Choke Design 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 → Core Materials Core Materials & Properties The core material of an inductor dramatically affects its performance. Choosing the right core is essential for achieving the desired inductance, Q factor, and frequency response in VIC applications. Why Use a Core? A magnetic core increases inductance by providing a low-reluctance path for magnetic flux: L = μ₀μᵣN²A/l The relative permeability (μᵣ) of the core multiplies the inductance compared to an air core. Core Material Comparison Material μᵣ (typical) Frequency Range Saturation Cost Air 1 Any N/A Free Iron Powder 10-100 1 kHz - 100 MHz High (0.5-1.5T) Low Ferrite (MnZn) 1000-10000 1 kHz - 1 MHz Low (0.3-0.5T) Medium Ferrite (NiZn) 50-1500 100 kHz - 500 MHz Low (0.3-0.4T) Medium Laminated Silicon Steel 2000-6000 50 Hz - 10 kHz High (1.5-2.0T) Low Amorphous Metal 10000-100000 50 Hz - 100 kHz High (1.5T) High Nanocrystalline 15000-100000 1 kHz - 1 MHz High (1.2T) High Core Losses All magnetic cores dissipate energy through two mechanisms: 1. Hysteresis Loss Energy lost each time the core is magnetized and demagnetized. P h ∝ f × B max n (n ≈ 1.6-2.5) Proportional to frequency and flux density. 2. Eddy Current Loss Circulating currents induced in the core material. P e ∝ f² × B max ² Proportional to frequency squared - dominates at high frequencies. Steinmetz Equation P core = k × f α × B β × Volume Where k, α, β are material-specific constants from datasheets. Ferrite Materials for VIC Ferrites are the most common choice for VIC frequencies (1-50 kHz): Material μᵢ Optimal Frequency Application 3C90 (TDK) 2300 25-200 kHz Power transformers N87 (EPCOS) 2200 25-500 kHz General purpose N97 (EPCOS) 2300 25-150 kHz Low loss 3F3 (Ferroxcube) 2000 100-500 kHz Higher frequency 77 Material (Fair-Rite) 2000 Up to 1 MHz EMI/RFI suppression Iron Powder Cores Micrometals and Amidon iron powder cores are popular for their: High saturation flux density Gradual saturation (soft saturation) Good temperature stability Self-gapping (distributed gap) Common Iron Powder Mixes Mix μ Color Frequency Range Mix 26 75 Yellow/White DC - 1 MHz Mix 52 75 Green/Blue DC - 3 MHz Mix 2 10 Red/Clear 1 - 30 MHz Mix 6 8 Yellow 10 - 50 MHz Core Shapes Toroidal Doughnut shape with closed magnetic path. Excellent flux containment, low EMI. Harder to wind but very efficient. E-Core / EI-Core E-shaped halves that mate together. Easy to wind on bobbin. Can add air gap easily. Pot Core Cylindrical with center post. Shields winding from external fields. Good for sensitive applications. Rod Core Simple cylindrical rod. Open magnetic path, lower inductance per turn but no saturation issues. Core Saturation When the magnetic flux density exceeds the saturation limit: Permeability drops dramatically Inductance decreases Current increases rapidly Core heating increases Avoiding Saturation: B peak = (L × I peak ) / (N × A e ) < B sat Always check that peak flux density stays below saturation limit of your core material. Recommendations for VIC Frequency Range Recommended Core Notes 1-10 kHz N97/3C90 ferrite or iron powder Low loss at these frequencies 10-50 kHz N87/3F3 ferrite Good balance of μ and loss 50-200 kHz 3F3/3F4 ferrite or Mix 26 powder Lower permeability, lower loss >200 kHz NiZn ferrite or Mix 2 powder Designed for high frequency VIC Matrix Calculator: The Choke Design module includes a core database with A L values and frequency recommendations. Select your core and it will calculate the required turns for your target inductance. Next: Wire Gauge & Material Selection → Wire Selection Wire Gauge & Material Selection The wire used to wind an inductor directly affects its DC resistance, current capacity, and Q factor. Proper wire selection is essential for maximizing VIC circuit performance. Wire Gauge Systems Wire size is commonly specified using the American Wire Gauge (AWG) system: AWG Diameter (mm) Area (mm²) Ω/m (Copper) Max Current (A) 18 1.024 0.823 0.0210 2.3 20 0.812 0.518 0.0333 1.5 22 0.644 0.326 0.0530 0.92 24 0.511 0.205 0.0842 0.58 26 0.405 0.129 0.1339 0.36 28 0.321 0.081 0.2128 0.23 30 0.255 0.051 0.3385 0.14 32 0.202 0.032 0.5383 0.09 Note: AWG follows logarithmic progression. Each 3 AWG steps doubles resistance, halves area. Wire Materials Material Resistivity (×10⁻⁸ Ω·m) Relative to Copper Use Case Copper 1.68 1.0× (reference) Best for high Q Aluminum 2.65 1.6× Lightweight applications SS304 72 ~43× Corrosion resistance SS316 74 ~44× Better corrosion resistance SS430 (Ferritic) ~100 ~60× Magnetic, high resistance Nichrome (80/20) 108 ~64× Heating elements, damping Kanthal A1 145 ~86× High-temp resistance wire Effect of Material on Q Factor Q Factor Relationship: Q = 2πfL / R Since R is proportional to resistivity, using high-resistivity wire dramatically reduces Q: Copper wire Q = 100 → SS316 wire Q ≈ 2.3 Copper wire Q = 50 → Nichrome wire Q ≈ 0.8 When to Use Resistance Wire Despite lower Q, resistance wire has valid uses: Current limiting: Built-in current limit without separate resistor Damping: Prevents excessive ringing Safety: Limits power in fault conditions Meyer's designs: Some original VIC designs used stainless steel wire Warning: Using resistance wire in a resonant circuit dramatically reduces voltage magnification. A Q of 2 means you only get 2× voltage gain instead of 50× or 100× with copper. Skin Effect At high frequencies, current flows primarily near the wire surface: Skin Depth (δ): δ = √(ρ / (π × f × μ₀ × μᵣ)) For Copper: δ(mm) ≈ 66 / √f(Hz) 1 kHz δ ≈ 2.1 mm 10 kHz δ ≈ 0.66 mm 100 kHz δ ≈ 0.21 mm Skin Effect Mitigation Litz wire: Multiple thin insulated strands twisted together Flat/ribbon wire: More surface area for same cross-section Use finer gauge: If wire radius ≈ δ, skin effect is minimal Magnet Wire Types Insulation Type Temp Rating Voltage Rating Notes Polyurethane (solderable) 130°C ~100V/layer Can solder through coating Polyester-imide 180°C ~200V/layer Good general purpose Polyamide-imide 220°C ~300V/layer High temp applications Heavy build (HN) Various ~500V/layer Thicker insulation Triple insulated Various ~3000V Safety-rated isolation Wire Selection Guidelines for VIC For Maximum Q (recommended): Use copper magnet wire Choose gauge based on skin depth at operating frequency Use largest gauge that fits the core/bobbin Consider Litz wire for frequencies >50 kHz For Current-Limited Applications: Use stainless steel or nichrome Calculate required resistance: R = V max /I limit Accept reduced Q factor as tradeoff Calculating Wire Length Wire Length for N Turns: l wire ≈ N × π × d coil Where d coil is the average coil diameter. Resulting DCR: R dc = ρ × l wire / A wire VIC Matrix Calculator: The Choke Design tool automatically calculates DCR based on your wire gauge, material, and number of turns. It shows the resulting Q factor and voltage magnification for your design. Next: Bifilar Winding Technique → Bifilar Windings Bifilar Winding Technique Bifilar winding is a special technique where two wires are wound together in parallel on a core. This configuration creates unique electromagnetic properties that are particularly relevant to VIC designs, including inherent capacitance between windings and special transformer-like coupling. What is Bifilar Winding? In a bifilar winding, two conductors are wound side-by-side along the entire length of the coil: Standard Winding: Bifilar Winding: ───────────── ═══════════════ │ │ │ │ │ │ ║A║B║A║B║A║B║ └─┘ └─┘ └─┘ ╚═╝ ╚═╝ ╚═╝ Single wire wound Two wires (A & B) around core wound together Cross-section view: Standard: Bifilar: ○ ○ ○ ○ ● ○ ● ○ ○ ○ ● ○ ● ○ ○ = Wire A ● = Wire B Bifilar Winding Properties Property Effect VIC Relevance High inter-winding capacitance Built-in C between A and B May replace discrete capacitor Near-unity coupling k ≈ 1 between windings Efficient energy transfer Cancellation modes Some flux cancellation possible Affects net inductance Lower SRF High C parasitic reduces SRF Consider in frequency selection Connection Configurations 1. Series Aiding (Same Direction): End of A connects to start of B → Fluxes add L total = L A + L B + 2M ≈ 4L (for k=1) 2. Series Opposing (Opposite Direction): End of A connects to end of B → Fluxes subtract L total = L A + L B - 2M ≈ 0 (for k=1) 3. Parallel Connection: Starts connected, ends connected → Current splits L total = L/2 (for identical windings) 4. Transformer Mode: A is primary, B is secondary → Voltage transformation V B /V A = N B /N A = 1 (for bifilar) Calculating Bifilar Capacitance Approximate Inter-Winding Capacitance: C winding ≈ ε₀ε r × (l wire × d wire ) / s Where: l wire = length of each wire d wire = wire diameter s = spacing between wires (≈ insulation thickness × 2) ε r = dielectric constant of insulation Typical Values: For magnet wire on ferrite: 10-100 pF per meter of winding Bifilar in VIC Context Meyer's designs reportedly used bifilar chokes in several ways: As Primary/Secondary Pair L1 and L2 wound as bifilar on same core: Tight coupling between primary and secondary Built-in capacitance may serve as C1 Simpler construction (single winding operation) As Choke Sets Matched pairs for symmetrical circuits: Identical L values guaranteed Common-mode rejection possible Push-pull drive configurations Winding Techniques Tips for Bifilar Winding: Keep wires parallel: Twist them together before winding or use a jig Maintain tension: Even tension prevents gaps and loose spots Mark the wires: Use different colors or tag ends carefully Wind in layers: Complete one layer before starting next Insulate between layers: Add tape for voltage isolation Measuring Bifilar Parameters Measurement Configuration What It Tells You L A alone Measure A, B open Inductance of winding A L series-aid A end to B start, measure L A + L B + 2M L series-opp A end to B end, measure L A + L B - 2M C winding Measure C between A and B Inter-winding capacitance Calculating Coupling Coefficient: M = (L series-aid - L series-opp ) / 4 k = M / √(L A × L B ) For true bifilar winding: k ≈ 0.95-0.99 Advantages and Disadvantages Advantages: Built-in capacitance may simplify circuit Excellent magnetic coupling Matched characteristics between windings Compact construction Disadvantages: Lower SRF due to high parasitic capacitance Difficult to adjust windings independently Insulation must handle full voltage difference More complex to wind correctly VIC Matrix Calculator: The Choke Design section includes options for bifilar windings. It can calculate the expected inter-winding capacitance and adjust the SRF estimate accordingly. When designing bifilar chokes, the calculator helps ensure compatibility with your target resonant frequency. Next: Parasitic Capacitance & SRF → Parasitic Effects Parasitic Capacitance & SRF Real inductors have parasitic capacitance between turns and layers that limits their useful frequency range. Understanding these effects is critical for VIC design, as they determine the maximum operating frequency and affect circuit tuning. Sources of Parasitic Capacitance Parasitic capacitance in inductors comes from several sources: 1. Turn-to-Turn Capacitance (C tt ) Capacitance between adjacent turns in the same layer. Depends on wire spacing and insulation. 2. Layer-to-Layer Capacitance (C ll ) Capacitance between winding layers. Often the largest contributor in multi-layer coils. 3. Winding-to-Core Capacitance (C wc ) Capacitance between the winding and the magnetic core (if conductive or grounded). 4. Winding-to-Shield Capacitance In shielded inductors, capacitance to the external shield. Self-Resonant Frequency (SRF) The parasitic capacitance resonates with the inductance at the Self-Resonant Frequency: SRF = 1 / (2π√(L × C parasitic )) Behavior at SRF: Impedance is maximum (parallel resonance) Inductor is neither inductive nor capacitive Phase angle crosses through 0° Above SRF: The "inductor" behaves as a capacitor ! Impedance decreases with frequency. Impedance vs. Frequency |Z| ↑ │ ╱╲ │ ╱ ╲ ← Peak at SRF │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ ╲ │ ╱ Inductive region ╲ Capacitive region │ ╱ |Z| = 2πfL ╲ |Z| = 1/(2πfC) └────────────────────────────────────────────→ f SRF Phase: +90° ───────────┬─────────── −90° 0° (at SRF) Operating Frequency Guidelines f op / SRF Behavior Recommendation < 0.1 (< 10%) Nearly ideal inductor Preferred range 0.1 - 0.3 (10-30%) Slight inductance increase Acceptable with correction 0.3 - 0.7 (30-70%) Significant deviation Caution - Q drops > 0.7 (> 70%) Near or past SRF Do not use Effective Inductance Near SRF As frequency approaches SRF, the apparent inductance increases: L eff = L dc / [1 - (f/SRF)²] Example: L dc = 10 mH, SRF = 100 kHz At 30 kHz: L eff = 10 / [1 - 0.09] = 11.0 mH (+10%) At 50 kHz: L eff = 10 / [1 - 0.25] = 13.3 mH (+33%) At 70 kHz: L eff = 10 / [1 - 0.49] = 19.6 mH (+96%) Minimizing Parasitic Capacitance Winding Techniques: Single-layer winding: Eliminates layer-to-layer capacitance Space-wound turns: Increases turn-to-turn distance Honeycomb/basket winding: Crosses turns to reduce adjacent voltage Bank winding: Winds in sections to reduce voltage across layers Progressive winding: Keeps voltage gradient low between adjacent turns Design Choices: Use fewer turns (requires higher permeability core) Use thinner insulation (but watch voltage ratings) Use air-core (eliminates winding-to-core capacitance) Choose toroidal cores (natural progressive winding) Calculating Parasitic Capacitance Turn-to-Turn Capacitance (Simplified) C tt ≈ ε₀ε r × l turn × d wire / s Where s is the spacing between adjacent turn centers. Layer-to-Layer Capacitance C ll ≈ ε₀ε r × A layer / t insulation Where A layer is the overlapping area between layers. Total Parasitic Capacitance The total equivalent capacitance is complex because the distributed capacitances see different voltages. For a rough estimate: C parasitic ≈ C ll /3 + C tt /N The 1/3 factor accounts for voltage distribution across layers. Measuring SRF Method 1: Impedance Analyzer Connect inductor to impedance analyzer Sweep frequency and plot |Z| SRF is where impedance peaks Method 2: Signal Generator + Oscilloscope Connect inductor in series with known resistor Drive with sine wave, sweep frequency Monitor voltage across inductor SRF is where voltage peaks (current minimum) Method 3: Resonance with Known Capacitor Measure inductance at low frequency Add known capacitor in parallel Find new resonant frequency Calculate parasitic C from the difference SRF in VIC Design Problem Symptom Solution Operating too close to SRF Resonance frequency higher than calculated Reduce tuning cap or use different choke Operating above SRF No resonance, circuit acts capacitive Must redesign with fewer turns Low SRF in bifilar winding Limited usable frequency range Accept limitation or use separate chokes VIC Matrix Calculator: The Choke Design module estimates SRF based on winding geometry and displays a warning if your operating frequency is too close to SRF. It also calculates the effective inductance at your operating frequency. Next: DC Resistance and Q Factor → DCR Effects DC Resistance and Q Factor The DC resistance (DCR) of an inductor is the primary factor limiting its Q factor and thus the voltage magnification achievable in a VIC circuit. Understanding and minimizing DCR is essential for high-performance designs. What is DCR? DCR is simply the resistance of the wire used to wind the inductor, measured with direct current: R dc = ρ × l wire / A wire Where: ρ = resistivity of wire material (Ω·m) l wire = total wire length (m) A wire = wire cross-sectional area (m²) DCR and Inductor Design For a given inductance, DCR depends on the design choices: Design Change Effect on L Effect on DCR Net Q Effect More turns L ∝ N² R ∝ N Q ∝ N (improves) Larger wire gauge No change R decreases Q improves Higher μ core L increases Fewer turns needed Variable* Larger core L increases Longer mean turn Often improves Copper vs. SS wire No change R × 40-60 Q ÷ 40-60 *Core losses may offset wire resistance reduction at high frequencies Q Factor Calculation Q Factor at Operating Frequency: Q = 2πfL / R total Total Resistance includes: R total = R dc + R skin + R proximity + R core At low frequencies, R dc dominates. At high frequencies, skin effect and core losses become significant. Voltage Magnification Impact Since voltage magnification equals Q at resonance: Example Comparison: Scenario L DCR Q @ 10kHz V out (12V in) 22 AWG Copper 10 mH 5 Ω 126 1,508 V 26 AWG Copper 10 mH 13 Ω 48 580 V 22 AWG SS316 10 mH 220 Ω 2.9 34 V 22 AWG Nichrome 10 mH 320 Ω 2.0 24 V Measuring DCR Method 1: Multimeter Simple and quick Set meter to lowest resistance range Subtract lead resistance Accuracy: ±1-5% Method 2: 4-Wire (Kelvin) Measurement Eliminates lead resistance error Required for low DCR (<1 Ω) Uses separate sense and current leads Accuracy: ±0.1% Method 3: LCR Meter Measures L and DCR together Can measure at different frequencies Shows equivalent series resistance (ESR) Best for complete characterization Optimizing DCR Design Strategies: Use the largest wire that fits: Fill the available winding area Choose copper: Unless current limiting is specifically needed Use higher permeability core: Fewer turns needed for same L Optimize core size: Larger cores have more room for thicker wire Consider parallel windings: Two parallel wires = half the DCR Practical Limits: Wire must fit on the core with proper insulation Multiple layers increase parasitic capacitance Very thick wire is hard to wind neatly Cost and availability of materials Temperature Effects Wire resistance increases with temperature: R(T) = R 20°C × [1 + α(T - 20)] Where α ≈ 0.00393 /°C for copper Example: At 80°C: R = R 20°C × 1.24 (+24% increase) This means Q drops by ~20% when the choke heats up! DCR in the VIC System The total resistance in a VIC circuit includes: Source Typical Range Mitigation L1 DCR 1-50 Ω Optimize winding L2 DCR 1-50 Ω Optimize winding Capacitor ESR 0.01-1 Ω Use low-ESR caps WFC solution resistance 10-10000 Ω Electrode design, electrolyte Connection resistance 0.01-1 Ω Solid connections Driver output resistance 0.1-10 Ω Low R ds(on) MOSFETs Practical Example Target: 10 mH inductor at 10 kHz with Q > 50 Required R max : Q = 2πfL/R → R = 2πfL/Q = 2π × 10000 × 0.01 / 50 = 12.6 Ω Wire selection (100 turns on 25mm toroid): Mean turn length ≈ 80mm, total wire = 8m 22 AWG copper: 8m × 0.053 Ω/m = 0.42 Ω ✓ 26 AWG copper: 8m × 0.134 Ω/m = 1.07 Ω ✓ 30 AWG copper: 8m × 0.339 Ω/m = 2.71 Ω ✓ 22 AWG SS316: 8m × 2.3 Ω/m = 18.4 Ω ✗ (Q = 34) Result: 22-30 AWG copper all meet the requirement. 22 AWG gives highest Q but may be harder to wind. VIC Matrix Calculator: Enter your wire gauge and material in the Choke Design tool. It calculates DCR automatically and shows how it affects Q factor and voltage magnification. The calculator warns if your DCR is too high for effective resonance. Chapter 5 Complete. Next: Water Fuel Cell Design →