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Table 1 Formulas approximate for how many turns are required to achieve a specified inductance

From: Energy harvesting for the implantable biomedical devices: issues and challenges

Formulas References
L = N 2 R µ 0 µ r ln 8 R a 0.2 [62]
L = r 2 N 2 2 r + 2.8 d * 10 3 [63]
L = 0.31 aN 2 6 a + 9 h + 10 b [64]
L = 2.9 ln 9 D K N 1.9 [65]