathrm{T}$ 1 with geometry coefficients

$10~\mu\mathrm{T}$ 2

Here again, the usefulness of PCB windings lies in the fact that $10~\mu\mathrm{T}$ 3 and $10~\mu\mathrm{T}$ 4 are fixed and knowable from the lithographic layout (DiMarco et al., 16 Sep 2025).

Inductive position sensors adopt the same geometry-first logic at MHz carrier frequency. The PCB transmitter coil excites a conductive rotor target, the receiver coils detect target-modulated coupling, and the demodulated outputs encode angle in quadrature: $10~\mu\mathrm{T}$ 5 For the sample sensor, $10~\mu\mathrm{T}$ 6, so the second receiver coil is rotated mechanically by $10~\mu\mathrm{T}$ 7 relative to the first (Kuntz et al., 18 Mar 2025).

3. Rotating-coil probes, field confinement, and self-calibration

PCB windings have been used most extensively in precision magnetic measurement, where geometric reproducibility directly affects harmonic accuracy. In rotating probes, lithographically matched loops at different radii enable unbucked (UB), dipole-bucked (DB), and dipole-quadrupole-bucked (DQB) circuits on the same board. The principal advantage is that calibration no longer has to determine all wire positions individually: it reduces to the rigid-body displacement of the PCB relative to the rotation axis, described by a horizontal/radial offset $10~\mu\mathrm{T}$ 8 and a vertical/transverse offset $10~\mu\mathrm{T}$ 9 (DiMarco et al., 2019).

The dynamic calibration method for rotating PCB probes exploits the fact that, in a quadrupole main field, the DB winding’s quadrupole measurement is essentially insensitive to both $p=5$ 0 and $p=5$ 1, whereas the UB winding is sensitive to both. Amplitude comparison identifies mainly the radial position, while phase comparison identifies mainly the transverse offset. Experimentally, the calibration found PCB position with repeatability better than 1 μm in both horizontal and vertical directions over repeated rotations; the average shift caused by shimming agreed closely between dynamic calibration and coordinate measuring machine data, with an average discrepancy of about 6 μm. In the same work, the quadrupole field strength measured by the DB PCB winding was 1.5847 T·m/m with standard deviation of the mean about 0.00012, compared with a stretched-wire reference of 1.5850 T·m/m, and the effective dipole bucking of the DB signal was about 560 (DiMarco et al., 2019).

The sextupole-probe literature extends this philosophy by insisting that each PCB layer independently provide DQS bucking. That avoids relying on interlayer registration for cancellation and lets multilayer stacks increase signal rather than compensate stacking errors. Two concrete examples are a 14-layer, 22.7 mm diameter probe for APSU and a 16-layer, 12 mm diameter probe for the NSLS-II upgrade. In tests with a translatable BNL quadrupole magnet over a 270 mm active length, the probe’s radial and transverse offset uniformity were both on the order of 10 microns along the length, and the DQS bucking ratio was above 100 at all positions and all tested rotation speeds (DiMarco, 2024).

A distinct measurement use is static field generation rather than flux pickup. The PCB confining-coil paper reported a field-confining coil entirely made from PCBs with sub- $p=5$ 2 field uniformity over a large fraction of the coil, measured with cesium magnetometers from 1 to 10 μT, for use in an atomic magnetometry-based current controller (Koss et al., 2017).

4. Representative application domains

PCB windings span several technical regimes, from low-frequency field metrology to MHz sensing and power conversion.

Domain	Representative winding architecture	Reported result
Rotating magnetic measurement	Multilayer radial PCB loops with UB, DB, DQB, or DQSBuck circuits	Repeatability better than 1 μm; DQS bucking ratio above 100
Rapid-cycling accelerator magnets	3.2 m curved flat-coil from 6 PCB segments, 15 windings per segment	Field resolution better than 0.01%
Inductive position sensing	Outer TX coil with inner differential RX coils on 4-layer PCB	Mechanical angle error less than 0.02° measured
Coreless transformer	Top/bottom concentric PCB spirals, 23/23 turns	Transfer magnitude about 0.72 below about 6.5 MHz
Micro axial-flux motor	48-layer HDI PCB stator from four 12-layer modules	45% copper fill in 19 mm diameter package

In accelerator instrumentation, the Fermilab rapid-cycling Booster study developed a curved PCB search coil specifically to measure integral, body, and end fields during the AC cycle. The main probe was 3.2 m long, sampled about 100 mm of aperture with 15 simultaneous windings, used 24-bit simultaneous acquisition at 200 kHz, and reported field strength and uniformity measurements with 0.01% resolution and inter-calibration of inductive pickup loops at less than 0.5 µm level. At 15 Hz and 20 Hz, the reported hysteresis and field residual profile were very similar (DiMarco et al., 16 Sep 2025).

In automotive-oriented inductive sensing, PCB windings form a coupled-coil eddy-current transducer rather than a flux pickup loop. The transmitter operates in the 3 MHz to 5 MHz range and surrounds the receiver coils and target. The receiver structures are differential, their enclosed areas alternate surface-normal orientation, and target modulation produces approximately sinusoidal quadrature channels. The demonstrated sample sensor, with two receiver coils, three windings each in series, and a 4-layer PCB, exhibited mechanical angle error below 0.02° in measurement and below 0.01° in FEM, while remaining robust against magnetic stray fields exceeding 4000 A/m (Kuntz et al., 18 Mar 2025).

In isolated power conversion, the coreless transformer paper shows PCB windings in a regime where low profile and elimination of magnetic-core loss are prioritized. The transformer used concentric planar windings on the top and bottom PCB layers, with equivalent parameters

$p=5$ 3

$p=5$ 4

$p=5$ 5

Its transfer-function magnitude was approximately 0.72 below about 6.5 MHz, and the transformer/converter study reported efficiencies of 72%, 79%, 88%, and 92% at 1.1, 1.4, 1.9, and 2.5 MHz, while also noting that overall converter efficiency does not necessarily continue improving above 1.9 MHz because of output-diode losses, AC resistance of the coreless transformer, and PCB-track losses (Ghaderloo et al., 2023).

In miniature electromechanics, the micro axial-flux motor uses PCB windings to address the copper-fill bottleneck of sub-20 mm machines. The winding stack comprises 48 single PCB layers formed from four 12-layer HDI modules, reports 45% copper fill, and achieves a terminal resistance of 4.70 Ω, terminal inductance of 3 mH, torque constant of 32.0 mNm/A, continuous stall torque of 23.4 mNm, and maximum efficiency of 60%. Back-EMF at 3000 rpm was simulated at 9.97 V peak and measured at approximately 9.48 V peak (Wang et al., 28 Sep 2025).

5. Design rules, trade-offs, and dominant error sources

A consistent design rule across the rotating-coil papers is that cancellation should be achieved within each etched layer plane. The reason is explicit: trace placement is most accurate within a layer, whereas stacking accuracy between layers is worse. Both the calibration paper and the sextupole-probe paper therefore favor per-layer self-bucking layouts, so the multilayer stack inherits bucking even if layer-to-layer spacing or alignment is imperfect (DiMarco et al., 2019, DiMarco, 2024).

Several layout heuristics recur. The sextupole-probe paper recommends fixed grid spacing because it is easier for designers, less susceptible to round-off errors, and less likely to inadvertently shift traces. It also reports that using around 70% of probe diameter for traces is typical for optimal sensitivities, while a comparative sensitivity example used 78% of the probe diameter. Among the DQSBuck topologies considered, the interleaved compact DQBuck combination gave the best sensitivity for available radial space (DiMarco, 2024).

Application-specific trade-offs are equally clear. In the curved flat-coil probe, the dominant calibration issue for the long probe was loop-width variation of about 3 units, corresponding to about 1 µm in winding width, whereas the short translating probe could show area variation among windings as large as 15 units when the soldered end connections sat inside magnetic field, corresponding to about 0.75 mm in effective length variation. As the short probe moved into lower field, the calibration returned to the integral-probe regime where width error dominated (DiMarco et al., 16 Sep 2025).

In MHz inductive position sensors, transmitter-turn count is an explicit trade-off. The paper gives

$p=5$ 6

and under constant-voltage resonant excitation

$p=5$ 7

so the effective excitation field and receiver signal scale roughly as $p=5$ 8. More turns reduce ASIC drive burden; fewer turns increase field and receiver amplitude. The same paper notes that copper resistance has temperature coefficient about 0.393%/K, so $p=5$ 9 is about 40% larger at $N_p/N_s = 23/23$ 0 than at room temperature (Kuntz et al., 18 Mar 2025).

In coreless PCB transformers, the major penalties are low magnetizing inductance, high leakage, interwinding capacitance, and thin-copper AC loss. The cited transformer had $N_p/N_s = 23/23$ 1, leakage inductance 3.9 μH, interwinding capacitance 16 pF, and per-side resistance 1.27 Ω. In the motor domain, improved copper fill does not eliminate thermal limitation: with an 8 W thermal load, the axial-flux PCB motor reached 143°C in simulation and 148°C in measurement, despite insulation and magnet thermal ratings of 200°C and 180°C (Ghaderloo et al., 2023, Wang et al., 28 Sep 2025).

A common misconception is that PCB windings are simply wound-wire coils reproduced in copper artwork. The rotating-coil calibration paper explicitly rejects that reduction: its key innovation is the use of photolithographically defined, radially separated, equal-area planar loops to create UB, DB, and DQB winding functions with analytically known harmonic sensitivities and strong lower-order suppression. The sextupole-probe paper frames the same idea more generally: PCB windings are fundamentally a precision conductor-placement technology, and harmonic suppression is a geometric problem encoded in conductor coordinates and signs (DiMarco et al., 2019, DiMarco, 2024).

At the same time, not every multilayer printed conductor architecture is a winding in the usual electrical-machine or sensor sense. The metasurface paper on multilayered PCB cascades is a useful limiting case: it uses three patterned metal layers separated by dielectrics, but “no vias,” “no spirals,” “no conventional wound coils,” and “no true loop resonators” in the demonstrated designs. Its meander lines are the closest geometry to a winding-like trace, yet the paper’s deeper point is different: stacked printed conductors can collectively emulate tangential and normal susceptibilities through multiple reflections and interlayer coupling rather than through literal turns (Shaham et al., 2024).

This suggests a useful boundary for the term. PCB windings, in the strict sense represented by the magnetic-measurement, sensor, transformer, and motor papers, are printed conductor paths intended to realize coil area, flux linkage, mutual coupling, or ampere-turn production directly. A plausible implication is that they belong to a broader family of multilayer PCB current-path architectures, but their distinguishing property remains the explicit encoding of inductive function in lithographically controlled conductor geometry (Shaham et al., 2024).