Experimental Validation

Experimental Validation Methods 

 Theoretical calculations and simulations must be validated with actual measurements. This page covers practical techniques for measuring VIC circuit parameters and comparing results to predictions. 

 Essential Test Equipment 

 Equipment 

 Purpose 

 Key Specifications 

 Oscilloscope 

 Waveform viewing, frequency measurement 

 2+ channels, 100+ MHz bandwidth 

 Function Generator 

 Provide test signals 

 1 Hz - 1 MHz, variable duty cycle 

 LCR Meter 

 Measure L, C, R 

 Multiple test frequencies (1 kHz, 10 kHz) 

 Multimeter 

 DC resistance, voltage 

 True RMS, low-ohm capability 

 Current Probe 

 Non-contact current measurement 

 AC/DC, appropriate bandwidth 

 High-Voltage Probe 

 Measure high voltages safely 

 1000:1 or 100:1, rated voltage 

 Component Verification 

 Measuring Inductance 

 Method 1: LCR Meter (Preferred) 

 

 

 Set LCR meter to inductance mode 

 Select test frequency (1 kHz typical) 

 Connect inductor, read value 

 Repeat at 10 kHz to check for frequency dependence 

 

 

 Method 2: Resonance with Known C 

 

 Connect inductor with known capacitor C 

 Drive with function generator, sweep frequency 

 Find resonant frequency f₀ (voltage peak) 

 Calculate: L = 1/(4π²f₀²C) 

 

 Measuring DCR 

 Four-Wire (Kelvin) Measurement: 

 For accurate low-resistance measurement, use 4-wire method to eliminate lead resistance: 

 

 

 Use dedicated low-ohm meter 

 Or use LCR meter in R mode 

 Allow reading to stabilize (self-heating) 

 

 

 Expected accuracy: ±1-5% compared to calculated value 

 Measuring WFC Capacitance 

 

 

 Fill WFC with water at operating temperature 

 Measure with LCR meter at 1 kHz and 10 kHz 

 Values should be similar (if EDL effects are small) 

 Note the ESR reading as well 

 

 

 Expected accuracy: ±10-20% compared to calculated value 

 Resonant Frequency Measurement 

 Frequency Sweep Method 

 Setup: 

 Function ──→ [VIC ] ──→ Oscilloscope

Generator [Circuit] Ch1: Input

 Ch2: Output (across WFC)

 

 Procedure: 

 

 

 Set function generator to low amplitude sine wave 

 Start at low frequency (1/10 of expected f₀) 

 Slowly increase frequency while watching Ch2 amplitude 

 Note frequency of maximum amplitude—this is f₀ 

 Also note -3dB frequencies (where amplitude = 0.707 × peak) 

 

 

 Calculate Q from Measurement: 

 Q = f₀ / (f high - f low ) = f₀ / BW 

 Phase Measurement Method 

 

 Display both input current and output voltage 

 Use X-Y mode or measure phase with oscilloscope 

 At resonance, phase difference = 0° 

 More accurate than amplitude peak for high-Q circuits 

 

 Q Factor Measurement 

 Method 1: Bandwidth 

 Measure -3dB bandwidth and calculate: 

 Q = f₀ / BW 

 Method 2: Ring-Down 

 

 

 Excite circuit with single pulse at f₀ 

 Observe decaying oscillation on oscilloscope 

 Count cycles to decay to 1/e (37%) 

 Q ≈ π × (number of cycles to 1/e decay) 

 

 

 Alternatively, measure time constant τ: 

 τ = 2L/R = Q/(πf₀) 

 Method 3: Voltage Magnification 

 

 

 Measure input voltage V in 

 Measure output voltage V out at resonance 

 Q ≈ V out /V in 

 

 

 Caution: This assumes lossless input coupling. Actual Q may be higher due to source impedance effects. 

 Comparing Calculated vs. Measured 

 Parameter 

 Acceptable Difference 

 If Larger Difference 

 Inductance 

 ±20% 

 Check core μᵣ, turn count 

 DCR 

 ±10% 

 Check wire gauge, connections 

 WFC Capacitance 

 ±20% 

 Check geometry, water level 

 Resonant Frequency 

 ±15% 

 Check L and C values 

 Q Factor 

 ±30% 

 Look for missing losses 

 Troubleshooting Discrepancies 

 Measured f₀ Lower than Calculated: 

 

 

 Stray capacitance adding to total C 

 Actual L higher than calculated 

 Check for loose connections (add L) 

 

 

 Measured f₀ Higher than Calculated: 

 

 

 Actual L lower (core saturation, wrong μᵣ) 

 WFC capacitance overestimated 

 Air bubbles reducing effective C 

 

 

 Measured Q Lower than Calculated: 

 

 

 Additional losses not accounted for 

 Core losses at operating frequency 

 Poor connections adding resistance 

 Radiation losses at high frequency 

 

 

 No Clear Resonance Observed: 

 

 Operating above SRF (choke is capacitive) 

 Very low Q (Q < 2) makes resonance hard to see 

 Measurement setup loading the circuit 

 

 Documentation Template 

 Record for Each Test: 

 Date: ___________

Circuit ID: ___________

COMPONENT VALUES (Calculated / Measured):

L1: _______ mH / _______ mH

L2: _______ mH / _______ mH

DCR1: _______ Ω / _______ Ω

DCR2: _______ Ω / _______ Ω

C_wfc: _______ nF / _______ nF

C1: _______ nF / _______ nF

RESONANCE (Calculated / Measured):

f₀_primary: _______ kHz / _______ kHz

f₀_secondary: _______ kHz / _______ kHz

PERFORMANCE (Calculated / Measured):

Q: _______ / _______

Bandwidth: _______ Hz / _______ Hz

V_magnification: _______ / _______

NOTES:

_________________________________

 

 Safety Considerations 

 ⚠️ High Voltage Warning: 

 

 

 VIC circuits can develop high voltages at resonance 

 Always use proper high-voltage probes 

 Keep one hand in pocket when probing live circuits 

 Discharge capacitors before handling 

 

 

 ⚠️ Gas Production: 

 

 WFC produces hydrogen and oxygen—ensure ventilation 

 No open flames or sparks near operating cell 

 Use appropriate gas collection if needed 

 

 Best Practice: Always compare measured values to calculator predictions. This builds confidence in both your construction skills and the calculator's accuracy. Document discrepancies—they often reveal important lessons about real-world effects. 

 Chapter 8 Complete. See Appendices for reference tables and formulas. →