VIC Matrix Calculator Calculator Overview VIC Matrix Calculator Overview The VIC Matrix Calculator is a comprehensive design tool that integrates all the concepts covered in this educational series. It allows you to design, simulate, and optimize complete VIC circuits by calculating component values, resonant frequencies, Q factors, and system behavior. Calculator URL: https://matrix.stanslegacy.com What the Calculator Does The calculator brings together multiple design domains: 1. Choke Design Module Calculate inductance, DCR, parasitic capacitance, and SRF for custom wound chokes. Core selection (ferrite, iron powder, air core) Wire gauge and material selection Bifilar winding support Multi-layer winding calculations 2. Water Profile Module Model the WFC as an electrical component with all relevant parameters. Electrode geometry (plates, tubes, arrays) Water conductivity effects Temperature compensation EDL and solution resistance 3. Circuit Profile Module Combine chokes and WFC into complete VIC circuits for analysis. Primary and secondary resonance Q factor and bandwidth Voltage magnification Ring-down characteristics 4. Simulation Module Visualize circuit behavior and optimize performance. Frequency response plots Time-domain waveforms Impedance analysis Sensitivity analysis Design Workflow The recommended workflow for using the calculator: Define Requirements: Target frequency, available components, constraints Design/Select Chokes: Use Choke Design module or enter measured values Configure Water Profile: Enter WFC geometry and water properties Create Circuit Profile: Combine components and select topology Run Simulation: Analyze resonance, Q, and system behavior Optimize: Adjust parameters to improve performance Build & Verify: Construct circuit and compare to predictions Key Features Feature Description Benefit Real-time Calculations Results update instantly as you change parameters Rapid design iteration Warning System Alerts for out-of-range values or design issues Avoid common mistakes Saved Profiles Store and recall choke, water, and circuit configurations Compare designs easily Interconnected Models Changes propagate through entire system See full system impact Educational Notes Tooltips and explanations throughout Learn while designing Input vs. Output Parameters You Provide (Inputs): Core dimensions and material properties Wire gauge, material, and turn count Electrode geometry and spacing Water conductivity and temperature Operating frequency or frequency range Calculator Provides (Outputs): Inductance (L), DCR, parasitic capacitance Self-resonant frequency (SRF) WFC capacitance and ESR Resonant frequency (f₀) Q factor, bandwidth, ring-down time Voltage magnification ratio Impedance characteristics Frequency response curves Accuracy and Limitations Parameter Typical Accuracy Notes Inductance ±10-20% Core properties vary; always verify DCR ±5% Depends on wire tables accuracy WFC Capacitance ±15% Fringe effects, water purity affect results Q Factor ±20-30% Multiple loss mechanisms; use as estimate Resonant Frequency ±10-15% Depends on L and C accuracy Important: The calculator provides design estimates. Always verify critical parameters with measurements on actual components. Real-world results may vary due to manufacturing tolerances, stray inductance/capacitance, and environmental factors. Getting Started To begin using the VIC Matrix Calculator: Navigate to the application dashboard Start with the module that matches your first design decision: If you have specific chokes → Start with Choke Design If you have a specific WFC → Start with Water Profile If you have target frequency → Work backwards from Circuit Profile Follow the guided workflow to complete your design Tip: The following pages in this chapter provide detailed guidance on each module. Work through them in order for the best understanding of the calculator's capabilities. Next: Component Input Parameters → Component Inputs Component Input Parameters This page details all input parameters used across the VIC Matrix Calculator modules. Understanding what each parameter means and how to determine its value is essential for accurate calculations. Choke Design Inputs Core Parameters Parameter Symbol Units Description Core Type — — Toroid, E-core, rod, bobbin, or air-core Core Material — — Ferrite mix, iron powder, or air Relative Permeability μᵣ — Material permeability (1 for air, 2000+ for ferrite) AL Value Aₗ nH/turn² Inductance factor (from core datasheet) Outer Diameter OD mm Core outer diameter (toroids) Inner Diameter ID mm Core inner diameter (toroids) Height H mm Core height/thickness Finding Core Parameters: Check manufacturer datasheet for Aₗ and μᵣ Measure physical dimensions with calipers For unknown cores, estimate μᵣ from material type Wire Parameters Parameter Symbol Units Description Wire Gauge AWG AWG American Wire Gauge number Wire Material — — Copper, aluminum, silver Number of Turns N turns Total turns wound on core Number of Layers n layers — Winding layers (affects parasitic C) Winding Style — — Single, bifilar, or multi-filar Bifilar-Specific Parameters Parameter Description Choke Role Primary (L1), Secondary (L2), or Bifilar Set Coupling Coefficient k value between bifilar windings (typically 0.95-0.99) Inter-winding Insulation Thickness and material of insulation between wires Water Profile Inputs Electrode Geometry Parameter Symbol Units Description Electrode Type — — Parallel plates, concentric tubes, tube array Electrode Area A cm² Active electrode surface area Electrode Gap d mm Distance between electrodes Inner Radius r i mm Inner tube radius (cylindrical) Outer Radius r o mm Outer tube radius (cylindrical) Tube Length L cm Submerged tube length Number of Tubes n — Tube pairs in array Water Properties Parameter Symbol Units Description Water Conductivity σ µS/cm Electrical conductivity of water Water Temperature T °C Operating temperature Dielectric Constant ε r — Relative permittivity (~80 for water at 20°C) Measuring Conductivity: Use a TDS or conductivity meter Distilled water: 1-10 µS/cm Tap water: 200-800 µS/cm If unknown, 500 µS/cm is a reasonable tap water estimate Circuit Profile Inputs Component Selection Parameter Description Primary Choke (L1) Select from saved choke designs or enter values Secondary Choke (L2) Select from saved choke designs or enter values Water Profile (WFC) Select from saved water profiles or enter values Primary Capacitor (C1) Capacitance value for primary resonance Tuning Capacitor Optional capacitor in parallel with WFC Operating Parameters Parameter Symbol Units Description Operating Frequency f op kHz Pulse generator frequency Input Voltage V in V Peak pulse voltage Duty Cycle D % Pulse on-time percentage Source Resistance R s Ω Driver output impedance Direct Value Entry If you have measured values for components (rather than designing from scratch), you can enter them directly: For Chokes: Inductance (measured at low frequency) DC Resistance (measured with ohmmeter) Self-Resonant Frequency (if known) For WFC: Capacitance (measured with LCR meter) ESR or solution resistance Best Practice: When possible, measure actual component values and compare to calculated values. This helps identify measurement errors and improves your understanding of the calculator's accuracy for your specific components. Next: Simulation Tab Explained → Simulation Tab Simulation Tab Explained The Simulation tab provides visual analysis of your VIC circuit design. It generates frequency response curves, time-domain waveforms, and key performance metrics that help you understand and optimize circuit behavior. Simulation Overview The simulation performs several types of analysis: 1. Frequency Domain Analysis Sweeps through a frequency range to show how the circuit responds at different frequencies. 2. Impedance Analysis Shows how circuit impedance varies with frequency, identifying resonant points. 3. Time Domain Analysis Simulates actual voltage and current waveforms during pulse operation. 4. Ring-down Analysis Shows how oscillations decay after excitation stops. Frequency Response Display The frequency response plot shows amplitude vs. frequency: Amplitude ↑ │ │ ╱╲ │ ╱ ╲ ← Secondary resonance │ ╱ ╲ │ ╱ ╲ │ ╱╲ ╱ ╲ │ ╱ ╲ ╱ ╲ │ ╱ ╲ ╱ ╲ │╱ ╳ ╲ └─────────────────────────→ Frequency (kHz) ↑ ↑ Primary Secondary resonance resonance Key Features in Plot Feature What It Means Ideal Characteristic Peak Height Voltage magnification at resonance Higher = more voltage gain Peak Sharpness Q factor (sharp = high Q) Depends on application Peak Location Resonant frequency f₀ Should match design target -3dB Bandwidth Frequency range at 70.7% of peak Narrower = higher Q Multiple Peaks Primary and secondary resonances Aligned for max transfer Calculated Metrics The simulation calculates and displays these key values: Resonance Parameters Primary f₀: Resonant frequency of L1-C1 tank Secondary f₀: Resonant frequency of L2-C wfc tank Match Status: How well primary and secondary are tuned Q Factor Metrics Primary Q: Q factor of primary circuit Secondary Q: Q factor of secondary circuit System Q: Effective Q of coupled system Performance Metrics Voltage Magnification: V out /V in at resonance Bandwidth: -3dB frequency range Ring-down Time: Time constant τ = 2L/R Ring-down Cycles: Oscillation cycles during decay Impedance Plot Shows circuit impedance magnitude and phase vs. frequency: |Z| (Ω) Phase ↑ ↑ │ ╱╲ │ ╱──── │ ╱ ╲ ← Peak at │ ╱ │ ╱ ╲ resonance │ ╱ │ ╱ ╲ │──────╳ ← 0° at f₀ │ ╱ ╲ │ ╱ │ ╱ ╲ │ ╱ │╱ ╲ │───╱──── └──────────────────→ f └──────────────→ f Interpreting Impedance Peak impedance: Maximum at parallel resonance Minimum impedance: At series resonance points Phase = 0°: Indicates resonant frequency Positive phase: Inductive behavior (current lags) Negative phase: Capacitive behavior (current leads) Time Domain Waveforms The time-domain view shows actual voltage and current over time: Waveforms Displayed: Input Voltage: The driving pulse waveform Primary Current: Current through L1 WFC Voltage: Voltage across the water cell WFC Current: Current through the cell What to Look For: Voltage build-up during resonance Ring-down oscillations after pulse ends Phase relationship between V and I Settling time and stability Ring-Down Display Shows oscillation decay after excitation stops: Voltage ↑ │╱╲ │ ╲╱╲ │ ╲╱╲ │ ╲╱╲ │ ╲╱╲ │ ╲╱╲ │ ╲╱─── → Envelope decay │ ╲ └────────────────────→ Time ←─── τ ───→ (63% decay) Ring-Down Metrics Metric Formula Significance Time Constant (τ) τ = 2L/R Time to decay to 37% Ring-down Cycles n ≈ 0.733 × Q Oscillations before decay Settling Time ~5τ for 99% decay Time to reach steady state Warning Indicators The simulation flags potential issues: Warning Meaning Action ⚠️ Near SRF Operating frequency close to choke SRF Reduce frequency or redesign choke ⚠️ Low Q Q factor below recommended threshold Reduce losses (DCR, water R) ⚠️ Frequency Mismatch Primary and secondary not aligned Adjust C1 or component values ⚠️ High Voltage Magnified voltage exceeds safe limits Verify insulation ratings Using Simulation Results Design Iteration Process: Run initial simulation with your component values Check if resonant frequency matches your target Evaluate Q factor—is it sufficient for your goals? Look for warnings and address them Adjust parameters and re-simulate Compare before/after to verify improvements Pro Tip: Save your circuit profile before making changes. This allows you to compare different configurations side-by-side and roll back if needed. Next: Circuit Optimization Strategies → Optimization Circuit Optimization Strategies This page covers practical strategies for optimizing your VIC circuit design using the calculator. Learn how to achieve specific goals like maximizing Q, hitting a target frequency, or optimizing voltage magnification. Optimization Goals Different applications may prioritize different characteristics: Goal Optimize For Trade-offs Maximum Voltage High Q, matched resonance Narrower bandwidth, critical tuning Stable Operation Moderate Q, wide bandwidth Lower peak voltage Frequency Flexibility Lower Q, broader response Reduced magnification Energy Efficiency Minimize losses (DCR, R sol ) May require larger components Strategy 1: Maximizing Q Factor Q determines voltage magnification and selectivity. To maximize Q: Reduce Choke DCR: Use larger wire gauge (lower AWG number) Use copper instead of aluminum Minimize wire length (fewer turns with higher-μ core) Consider Litz wire for high frequencies Reduce Solution Resistance: Increase water conductivity slightly (add small amount of electrolyte) Increase electrode area Decrease electrode gap (but watch capacitance change) Ensure good electrode contact Increase L or Decrease C: Higher L/C ratio raises Z₀ = √(L/C) Q = Z₀/R, so higher Z₀ means higher Q Must maintain same f₀ = 1/(2π√LC) Q Factor Relationships: Q = 2πf₀L/R = Z₀/R = √(L/C)/R To double Q: halve R, or quadruple L (while quartering C to maintain f₀) Strategy 2: Hitting Target Frequency When you need a specific resonant frequency: Approach A: Fixed L, Adjust C Design or select choke for desired L Calculate required C: C = 1/(4π²f₀²L) If C wfc ≠ required C: Add parallel capacitor if C wfc is too low Modify electrode geometry if adjustment is large Approach B: Fixed C, Adjust L Measure or calculate WFC capacitance Calculate required L: L = 1/(4π²f₀²C) Design choke for that inductance Approach C: Adjust Both Start with practical component ranges Use calculator to explore L/C combinations Choose combination that also optimizes Q Fine-Tuning Frequency Adjustment Effect on f₀ Typical Range Add parallel capacitor Decreases f₀ 1-50 nF typical Adjust core gap (if gapped) Changes L → changes f₀ ±20% L adjustment Add/remove turns Changes L significantly L ∝ N² Change water level Changes C → changes f₀ Proportional to area Strategy 3: Matching Primary to Secondary For maximum energy transfer, align primary and secondary resonances: Exact Match (f₀ pri = f₀ sec ): Maximum voltage transfer at resonance Narrow combined response Requires precise tuning Slight Offset (5-10% difference): Broader frequency response More tolerant of drift Slightly reduced peak transfer Calculator Approach: Design secondary (L2 + WFC) first—this is usually more constrained Calculate secondary f₀ Select C1 to tune primary to match: C1 = 1/(4π²f₀²L1) Verify with simulation Strategy 4: Optimizing for Available Components When working with existing components: Step 1: Characterize What You Have Measure L of available chokes Measure C of your WFC Note DCR values Step 2: Calculate Natural Resonance f₀ = 1/(2π√LC) This is where your circuit wants to resonate. Step 3: Evaluate Performance Is f₀ in your driver's range? Is Q acceptable at this frequency? Are there SRF issues? Step 4: Adjust as Needed Add tuning capacitor if f₀ is too high Consider different choke if f₀ is way off Accept the natural f₀ if performance is good Sensitivity Analysis Understanding how sensitive your design is to variations: Parameter Change Effect on f₀ Effect on Q L +10% f₀ -5% Q +5% C +10% f₀ -5% Q -5% R +10% No change Q -10% Temperature +10°C f₀ +2% (due to ε r drop) Q +5% (R sol drops) Common Optimization Mistakes ❌ Chasing Extreme Q Very high Q makes the circuit sensitive to drift and hard to tune. Q of 50-100 is often more practical than Q > 200. ❌ Ignoring SRF A design that works on paper fails if operating frequency is too close to SRF. Always check this! ❌ Forgetting Water Resistance Solution resistance often dominates losses. Pure distilled water has higher resistance than you might expect. ❌ Not Accounting for Parasitics Real circuits have stray inductance and capacitance. Leave margin for these effects. ❌ Over-constraining the Design If you fix too many parameters, you may have no degrees of freedom for optimization. Optimization Checklist ☐ Define your primary optimization goal ☐ Identify fixed constraints (available components, frequency range) ☐ Calculate baseline performance ☐ Identify largest loss contributor (DCR vs R sol ) ☐ Make targeted improvements to dominant loss ☐ Verify SRF is >3× operating frequency ☐ Check that primary/secondary are reasonably matched ☐ Run simulation to verify improvements ☐ Consider sensitivity to variations ☐ Document final design parameters Remember: Optimization is iterative. The calculator makes it easy to try variations quickly. Don't expect to find the optimal design on the first try—explore the design space! Next: Interpreting Calculation Results → Interpreting Results Interpreting Calculation Results Understanding what the calculator's output values mean and how to use them for practical circuit construction. This page helps you translate numbers into actionable design decisions. Understanding Output Values Inductance Results Output Typical Range What It Means L (inductance) 1-100 mH Primary choke property, affects f₀ and Q DCR 0.1-50 Ω Wire resistance, major Q limiter SRF 50 kHz - 1 MHz Maximum usable frequency C parasitic 10-500 pF Stray capacitance, determines SRF Wire Length 1-50 m Total wire needed for winding Capacitance Results Output Typical Range What It Means C wfc 1-100 nF WFC capacitance, sets resonance with L R solution 0.1-100 Ω Water resistance, affects Q Z₀ (characteristic) 100-10,000 Ω √(L/C), impedance at resonance Circuit Results Output Typical Range Interpretation f₀ (resonant freq) 1-100 kHz Where circuit resonates naturally Q factor 5-200 Resonance sharpness, voltage gain Bandwidth 50 Hz - 5 kHz Usable frequency range around f₀ V magnification 5× - 200× Voltage gain at resonance Ring-down τ 0.1-10 ms Decay time constant Ring-down cycles 3-150 Oscillations during decay What "Good" Values Look Like ✓ Well-Designed VIC Circuit: Q factor: 30-100 (good balance of gain vs. stability) f₀: Within your driver's frequency range Operating frequency: < 30% of SRF (preferably < 10%) Primary/Secondary f₀ match: Within 5-10% Bandwidth: Wide enough to accommodate drift Voltage magnification: As needed for your application ✗ Warning Signs: Q < 10: Very low—circuit barely resonates Q > 300: Extremely sharp—hard to tune, sensitive to drift f op > 0.5 × SRF: Operating too close to SRF DCR > Z₀/10: Resistance dominates, poor Q Primary/Secondary mismatch > 20%: Poor energy transfer Translating Results to Construction Wire Length and Turns The calculator provides wire length and turn count. When winding: Add 10-20% to wire length for lead connections and margins Count turns carefully —L varies as N², so turn count is critical Verify L after winding —actual may differ from calculated Component Selection Calculated Value Selection Guidance C1 = 47.3 nF Use 47 nF standard value (within 1%) C1 = 31.2 nF Use 33 nF or parallel 22+10 nF L = 15.7 mH Wind for 16 mH, fine-tune with parallel C Understanding Accuracy Limits Know what to expect from calculated vs. measured values: Parameter Expected Accuracy Why Variation Occurs Inductance ±10-20% Core μᵣ varies, winding geometry imperfect DCR ±5% Wire tables accurate, but length varies SRF ±30% Parasitic C is hard to model precisely C wfc ±15% Fringe effects, water purity variation R solution ±20% Conductivity varies with temperature f₀ (calculated) ±15% Depends on L and C accuracy Q factor ±25% Multiple loss mechanisms combine Comparing Calculated vs. Measured When Measured f₀ is Lower Than Calculated: Actual L is higher than calculated Stray capacitance adding to C total WFC capacitance underestimated When Measured f₀ is Higher Than Calculated: Actual L is lower than calculated Core saturation reducing effective L WFC capacitance overestimated When Measured Q is Lower Than Calculated: Additional losses not accounted for (core loss, skin effect) Poor connections adding resistance Water conductivity different than assumed Using Results for Troubleshooting Observation Calculator Check Likely Issue No resonance found Check SRF vs. operating frequency Operating above SRF Very weak resonance Check calculated Q High losses, low Q Resonance at wrong frequency Verify L and C inputs Input error or mismeasurement Less voltage gain than expected Compare Q values Actual losses higher Resonance drifts during use Check temperature effects Water heating, capacitance changing Results Summary Checklist Before building, verify these from your results: ☐ f₀ is within driver frequency range ☐ f₀ is < 30% of SRF (ideally < 10%) ☐ Q is in acceptable range (typically 20-150) ☐ Voltage magnification won't exceed component ratings ☐ Wire gauge handles expected current ☐ Primary and secondary frequencies are matched ☐ No warning indicators are present ☐ Results are saved for reference Final Advice: The calculator gives you an excellent starting point. Always plan to measure your actual circuit and iterate. The goal is to get close enough that minor tuning (adjusting C1, trimming frequency) achieves optimal performance. Chapter 7 Complete. Next: Advanced Topics → VIC Matrix Calculator Application The VIC Matrix Calculator (v6) can be found at the following url: https://matrix.stanslegacy.com