PCB Coil Inductance Calculator
Calculate planar spiral PCB coil inductance using Wheeler's approximation. Estimate inner diameter, average radius, and fill ratio for circular planar inductors in mil and mm for RF and wireless design.
PCB Coil Inductance Calculator
How to Use PCB Coil Inductance Calculator
Calculating the self-inductance of planar spiral copper coils on printed circuit boards is simplified using our interactive utility. It helps layout engineers determine winding parameters for RF and wireless filters without running complex field solver algorithms initially. Follow this professional workflow to calculate your PCB inductor dimensions:
- 1Enter outer diameter. Input the total outer circular boundary limit of the spiral coil trace in the selected unit.
- 2Enter trace width. Input the width of the copper conductor trace forming the coil windings.
- 3Enter spacing. Input the space separating adjacent copper tracks on the substrate.
- 4Enter number of turns. Input the total number of concentric turns designed for the inductor.
- 5Select unit. Choose between millimeters (mm) and thousandths of an inch (mil) for dimensional inputs.
- 6Click calculate. Click the Calculate button to run the Wheeler spiral approximation algorithm.
- 7Read inductance and dimensions. Review the calculated inductance in microhenries along with the computed inner diameter, average radius, and fill ratio.
How to Calculate PCB Coil Inductance
Determining the electrical inductance of planar spiral coils on a PCB substrate requires evaluating the coil geometry and using specialized empirical formulas. Wheeler's planar spiral coil approximation is the industry-standard equation for estimating circular flat coil inductance. The math involved in this estimation is presented below:
Average Radius
Fill Ratio
Inductance
Where the variables in these geometric calculations are defined as:
- L: Inductance in microhenries (µH)
- ravg: Average radius of the winding in inches
- N: Total number of concentric turns
- w: Radial width of the winding in inches (rout − rin)
- rout: Outer radius of the spiral winding in inches (Dout ÷ 2)
- rin: Inner radius of the spiral winding in inches (Din ÷ 2)
- ρ: Fill ratio representing layout density (dimensionless)
The inner diameter is calculated using the track parameters: Din = Dout − 2 × N × trace width − 2 × (N − 1) × spacing. All metric units are converted to inches before running the Wheeler inductance equation.
Step-by-Step Engineering Worked Example
To demonstrate this calculation method, let's solve a typical layout scenario with these design parameters:
- Outer Diameter (Dout): 40 mm
- Trace Width (trace width): 0.5 mm
- Trace Spacing (spacing): 0.3 mm
- Turns (N): 8
Step 1: Calculate the inner diameter in mm
Din = 40 − 2 × 8 × 0.5 − 2 × (8 − 1) × 0.3 = 40 − 8 − 4.2 = 27.8 mm
Step 2: Convert metric dimensions to inches
Dout in inches = 40 ÷ 25.4 = 1.5748 in (giving rout = 0.7874 in)
Din in inches = 27.8 ÷ 25.4 = 1.0945 in (giving rin = 0.5472 in)
Step 3: Calculate the average radius and winding width
ravg = (0.7874 + 0.5472) ÷ 2 = 0.6673 in
w = 0.7874 − 0.5472 = 0.2402 in
Step 4: Compute fill ratio
ρ = (0.7874 − 0.5472) ÷ (0.7874 + 0.5472) = 0.2402 ÷ 1.3346 = 0.1800
Step 5: Calculate planar coil inductance using Wheeler's formula
L = (31.33 × ravg² × N²) ÷ (8 × ravg + 11 × w)
L = (31.33 × 0.6673² × 8²) ÷ (8 × 0.6673 + 11 × 0.2402)
L = (31.33 × 0.4453 × 64) ÷ (5.3384 + 2.6422)
L = 892.98 ÷ 7.9806 = 111.90 µH
Final Output Values:
- Inductance (L): 111.90 µH
- Inner Diameter (Din): 27.80 mm
- Average Radius (ravg): 16.95 mm
- Fill Ratio (ρ): 0.1800
PCB Coil Inductance Chart
This reference chart displays calculated planar spiral PCB coil inductance and dimensions for typical layout geometries in millimeters. Inductance calculations are computed using Wheeler's circular spiral approximation formula.
| Outer Diameter (mm) | Turns | Trace Width (mm) | Spacing (mm) | Approximate Inductance (µH) |
|---|---|---|---|---|
| 20 mm | 5 | 0.4 mm | 0.2 mm | 22.90 µH |
| 30 mm | 6 | 0.5 mm | 0.2 mm | 50.71 µH |
| 40 mm | 8 | 0.5 mm | 0.3 mm | 111.89 µH |
| 50 mm | 10 | 0.6 mm | 0.3 mm | 201.60 µH |
| 60 mm | 12 | 0.8 mm | 0.4 mm | 277.99 µH |
Note: actual inductance may vary depending on copper thickness, substrate material and operating frequency.
Frequently Asked Questions (FAQs)
A PCB trace coil is a type of inductor created directly on a printed circuit board using copper traces arranged in a spiral or circular pattern. These integrated inductors are commonly used in radio frequency circuits, wireless power transfer, and high-frequency filtering to save board space.
Calculating PCB coil inductance involves complex formulas that account for the outer and inner diameters, the number of turns, the trace width, and the spacing between traces. Online calculators typically use the Wheeler formula or modifications of it to estimate planar spiral inductance values.
The inductance of a PCB coil is primarily affected by the total number of turns, the area enclosed by the coil, and the geometry of the traces. Increasing the number of turns or the outer diameter increases the inductance, while widening the trace or increasing trace spacing can alter the value.
PCB coils are very effective for specific high-frequency applications where only small inductance values are required. However, they typically cannot achieve the high inductance or handle the high currents of traditional wire-wound components, and they occupy a relatively large footprint area.
Yes, you can simulate PCB coil inductance using specialized electromagnetic field simulation software. While simple calculators provide good approximations, tools like finite element analysis offer highly precise results by accounting for parasitic capacitance, skin depth, and substrate properties.