Structure-Aware Design of a Partially Overlapped Segmented Transmitter with a Position-Dependent Excitation Strategy for Automotive Power-Seat Wireless Power Transfer Under Wide Misalignment

Abstract

Wireless power transfer (WPT) can eliminate moving power-supply harnesses in automotive power-seat systems, but seat travel and nearby metallic structures cause substantial variations in magnetic coupling and electromagnetic loss. This paper proposes a structure-aware, partially overlapped segmented transmitter and evaluates two predefined excitation states according to receiver position. In the single-segment state, only the reference segment CP1 is energized; in the simultaneous dual-segment state, CP1 and the adjacent segment CP2 are energized together. Three-dimensional finite element method (FEM) simulations compare candidate transmitter structures and evaluate the electromagnetic influence of the aluminum lower rail, steel upper rail, and steel seat frame. The transmitter geometry is determined by considering mutual inductance, winding loss, structural eddy-current loss, and partial-overlap characteristics. A three-coil equivalent circuit clarifies the branch-current distribution, and a two-state switched-capacitor network accommodates the different equivalent transmitter impedances. A 100 W, 110 kHz prototype separately evaluates representative states at x = 0 and 80 mm; automatic position-based state switching is not implemented. At x = 0 mm, CP1-only excitation achieves 78.79% efficiency. At x = 80 mm, CP1 + CP2 excitation produces 32.13 V and 72.15%, compared with 18.78 V and 67.84% under CP1-only excitation, thereby satisfying the 30 V minimum output requirement.

1. Introduction

As vehicle electrification and autonomous-driving technologies advance, automotive seats are increasingly required to accommodate electrical loads such as heating, ventilation, and massage systems in addition to conventional position-adjustment actuators. These loads are typically supplied through wiring harnesses connected to the vehicle power source. However, repeated forward–backward movement and rotation of the seat subject the wiring to continuous bending and friction. This can cause insulation abrasion, mechanical fatigue, and conductor failure over long-term operation. Wiring harnesses also restrict the available range of seat motion, complicate mechanical design, and require dedicated routing space.

Wireless power transfer (WPT) provides an alternative means of supplying power between a stationary vehicle structure and a movable seat assembly without direct electrical contact. Recent reviews have summarized EV-oriented WPT technologies, including inductive couplers, compensation networks, misalignment, control, and safety considerations [1,2]. Capacitive WPT has also been reviewed as a complementary approach with distinct coupler, electric-field, and compensation-network requirements [3,4]. The present study focuses on magnetically coupled inductive power transfer (IPT) for an automotive power seat.

An early vehicle-seat-related study transferred power through a military vehicle seat to electronic equipment carried by the occupant, demonstrating the feasibility of WPT around a vehicle seat [5]. However, that system was intended for power transfer through a stationary seat and did not address the wide rail-direction displacement required for a movable automotive power seat. More recently, an automotive power-seat WPT system was proposed in which the transmitter and receiver coils were embedded within the seat rail and the magnetic-core structure was optimized to reduce leakage magnetic fields [6]. Because the magnetic coupler was installed inside the rail, that approach requires a rail structure capable of accommodating the coils and magnetic cores. In contrast, the present study considers repeated transmitter segments installed alongside the rail without requiring modification of the internal rail structure.

Automotive power-seat WPT systems are subject to design constraints that differ from those of conventional stationary charging systems. The receiver pad must fit within the limited space among the seat frame, actuator motors, rails, and brackets. In addition, the transmitter and receiver are positioned close to aluminum and steel structures. These structures alter the magnetic-flux distribution, inductance, ac resistance, and electromagnetic loss. Because the receiver travels along a rail that is considerably longer than the pad dimensions, a single fixed transmitter cannot readily maintain favorable coupling over the entire travel range. Furthermore, because the magnetic coupler is located directly beneath the seat, the stray magnetic field toward the occupant-side region is also an important design consideration. Consequently, the magnetic-coupler geometry, surrounding metallic structures, transmitter segmentation, position-dependent operating condition, and occupant-side field distribution should be considered within an integrated design procedure.

Various magnetic couplers, including circular pads (CPs), double-D pads (DDPs), and bipolar pads (BPPs), have been investigated to improve coupling and misalignment tolerance. A CP has a simple geometry and provides strong coupling under aligned conditions, but its coupling decreases considerably with horizontal misalignment [7]. A DDP produces a directional bipolar magnetic field and can provide improved lateral tolerance when paired with a compatible polarized receiver [8]. In the present application, however, the receiver is constrained to a compact, non-polarized CP because of the limited installation space beneath the seat. Accordingly, adjacent D-shaped transmitter coils are considered only as a comparison configuration for evaluating their interaction with the selected CP receiver.

A commonly reported BPP configuration employs multiple constituent coils whose current magnitudes and relative phases can be controlled to synthesize different magnetic-field distributions [1,9,10]. The transmitter investigated in this study differs from such conventional BPP couplers. Rather than employing a physically separate bipolar pad, it is constructed from repeated CP segments with intentional partial overlap. The electromagnetic interaction between adjacent segments is therefore explicitly considered as part of the transmitter design.

Segmented transmitter tracks and selectively energized transmitter arrays provide another approach for supplying power over a long travel path. Segmented IPT tracks have been investigated for continuous power delivery to moving loads [11], while selective activation of multiple transmitter coils according to receiver position has been proposed to reduce unnecessary excitation and leakage magnetic fields [12]. The spacing between adjacent transmitters is an important design parameter because it affects both intersegment interaction and magnetic-field coverage [1]. Overlapping transmitter arrays have also been investigated to increase magnetic-field coverage and reduce weak-field regions for moving receivers [13]. Pahlavan et al. used overlapped resonators to improve field uniformity and reduce blank spots for a freely moving receiver [13]. They subsequently proposed star-shaped overlapping transmitter coils to improve receiver-rotation tolerance [14]. These studies primarily addressed planar free motion or receiver rotation rather than the one-dimensional transition of a compact CP receiver between repeated transmitter segments in a metallic automotive seat environment.

Table 1. Quantitative comparison of representative related WPT studies and this work.

Study and Application	Reported Result	Relation to This Work
[5] Stationary military-seat WPT	Feasibility demonstrated; no rail-position sweep reported	Seat WPT; fixed, non-segmented configuration
[6] Rail-embedded automotive power-seat coupler	70 W; 80% overall efficiency; up to 90% leakage-field reduction	Inside-rail installation; no external overlapping segments
[12] Position-selective multiple-transmitter WPT	300 W class; about 53% magnetic-field reduction	Selective activation; non-seat and non-overlapped rail geometry
[13] 50%-overlapped array for a freely moving receiver	Maximum power variation: 10% (approximately 50% without overlap)	Planar free-motion coverage; not a compact seat-rail transition
This work: rail-adjacent partially overlapped segments	100 W, 110 kHz; dc-to-dc efficiency: 78.79% at x = 0 mm under single-segment excitation and 72.15% at x = 80 mm under dual-segment excitation	Seat-metal FEM; predefined single-/dual-segment states

summarizes the quantitative scope of the most directly related seat, segmented-transmitter, selective-activation, and overlapped-array studies. The comparison distinguishes their reported objectives from the rail-adjacent, metallic-seat, and predefined two-state evaluation considered here.

Surrounding metallic structures further complicate the design of such a segmented transmitter. Eddy currents induced in conductive vehicle structures generate additional loss and alter the leakage-field distribution. Their magnitude depends on material properties, geometry, pad-to-structure distance, operating frequency, and coil-current condition [15]. The transmitter geometry therefore cannot be selected solely from the coupling coefficient of an isolated magnetic coupler. Moreover, receiver displacement changes the transmitter–receiver mutual inductance and consequently the coil-current condition. Winding loss, ferrite-core loss, and structural eddy-current loss can therefore exhibit different position dependencies for different excitation states. A position-dependent electromagnetic-loss assessment provides an important design basis for comparing single- and dual-segment excitation as the receiver moves along the rail.

The electrical operating condition also changes when the number of active transmitter segments is altered. Variations in mutual inductance modify the receiver-reflected impedance. Simultaneous excitation of two adjacent segments additionally introduces intersegment coupling and changes the equivalent transmitter inductance. The power-transfer capability, reflected impedance, and zero-phase-angle characteristics of IPT compensation networks have been extensively investigated [16]. Switched-capacitor techniques have also been proposed to adapt compensation parameters when coupling or coil configurations vary [17]. In the present work, reconfigurable compensation is therefore used as an enabling technique rather than as the primary contribution. Two predetermined transmitter-side capacitance states are employed for the evaluated single- and dual-segment excitation conditions.

Despite these advances, several issues remain insufficiently addressed for automotive power-seat WPT. First, conventional segmented-transmitter studies establish the usefulness of selective transmitter activation. However, they do not directly address the transition between intentionally partially overlapped segments under the restricted installation constraints of a power-seat rail. Second, conventional BPP and overlapping-array studies demonstrate multi-coil field shaping and improved spatial coverage. Their magnetic structures and operating objectives differ from those of repeated CP segments coupled to a compact non-polarized CP receiver. Third, a segmented transmitter installed close to aluminum and steel seat structures requires simultaneous consideration of coupling transition, branch-current distribution, position-dependent electromagnetic loss, compensation condition, and occupant-side stray magnetic field. These coupled design aspects motivate a structure- and position-aware design procedure, rather than independent consideration of the magnetic coupler and resonant circuit.

Accordingly, this study investigates a partially overlapped segmented transmitter composed of repeated CP segments. Near the center of a reference segment, only that segment is energized, which is referred to as single-segment excitation. In the transition region, the adjacent segment is simultaneously energized, which is referred to as dual-segment excitation. The dual-segment state modifies the magnetic-field distribution through the simultaneous excitation of two adjacent CP segments while remaining an operating state of the same segmented transmitter. The two adjacent transmitter segments considered in the quantitative analysis are denoted CP1 and CP2. The comparison therefore focuses on CP1-only and CP1 + CP2 excitation as the receiver moves from the CP1 center toward CP2. The position-dependent strategy is analyzed theoretically and through FEM, while representative excitation and compensation states are experimentally evaluated. The prototype evaluates predefined excitation and compensation states; real-time position-based switching and continuous-transition testing are outside the present scope.

The main contributions of this study are summarized as follows:

• Candidate transmitter structures are evaluated under the constrained CP-receiver condition, and a partially overlapped architecture is established for the local intersegment transition representative of repeated rail-direction coverage; the effects of segment dimensions and partial overlap are considered in establishing the transmitter geometry;
• A structure-aware three-dimensional finite element method (FEM) model incorporating the aluminum lower rail, steel upper rail, and steel seat frame is used to assess magnetic coupling, winding loss, ferrite-core loss, structural eddy-current loss, and occupant-side stray magnetic-field characteristics;
• Under a common electrical reference condition, position-dependent coupling, fundamental coil currents, and electromagnetic-loss characteristics of the single- and dual-segment states are evaluated, and a three-coil equivalent-circuit model is used to characterize the branch-current distribution during dual-segment excitation; and
• A two-state transmitter-side compensation network accommodates the different equivalent transmitter conditions, and representative operating states are experimentally evaluated using a 100 W, 110 kHz prototype.

This paper substantially extends the authors’ previous conference study [18], which focused primarily on magnetic-parameter variations and structural eddy-current losses using simplified aluminum and steel plate models. The present study further considers the segmented-transmitter architecture, seat-structure-based geometry design, partial-overlap characteristics, position-dependent single- and dual-segment excitation, coupled branch-current behavior, reconfigurable compensation, and representative prototype validation.

2. System Requirements and Evaluation Criteria

2.1. Installation Environment and Design Constraints

Figure 1 shows the conceptual installation environment of the automotive power-seat WPT system. The transmitter is installed on a stationary structure near the seat rail, and the receiver is placed on the underside of the movable seat assembly. As the seat travels along the rail, the relative position and magnetic coupling between the transmitter and receiver continuously change.

The receiver installation area is limited by the seat frame, actuator motors, rails, and brackets. Accordingly, a compact non-polarized CP is employed as the receiver because of its simple geometry and limited installation footprint. This selection reflects the spatial constraints of the present application and does not imply that polarized DDP or BPP receivers are generally unsuitable.

The transmitter is located close to the lower rail, upper rail, and seat frame. These surrounding metallic structures constitute important design constraints because they can alter the magnetic-flux path, inductance, ac resistance, and electromagnetic loss.

The transmitter is composed of repeated segments arranged along the rail direction. The present study evaluates single-segment and dual-segment excitation as the receiver moves between adjacent transmitter segments. The transmitter architecture, segment geometry, and position-dependent characteristics of these excitation states are developed in Section 3, Section 4 and Section 5.

2.2. Misalignment Definition and Representative Positions

The seat-rail direction is defined as the x-axis. The seat-rail travel of the considered seat structure is approximately 1050 mm, which is substantially longer than a single transmitter segment. In the local analysis between two adjacent segments, CP1 is designated as the reference transmitter segment, and x = 0 mm denotes the position at which the receiver center coincides with the CP1 center.

The receiver is displaced from the CP1 center toward the adjacent segment CP2 along the positive x-direction, which is used as the reference direction for the local transition analysis. The position-dependent electromagnetic characteristics are evaluated over x = 0–80 mm to examine the gradual change from a CP1-dominant coupling condition to a region in which the contribution of CP2 becomes significant.

For the partially overlapped geometry considered in this study, the overlap-length comparison is presented in Section 3.6, while the final segment dimensions are established through the seat-structure-based analysis in Section 4. The resulting segment length and overlap length are 190 and 90 mm, respectively, corresponding to a center-to-center segment pitch of 100 mm. Accordingly, x = 50 mm corresponds to the geometric midpoint between the centers of CP1 and CP2. This position is used as a representative intermediate evaluation position rather than as a predetermined switching boundary.

The positions x = 0, 50, and 80 mm are retained as representative points for detailed comparison and experimental interpretation. The x = 0 mm condition represents alignment with CP1, whereas x = 80 mm represents a large displacement from CP1 where its transmitter-to-receiver coupling is substantially reduced. These representative positions do not define universal excitation-switching boundaries and should not be interpreted as covering the entire 1050 mm seat travel. In a repeated multi-segment implementation, the same local transition concept is applied between adjacent transmitter segments.

2.3. Electrical Specifications and Comparison Conditions

The electrical specifications and evaluation targets used in this study are summarized in

Table 2. Electrical specifications and evaluation targets.

Parameter	Value
Target output power	100 W
Required dc output voltage	30–60 V
Minimum acceptable dc output voltage	30 V
Nominal prototype dc-link voltage	16 V
Operating frequency	110 kHz

. They are prototype-level design targets adopted for the present evaluation and are not standardized automotive power-seat ratings. The target output power is 100 W, and the required dc output-voltage range is 30–60 V. The lower bound of 30 V is used as the minimum acceptable dc output voltage when the representative operating states are evaluated at approximately 100 W. A nominal dc-link voltage of 16 V is used as the prototype inverter input condition, and the operating frequency is fixed at 110 kHz throughout the electromagnetic, circuit, and prototype evaluations.

A single high-frequency inverter is shared by the transmitter segments in the final system. According to the evaluated excitation state, either one transmitter segment or two adjacent segments are connected to the inverter. The CP1 and CP2 notation and the corresponding single- and dual-segment excitation states apply to the partially overlapped segmented transmitter selected through the topology-screening process.

In the initial topology screening presented in Section 3, however, each candidate winding arrangement is evaluated as a complete transmitter-pad configuration under its assigned electrical connection and winding-polarity condition. Thus, the initial comparison does not represent independent CP1 and CP2 activation or a position-dependent excitation strategy. The candidate transmitter configurations are compared using the same receiver, transmitter-to-receiver air gap, operating frequency, number of turns, and litz-wire specification. The signed coupling coefficient is used only as an initial topology-screening index [19]. Its sign follows the winding-polarity and reference-direction conventions assigned in the FEM model. Mutual inductance and electromagnetic loss are subsequently considered because the candidate structures differ in self-inductance, conductor length, and winding configuration.

The specifications in Table 2 define the target operating conditions of the prototype. In the position-dependent comparative analysis presented in Section 5, a common electrical reference condition is applied to the single-segment and simultaneous dual-segment excitation states to examine variations in fundamental coil current and electromagnetic loss with receiver position. This comparative condition is not intended to impose identical output power at every receiver position. The reference-load condition and its FHA-equivalent resistance are defined in Section 5.2.

3. Comparison of Candidate Transmitter Structures and Selection of the Segmented Architecture

The initial topology screening was performed using a reference single-pad design area with x- and y-axis dimensions of 210 and 150 mm, respectively. Each component winding has eight turns and uses the same 1.6 mm diameter litz wire. The same receiver, transmitter-to-receiver air gap, operating frequency, and winding specification were maintained throughout the comparison. The extended-CP configurations intentionally exceed the reference x-axis dimension to investigate whether the required rail-direction coverage can be achieved by extending a single continuous transmitter winding.

Figure 2 shows the four transmitter configurations considered in the initial topology screening: a single circular pad (CP), a continuous extended CP, two adjacent D-shaped windings under same-polarity excitation, and partially overlapped CP windings. Figure 2b presents the representative 2D_x = 420 mm extended configuration, while both the 2D_x = 420 mm and 3D_x = 630 mm configurations are included in Figure 3. For the partially overlapped configuration, an overlap length of 90 mm is used as a representative baseline. The influence of the overlap length is evaluated separately in Section 3.6 using the selected segmented configuration with a fixed 190 mm segment length within the common maximum design envelope.

For the candidate configurations composed of two windings, the winding connection and polarity assigned in the FEM model were maintained throughout the position sweep. At this topology-screening stage, these windings are treated as components of each candidate pad configuration rather than as independently selectable CP1 and CP2 segments.

Figure 3 compares the signed coupling coefficients obtained directly from the FEM models. The sign follows the fixed winding-polarity and reference-direction conventions used for each configuration. Accordingly, a negative coupling coefficient indicates a reversal in the direction of the mutual flux linkage, rather than a negative coupling magnitude. The coupling coefficient is used only as an initial magnetic-topology screening index. A higher coupling coefficient does not necessarily correspond to higher output power or efficiency because the candidate structures have different self-inductances, conductor lengths, winding arrangements, and electromagnetic-loss characteristics. The subsequent design stages therefore consider mutual inductance, winding loss, structural eddy-current loss, circuit operating conditions, and leakage-field distribution in addition to the initial coupling trend.

3.1. Single Circular Pad

The single CP provides strong coupling near the aligned position because its magnetic flux is concentrated around the compact receiver. However, as shown in Figure 3, the coupling coefficient decreases rapidly as the receiver moves away from the transmitter center and approaches zero at large rail-direction displacement. The coupling direction is subsequently reversed according to the fixed winding-reference convention.

This strong position dependence indicates that maintaining the required operating condition over a wide displacement range would require a substantial variation in the transmitter current or circuit operating point. Therefore, a single fixed CP does not provide a sufficiently broad coupling region for the wide seat-travel range considered in this application.

3.2. Extended Circular Pad

To examine whether the wide rail-direction displacement can be accommodated by simply extending a continuous transmitter, extended-CP configurations with x-axis lengths of 2D_x = 420 mm and 3D_x = 630 mm were evaluated. As shown in Figure 3, increasing the transmitter length broadens the region over which the coupling coefficient remains relatively stable compared with that of the single CP.

Figure 4 compares the leakage magnetic-flux-density distributions of the single and extended CPs under identical excitation conditions. A common display range of 0–40 µT is used for both configurations to emphasize the spatial extent of the high-flux-density regions. Values above the upper display limit are represented by the saturated red region. The common scale is used solely for cross-structure comparison of the leakage-field distribution.

The extended CP produces a wider high-flux-density region along the rail direction than the single CP. Increasing the winding length also increases conductor usage and winding resistance and enlarges the region in which the generated field can interact with nearby metallic seat structures. Therefore, although a continuous extended CP broadens the coupling region, extending a single transmitter winding over the rail direction is not selected as the preferred architecture for the present application.

3.3. Adjacent D-Shaped Windings Under Same-Polarity Excitation

Two adjacent D-shaped transmitter windings are included as a comparison configuration. Because the selected receiver is a compact non-polarized CP, the two D-shaped windings are assigned the same excitation polarity to investigate whether simple adjacent placement can establish a continuous coupling region with the selected receiver.

Figure 5a shows the magnetic-field-strength H vector distribution for the adjacent D-shaped winding configuration. Under the same-polarity excitation condition, the interaction between the two windings produces a local magnetic-field-cancelation region near their common boundary. This local field cancelation weakens the magnetic-field contribution toward the receiver around the inter-winding region.

The coupling-coefficient trend in Figure 3 also shows that the adjacent D-shaped winding configuration provides a lower coupling coefficient than the partially overlapped CP-winding configuration within the representative receiver-position range used in the subsequent detailed analysis. Therefore, simple adjacent placement is not selected for the compact CP receiver considered in this study. This result is specific to the same-polarity excitation and compact non-polarized receiver condition and should not be generalized to D-shaped couplers designed for operation with a compatible polarized receiver.

3.4. Partially Overlapped CP Windings

The partially overlapped configuration is formed by arranging two CP-shaped windings with an intentional overlap along the rail direction. Unlike simple adjacent placement, the overlap changes the spatial relationship between the winding boundaries and modifies the magnetic-field superposition in the intermediate region.

Figure 5b shows the magnetic-field-strength H vector distribution of the partially overlapped CP-winding configuration. Compared with the adjacent D-shaped winding configuration shown in Figure 5a, the partially overlapped geometry produces a more continuous magnetic-field distribution toward the compact CP receiver across the intermediate region. The corresponding coupling-coefficient trend in Figure 3 maintains a comparatively high coupling level near the reference winding and throughout the inter-winding transition region.

At this topology-screening stage, the partially overlapped winding arrangement is evaluated within the same maximum design envelope used for the other candidate configurations. The influence of the overlap length is examined separately in Section 3.6 before the selected geometry is applied to the seat-structure-based analysis in Section 4.

3.5. Selection of the Segmented Transmitter Architecture

The single CP provides strong coupling near alignment but exhibits rapid coupling degradation with rail-direction displacement. Extending a continuous CP broadens the coupling region but increases the winding length and the spatial extent of the high-flux-density region. The adjacent D-shaped windings under same-polarity excitation exhibit local magnetic-field cancelation near their common boundary under the selected compact CP-receiver condition.

In comparison, the partially overlapped CP-winding configuration produces a more continuous magnetic-field distribution across the intermediate region and maintains a relatively high coupling coefficient over the receiver-position range considered in the subsequent detailed analysis. In addition, its repeated winding geometry can be implemented as independently selectable transmitter segments without requiring one continuous winding to extend over the entire rail length.

Based on this topology-level comparison, the partially overlapped segmented transmitter is selected for the subsequent design stages. This selection establishes the transmitter architecture but does not yet determine the overlap length or the final segment dimensions. The influence of the overlap length is evaluated in Section 3.6 using the selected 190 mm segment geometry within the common maximum design envelope, after which the selected overlap is applied to the structure-aware segment-dimension study in Section 4.

3.6. Influence of Overlap Length on Segment Coupling Characteristics

The 210 mm x-axis dimension used in Section 3.1, Section 3.2, Section 3.3, Section 3.4 and Section 3.5 represents the common maximum design envelope for topology-level screening. Following selection of the partially overlapped architecture, the x-axis outer length of each transmitter segment is set to D_x = 190 mm. Relative to the common envelope, this retains a total of 20 mm geometric clearance for the winding bends and separation from the ferrite-sheet boundary. Figure 6 defines the overlap length O_ov and center-to-center pitch p = D_x − O_ov. Overlap lengths of 50, 70, 90, 110, and 130 mm are evaluated, corresponding to pitches of 140, 120, 100, 80, and 60 mm, respectively. The receiver geometry, air gap, operating frequency, and winding specifications are maintained throughout the comparison.

Figure 7 shows the signed coupling coefficients k_1s and k_2s between the receiver and CP1 and CP2, respectively. As the receiver moves from the CP1 center along the positive x-direction, k_1s decreases while k_2s increases. A larger overlap reduces the segment pitch and causes the CP2 coupling contribution to become significant at an earlier receiver position. At x = 0 mm, k_1s changes only slightly among the evaluated overlap lengths because the receiver remains aligned with the CP1 center. In contrast, k_2s changes from negative to positive coupling and increases substantially as the overlap length increases. The extent of this overlap-dependent variation is comparable to the position-dependent variation in k_1s over the evaluated receiver-position range, demonstrating that the overlap length materially affects the coupling transition between adjacent segments.

The vertical lines in Figure 7 indicate the geometric midpoint (x = p/2) for the representative configurations shown in Figure 6. The common x = 0–80 mm range is used to compare all overlap configurations over the same physical receiver displacement from the CP1 center. The vertical markers at x = p/2 identify the geometry-dependent midpoint between adjacent segment centers; data beyond each marker are retained for the common-position comparison and are not interpreted as a normalized transition interval. These locations do not necessarily correspond to identical k_1s and k_2s values or predetermined excitation-switching boundaries. Increasing the overlap from 50 to 130 mm also reduces the pitch from 140 to 60 mm, increasing the nominal segment density required per unit rail length by a factor of (140/60 = 2.33). Thus, a larger overlap promotes an earlier contribution from the adjacent segment but reduces the rail length covered by each repeated segment interval and increases the potential implementation complexity.

Figure 8 compares the minimum and maximum signed intersegment coupling coefficients k₁₂ obtained over the evaluated receiver-position range for each overlap length. Although k₁₂ varies with receiver position, the variation within each overlap configuration is smaller than the change produced by varying the overlap length. The 50 mm overlap maintains negative k₁₂ values over the evaluated positions, whereas the 70 mm overlap produces a small positive coupling range. Increasing the overlap to 90, 110, and 130 mm results in progressively stronger positive intersegment coupling. These results confirm that the overlap length is a dominant geometric factor governing the direct magnetic interaction between adjacent transmitter segments. Nevertheless, the sign and magnitude of k₁₂ alone do not determine branch-current division or circuit performance, which are examined later using the three-coil equivalent-circuit model.

The 90 mm overlap provides an intermediate 100 mm pitch, for which x = 50 mm corresponds to the geometric midpoint between the segment centers. Around this representative intermediate position, both k_1s and k_2s remain positive and appreciable, while k₁₂ remains at a moderate positive level relative to the larger-overlap configurations. The 90 mm overlap also avoids the high segment density and strong intersegment interaction associated with the 110 and 130 mm overlaps, as well as the near-decoupled or reversed mutual-flux-linkage conditions associated with the smaller overlaps. These geometry-level trends identify the 90 mm overlap as a balanced design point for the coupling transition, intersegment interaction, segment pitch, and nominal segment density. This geometry is used in the structure-aware segment-dimension and electromagnetic-loss analyses of Section 4.

4. Segment-Dimension Selection Considering the Seat Structure

4.1. Fundamental Analysis Using a Metallic-Plate Model

Figure 9 shows the simplified metallic-plate model and defines the pad-to-plate distance. The resulting eddy-current losses are compared in Figure 10. A simplified metallic-plate model was used to isolate the effects of material and pad-to-plate distance. The transmitter-to-receiver air gap was fixed at 50 mm, and the plate distance was varied from 0 to 30 mm for aluminum and steel.

The structural eddy-current loss was obtained by integrating the volumetric ohmic loss from the FEM solution over the metallic structure. The steel-structure loss reported here includes only the ohmic loss caused by induced currents and excludes magnetic hysteresis loss.

Aluminum forms shielding eddy currents because of its high conductivity, while the high permeability of steel can concentrate flux and alter the current-density distribution. The loss magnitude cannot be generalized from conductivity or permeability alone and depends on geometry, distance, frequency, and flux distribution. Under the present geometry, the losses in both materials decrease with distance, and the steel eddy-current loss is larger at small distances.

4.2. Seat-Structure FEM Model

Three-dimensional electromagnetic FEM simulations were performed using Ansys Maxwell. In the FEM simulation, the lower rail was modeled as aluminum, whereas the upper rail and seat frame were modeled as steel. Figure 11 shows the generalized lower-seat FEM model used to evaluate the influence of the surrounding metallic structures. The model is not intended to reproduce a specific commercial seat in detail but captures the principal metallic components affecting the magnetic coupler. The mutual inductances between CP1 and the secondary receiver coil and between CP2 and the secondary receiver coil are denoted M_1s and M_2s, respectively, while M₁₂ denotes the direct mutual inductance between CP1 and CP2. The subscript s identifies the secondary receiver side.

The x-axis outer dimensions of the transmitter segment and receiver pad are both D_x = 190 mm. The transmitter-segment y-axis outer dimension D_y is varied from 110 to 150 mm in 10 mm increments. Each transmitter segment has eight turns and uses a 1.6 mm diameter litz wire. The final overlap length is 90 mm, resulting in a center-to-center segment pitch of 100 mm and an overall two-segment transmitter-assembly length of 290 mm.

A fixed root-mean-square (rms) current of 1 A was applied to all candidate geometries under the corresponding current-direction condition. The losses in this section therefore represent comparative losses under identical excitation rather than final losses at the required output condition.

The principal solver and material settings are summarized in

Table 3. Key FEM model and analysis conditions for the seat-structure-based evaluations.

Parameter	Condition	Parameter	Condition
FEM software	Ansys Maxwell 3D 2023 R2	Initial curved-surface mesh	Maximum count (level 9)
Solution type	Eddy Current	Coil skin-depth mesh	0.19 mm; 2 layers
Adaptive solution frequency	110 kHz	Maximum adaptive passes	15
Region transverse padding	10% transverse offset	Convergence criterion	1%
Current excitation	Stranded-current excitation	Mesh refinement per pass	20%
Litz-wire model	Equivalent bundle; 100 × Ø0.12 mm	Winding resistance	110 kHz Matrix self-R
Ferrite sheet	PM12; 2 mm; B–H/B–P data	Aluminum shield	1 mm; Tx/Rx pads

. Both the transmitter and receiver pads incorporate a 2 mm-thick PM12 ferrite sheet and a 1 mm-thick aluminum shield. Supplier-provided B–H and B–P material tables based on toroidal-specimen characterization were assigned to PM12. The B–H data represent the nonlinear magnetic behavior, whereas the B–P data were used to evaluate the ferrite-core loss. The frequency-dependent winding self-resistances were extracted from the 110 kHz Eddy Current Matrix using the equivalent litz-wire representation; the individual strands were not explicitly modeled as separate three-dimensional conductors.

4.3. Mutual Inductance Versus Segment Width

Figure 12 shows the transmitter-segment geometry used for the D_y variation, and Figure 13 compares the corresponding transmitter-to-receiver mutual inductances. At x = 0 mm, M_1s increases with D_y, but the incremental improvement decreases as the segment becomes wider. The increases over the 110–120, 120–130, 130–140, and 140–150 mm intervals are approximately 8.30%, 6.20%, 4.60%, and 3.10%, respectively. At x = 50 mm, both CP1 and CP2 contribute to receiver coupling. The following first-order geometric screening index is therefore defined:

$$M_{sum} = M_{1s} + M_{2s}$$

(1)

The calculated M_sum values for D_y = 110, 120, 130, 140, and 150 mm are 16.01, 16.34, 16.55, 15.92, and 14.91 µH, respectively, with the maximum at 130 mm. Because M_sum does not include M₁₂ or the transmitter branch impedances, it is used only as a first-order geometric screening index. The complete transmitter branch-current relationship under simultaneous dual-segment excitation is analyzed in Section 6.

4.4. Winding Loss Under 1 A rms Excitation

Figure 14 and Figure 15 show the winding-loss and structural eddy-current-loss trends, respectively. The total winding loss, including the CP1, CP2, and receiver windings, increases with D_y because the transmitter winding length and ac resistance increase, whereas the receiver-pad geometry is unchanged. At x = 0 mm, it rises from 277.84 mW at D_y = 110 mm to 322.66 mW at D_y = 150 mm. These values were obtained under the common 1 A rms condition using the same Matrix-resistance-based I²R procedure described in Section 5.2. However, a smaller segment also provides lower mutual inductance and may require a larger operating current; the final dimension cannot therefore be selected from the common-current total winding loss alone.

4.5. Structural Eddy-Current Loss Under 1 A rms Excitation

The structural eddy-current loss increases as the leakage-field region expands with D_y. At x = 0 mm, the combined eddy-current loss in the aluminum lower rail, steel upper rail, and steel seat frame increases from 15.56 mW at D_y = 110 mm to 34.46 mW at D_y = 150 mm. The steel upper rail exhibits the largest increase because it is located close to the transmitter.

4.6. Final Segment Dimensions

The D_y = 110 mm segment provides the lowest total winding loss and structural eddy-current loss under the common 1 A rms excitation condition, but also the lowest mutual inductance. Increasing D_y beyond 130 mm yields only a limited improvement in aligned mutual inductance, while the total winding loss and structural eddy-current loss continue to increase. In addition, M_sum at x = 50 mm decreases when D_y exceeds 130 mm. Based on these trends, D_y = 130 mm provides a balanced design point by retaining most of the mutual-inductance benefit while limiting the increases in total winding loss and structural eddy-current loss under the common 1 A rms condition.

The final outer dimensions of the transmitter segment and receiver pad are both 190 × 130 mm. The 90 mm overlap produces a 100 mm center-to-center segment pitch and a 290 mm overall length for the two-segment transmitter assembly. The initial 210 mm x-axis dimension in Section 3 represents the maximum candidate-comparison area, whereas the final D_x = 190 mm maintains a winding margin within the ferrite boundary. The 90 mm overlap was selected through the topology-level parametric comparison in Section 3.6 and was subsequently maintained during the structure-aware segment-dimension study.

5. Position-Dependent Single- and Dual-Segment Excitation Strategy

5.1. Evaluated Excitation States

Figure 16 illustrates the conceptual excitation sequence. Near the CP1 center, only CP1 is energized. As the receiver moves away from CP1 toward the overlap region with CP2, simultaneous CP1 + CP2 excitation can utilize both transmitter-to-receiver coupling paths. The present analysis compares these two predefined states as a function of receiver position.

Real-time implementation could use a position-dependent lookup table with hysteresis or a minimum dwell time, but position sensing and dynamic state switching were not tested in the present prototype.

5.2. Comparison Under a Common Fixed-Source and Fixed-Load Condition

The 1 A rms analysis in Section 4 identifies geometry-dependent trends, but the calculated operating currents vary with receiver position and excitation state. The two excitation states were therefore evaluated using the same FHA source model, derived from the nominal 16 V dc-link condition in Table 2, and a common fixed load. This sweep quantifies position-dependent current, output-power, and electromagnetic-loss trends without enforcing identical output power at every position.

Figure 17 summarizes the calculated fundamental rms coil currents and corresponding unregulated output powers under the fixed-source and fixed-load condition. A fixed dc-side load of R_dc = 22 Ω was used. Under the full-wave-rectifier FHA, this corresponds to R_L = 8R_dc/π² = 17.83 Ω, and the plotted output power was calculated as P_o(x) = |I_s(x)|²R_L. Under single-segment excitation, I₁ denotes the active transmitter-segment current phasor. Under simultaneous dual-segment excitation, I₁ and I₂ denote the CP1 and CP2 branch-current phasors, respectively, and I_s denotes the receiver-current phasor. The individual complex branch-current phasors were applied separately in the FEM loss calculation.

The plotted currents are fundamental rms coil-current magnitudes calculated using the FHA model and should not be directly compared with the measured dc-link current. Because the calculated output power differs among receiver positions and excitation states under the fixed-source and fixed-load condition, the absolute loss values do not represent an equal-output efficiency comparison. They are used only to characterize the position-dependent electromagnetic-loss trends of the two excitation states. Consequently, output-power values exceeding 100 W in Figure 17 are unregulated model results rather than intended prototype operating points. The branch-current distribution under simultaneous dual-segment excitation is interpreted in Section 6.3.

The winding loss was calculated using the FHA-derived rms coil-current magnitudes and the frequency-dependent winding self-resistances extracted from the 110 kHz Eddy Current Matrix. For each excitation condition, the winding-loss summation includes the active transmitter winding or windings and the receiver winding. The litz-wire conductors were represented as equivalent bundles of 100 round strands with a strand diameter of 0.12 mm; the individual strands were not explicitly meshed. The Matrix-derived self-resistances include the skin- and proximity-effect contributions represented by the adopted litz-wire model. The ferrite-core, aluminum-shield eddy-current, and surrounding-structure eddy-current losses were obtained from the corresponding FEM field quantities. The PM12 ferrite-core loss was evaluated using the assigned B–P data.

Figure 18 compares the calculated electromagnetic-loss breakdown under single-segment and simultaneous dual-segment excitation over the receiver-position range from x = 0 to 80 mm. The reported values include the transmitter and receiver winding losses, ferrite-core loss, aluminum-shield eddy-current loss, and eddy-current losses in the surrounding seat structures. Losses in the inverter, compensation capacitors, segment-selection switches, wiring, rectifier, and load are not included.

CP1 excitation produces the lower calculated electromagnetic loss over x = 0–20 mm. Its total loss is 2.12 W at x = 0 mm and remains below the CP1 + CP2 result up to x = 20 mm. From x = 30 mm, CP1 + CP2 excitation yields the lower loss. At x = 50 mm, the calculated loss decreases from 4.92 W under CP1 excitation to 2.27 W under CP1 + CP2 excitation. At x = 80 mm, the corresponding values are 18.42 and 2.44 W, respectively. The rapid increase under CP1 excitation is associated with the increase in the calculated transmitter current as M_1s decreases, whereas simultaneous excitation of CP1 and CP2 maintains a comparatively low loss over the transition region.

Under the stated fixed-source and fixed-load condition, the offline comparison favors CP1 excitation near the CP1 center and CP1 + CP2 excitation farther from CP1 with respect to the modeled electromagnetic-loss trend. This ranking is not an equal-output efficiency comparison and does not constitute a dynamically implemented switching law. The individual branch-current distribution under CP1 + CP2 excitation is analyzed in Section 6.

5.3. Comparative Occupant-Side Stray-Field Evaluation

To compare the stray magnetic field in a representative occupant-side region, an 800 × 500 × 400 mm rectangular evaluation surface was defined around the seat-cushion space shown in Figure 19. This installation-specific surface is used as a spatial sampling region.

The magnetic-flux-density distributions were calculated at 110 kHz using the rms coil-current phasors from Section 5.2. Phase-resolved field distributions were examined at the discrete phase angles included in the solver sweep. For the four evaluated endpoint conditions, the largest spatial maximum among those sampled phases occurred at the cosine-referenced phase of 0°, and Figure 20 presents the corresponding distributions. Here, B_max denotes the maximum spatial value on the modeled surface at the displayed phase.

At x = 0 mm, B_max is 14.230 μT under CP1 excitation and 30.382 μT under CP1 + CP2 excitation. At x = 80 mm, B_max is 36.638 μT under CP1 excitation and 25.717 μT under CP1 + CP2 excitation. With respect only to this modeled surface-maximum indicator, the lower value occurs for CP1 excitation at x = 0 mm and for CP1 + CP2 excitation at x = 80 mm. Only these two receiver positions were assessed; therefore, a worst-case field condition over the complete 0–80 mm sweep has not been established.

Because the installation-specific sampling surface and phase-resolved spatial maxima do not follow standardized dosimetric geometry or rms averaging procedures, the reported values cannot be directly compared with the ICNIRP reference levels [20]. Accordingly, these results are used only for comparison among the evaluated excitation states and establish neither compliance nor non-compliance; a standards-based full-position exposure assessment remains future work.

5.4. Design Criterion for Position-Dependent State Selection

For the present offline evaluation, the preferred excitation state is the state that satisfies the minimum output-voltage requirement, maintains inductive input operation, and yields the lower modeled electromagnetic loss. Under the common fixed-source and fixed-load condition, the electromagnetic-loss ranking changes between x = 20 and 30 mm. This interval is treated as a candidate crossover region rather than an implemented switching boundary. The receiver positions x = 0, 50, and 80 mm are retained as representative evaluation points. The final switching boundary of an implemented system should also consider position uncertainty, compensation state, and transition hysteresis.

6. Equivalent-Circuit Analysis and Reconfigurable Compensation

6.1. Single-Segment Excitation

Figure 21a shows the FHA equivalent circuit under single-segment excitation. In the single-segment state, the segment-selection circuit disconnects CP2 from both the inverter and the transmitter-side compensation network. CP2 therefore forms an open loop, so no branch current flows and no receiver-reflected impedance appears through CP2 in Figure 21a. The geometric coupling M₁₂ and the corresponding open-circuit induced voltage remain, whereas switch off-state parasitics are outside the scope of this idealized model. One transmitter segment and the receiver form a two-coil series–series compensated circuit. In Figure 21, U_in denotes the rms fundamental inverter-output voltage applied to the compensation network, whereas V_Tx denotes the rms fundamental voltage across the coupled transmitter-coil network after the common transmitter-side series compensation capacitor. The inverter dc-link voltage used in the experiment is denoted separately by V_DC. In the phasor-domain FHA model, j represents a 90° phase shift, and ω denotes the angular operating frequency.

The active transmitter-coil impedance and the compensated receiver-side impedance are defined as

$$\begin{array}{cc}{Z}_1=R_1+j\omega L_1, & Z_s=R_s+R_L+j\left(\omega L_s-{\displaystyle \frac{1}{\omega C_s}}\right)\end{array}$$

(2)

Here, R₁ and R_s are the equivalent ac resistances of the active transmitter segment and receiver coil, respectively; L₁ and L_s are their self-inductances; C_s is the receiver-side series compensation capacitance; and R_L is the FHA-equivalent ac load resistance referred to the receiver-coil terminals. The receiver-reflected impedance and the equivalent impedance of the coupled transmitter network under single-segment excitation are

$$\begin{array}{cc}{Z}_{r,single}={\displaystyle \frac{{\omega }^2{M_{1s}}^2}{Z_s}}, & Z_{Tx,single}=Z_1+Z_{r,single}\end{array}$$

(3)

Including the common transmitter-side series compensation capacitor, the inverter-side input impedance is

$$Z_{in,single}={\displaystyle \frac{1}{j\omega C_{Tx,single}}}+Z_{Tx,single}$$

(4)

The implemented value of C_Tx,single is introduced with the reconfigurable compensation network in Section 6.4. As the receiver moves away from the CP1 center, M_1s and the corresponding reflected impedance vary, thereby changing both the magnitude and phase of Z_in,single.

6.2. Simultaneous Dual-Segment Excitation and Reflected-Impedance Decomposition

Figure 21b shows the simultaneous dual-segment excitation circuit. CP1 and CP2 form parallel transmitter branches after the common transmitter-side series compensation capacitor and therefore share the same network voltage V_Tx. Together with the receiver, the two transmitter segments form a three-coil system. Based on the current directions and dot convention shown in Figure 21b, the KVL equations are

$$\left[\begin{array}{c}{V}_{Tx}\\ V_{Tx}\\ 0\end{array}\right]=\left[\begin{array}{ccc}{Z}_1& j\omega M_{12}& -j\omega M_{1s}\\ j\omega M_{12}& Z_2& -j\omega M_{2s}\\ -j\omega M_{1s}& -j\omega M_{2s}& Z_s\end{array}\right]\left[\begin{array}{c}{I}_1\\ I_2\\ I_s\end{array}\right]$$

(5)

Here, Z₂ = R₂ + jωL₂, and I₁, I₂, and I_s are the complex rms current phasors of CP1, CP2, and the receiver, respectively. M₁₂ is the direct mutual inductance between CP1 and CP2, whereas M_1s and M_2s are the mutual inductances between each transmitter segment and the receiver. The negative transmitter–receiver coupling terms follow the selected current references and dot convention. The 3 × 3 impedance matrix remains symmetric, consistent with electromagnetic reciprocity, and the receiver-loop equation represents the condition that the induced electromotive forces and receiver-side impedance voltage sum to zero.

Defining the total transmitter current as I_Tx = I₁ + I₂, the KVL equations can be reorganized into one reflected-impedance term common to the transmitter port and two branch-differential reflected-impedance terms. These components are defined as

$$\left\{\begin{array}{c}{Z}_{r12}={\displaystyle \frac{{\omega }^2{M}_{1s}{M}_{2s}}{Z_s}}\\ Z_{r1}={\displaystyle \frac{{\omega }^2{M}_{1s}\left(M_{1s}-M_{2s}\right)}{Z_s}}\\ Z_{r2}={\displaystyle \frac{{\omega }^2{M}_{2s}\left(M_{2s}-M_{1s}\right)}{Z_s}}=-{\displaystyle \frac{{\omega }^2{M}_{2s}∆M}{Z_s}}\end{array}\right.$$

(6)

The term Z_r12 is the receiver-mediated reflected impedance common to both transmitter branches. In contrast, Z_r1 and Z_r2 are differential reflected impedances arising from the difference between M_1s and M_2s. These terms are an algebraic decomposition of the coupled three-coil impedance rather than three independent physical loads. When M_1s = M_2s, Z_r1 and Z_r2 become zero, and the receiver-reflected contribution is represented only by the common term Z_r12. In this notation, the subscript r denotes a reflected-impedance component, whereas s denotes the secondary receiver side.

The equivalent impedance of the coupled transmitter-coil network excluding the common series compensation capacitor is therefore

$$Z_{Tx,dual}=j\omega M_{12}+Z_{r12}+\left(Z_1-j\omega M_{12}+Z_{r1}\right)\parallel \left(Z_2-j\omega M_{12}+Z_{r2}\right)$$

(7)

Equation (7) separates the common port component, jωM₁₂ + Z_r12, from the parallel combination of the two differential branch impedances. Including the common transmitter-side series compensation capacitor, the inverter-side input impedance under simultaneous dual-segment excitation is

$$Z_{in,dual}={\displaystyle \frac{1}{j\omega C_{Tx,dual}}}+Z_{Tx,dual}$$

(8)

The implemented value of C_Tx,dual is presented in Section 6.4. Equations (6)–(8) provide a circuit-level interpretation of the simultaneous dual-segment input impedance without requiring the intermediate KVL solution to be expanded in the main text.

6.3. Branch-Current Distribution Under Simultaneous Dual-Segment Excitation

The common port component jωM₁₂ + Z_r12 affects the total simultaneous dual-segment input impedance but is identical for the two transmitter branches and therefore does not directly determine their current division. Removing this common voltage component from the two branch equations gives the branch-current ratio

$${\displaystyle \frac{I_2}{I_1}}={\displaystyle \frac{\left(Z_1-j\omega M_{12}+Z_{r1}\right)}{\left(Z_2-j\omega M_{12}+Z_{r2}\right) }}$$

(9)

Because CP1 and CP2 have the same geometry, number of turns, conductor specification, and nominal compensation condition, their coil impedances can be approximated as Z₁ ≈ Z₂ ≡ Z₀. Defining the mutual-inductance difference as ΔM = M_1s − M_2s, Equation (9) can be written as

$${\displaystyle \frac{I_2}{I_1}} \approx {\displaystyle \frac{Z_s\left(Z_0-j\omega M_{12}\right)+{\omega }^2{M}_{1s}∆M}{Z_s\left(Z_0-j\omega M_{12}\right)-{\omega }^2{M}_{2s}∆M}}$$

(10)

Equation (10) shows that the branch-current ratio is not governed by ΔM alone. The difference between M_1s and M_2s enters through the differential reflected terms ω²M_1sΔM/Z_s and −ω²M_2sΔM/Z_s. Their influence is determined relative to the common branch term Z₀ − jωM₁₂, which appears in both the numerator and denominator. Therefore, even when M_1s and M_2s differ, the current ratio remains close to unity when the differential reflected terms are small compared with the common branch term.

The branch-current imbalance ratio is defined as

$${\gamma }_i\left(x\right)={\displaystyle \frac{\left|\left|I_1\left(x\right)\right|-\left|I_2\left(x\right)\right|\right|}{\left|\left|I_1\left(x\right)\right|+\left|I_2\left(x\right)\right|\right|/2}}\times 100\%$$

(11)

At x = 50 mm, the calculated rms branch-current magnitudes are 2.28 A for CP1 and 2.37 A for CP2, corresponding to an imbalance ratio of 3.87%. Thus, under the investigated transition-region condition, the unequal transmitter-to-receiver mutual inductances produce only a limited branch-current imbalance. This result applies only to the analyzed geometry and compensation condition and does not imply balanced branch currents at all receiver positions or under all parameter tolerances.

6.4. Reconfigurable Compensation and Inductive Input-Impedance Region

Single- and dual-segment excitation produce different equivalent transmitter impedances because the active-segment count and contribution of M₁₂ differ. A single fixed transmitter-side compensation capacitance cannot therefore maintain the intended input-impedance phase under both excitation states.

The two-state network in Figure 22 uses a 66 nF base transmitter capacitor under single-segment excitation. Under simultaneous dual-segment excitation, an additional 33 nF capacitor is connected in parallel, increasing the effective transmitter-side capacitance to 99 nF. The receiver-side series compensation capacitance C_s is fixed at 56 nF. The representative equivalent transmitter inductances used in the compensation analysis are 33.2 μH under single-segment excitation and 21.3 μH under simultaneous dual-segment excitation.

To assess the first-order sensitivity of the compensation network, the effective transmitter-side capacitance C_Tx and receiver-side capacitance C_s were independently varied by ±10%, while the remaining circuit parameters were fixed at their nominal values. For the dual-segment state, the ±10% variation was applied to the effective total transmitter capacitance of 99 nF, representing the same-direction worst-case deviation of the 66 and 33 nF capacitor banks.

Figure 23 shows nominal ZPA points of 31.7 and 21.1 μH for the single- and simultaneous dual-segment compensation states, respectively. Variation in C_Tx produces a larger shift in the ZPA point than the corresponding variation in C_s. At representative equivalent transmitter inductances of 33.2 and 21.3 μH, the nominal input-impedance phases are 9.32° and 7.22°, respectively. These positive phase angles indicate nominal inductive operation but do not guarantee ZVS. Under adverse capacitor-tolerance combinations, the ZPA point may shift beyond the representative operating inductance and cause capacitive operation. Tight-tolerance capacitors or post-assembly compensation adjustment may therefore be required.

7. Experimental Results

7.1. Prototype and Test Conditions

Figure 24 shows the fabricated pads and experimental setup, and

Table 4. Fabricated pad and compensation parameters.

Fabricated-Pad Parameter	Value	Electrical Parameter	Value
Segment/assembly/ receiver dimensions	190 × 130/290 × 130/ 190 × 130 mm	LTx,single/LTx,dual	33.2/21.3 μH
Turns/litz-wire diameter	8/1.6 mm	CTx,single/CTx,dual	66/99 nF
Overlap/air gap	90/50 mm	Ls/Cs	35.9 μH/56 nF

summarizes the coupler and compensation parameters. The 100 W prototype comprises two partially overlapped CP transmitter segments, a single-CP receiver, an inverter with segment selection and two-state transmitter compensation, and a receiver-side series capacitor, rectifier, and adjustable electronic dc load. Because the mutual inductance and receiver current differ by excitation state, the load setting was adjusted at each position to establish an approximately 100 W output point. The reported output values therefore represent rated-power operation rather than a fixed-load voltage-gain comparison.

The endpoint tests were selected to assess the limiting conditions of single-segment excitation rather than to locate the state-transition boundary. Single-segment excitation was expected to satisfy the output requirement at x = 0 mm but not at x = 80 mm because of the reduced CP1-to-receiver coupling. Intermediate-position and dynamic-transition validation remain future work.

7.2. Comparison of FEM and Measured Magnetic Parameters

Figure 25 compares the FEM-calculated and measured magnetic parameters. In Figure 25b, M_1s denotes the mutual inductance between CP1 and the receiver under single-segment excitation, whereas M_eq denotes the equivalent transmitter-to-receiver mutual inductance measured at the paralleled CP1–CP2 transmitter terminals under simultaneous dual-segment excitation. As the receiver moves away from the CP1 center, M_1s decreases, whereas M_eq remains within a narrower range over the evaluated positions because both transmitter-to-receiver coupling paths contribute. The FEM-calculated and measured self, equivalent, and mutual inductances exhibit similar position-dependent trends, supporting the use of the FEM-derived parameters in the equivalent-circuit and loss analyses.

7.3. Output and Efficiency Characteristics

Figure 26 summarizes the measured power-transfer performance under the four evaluated conditions. The efficiency values are the direct dc-to-dc efficiency readings from the power analyzer. The displayed voltages, currents, and powers are independently rounded; therefore, efficiencies recalculated from the rounded table values may differ slightly from the reported readings. The corresponding effective dc loads, calculated from the measured output voltage and current, were 18.80, 12.02, 3.52, and 10.28 Ω for the x = 0 mm single-segment, x = 0 mm dual-segment, x = 80 mm single-segment, and x = 80 mm dual-segment conditions, respectively.

7.3.1. Results at 0 mm

At x = 0 mm, CP1 excitation produces a dc output voltage of 43.38 V, a dc output power of 100.10 W, and a dc-to-dc efficiency of 78.79%. CP1 + CP2 excitation produces 34.73 V, approximately 100 W, and 72.09%, respectively. CP1 excitation is therefore higher by 6.70 percentage points. Near the CP1 center, activating CP2 adds an energized winding and conduction path without a corresponding coupling benefit. The individual converter-component losses were not separately measured, so the efficiency difference is not assigned to a specific component.

7.3.2. Results at 80 mm Relative to the CP1 Center

At x = 80 mm relative to the CP1 center, CP1 excitation establishes an approximately 100 W operating point at a dc output voltage of 18.78 V and a dc-to-dc efficiency of 67.84%. However, the output voltage is below the required minimum of 30 V. CP1 + CP2 excitation establishes the approximately 100 W operating point at 32.13 V and 72.15%, satisfying the voltage requirement and improving efficiency by 4.31 percentage points relative to CP1 excitation.

The electromagnetic losses in Figure 18 and the measured dc-to-dc efficiencies in Figure 26 were obtained under different operating conditions. Figure 18 uses a common 16 V source and a fixed 22 Ω dc-side load, whereas the experimental electronic-load operating point was adjusted for each excitation state to establish approximately 100 W. The FEM and experimental results are therefore compared at the state-ranking level rather than through direct loss closure. At both evaluated positions, the excitation state with the lower calculated electromagnetic loss also exhibits the higher measured dc-to-dc efficiency.

7.4. Verification of Inductive Operation

Figure 27 shows the measured switching waveforms used to verify ZVS. Under both representative conditions, the input impedance is inductive. More importantly, the measured drain–source voltage decreases to near zero before the gate–source voltage is applied. The measured drain–source voltage, gate–source voltage, and inverter-current waveforms therefore verify ZVS for the tested switches, dc-link voltage, and dead-time conditions. The phase analysis in Figure 23 identifies inductive regions favorable for ZVS, whereas the measured switching waveforms provide the direct verification.

8. Discussion

The results show that excitation-state selection should not be based on coupling coefficient alone. At x = 0 mm, near the CP1 center, CP1 excitation provides sufficient coupling and lower total electromagnetic loss. As the receiver moves away from CP1, maintaining CP1 excitation requires a rapid increase in |I₁|. This raises the CP1 winding loss and may produce an output voltage below the specified range, even when an approximately 100 W operating point is established by adjusting the electronic dc load.

At x = 50 mm, CP1 + CP2 excitation reduces the absolute modeled electromagnetic loss by 53.9% relative to CP1 excitation at their respective calculated operating points under the common fixed-source and fixed-load condition. This percentage is not an equal-output efficiency improvement. At x = 80 mm, the separately adjusted approximately 100 W prototype test shows that CP1 + CP2 excitation establishes an output voltage above the 30 V minimum and improves the measured dc-to-dc efficiency relative to continued CP1 excitation.

The first-order geometric screening index M_sum is useful for selecting the transmitter-segment width but does not represent the complete performance under simultaneous dual-segment excitation because it excludes M₁₂, the transmitter branch impedances, and the complex current distribution. The three-coil analysis decomposes the receiver-reflected impedance into the common term Z_r12 and the branch-differential terms Z_r1 and Z_r2. The common port component jωM₁₂ + Z_r12 affects the total input impedance but does not directly determine current division. Instead, the branch-current ratio is governed by the two differential branch impedances. Under the investigated transition-region condition, these differential reflected terms remain small relative to the common branch term, resulting in a calculated current imbalance of 3.87% at x = 50 mm. Similarly, the losses calculated under the common 1 A rms condition in Section 4 are comparative design indicators, whereas the position-dependent total electromagnetic losses in Section 5 use the calculated operating-current phasors.

The calculated total electromagnetic loss includes the transmitter and receiver winding losses, ferrite-core loss, aluminum-shield eddy-current loss, and eddy-current losses in the surrounding seat structures. The measured dc-to-dc loss additionally includes the inverter, compensation capacitors, segment-selection devices, wiring, rectifier, and output stage. The FEM results should therefore be interpreted as magnetic-coupler design indicators rather than direct predictions of total system efficiency.

The two-state reconfigurable transmitter-side compensation network uses discrete single- and dual-segment compensation states rather than continuous online tuning. The input-impedance phase analysis establishes inductive operating regions, but actual ZVS also depends on current magnitude, switch output charge, dc-link voltage, and dead time. The measured switching waveforms verify ZVS only for the tested operating points. The first-order capacitor-tolerance analysis does not constitute a complete position–load input-phase map and does not include the on-resistance of the segment-selection switches or layout parasitics.

The present FEM study is limited to rail-direction receiver displacement under nominal geometry and material properties. Manufacturing tolerances, transverse or rotational misalignment, and temperature-dependent material and winding parameters were not evaluated. Long-term coil aging and the resulting drift in winding resistance and inductance were not separately evaluated and should be included in future robustness testing. Experimental validation was limited to static endpoint operation; the full load range and quantitative ZVS-current limits also remain to be established. Future work will address sensitivity to position uncertainty, hysteresis-band design, and dynamic state transitions. Circuit-level overlap optimization, detailed converter-loss separation, system-level thermal behavior, and battery-load validation also remain for future study.

9. Conclusions

This paper proposed a structure-aware, partially overlapped segmented transmitter with a position-dependent single- and simultaneous dual-segment excitation strategy for automotive power-seat WPT. Candidate magnetic couplers were compared under a compact CP-receiver condition, and a seat-structure FEM model incorporating the aluminum lower rail, steel upper rail, and steel seat frame was used to select 190 × 130 mm transmitter segments. The final overlap length, center-to-center pitch, and overall two-segment transmitter-assembly length are 90, 100, and 290 mm, respectively.

The common 1 A rms FEM simulations showed that increasing D_y beyond 130 mm provides limited mutual-inductance benefit while increasing total winding loss and structural eddy-current loss. Under the common fixed-source and fixed-load condition, CP1 excitation produced lower total electromagnetic loss at x = 0 mm, whereas CP1 + CP2 excitation produced lower loss at x = 50 and 80 mm. The three-coil equivalent-circuit analysis decomposed the dual-segment receiver-reflected impedance into Z_r12, Z_r1, and Z_r2 and showed that current division is governed by the differential branch impedances rather than by M_1s and M_2s alone. At x = 50 mm, the calculated branch-current imbalance was 3.87%.

The two-state compensation network provides effective transmitter capacitances of 66 nF under single-segment excitation and 99 nF under simultaneous dual-segment excitation, while the receiver-side capacitance remains 56 nF. At x = 0 mm, CP1 excitation achieved a dc-to-dc efficiency of 78.79%, 6.70 percentage points higher than CP1 + CP2 excitation. At x = 80 mm, CP1 + CP2 excitation established the approximately 100 W operating point at a dc output voltage of 32.13 V and a dc-to-dc efficiency of 72.15%, compared with 18.78 V and 67.84% under CP1 excitation. ZVS was verified using the measured drain–source voltage, gate–source voltage, and inverter-current waveforms.

The results support the offline design rationale for changing from CP1 to CP1 + CP2 excitation as the receiver moves away from the CP1 center. Future work will implement position sensing with hysteretic state selection and validate dynamic transitions during continuous seat movement, followed by thermal and battery-load evaluations.