# 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

<table id="bkmrk-equipment-purpose-ke" style="width: 100%; border-collapse: collapse; margin: 20px 0;"><thead><tr style="background: #007bff; color: white;"><th style="padding: 10px; border: 1px solid #ddd;">Equipment</th><th style="padding: 10px; border: 1px solid #ddd;">Purpose</th><th style="padding: 10px; border: 1px solid #ddd;">Key Specifications</th></tr></thead><tbody><tr><td style="padding: 10px; border: 1px solid #ddd;">Oscilloscope</td><td style="padding: 10px; border: 1px solid #ddd;">Waveform viewing, frequency measurement</td><td style="padding: 10px; border: 1px solid #ddd;">2+ channels, 100+ MHz bandwidth</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">Function Generator</td><td style="padding: 10px; border: 1px solid #ddd;">Provide test signals</td><td style="padding: 10px; border: 1px solid #ddd;">1 Hz - 1 MHz, variable duty cycle</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">LCR Meter</td><td style="padding: 10px; border: 1px solid #ddd;">Measure L, C, R</td><td style="padding: 10px; border: 1px solid #ddd;">Multiple test frequencies (1 kHz, 10 kHz)</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">Multimeter</td><td style="padding: 10px; border: 1px solid #ddd;">DC resistance, voltage</td><td style="padding: 10px; border: 1px solid #ddd;">True RMS, low-ohm capability</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">Current Probe</td><td style="padding: 10px; border: 1px solid #ddd;">Non-contact current measurement</td><td style="padding: 10px; border: 1px solid #ddd;">AC/DC, appropriate bandwidth</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">High-Voltage Probe</td><td style="padding: 10px; border: 1px solid #ddd;">Measure high voltages safely</td><td style="padding: 10px; border: 1px solid #ddd;">1000:1 or 100:1, rated voltage</td></tr></tbody></table>

## Component Verification

### Measuring Inductance

#### Method 1: LCR Meter (Preferred)

<div id="bkmrk-set-lcr-meter-to-ind" style="background: #e7f3ff; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #e7f3ff; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Set LCR meter to inductance mode
2. Select test frequency (1 kHz typical)
3. Connect inductor, read value
4. Repeat at 10 kHz to check for frequency dependence

</div></div>#### Method 2: Resonance with Known C

<div id="bkmrk-connect-inductor-wit" style="background: #e7f3ff; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Connect inductor with known capacitor C
2. Drive with function generator, sweep frequency
3. Find resonant frequency f₀ (voltage peak)
4. Calculate: L = 1/(4π²f₀²C)

</div>### Measuring DCR

#### Four-Wire (Kelvin) Measurement:

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

<div id="bkmrk-use-dedicated-low-oh" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">- Use dedicated low-ohm meter
- Or use LCR meter in R mode
- Allow reading to stabilize (self-heating)

</div></div>**Expected accuracy:** ±1-5% compared to calculated value

### Measuring WFC Capacitance

<div id="bkmrk-fill-wfc-with-water-" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Fill WFC with water at operating temperature
2. Measure with LCR meter at 1 kHz and 10 kHz
3. Values should be similar (if EDL effects are small)
4. Note the ESR reading as well

</div></div>**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:

<div id="bkmrk-set-function-generat" style="background: #d4edda; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #d4edda; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Set function generator to low amplitude sine wave
2. Start at low frequency (1/10 of expected f₀)
3. Slowly increase frequency while watching Ch2 amplitude
4. Note frequency of maximum amplitude—this is f₀
5. Also note -3dB frequencies (where amplitude = 0.707 × peak)

</div></div>#### Calculate Q from Measurement:

Q = f₀ / (f<sub>high</sub> - f<sub>low</sub>) = f₀ / BW

### Phase Measurement Method

<div id="bkmrk-display-both-input-c" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Display both input current and output voltage
2. Use X-Y mode or measure phase with oscilloscope
3. At resonance, phase difference = 0°
4. More accurate than amplitude peak for high-Q circuits

</div>## Q Factor Measurement

### Method 1: Bandwidth

Measure -3dB bandwidth and calculate:

Q = f₀ / BW

### Method 2: Ring-Down

<div id="bkmrk-excite-circuit-with-" style="background: #e7f3ff; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #e7f3ff; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Excite circuit with single pulse at f₀
2. Observe decaying oscillation on oscilloscope
3. Count cycles to decay to 1/e (37%)
4. Q ≈ π × (number of cycles to 1/e decay)

</div></div>Alternatively, measure time constant τ:

τ = 2L/R = Q/(πf₀)

### Method 3: Voltage Magnification

<div id="bkmrk-measure-input-voltag" style="background: #fff3cd; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #fff3cd; padding: 20px; border-radius: 5px; margin: 20px 0;">1. Measure input voltage V<sub>in</sub>
2. Measure output voltage V<sub>out</sub> at resonance
3. Q ≈ V<sub>out</sub>/V<sub>in</sub>

</div></div>**Caution:** This assumes lossless input coupling. Actual Q may be higher due to source impedance effects.

## Comparing Calculated vs. Measured

<table id="bkmrk-parameter-acceptable" style="width: 100%; border-collapse: collapse; margin: 20px 0;"><thead><tr style="background: #17a2b8; color: white;"><th style="padding: 10px; border: 1px solid #ddd;">Parameter</th><th style="padding: 10px; border: 1px solid #ddd;">Acceptable Difference</th><th style="padding: 10px; border: 1px solid #ddd;">If Larger Difference</th></tr></thead><tbody><tr><td style="padding: 10px; border: 1px solid #ddd;">Inductance</td><td style="padding: 10px; border: 1px solid #ddd;">±20%</td><td style="padding: 10px; border: 1px solid #ddd;">Check core μᵣ, turn count</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">DCR</td><td style="padding: 10px; border: 1px solid #ddd;">±10%</td><td style="padding: 10px; border: 1px solid #ddd;">Check wire gauge, connections</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">WFC Capacitance</td><td style="padding: 10px; border: 1px solid #ddd;">±20%</td><td style="padding: 10px; border: 1px solid #ddd;">Check geometry, water level</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">Resonant Frequency</td><td style="padding: 10px; border: 1px solid #ddd;">±15%</td><td style="padding: 10px; border: 1px solid #ddd;">Check L and C values</td></tr><tr><td style="padding: 10px; border: 1px solid #ddd;">Q Factor</td><td style="padding: 10px; border: 1px solid #ddd;">±30%</td><td style="padding: 10px; border: 1px solid #ddd;">Look for missing losses</td></tr></tbody></table>

## Troubleshooting Discrepancies

#### Measured f₀ Lower than Calculated:

<div id="bkmrk-stray-capacitance-ad" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">- Stray capacitance adding to total C
- Actual L higher than calculated
- Check for loose connections (add L)

</div></div>#### Measured f₀ Higher than Calculated:

<div id="bkmrk-actual-l-lower-%28core" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">- Actual L lower (core saturation, wrong μᵣ)
- WFC capacitance overestimated
- Air bubbles reducing effective C

</div></div>#### Measured Q Lower than Calculated:

<div id="bkmrk-additional-losses-no" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">- Additional losses not accounted for
- Core losses at operating frequency
- Poor connections adding resistance
- Radiation losses at high frequency

</div></div>#### No Clear Resonance Observed:

<div id="bkmrk-operating-above-srf-" style="background: #f8f9fa; padding: 20px; border-radius: 5px; margin: 20px 0;">- Operating above SRF (choke is capacitive)
- Very low Q (Q &lt; 2) makes resonance hard to see
- Measurement setup loading the circuit

</div>## 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:

<div id="bkmrk-vic-circuits-can-dev" style="background: #f8d7da; padding: 20px; border-radius: 5px; margin: 20px 0;"><div style="background: #f8d7da; padding: 20px; border-radius: 5px; margin: 20px 0;">- 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

</div></div>#### ⚠️ Gas Production:

<div id="bkmrk-wfc-produces-hydroge" style="background: #f8d7da; padding: 20px; border-radius: 5px; margin: 20px 0;">- WFC produces hydrogen and oxygen—ensure ventilation
- No open flames or sparks near operating cell
- Use appropriate gas collection if needed

</div>**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. →*