Voltage Magnification

Voltage Magnification at Resonance 

 Voltage magnification is the cornerstone of VIC circuit operation. At resonance, the voltage across reactive components (inductors and capacitors) can be many times greater than the input voltage. This is how the VIC develops high voltages across the water fuel cell while drawing modest current from the source. 

 The Principle of Voltage Magnification 

 In a series resonant circuit, even though the total impedance is at minimum (just resistance), the individual voltages across L and C can be much larger than the source voltage. This isn't "free energy"—it's the result of energy continuously cycling between the inductor and capacitor. 

 Key Insight: 

 At resonance, V L and V C are equal in magnitude but opposite in phase. They cancel each other in the circuit loop, but individually each represents a real voltage that can do work. 

 Voltage Magnification Formula 

 Q-Based Magnification: 

 V output = Q × V input 

 Impedance-Based Magnification: 

 Magnification = Z₀ / R = (1/R) × √(L/C) 

 Both formulas give the same result since Q = Z₀/R for a series circuit. 

 Practical Examples 

 Input Voltage 

 Q Factor 

 Output Voltage 

 Application 

 12V 

 10 

 120V 

 Low-Q experimental setup 

 12V 

 50 

 600V 

 Typical VIC circuit 

 12V 

 100 

 1200V 

 High-Q optimized circuit 

 24V 

 50 

 1200V 

 Higher input voltage approach 

 Where the Magnified Voltage Appears 

 In a Series LC Circuit 

 Across the inductor: V L = Q × V source (leads current by 90°) 

 Across the capacitor: V C = Q × V source (lags current by 90°) 

 Across resistance: V R = V source (in phase with current) 

 In the VIC Circuit 

 The water fuel cell acts as the capacitor, so the magnified voltage appears directly across the water: 

 VIC Voltage Path: 

 Source → L1 → C1 (series resonance for initial magnification) 

 Transformed via coupling to → L2 → WFC (secondary resonance) 

 Result: High voltage across water fuel cell electrodes 

 Two Approaches to Magnification 

 Method 1: Maximize Q 

 Increase Q by reducing resistance: 

 Use copper wire instead of resistance wire 

 Use larger gauge wire 

 Minimize connection resistances 

 Use low-ESR capacitors 

 Method 2: Optimize Z₀/R Ratio 

 Increase characteristic impedance relative to resistance: 

 Increase inductance (more turns, larger core) 

 Decrease capacitance (for same resonant frequency, requires more inductance) 

 The ratio √(L/C) determines Z₀ 

 Design Trade-off: 

 For a given resonant frequency f₀ = 1/(2π√LC): 

 

 

 Higher L with lower C → Higher Z₀ → Higher magnification (but more wire, more DCR) 

 Lower L with higher C → Lower Z₀ → Lower magnification (but less wire, less DCR) 

 

 

 The optimal design balances these factors. 

 Energy Considerations 

 Voltage magnification doesn't violate energy conservation: 

 Power In = Power Dissipated 

 At steady-state resonance: 

 

 

 Current through circuit: I = V source /R 

 Power from source: P = V source × I = V source ²/R 

 Power dissipated in R: P = I²R = V source ²/R (same!) 

 

 

 The high voltage across L and C represents reactive power —energy that sloshes back and forth but isn't consumed. 

 Real Power vs. Reactive Power 

 Type 

 Symbol 

 Unit 

 Description 

 Real Power 

 P 

 Watts (W) 

 Actually consumed, heats resistors 

 Reactive Power 

 Q (or VAR) 

 Volt-Amperes Reactive 

 Oscillates, stored in L and C 

 Apparent Power 

 S 

 Volt-Amperes (VA) 

 Total power flow 

 Magnification in the VIC Matrix Calculator 

 The VIC Matrix Calculator displays voltage magnification in several ways: 

 In Choke Designs 

 Q Factor: Calculated from inductance and DCR 

 Voltage Magnification: Equals Q for series resonance 

 Z₀/R Magnification: Alternative calculation method 

 Example Output: Shows actual voltage with 12V input 

 In Circuit Profiles 

 Q_L1C: Q factor of primary side (L1 with C1) 

 Q_L2: Q factor of secondary side (L2 with WFC) 

 Voltage Magnification: Expected magnification at resonance 

 Practical Note: Real circuits achieve somewhat less than theoretical magnification due to losses not accounted for in simple models (core losses, radiation, dielectric losses in capacitors, etc.). Expect 70-90% of calculated values in practice. 

 Safety Warning 

 ⚠️ High Voltage Hazard 

 Resonant circuits can develop dangerous voltages even from low-voltage sources: 

 

 A 12V source with Q=50 produces 600V peaks 

 These voltages can cause electric shock or burns 

 Energy stored in capacitors remains after power is removed 

 Always discharge capacitors before handling circuits 

 Use appropriate insulation and safety equipment 

 

 Chapter 1 Complete. Next: The Electric Double Layer (EDL) →