When three-phase sinusoidal signals that are 120 degrees to each other are sensed, it is well known that the Clarke transformation converts the three-phase sinusoidal signals ‒ sin(θ), sin(θ-120°), sin(θ-240°) ‒ into two-phase orthogonal signals of sin(θ) and cos(θ). The present-day sensing technology that is based on the two-phase orthogonal signals has not been changed since the inception of the technology.
The generalized conversion method for arbitrary N-phase sinusoidal signals, that are shifted 360°/N from each other, has been unknown until the finding of the ZF Transform that is recently published in “Multiphase Sensor Signal Processing” (https://ieeexplore.ieee.org/document/9773991).
The applications of the ZF Transform are very diverse such as in position sensing, phase modulated digital communications, or time of flight (ToF) ranging, especially when the phases of the sin(θ) and cos(θ) signals carry the information that needs to be extracted.

Applications of the ZF Transform

• • Position Sensing (Rotary or Linear Motors)
  • Time of Fight (ToF) Ranging
  • Phase Modulated Digital Communications

The ZF Transform Offers

• • to Facilitate the Architectural Change in Position Sensing Devices
  • to Improve the Sensing Accuracy
  • to Relax the Manufacturing Requirements
  • to Introduce the Digital Type Signal Sensing
  • to Design the Devices Flexibly

Characteristics of the ZF Transform

• • Preserve the Fundamental Signal Component from the Sensed Input Multiphase Signals.
  • Harmonic Components are Removed from the Input Signals.
  • Amplitude of the Output Signal is Adjusted during the Transformation
  • Phase of the Output Signal can be Shifted during the Transformation.
  • Common Mode Noise in the Input Signals are Completely Canceled.
  • Conveniently Implemented by the Operational Amplifiers.