Resonant Matching

Matching WFC to Circuit 

 For optimal VIC performance, the WFC must be properly matched to the circuit—its capacitance must resonate with the secondary choke at the desired operating frequency. This page covers the matching process and strategies for achieving good resonance. 

 The Matching Problem 

 In a VIC circuit, we have three interdependent parameters: 

 f₀ = 1 / (2π√(L₂ × C wfc )) 

 Design Challenge: 

 

 f₀ is set by the pulse generator (typically 1-50 kHz) 

 C wfc is constrained by electrode geometry and water properties 

 L₂ must be designed to complete the resonant match 

 

 Matching Strategies 

 Strategy 1: Design L₂ for Given WFC 

 When WFC geometry is fixed (existing cell): 

 

 

 Measure C wfc with LCR meter 

 Choose target frequency f₀ 

 Calculate required L₂: 

 

 

 L₂ = 1 / (4π²f₀²C wfc ) 

 Example: 

 

 C wfc = 10 nF (measured) 

 f₀ = 10 kHz (desired) 

 L₂ = 1 / (4π² × 10⁴² × 10⁻⁸) = 25.3 mH 

 

 Strategy 2: Design WFC for Given L₂ 

 When using a pre-wound or available choke: 

 

 

 Measure L₂ with LCR meter 

 Choose target frequency f₀ 

 Calculate required C wfc : 

 

 

 C wfc = 1 / (4π²f₀²L₂) 

 

 Design electrodes to achieve that capacitance 

 

 Strategy 3: Tune with Additional Capacitor 

 When exact match isn't achievable: 

 If C wfc is too low: 

 Add capacitor in parallel with WFC 

 C total = C wfc + C tune 

 If C wfc is too high: 

 Add capacitor in series with WFC (less common) 

 1/C total = 1/C wfc + 1/C series 

 Impedance Matching Considerations 

 Beyond frequency matching, impedance levels affect energy transfer: 

 Secondary Characteristic Impedance: 

 Z₀ = √(L₂/C wfc ) 

 Example Comparison: 

 

 

 L₂ 

 C wfc 

 f₀ 

 Z₀ 

 10 mH 

 25 nF 

 10 kHz 

 632 Ω 

 50 mH 

 5 nF 

 10 kHz 

 3162 Ω 

 100 mH 

 2.5 nF 

 10 kHz 

 6325 Ω 

 

 

 Higher Z₀ = Higher voltage for same energy 

 Primary-Secondary Matching 

 For dual-resonant VIC with both L1-C1 and L2-WFC tanks: 

 Configuration 

 Condition 

 Effect 

 Same frequency 

 f₀ pri = f₀ sec 

 Maximum voltage magnification 

 Slight offset 

 f₀ sec ≈ 0.95-1.05 × f₀ pri 

 Broader response, easier tuning 

 Harmonic 

 f₀ sec = 2× or 3× f₀ pri 

 Secondary resonates on harmonic 

 Finding Resonance 

 Method 1: Frequency Sweep 

 Connect oscilloscope across WFC 

 Sweep generator frequency slowly 

 Watch for voltage peak 

 Note frequency of maximum amplitude 

 Method 2: Phase Measurement 

 Monitor current and voltage simultaneously 

 At resonance, current and voltage are in phase (phase = 0°) 

 Below resonance: capacitive (current leads) 

 Above resonance: inductive (current lags) 

 Method 3: Minimum Current 

 For a series resonant circuit driven from a voltage source: 

 Current is minimum at anti-resonance (parallel resonance) 

 May need to reconfigure measurement 

 Troubleshooting Mismatch 

 Symptom 

 Likely Cause 

 Solution 

 No clear resonance peak 

 Very low Q (high losses) 

 Reduce water conductivity, lower DCR 

 Resonance far from expected 

 Wrong L or C values 

 Measure components, recalculate 

 Resonance drifts during operation 

 Temperature change, bubbles 

 Allow warmup, improve gas venting 

 Multiple resonance peaks 

 Coupled modes, parasitics 

 Check for stray coupling 

 Fine Tuning Tips 

 For L₂ Adjustment: 

 

 

 Add/remove turns (large adjustment) 

 Adjust core gap if gapped (medium) 

 Use adjustable ferrite slug (fine) 

 

 

 For C wfc Adjustment: 

 

 

 Add parallel capacitor (increases C) 

 Change water level (changes effective area) 

 Adjust electrode spacing (if possible) 

 

 

 For Frequency Adjustment: 

 

 PLL feedback to track resonance 

 Variable frequency oscillator 

 Multiple operating modes 

 

 Complete Matching Checklist 

 

 ☐ Measure or calculate C wfc 

 ☐ Measure or calculate L₂ 

 ☐ Calculate expected f₀ = 1/(2π√(L₂C)) 

 ☐ Verify f₀ is within driver frequency range 

 ☐ Calculate Z₀ = √(L₂/C) 

 ☐ Estimate R total (DCR + solution R) 

 ☐ Calculate Q = Z₀/R 

 ☐ Build circuit and measure actual resonance 

 ☐ Fine-tune as needed 

 ☐ Verify Q meets design goals 

 

 VIC Matrix Calculator: The Simulation tab performs complete matching analysis. Enter your choke and WFC parameters, and it calculates resonant frequency, Q factor, voltage magnification, and shows warnings if components are mismatched. 

 Chapter 6 Complete. Next: The VIC Matrix Calculator →