Inductor sizing equation

Chapter 1.6 Inductor sizing equation

Lessons In Electric Circuits Volume V – Reference Book
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Lessons In Electric Circuits Volume V – Reference Book

  • 8CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS1.6Inductor sizing equationWhere,N = Number of turns in wire coil (straight wire = 1)L =N2µAlL =µ =A =l =Inductance of coil in HenrysPermeability of core material (absolute, not relative)Area of coil in square meters = πr2Average length of coil in metersµ = µr µ0µr =µ0 =Relative permeability, dimensionless (µ0=1 for air)1.26 x 10 -6 T-m/At permeability of free spacerlWheeler’s formulas for inductance of air core coils which follow are useful for radio fre-quency inductors. The following formula for the inductance of a single layer air core solenoidcoil is accurate to approximately 1% for 2r/l < 3. The thick coil formula is 1% accurate whenthe denominator terms are approximately equal. Wheeler’s spiral formula is 1% accurate forc>0.2r. While this is a ”round wire” formula, it may still be applicable to printed circuit spiralinductors at reduced accuracy.Where,N = Number of turns of wire L =N2r29r + 10⋅lL =r =l =Inductance of coil in microhenrysMean radius of coil in inchesLength of coil in incheslrc = Thickness of coil in inchesrcrclL =N2r2L =0.8N2r28r + 11c6r + 9⋅l + 10c