Formula & Calculator
Encoder Angular Resolution
Calculates the smallest angular increment a rotary encoder can measure based on its counts-per-revolution rating.
Interpretation
δθ = 360 / CPR. Resolution in degrees per count. CPR is counts per revolution. Used to determine measurement precision.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| delta_theta | Smallest measurable angular increment | degrees |
| CPR | Encoder counts per revolution |
What it means
An incremental encoder outputs a certain number of pulses per revolution (CPR). The angular resolution is the angle corresponding to one count. Higher CPR gives better resolution. This is used to choose encoders for precise motion control. Understanding resolution is important for estimating position accuracy.
Worked example
Encoder Angular Resolution – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| CPR | 360 |
| Parameter | Value |
|---|---|
| CPR | 4096 |
Common mistakes
- Encoder angular resolution: δθ = 360 / CPR – where CPR is counts per revolution.
- CPR: The number of pulses per full rotation – for quadrature encoders, this is often the number of cycles per revolution (multiply by 4 for edge counts).
- Units: δθ in degrees – can also be in radians (δθ = 2π/CPR).
- Resolution: Smaller δθ means higher resolution.
- Interpolation: Some encoders have interpolation to increase resolution beyond the native CPR.
Applications
Encoder angular resolution, δθ = 360/CPR, gives the smallest angular increment measurable by an incremental encoder, where CPR is counts per revolution. This is essential for determining the positioning accuracy of motors and joints. Engineers use it to select an encoder with sufficient resolution for the required precision, to calculate velocity from counts, and to assess the noise and repeatability of measurements. Higher resolution allows finer control but may increase cost and processing requirements. This formula is used in servo systems, robotic joints, and CNC machinery. Understanding encoder resolution is crucial for high‑performance motion control.
- Selection of encoders for precision motion control
- Calculation of position and velocity from encoder feedback
- Design of closed‑loop servo systems
- Quality assessment of motion control accuracy
- Integration with motor drivers and controllers
Frequently Asked Questions
The angular resolution is the smallest detectable change in angle. For a rotary encoder with CPR (counts per revolution), the resolution in degrees is Δθ = 360 / CPR. If quadrature decoding is used, the effective CPR is multiplied by 4.
Confusing counts per revolution (CPR) with pulses per revolution (PPR). Quadrature decoding often multiplies the effective count by 4. Always check whether the CPR is raw or after decoding.
Quadrature decoding multiplies the resolution by 4, so the effective resolution becomes Δθ = 360 / (4 × CPR). This improves precision without additional hardware.
Effective CPR = 1000 × 4 = 4000 counts/rev. Resolution = 360 / 4000 = 0.09° per count.
Higher resolution allows finer position control and smoother velocity estimation. However, it also increases the data rate and computational load.
The maximum speed is limited by the encoder's maximum frequency and the controller's sampling rate. The speed is related to the frequency of the encoder pulses: RPM = (freq × 60) / (CPR × 4) for quadrature.
Incremental (relative) and absolute encoders. Incremental encoders provide relative position, while absolute encoders give a unique code for each position.
It is determined by the number of bits: resolution = 360 / 2^n, where n is the number of bits.
Motor position and speed feedback, robotics (joint angle sensing), and industrial automation.
Choose a resolution that meets the required positioning accuracy and speed measurement needs. Higher resolution improves accuracy but increases cost and data rate.