Coil shapes have played a profound role in the performance of wireless power transfer, especially with the coupling coefficient, output power, and energy transmission. We will examine how square, circular, and pentagonal coils have fared against each other. While there are many more shapes, these three form the basis of other shapes and, therefore, require careful consideration.

### Square-shaped coils for wireless power transfer

Square coils (**Figure 1**) can provide a better coupling coefficient over various distances between the transmitter and receiver coil. These coils perform better under misalignment conditions; therefore, they are the preferred structure where precise alignment is challenging.

One major drawback with this shape is the perpendicular bendings, which result in higher resistive losses than other shapes. Even when designing PCBs, sharp bends are usually avoided to remove resistances. Therefore, the same principle applies to square coils for wireless power transfer.

Rectangular coils can be taken as a variant of the square coils, which find applications in specific cases where the product shape and size determine the use case. However, Figure 1 shows these coils have a much lesser coupling coefficient than square and circular ones.

### Spiral-shaped coils for wireless power transfer

Spiral or circular coils (**Figure 2**) benefit from a uniform magnetic field, as they avoid sharp curves like square or rectangular coils. Due to their geometry, spiral or circular coils take minimal cover and are often preferred in compact products such as smartwatches and mobile phones. The coils can be easily customized in size and number of turns. Therefore, they are preferred during the initial stages of research and development of wireless charging products.

The same geometry of the spiral coils also poses various challenges. They are more sensitive to misalignment because they have a smaller coverage area than square and rectangular coils. The degree of alignment for spiral coils is critical for the best power transfer efficiency.

### Pentagonal-shaped coils for wireless power transfer

Pentagonal coils (**Figure 3**) blend circular and square coils, providing a unique compromise in space utilization and design adaptability for specific applications. Their magnetic field distribution uses a wider cover area as with square coils while trying to achieve a smoother shape like the circular coil.

However, the design of a pentagonal coil is tricky and requires more care than its counterparts. The spacing between turns has to be uniform over the entire length, and the curves must be aligned. Their design usually has a trade-off between misalignment and coupling coefficient.

### Case study

Here is a case study comparing the performances of square, spiral, and pentagonal coils due to the variations in distances between the coils. During the study, the surface area of the coils is kept at 110-120 mm^{2}. The spiral coil was noted to have 15 turns, while the pentagonal and square coils were kept at 14 turns. Note that both the transmitter and received coils are of the same shape.

**Figure 4** shows how the increased distance between the coils decreases output power, energy efficiency, and coupling coefficiency. This is obvious to any electrical engineer. However, the spiral coil has an interesting pattern.

From all three parameters, one can observe that the spiral coil takes a noticeable sag when the distance between the coils reaches 20 mm. After that, the curve tends to be linear.

Another interesting observation is the relationship between the square and spiral coils. The performance starts at the same point, 10 mm, and ends at nearly the same point, 40 mm. However, the differences bulge at 20 mm and then converge.

However, the three graphs clearly show that the pentagonal coil outperforms its counterparts by a large margin, at least during the first half. When the distance reaches the 30 to 40 mm range, the performance differences shrink, especially for output power and energy transmission efficiency.

Engineers should note that the graph curves and the ranges in Figure 4 for all three coil shapes are applicable for the assumed number of turns and surface area of coils. Hence, when making a larger or smaller surface area of the coil with changes in the number of turns, the graphs are expected to change, especially on the x-axis for the distance range. Therefore, this is a good starting point if you consider expanding the study.

### Summary

Understanding the performance of square, circular, and pentagonal coils gives us fundamental knowledge that can be expanded to other derivative shapes. In a case study, we have seen that pentagonal coils performed better than their counterparts for various parameters. However, due to their geometry, pentagonal coils require better design understanding, which can be challenging.

### References

Design and Analysis of Magnetic Coils for Optimizing the Coupling Coefficient in an Electric Vehicle Wireless Power Transfer System, Energies, MDPI

Study of the Circular Flat Spiral Coil Structure Effect on Wireless Power Transfer System Performance, Energies, MDPI

A polygonal double-layer coil design for high-efficiency wireless power transfer, AIP Publishing

Wireless Power Transfer—A Review, Energies, MDPI

Analysis on Shape and Geometry Effects of Primary Secondary Coils for Dynamic Wireless Power Transfer System, International Journal of Intelligent Systems and Applications in Engineering

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