SNOA930C March   2015  – May 2021 LDC0851 , LDC1001 , LDC1001-Q1 , LDC1041 , LDC1051 , LDC1101 , LDC1312 , LDC1312-Q1 , LDC1314 , LDC1314-Q1 , LDC1612 , LDC1612-Q1 , LDC1614 , LDC1614-Q1 , LDC2112 , LDC2114 , LDC3114 , LDC3114-Q1

 

  1.   Trademarks
  2. 1The Sensor
    1. 1.1 Sensor Frequency
    2. 1.2 RS and RP
      1. 1.2.1 AC Resistance
      2. 1.2.2 Skin Effect
  3. 2Inductor Characteristics
    1. 2.1 Inductor Shape
      1. 2.1.1 Example Uses of Different Inductor Shapes
    2. 2.2 Number of Turns
    3. 2.3 Multiple Layers
      1. 2.3.1 Mutual Inductance of Coils in Series
      2. 2.3.2 Multi-Layer Parallel Inductor
      3. 2.3.3 Temperature Compensation
    4. 2.4 Inductor Size
    5. 2.5 Self-Resonance Frequency
      1. 2.5.1 Measurement of SRF
      2. 2.5.2 Techniques to Improve SRF for Wire-wound Inductors
  4. 3Capacitor Characteristics
    1. 3.1 Capacitor RS, Q, and SRF
    2. 3.2 Effect of Parasitic Capacitance
      1. 3.2.1 Recommended Capacitor Values
    3. 3.3 Capacitor Placement
  5. 4Physical Coil Design
    1. 4.1 Example Design Procedure Using WEBENCH
      1. 4.1.1 General Design Sequence
    2. 4.2 PCB Layout Recommendations
      1. 4.2.1 Minimize Conductors Near Sensor
      2. 4.2.2 Sensor Vias and Other Techniques for PCBs
  6. 5Summary
  7. 6References
  8. 7Revision History

2.2 Number of Turns

GUID-4129319B-B37F-428F-BE92-72DC8CC4E4BE-low.gifFigure 2-4 Flat Circular Spiral Inductor

For a single-layer PCB spiral inductor, Mohan’s Equation, as discussed in Reference [1], is useful for understanding how inductance is related to coil geometry. This equation can be used to calculate the overall inductance of a coil for various geometries:

Equation 2. GUID-B4CEB424-E63F-4C09-9390-27D552ACA598-low.png

where

  • K1 and K2 are geometry dependent, based on the shape of the inductor
  • μo is the permeability of free space, 4π×10−7
  • n is the number of turns of the inductor
  • davg is the average diameter of the turns = (dOUT + dIN)/2
  • ρ = (dOUT – dIN)/(dOUT + dIN), and represents the fill ratio of the inductor – small values of ρ are a hollow inductor (dOUT ≈ dIN), while large values correspond to (dOUT ≫ dIN)
  • ci are layout dependent factors based on the geometry (for a circle, use c1 = 1.0, c2 = 2.46, c3 = 0, c4 = 0.20), refer to [1] for additional shapes

As the total inductance is proportional to the number of turns, adjusting the number of turns is an effective control on the total inductance. However, when adding inner turns (which reduces the inner diameter), the davg value begins to decrease, which reduces the additional inductance from the extra turns. For most applications, the ratio of dIN/dOUT must be greater than 0.3 for a higher inductor Q. The reason for this guideline is that the inner turns, which do not have a significant area, do not contribute significantly to the overall inductance while they still increase RS. However, for applications where the target is very close to the sensor, such as touch-on-metal, a ratio as low as 0.05 is often acceptable, as the inner turns provide increased sensitivity. Refer to Reference [2] for more information.

GUID-D394BD59-A285-40FB-A54C-06585950E9A5-low.pngFigure 2-5 Inductance Versus Number of Turns for 18-mm Circular Inductor

A key limitation on the number of turns that can be added is the practical minimum PCB trace width – a common value is 0.1 mm (or 0.004 in.). Under this constraint, with each increase of 2 mm in sensor diameter up to 5 additional turns can be added to a PCB inductor.

In Figure 2-5, it can be seen that the first few turns contribute the most inductance, while the last few turns contribute less inductance. This example with an 18-mm outer diameter coil with 0.15-mm trace width and trace spacing shows that the total inductance levels off at approximately 20 turns.