Skip to main content

DCR Effects

DC Resistance and Q Factor

The DC resistance (DCR) of an inductor is the primary factor limiting its Q factor and thus the voltage magnification achievable in a VIC circuit. Understanding and minimizing DCR is essential for high-performance designs.

What is DCR?

DCR is simply the resistance of the wire used to wind the inductor, measured with direct current:

Rdc = ρ × lwire / Awire

Where:

  • ρ = resistivity of wire material (Ω·m)
  • lwire = total wire length (m)
  • Awire = wire cross-sectional area (m²)

DCR and Inductor Design

For a given inductance, DCR depends on the design choices:

Design Change Effect on L Effect on DCR Net Q Effect
More turns L ∝ N² R ∝ N Q ∝ N (improves)
Larger wire gauge No change R decreases Q improves
Higher μ core L increases Fewer turns needed Variable*
Larger core L increases Longer mean turn Often improves
Copper vs. SS wire No change R × 40-60 Q ÷ 40-60

*Core losses may offset wire resistance reduction at high frequencies

Q Factor Calculation

Q Factor at Operating Frequency:

Q = 2πfL / Rtotal

Total Resistance includes:

Rtotal = Rdc + Rskin + Rproximity + Rcore

At low frequencies, Rdc dominates. At high frequencies, skin effect and core losses become significant.

Voltage Magnification Impact

Since voltage magnification equals Q at resonance:

Example Comparison:

Scenario L DCR Q @ 10kHz Vout (12V in)
22 AWG Copper 10 mH 5 Ω 126 1,508 V
26 AWG Copper 10 mH 13 Ω 48 580 V
22 AWG SS316 10 mH 220 Ω 2.9 34 V
22 AWG Nichrome 10 mH 320 Ω 2.0 24 V

Measuring DCR

Method 1: Multimeter

  • Simple and quick
  • Set meter to lowest resistance range
  • Subtract lead resistance
  • Accuracy: ±1-5%

Method 2: 4-Wire (Kelvin) Measurement

  • Eliminates lead resistance error
  • Required for low DCR (<1 Ω)
  • Uses separate sense and current leads
  • Accuracy: ±0.1%

Method 3: LCR Meter

  • Measures L and DCR together
  • Can measure at different frequencies
  • Shows equivalent series resistance (ESR)
  • Best for complete characterization

Optimizing DCR

Design Strategies:

  1. Use the largest wire that fits: Fill the available winding area
  2. Choose copper: Unless current limiting is specifically needed
  3. Use higher permeability core: Fewer turns needed for same L
  4. Optimize core size: Larger cores have more room for thicker wire
  5. Consider parallel windings: Two parallel wires = half the DCR

Practical Limits:

  • Wire must fit on the core with proper insulation
  • Multiple layers increase parasitic capacitance
  • Very thick wire is hard to wind neatly
  • Cost and availability of materials

Temperature Effects

Wire resistance increases with temperature:

R(T) = R20°C × [1 + α(T - 20)]

Where α ≈ 0.00393 /°C for copper

Example:

At 80°C: R = R20°C × 1.24 (+24% increase)

This means Q drops by ~20% when the choke heats up!

DCR in the VIC System

The total resistance in a VIC circuit includes:

Source Typical Range Mitigation
L1 DCR 1-50 Ω Optimize winding
L2 DCR 1-50 Ω Optimize winding
Capacitor ESR 0.01-1 Ω Use low-ESR caps
WFC solution resistance 10-10000 Ω Electrode design, electrolyte
Connection resistance 0.01-1 Ω Solid connections
Driver output resistance 0.1-10 Ω Low Rds(on) MOSFETs

Practical Example

Target: 10 mH inductor at 10 kHz with Q > 50

Required Rmax:

Q = 2πfL/R → R = 2πfL/Q = 2π × 10000 × 0.01 / 50 = 12.6 Ω

Wire selection (100 turns on 25mm toroid):

Mean turn length ≈ 80mm, total wire = 8m

  • 22 AWG copper: 8m × 0.053 Ω/m = 0.42 Ω ✓
  • 26 AWG copper: 8m × 0.134 Ω/m = 1.07 Ω ✓
  • 30 AWG copper: 8m × 0.339 Ω/m = 2.71 Ω ✓
  • 22 AWG SS316: 8m × 2.3 Ω/m = 18.4 Ω ✗ (Q = 34)

Result: 22-30 AWG copper all meet the requirement. 22 AWG gives highest Q but may be harder to wind.

VIC Matrix Calculator: Enter your wire gauge and material in the Choke Design tool. It calculates DCR automatically and shows how it affects Q factor and voltage magnification. The calculator warns if your DCR is too high for effective resonance.

Chapter 5 Complete. Next: Water Fuel Cell Design →

Back to top