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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, VL and VC 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:

Voutput = Q × Vinput

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: VL = Q × Vsource (leads current by 90°)
  • Across the capacitor: VC = Q × Vsource (lags current by 90°)
  • Across resistance: VR = Vsource (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 = Vsource/R
  • Power from source: P = Vsource × I = Vsource²/R
  • Power dissipated in R: P = I²R = Vsource²/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) →

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