Optical Quadrature Encoders: Decoding & Velocity Estimation

1. Overview & Concept Definition

Rotary electromechanical sensor that converts the angular displacement and rotational velocity of a mechanical shaft into two square-wave digital output signals phase-shifted by 90 electrical degrees.

2. Engineering & Industrial Significance

Enables closed-loop positioning and speed regulation in motor control, CNC milling machines, and autonomous robotics with sub-millimeter positioning precision and immediate direction sensing.

3. Physical Working Principle & Transducer Dynamics

An etched glass or slotted plastic code disc spins between infrared LED emitters and photodiode receivers. The optical gratings produce two square-wave channels ($A$ and $B$) in electrical quadrature ($90^\circ$ relative phase shift). Clockwise rotation causes Channel A to lead Channel B; counter-clockwise rotation causes Channel B to lead Channel A. By monitoring rising and falling edges of both channels, a 4X hardware decoding counter achieves four counting pulses per physical grating cycle ($CPR_{effective} = 4 \times CPR_{optical}$). An optional Channel Z (Index) pulse fires once per mechanical revolution for absolute zero-reference homing.

// C++: State-Machine Quadrature Decoder Table (4X Resolution)
#include <stdint.h>

// Gray code state-transition table: returns +1 (CW), -1 (CCW), 0 (no move), 2 (invalid/missed step)
static const int8_t QUAD_TABLE[16] = {
     0, -1,  1,  2,
     1,  0,  2, -1,
    -1,  2,  0,  1,
     2,  1, -1,  0
};

struct QuadratureEncoder {
    volatile int64_t positionCount;
    uint8_t prevState;

    void init(uint8_t pinA, uint8_t pinB) {
        positionCount = 0;
        prevState = ((pinA & 1) << 1) | (pinB & 1);
    }

    void update(uint8_t pinA, uint8_t pinB) {
        uint8_t currentState = ((pinA & 1) << 1) | (pinB & 1);
        uint8_t index = (prevState << 2) | currentState;
        int8_t movement = QUAD_TABLE[index];
        if (movement != 2) {
            positionCount += movement;
        }
        prevState = currentState;
    }
};

6. Common Engineering Pitfalls & Troubleshooting

7. Applications & Physical Constraints