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: 

 E L = ½LI² (energy in inductor) E C = ½CV² (energy in capacitor) 

 At Resonance: 

 E total = E L,max = E C,max = ½CV peak ² 

 Peak Energy (example): 

 

 C = 10 nF, V peak = 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 = I²R DCR 

 Use larger wire, copper 

 Solution Resistance 

 P = I²R sol 

 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: 

 ΔE cycle = 2π × E stored / 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 

 P in = V in × I in × cos(φ) 

 For pulsed operation: 

 P avg = (1/T) × ∫V(t)I(t)dt 

 Dissipated Power 

 P diss = I rms ² × R total 

 Where R total = R DCR1 + R DCR2 + R sol + R other 

 Useful Power 

 Power available for electrochemical work: 

 P useful = P in - P diss 

 Or, for the WFC specifically: 

 P wfc = V wfc × I wfc × cos(φ wfc ) 

 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 = P wfc /P in 

 50-90% 

 Voltage Multiplication η 

 V out /V in (at resonance) 

 10-100× typical 

 Energy Balance Verification 

 To verify your analysis is correct, energy must balance: 

 Steady State: 

 P in = P DCR1 + P DCR2 + P sol + P core + P other 

 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% 

 R solution 

 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: 

 

 

 Reduce largest loss first: In example above, R sol is 40%—optimize water conductivity 

 Use larger wire: Each AWG step down reduces DCR by ~25% 

 Choose better core: Low-loss ferrite vs. iron powder 

 Optimize water conductivity: Not too high (electrolysis), not too low (resistance loss) 

 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 →