# Textile-Based Flexible Coils for Wireless Inductive Power Transmission
## 3 Design  
The flat coil was designed as a circular spiral shape to provide the desired inductance as well as to retain flexibility for both TX and RX coils as shown in Figure 2. The external diameter of the coils was specified based on the target application. As the printed coils increase the thickness of a textile this reduces the flexibility and breathability of the textile. Therefore, the coil size is limited to ensure that the WPT system enabled textile is as comfortable as possible. An area less than 140 mm \(\times\) 140 mm is an acceptable size for flexibility and fits the printable area of the semi-automatic screen printer used in this paper. The external diameter was 138 mm and the remaining space was for the connection pads and screen-printing alignment marks.  
[PERSON] et al. [20] presented experimental work on a geometric approach for the enhancement of the unloaded \(Q\) factor and the coupling coefficient of flat coils. They concluded that when \(d_{inner}\approx 0.4\times d_{ext}\), the optimum unloaded \(Q\) factor is obtained for a given coupling coefficient. Therefore, the inner diameter of the coil was set as 53 mm to get an integral number of turns for the coil.  
[PERSON] et al. [11] found that the optimal spacing depended on the size of coil and is essential to improve the unloaded \(Q\) factor. In this paper, the coils have a 2 mm spacing between conductive tracks, the spacing has been standardized at this value to reduce inter-turn proximity effects while leaving scope for the width of the conductive track to be varied within the overall coil-dimension limits.  
When increasing the number of turns, \(N\), of a coil, both the numerator and denominator of its unloaded \(Q\) factor in Equation (6) are increased. The relationship between \(N\) and unloaded \(Q\) factor is simulated and illustrated in Figure 3 with parameters as \(d_{ext}=138\) mm, \(d_{inner}=53\) mm, \(S=2\) mm, for both circular and square forms, and using a sheet resistance \(R_{sheet}=24\) m\(\Omega/\square\) given from the manufacturer (specified as \(\Omega\) per square area for their recommended printed thickness, denoted as \(\Omega/\square\)). The width of the track was varied in simulation to fit a given number of turns within the specified area, varying the width for a given printed thickness affects the effective conductor size as the resulting cross-sectional area changes. For both circular and square coils the 6-turn coil has the highest unloaded \(Q\) factor and the width of the track \(W\) is 4.5 mm with a pitch of 6.5 mm. By comparing coils with different shapes, it was found that the circular coils have a larger \(Q\), a shorter length of track and a lower resistance than the square coil for the same number of turns. The resistance of the printed coils is approximately 50 times higher than that of a wound copper coil because of the limitation in respect of conductivity of the screen-printable conductive paste caused by the non-conductive polymer binder and gaps between the metal particles in the printed paste. This material-based limitation makes resistance the limiting factor of the unloaded \(Q\) factor of the printed coil. As a result, the circular coil has a higher unloaded \(Q\) factor than the square one due to the longer track length in the square coil.