# 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](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:

1. **Define Requirements:** Target frequency, available components, constraints 2. **Design/Select Chokes:** Use Choke Design module or enter measured values 3. **Configure Water Profile:** Enter WFC geometry and water properties 4. **Create Circuit Profile:** Combine components and select topology 5. **Run Simulation:** Analyze resonance, Q, and system behavior 6. **Optimize:** Adjust parameters to improve performance 7. **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: 1. Navigate to the application dashboard 2. 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 3. 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:

1. Run initial simulation with your component values 2. Check if resonant frequency matches your target 3. Evaluate Q factor—is it sufficient for your goals? 4. Look for warnings and address them 5. Adjust parameters and re-simulate 6. 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

1. Design or select choke for desired L 2. Calculate required C: C = 1/(4π²f₀²L) 3. 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

1. Measure or calculate WFC capacitance 2. Calculate required L: L = 1/(4π²f₀²C) 3. Design choke for that inductance

#### Approach C: Adjust Both

1. Start with practical component ranges 2. Use calculator to explore L/C combinations 3. 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:

1. Design secondary (L2 + WFC) first—this is usually more constrained 2. Calculate secondary f₀ 3. Select C1 to tune primary to match: C1 = 1/(4π²f₀²L1) 4. 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

1. ☐ Define your primary optimization goal 2. ☐ Identify fixed constraints (available components, frequency range) 3. ☐ Calculate baseline performance 4. ☐ Identify largest loss contributor (DCR vs R_sol) 5. ☐ Make targeted improvements to dominant loss 6. ☐ Verify SRF is >3× operating frequency 7. ☐ Check that primary/secondary are reasonably matched 8. ☐ Run simulation to verify improvements 9. ☐ Consider sensitivity to variations 10. ☐ 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:

1. ☐ f₀ is within driver frequency range 2. ☐ f₀ is < 30% of SRF (ideally < 10%) 3. ☐ Q is in acceptable range (typically 20-150) 4. ☐ Voltage magnification won't exceed component ratings 5. ☐ Wire gauge handles expected current 6. ☐ Primary and secondary frequencies are matched 7. ☐ No warning indicators are present 8. ☐ 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](https://matrix.stanslegacy.com)