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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 × Cwfc))

Design Challenge:

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

  1. Measure Cwfc with LCR meter
  2. Choose target frequency f₀
  3. Calculate required L₂:

L₂ = 1 / (4π²f₀²Cwfc)

Example:

  • Cwfc = 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:

  1. Measure L₂ with LCR meter
  2. Choose target frequency f₀
  3. Calculate required Cwfc:

Cwfc = 1 / (4π²f₀²L₂)

  1. Design electrodes to achieve that capacitance

Strategy 3: Tune with Additional Capacitor

When exact match isn't achievable:

If Cwfc is too low:

Add capacitor in parallel with WFC

Ctotal = Cwfc + Ctune

If Cwfc is too high:

Add capacitor in series with WFC (less common)

1/Ctotal = 1/Cwfc + 1/Cseries

Impedance Matching Considerations

Beyond frequency matching, impedance levels affect energy transfer:

Secondary Characteristic Impedance:

Z₀ = √(L₂/Cwfc)

Example Comparison:

L₂ Cwfc 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 f₀pri = f₀sec Maximum voltage magnification
Slight offset f₀sec ≈ 0.95-1.05 × f₀pri Broader response, easier tuning
Harmonic f₀sec = 2× or 3× f₀pri Secondary resonates on harmonic

Finding Resonance

Method 1: Frequency Sweep

  1. Connect oscilloscope across WFC
  2. Sweep generator frequency slowly
  3. Watch for voltage peak
  4. Note frequency of maximum amplitude

Method 2: Phase Measurement

  1. Monitor current and voltage simultaneously
  2. At resonance, current and voltage are in phase (phase = 0°)
  3. Below resonance: capacitive (current leads)
  4. 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 Cwfc 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

  1. ☐ Measure or calculate Cwfc
  2. ☐ Measure or calculate L₂
  3. ☐ Calculate expected f₀ = 1/(2π√(L₂C))
  4. ☐ Verify f₀ is within driver frequency range
  5. ☐ Calculate Z₀ = √(L₂/C)
  6. ☐ Estimate Rtotal (DCR + solution R)
  7. ☐ Calculate Q = Z₀/R
  8. ☐ Build circuit and measure actual resonance
  9. ☐ Fine-tune as needed
  10. ☐ 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 →

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