TIDUFF8 September   2025

 

  1.   1
  2.   Description
  3.   Resources
  4.   Features
  5.   Applications
  6.   6
  7. 1System Description
    1. 1.1 Key System Specifications
  8. 2System Overview
    1. 2.1 Block Diagram
    2. 2.2 Design Considerations
    3. 2.3 Highlighted Products
      1. 2.3.1 LDC5072-Q1
      2. 2.3.2 MSPM0G3507
      3. 2.3.3 TPSM365R3
      4. 2.3.4 TLV9062
  9. 3System Design Theory
    1. 3.1 Hardware Design
      1. 3.1.1 Target PCB
      2. 3.1.2 Coil PCB
      3. 3.1.3 Signal Chain PCB
        1. 3.1.3.1 Inductive Angle Position Sensor Front-End Schematic
        2. 3.1.3.2 Differential to Single-Ended Signal Conversion
      4. 3.1.4 MSPM0G3507 Schematic Design
      5. 3.1.5 Power Supply Design
    2. 3.2 Absolute Position Calculation
    3. 3.3 Software Design
      1. 3.3.1 Angle Calculation Timing
      2. 3.3.2 Rotary Angle Error Sources and Compensation
  10. 4Hardware, Software, Testing Requirements, and Test Results
    1. 4.1 Hardware Requirements
      1. 4.1.1 PCB Overview
      2. 4.1.2 Encoder Interface
    2. 4.2 Software
    3. 4.3 Test Setup
    4. 4.4 Test Results
      1. 4.4.1 Inductive Sensor Sine and Cosine Noise Measurement
      2. 4.4.2 Absolute Angle Noise Measurement
      3. 4.4.3 Rotary Angle Accuracy Measurement
      4. 4.4.4 Impact of Air Gap on Noise, 4th Electrical Harmonics and Total Angle Accuracy
      5. 4.4.5 Power Consumption Measurement
  11. 5Design and Documentation Support
    1. 5.1 Design Files
      1. 5.1.1 Schematics
      2. 5.1.2 BOM
      3. 5.1.3 PCB Layout
      4. 5.1.4 Altium Project Files
      5. 5.1.5 Gerber Files
      6. 5.1.6 Assembly Drawings
    2. 5.2 Tools and Software
    3. 5.3 Documentation Support
    4. 5.4 Support Resources
    5.     Trademarks
  12. 6About the Author

3.2 Absolute Position Calculation

To get absolute position, this reference design uses dual track coils with coprime periods. The outer side track uses 16 periods coils while the inner track uses 15 periods coils.

To better illustrate how to calculate the absolute position, the design guide takes the outer coil with four periods and the inner coil with three periods, for example.

Figure 3-8 illustrates the relationship between the electrical angle of the outer coils and inner coils over one mechanical revolution with a lower period count of four and three for simplicity.

TIDA-010961 Outer and Inner Coil Angle Relationship With Coprime Four and Three Periods Figure 3-8 Outer and Inner Coil Angle Relationship With Coprime Four and Three Periods

The absolute mechanical angle is determined by the electrical angle difference between the coprime coils in the example 4 and 3.

Table 3-1 Relationship Between Electrical Angle Difference and Absolute Angle
DIFFERENCE ANGLE (°)ABSOLUTE ANGLE (°)
0 to 90N4(1)
–270 to –24090 + N4(1)
120 to 18090 + N4(1)
–180 to 120180 + N4(1)
240 to 270180 + N4(1)
–90 to 0270 + N4(1)
(1) N4 means the outer coils mechanical angle.

In this reference design, coprime 16 and 15 coils are used. The 16 periods coils divide the absolute angle into 16 sectors. Assuming the absolute angle falls within nth sector, the outer coils angle are either n × 22.5° greater than or 360 – n × 22.5° less than the inner coils angle. Equation 3 calculates the sector number.

Equation 3. sector=FLOORoutercoilangle-innercoilangle22.5outercoilangle≥innercoilangleFLOORoutercoilangle-innercoilangle+36022.5outercoilangle<innercoilangle

Then, the absolute angle can be calculated as:

Equation 4. absoluteposition=sector×22.5°+fineangle/16

Figure 3-9 shows the absolution position calculation flow chart in a Nonius encoder.

TIDA-010961 Rotary Angle Calculation Flow ChartFigure 3-9 Rotary Angle Calculation Flow Chart