# Primary Side # Primary Side (L1-C1) Analysis The primary side of the VIC consists of the first inductor (L1) and tuning capacitor (C1). This stage receives the driving signal and provides the first stage of voltage magnification. Understanding its behavior is crucial for successful VIC design. ## Primary Tank Circuit L1 and C1 form a series resonant tank circuit. At the resonant frequency, this circuit: - Has minimum impedance (ideally just the DC resistance) - Draws maximum current from the source - Develops magnified voltage across L1 and C1 ``` R1 (DCR of L1) │ Pulse ┌────────┴────────┐ Generator │ │ ○──────┤ L1 ├────────┬────── To L2 │ │ │ └─────────────────┘ ─┴─ ─┬─ C1 │ ─┴─ GND V_in ────▶ [ L1 + R1 ] ────▶ [ C1 ] ────▶ V_out At resonance: V_C1 = Q × V_in ``` ## Resonant Frequency Calculation #### Primary Resonant Frequency: f₀ = 1 / (2π√(L1 × C1)) #### Rearranging to Find Components: L1 = 1 / (4π²f₀²C1) C1 = 1 / (4π²f₀²L1) ### Example Calculations
Target f₀Given L1Required C1
10 kHz1 mH253 nF
10 kHz10 mH25.3 nF
25 kHz1 mH40.5 nF
50 kHz500 µH20.3 nF
## Q Factor of Primary Side The Q factor determines voltage magnification: #### Q Factor: QL1C = (2π × f₀ × L1) / R1 = XL1 / R1 #### Voltage Magnification: VC1 = QL1C × Vin #### Example:
- f₀ = 10 kHz, L1 = 10 mH, R1 = 10 Ω - XL1 = 2π × 10,000 × 0.01 = 628 Ω - Q = 628 / 10 = 62.8 - With 12V input: VC1 = 62.8 × 12 = 754V
## Characteristic Impedance The characteristic impedance of the primary tank affects matching: Z₀ = √(L1 / C1) #### Relationship to Q: Q = Z₀ / R1 Higher Z₀ (more L, less C) means higher Q for same resistance. ## Design Trade-offs
Design ChoiceAdvantagesDisadvantages
**High L1, Low C1**Higher Z₀, potentially higher QMore wire, higher DCR, harder to wind
**Low L1, High C1**Less wire, lower DCR, easier constructionLower Z₀, may need larger capacitor
**High frequency**Smaller components, lower SRF concernSkin effect losses, harder switching
**Low frequency**Lower losses, easier switchingLarger components, SRF may be issue
## Current and Power Considerations At resonance, the circuit draws maximum current: #### Resonant Current: Ires = Vin / R1 #### Power from Source: Pin = Vin² / R1 = Ires² × R1 #### Reactive Power (circulating): Preactive = VC1 × Ires = Q × Pin **Note:** The reactive power circulates between L1 and C1 but is not consumed. ## Bandwidth and Tuning Sensitivity The 3dB bandwidth of the primary tank: BW = f₀ / QL1C #### Example: f₀ = 10 kHz, Q = 50 → BW = 200 Hz The driving frequency must be within ±100 Hz of f₀ for good response. #### Practical Implication: High-Q circuits are sensitive to component tolerances and temperature drift. You may need PLL (Phase-Locked Loop) control to maintain resonance. ## Component Selection Guidelines ### L1 (Primary Choke) - **Inductance:** 100 µH to 100 mH typical - **DCR:** As low as practical (determines Q) - **SRF:** Should be well above operating frequency (10× minimum) - **Core:** Ferrite, iron powder, or air-core depending on frequency - **Wire:** Copper preferred; resistance wire reduces Q ### C1 (Tuning Capacitor) - **Value:** Selected to resonate with L1 at desired frequency - **Voltage rating:** Must exceed Q × Vin - **Type:** Film (polypropylene, polyester) or ceramic - **ESR:** Low ESR for minimal losses - **Temperature stability:** NPO/C0G ceramic or film preferred ## Practical Assembly Tips 1. **Measure L1 accurately:** Use an LCR meter at multiple frequencies 2. **Start with calculated C1:** Then fine-tune for best response 3. **Use variable capacitor or parallel caps:** For easy tuning 4. **Check for SRF:** Ensure L1's SRF is well above f₀ 5. **Monitor temperature:** Component values drift with heat **VIC Matrix Calculator:** The calculator determines optimal L1 and C1 values based on your target frequency and available components. It also shows the expected Q factor and voltage magnification. *Next: Secondary Side (L2-WFC) Analysis →*