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Energy Efficiency

Energy Efficiency Analysis

Understanding energy flow in VIC circuits helps optimize performance and evaluate system efficiency. This page covers how to analyze energy storage, transfer, and dissipation in resonant VIC systems.

Energy in Resonant Circuits

In an LC resonant circuit, energy oscillates between the inductor and capacitor:

Energy Storage:

EL = ½LI² (energy in inductor)
EC = ½CV² (energy in capacitor)

At Resonance:

Etotal = EL,max = EC,max = ½CVpeak²

Peak Energy (example):

  • C = 10 nF, Vpeak = 1000 V
  • E = ½ × 10×10⁻⁹ × 1000² = 5 mJ

Energy Flow Diagram

                    Input Power
                         │
                         ↓
    ┌─────────────────────────────────────────────┐
    │              VIC CIRCUIT                     │
    │                                              │
    │  ┌──────┐      ┌──────┐      ┌──────┐       │
    │  │ L1   │──────│ L2   │──────│ WFC  │       │
    │  │ DCR  │      │ DCR  │      │ ESR  │       │
    │  └──────┘      └──────┘      └──────┘       │
    │      │             │             │          │
    │      ↓             ↓             ↓          │
    │  Heat Loss    Heat Loss     Heat Loss       │
    │  (copper)     (copper)      (solution)      │
    │                                  │          │
    │                                  ↓          │
    │                           Electrochemical   │
    │                           Work (desired)    │
    └─────────────────────────────────────────────┘

Loss Mechanisms

Loss Type Formula How to Minimize
Choke DCR Loss P = I²RDCR Use larger wire, copper
Solution Resistance P = I²Rsol Optimize water conductivity
Core Loss P ∝ f^α × B^β Choose low-loss core material
Skin Effect Loss Increases R at high f Use Litz wire at high f
Dielectric Loss P = ωCV² × tan(δ) Use low-loss capacitors

Q Factor and Efficiency

Q factor is directly related to energy efficiency per cycle:

Energy Loss Per Cycle:

ΔEcycle = 2π × Estored / Q

Interpretation:

  • Q = 10: Lose 63% of energy per cycle
  • Q = 50: Lose 13% of energy per cycle
  • Q = 100: Lose 6% of energy per cycle
  • Q = 200: Lose 3% of energy per cycle

Energy Retention:

After n cycles: E(n) = E₀ × e^(-2πn/Q)

Power Flow Analysis

Input Power

Pin = Vin × Iin × cos(φ)

For pulsed operation:

Pavg = (1/T) × ∫V(t)I(t)dt

Dissipated Power

Pdiss = Irms² × Rtotal

Where Rtotal = RDCR1 + RDCR2 + Rsol + Rother

Useful Power

Power available for electrochemical work:

Puseful = Pin - Pdiss

Or, for the WFC specifically:

Pwfc = Vwfc × Iwfc × cos(φwfc)

Efficiency Calculations

Efficiency Type Formula Typical Values
Resonant Tank η η = Q/(Q+1) ≈ 1 - 1/Q 90-99% for high Q
Power Transfer η η = Pwfc/Pin 50-90%
Voltage Multiplication η Vout/Vin (at resonance) 10-100× typical

Energy Balance Verification

To verify your analysis is correct, energy must balance:

Steady State:

Pin = PDCR1 + PDCR2 + Psol + Pcore + Pother

Check:

  • Sum all loss mechanisms
  • Compare to measured input power
  • Large discrepancy indicates missing loss or measurement error

Loss Breakdown Example

Component Resistance Power Loss (at 1A) % of Total
L1 DCR 2.5 Ω 2.5 W 25%
L2 DCR 3.0 Ω 3.0 W 30%
Rsolution 4.0 Ω 4.0 W 40%
Other (core, leads) 0.5 Ω 0.5 W 5%
Total 10 Ω 10 W 100%

Improving Efficiency

High-Impact Improvements:

  1. Reduce largest loss first: In example above, Rsol is 40%—optimize water conductivity
  2. Use larger wire: Each AWG step down reduces DCR by ~25%
  3. Choose better core: Low-loss ferrite vs. iron powder
  4. Optimize water conductivity: Not too high (electrolysis), not too low (resistance loss)
  5. Reduce connection resistance: Good solder joints, clean contacts

Diminishing Returns:

Once a loss mechanism is <10% of total, further improvement has limited benefit. Focus on the dominant losses.

Thermal Considerations

All dissipated power becomes heat:

Component Heat Concern Mitigation
Choke windings Wire insulation damage Adequate wire size, ventilation
Ferrite core Curie temp, permeability change Keep below rated temperature
Water/WFC Boiling, capacitance drift Monitor temperature, allow cooling
Capacitors ESR heating, life reduction Use low-ESR types, derate

VIC Matrix Calculator: The simulation module calculates expected power dissipation in each component. Use this to identify thermal hotspots and verify your design won't overheat during operation.

Next: Experimental Validation Methods →

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