Choke Fundamentals

Inductor/Choke Fundamentals 

 Inductors, commonly called "chokes" in VIC terminology, are the workhorses of the resonant circuit. They store energy in their magnetic field and, together with capacitors, determine the resonant frequency and voltage magnification capability of the VIC. 

 What is an Inductor? 

 An inductor is a passive electrical component that stores energy in a magnetic field when current flows through it. The fundamental properties are: 

 Inductance (L): 

 Measured in Henries (H), inductance quantifies the magnetic flux linkage per unit current: 

 L = NΦ/I = N²μA/l 

 Where: 

 

 N = number of turns 

 Φ = magnetic flux 

 I = current 

 μ = permeability of core material 

 A = cross-sectional area of core 

 l = magnetic path length 

 

 Key Inductor Parameters 

 Parameter 

 Symbol 

 Units 

 Importance 

 Inductance 

 L 

 Henry (H) 

 Determines resonant frequency with C 

 DC Resistance 

 DCR, R dc 

 Ohms (Ω) 

 Limits Q factor and causes losses 

 Self-Resonant Frequency 

 SRF 

 Hz 

 Must be > operating frequency 

 Quality Factor 

 Q 

 Dimensionless 

 Ratio of reactance to resistance 

 Saturation Current 

 I sat 

 Amps (A) 

 Max current before inductance drops 

 Inductor Construction 

 A practical inductor consists of: 

 Wire: Conductor wound into coils (turns) 

 Core: Material inside the coil (air, ferrite, iron, etc.) 

 Form: Structure that holds the winding 

 Types of Cores 

 Core Type 

 Permeability 

 Frequency Range 

 VIC Application 

 Air core 

 1 (reference) 

 Any (no losses) 

 High-Q, low inductance 

 Iron powder 

 10-100 

 Up to ~10 MHz 

 Good for VIC frequencies 

 Ferrite 

 100-10000 

 10 kHz - 100 MHz 

 Most common for VIC 

 Laminated iron 

 1000-10000 

 50/60 Hz to ~10 kHz 

 Lower VIC frequencies 

 Inductance Formulas 

 Single-Layer Solenoid (air core): 

 L = (N²μ₀A)/l = (N²r²)/(9r + 10l) µH 

 Where r and l are in inches (Wheeler's formula) 

 With Magnetic Core: 

 L = A L × N² (nH) 

 Where A L is the inductance factor of the core (nH/turn²) 

 Toroidal Core: 

 L = (μ₀μ r N²A) / (2πr mean ) 

 DC Resistance (DCR) 

 The DC resistance is determined by the wire properties: 

 R dc = ρ × l wire / A wire 

 Where: 

 

 ρ = resistivity of wire material (Ω·m) 

 l wire = total wire length ≈ N × π × d coil 

 A wire = wire cross-sectional area 

 

 Q Factor of Inductors 

 Inductor Q Factor: 

 Q = ωL/R = 2πfL/R total 

 R total includes: 

 

 DC resistance of wire 

 Skin effect losses (increases with frequency) 

 Proximity effect losses 

 Core losses (hysteresis + eddy currents) 

 

 Self-Resonant Frequency (SRF) 

 Every inductor has parasitic capacitance between turns and layers: 

 SRF = 1 / (2π√(LC parasitic )) 

 Design Rule: 

 SRF should be at least 10× the operating frequency. 

 At frequencies above SRF, the inductor acts like a capacitor! 

 VIC Choke Design Goals 

 Target inductance: Sets resonant frequency with capacitor 

 Low DCR: Maximizes Q factor 

 High SRF: Ensures proper operation at intended frequency 

 Adequate current rating: Won't saturate or overheat 

 Appropriate core: Low losses at operating frequency 

 Key Tradeoff: More turns = more inductance, but also more wire = more DCR. The design challenge is achieving the target inductance with minimum resistance, which means selecting appropriate wire gauge, core material, and winding technique. 

 Next: Core Materials & Properties →