Magnetic Field Angle Determination Using Arcsin Arccos Approximations
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Solution Overview
Problem
Existing methods for determining the angle of a magnetic field using two orthogonal components are prone to measurement errors, requiring high-bit encoding and complex implementations, which increase ADC conversion time and power consumption.
Innovation Solution
A method using a digital signal processor that determines the angle by receiving digital measurements of magnetic field components Bx and Bz, calculating absolute values, and using arcsin or arccos approximations to minimize error propagation, with reduced bit precision and employing lookup tables to simplify computations, thereby reducing power consumption and on-chip area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the arctan formula is used to calculate the angle from Bx and Bz components, then the angle can be determined, but measurement errors in Bx and Bz are strongly propagated to the resulting angle and high-bit encoding is required
Solution Approach 1:
The patent changes the mathematical parameters from using arctan(Bx/Bz) to using arcsin(Bz/B) or arccos(Bx/B) where B is the magnetic field magnitude. This parameter transformation eliminates the division operation that causes error propagation, allowing accurate angle determination with lower bit encoding (e.g., 8 bits instead of 16 bits) while maintaining measurement precision.
2Measurement precision
If high-bit encoding is used for Bx and Bz to mitigate measurement errors, then angle precision is improved, but ADC conversion time increases and implementation becomes more complex
Solution Approach 1:
By changing the calculation formula to arcsin(Bz/B) or arccos(Bx/B), the patent reduces the required encoding bits from 16 to 8 bits. This reduction directly decreases ADC conversion time and simplifies implementation while maintaining the same angle determination precision through the mathematical transformation.
3Ease of operation
If the arctan computation is implemented, then the angle can be calculated, but the implementation becomes complex and requires more on-chip area and power consumption
Solution Approach 1:
The patent replaces the complex arctan computation with simpler arcsin or arccos calculations based on the ratio of magnetic field components to the total field magnitude. This parameter change simplifies the computational logic, reduces on-chip area requirements, and lowers power consumption while maintaining full angle calculation capability.
Solution Approach 2:
The patent segments the angle calculation into two cases: when |Bx| ≥ |Bz| use arccos(Bx/B), and when |Bx| < |Bz| use arcsin(Bz/B). This segmentation simplifies the computational path by avoiding the need for full arctan implementation, reducing both power consumption and hardware complexity.
Data Source
AI summary
A method of determining an absolute angle of a magnetic field includes receiving a first digital measurement value Bx of a first magnetic field component indicating intensity of the magnetic field along a first axis; receiving a second digital measurement value Bz of a second magnetic field component indicating the intensity of the magnetic field along a second axis, orthogonal to the first axis; determining absolute values for the first and second magnetic field components; and determining the angle of the magnetic field with respect to the first or second axis. The angle is determined so that the angle is derivable from the value of arcsin of Bz or of its approximation, when the absolute value of Bz≤ the absolute value of Bx, and derivable from the value of arccos of Bx or of its approximation, when the absolute value of Bz> the absolute value of Bx.