Engineering Reference
Stepper, Encoder and BLDC Timing Reference
Lookup for step angle, microsteps, pulse rate, encoder PPR and decoded CPR, gear ratios, BLDC pole pairs, electrical RPM, electrical frequency, and commutation timing.
- Reading Time
- 11 min
- Format
- Motion timing lookup
- Updated
- September 29, 2026
Timing and Count Terms
| Term | Unit | Meaning | Boundary |
|---|---|---|---|
| Full-step angle | degrees/full step | Mechanical command increment of a stepper in full-step mode | Does not guarantee equal static position accuracy |
| Full steps/rev | steps/rev | 360° divided by full-step angle | Motor construction and drive mode must match |
| Microstep divisor | microsteps/full step | Command subdivisions generated by the driver | Microsteps are not equivalent to absolute accuracy or torque equality |
| Command counts/rev | counts/rev | Full steps/rev multiplied by microstep divisor | Gearbox and controller pulse conventions may add factors |
| Encoder PPR | pulses/rev | Base cycles or pulses per mechanical revolution under a stated channel convention | Manufacturers use PPR/CPR terminology inconsistently |
| Decoded CPR | counts/rev | Digital edge counts per revolution after x1/x2/x4 decoding | State whether quadrature multiplier is already included |
| Mechanical RPM | r/min | Shaft revolutions per minute | Not electrical RPM |
| Electrical RPM | ERPM | Electrical cycles per minute | ERPM = mechanical RPM × pole pairs |
| Electrical frequency | Hz | Electrical cycles per second | fe = mechanical RPM × pole pairs / 60 |
| Pole pairs | pairs | Half the even magnetic pole count | Do not use total pole count directly in the pole-pair formula |
| Six-step sector rate | transitions/s | Six ideal commutation sectors per electrical cycle | Controller and sensor edge definitions can differ |
| Gear ratio | input rev/output rev | Speed reduction and ideal torque multiplication convention | Always state ratio direction and efficiency |
Core Relationships
| Need | Relationship | Boundary |
|---|---|---|
| Stepper full steps | Nfull = 360° / step angle | Mechanical full-step specification |
| Stepper command counts | Ncmd = Nfull × microstep divisor | Command resolution, not guaranteed accuracy |
| Pulse frequency | fpulse = RPM × Ncmd / 60 | Motor must follow acceleration and load |
| Encoder RPM | RPM = fedge × 60 / effective CPR | Decoder convention must match CPR |
| Encoder resolution | degrees/count = 360° / effective CPR | Backlash and interpolation error are separate |
| BLDC electrical frequency | fe = mechanical RPM × pole pairs / 60 | Pole pairs = total poles / 2 |
| Electrical RPM | ERPM = mechanical RPM × pole pairs | Not shaft RPM |
| Gearbox output speed | RPMout = RPMin / ratio | Ratio direction must be declared |
Canonical Calculation Anchors
| Case | Result | Interpretation |
|---|---|---|
| 1.8° stepper | 200 full steps/rev | Mechanical full-step count |
| 200 steps, 16 microsteps | 3200 command counts/rev | 0.1125° command increment |
| 300 RPM at 3200 counts/rev | 16000 pulses/s | Command rate before acceleration limits |
| 1024 effective CPR at 1500 RPM | 25600 edges/s | 0.351563° per count |
| 14-pole BLDC | 7 pole pairs | Use seven, not fourteen, in electrical-cycle formula |
| 3000 RPM, 7 pole pairs | 350 Hz; 21000 ERPM | 2100 ideal six-step sectors/s |
| 3000 RPM through 10:1 reduction | 300 RPM output | Ideal speed relation; efficiency affects torque/power |
Practical Boundaries
| Topic | Why arithmetic is not enough |
|---|---|
| Stepper motion | Acceleration, resonance, current control, voltage, load inertia and torque determine whether commanded steps are followed |
| Microstepping | Current-vector interpolation improves smoothness but incremental torque and position are nonlinear |
| Encoder measurement | Edge jitter, count-window length, quantization, missed edges and index alignment affect estimate |
| Gearing | Backlash, compliance, tooth error and efficiency separate command resolution from output accuracy |
| BLDC commutation | Back-EMF shape, Hall placement, sensorless detection and control strategy shift practical timing |
| High-speed control | Controller interrupt rate, timer resolution and driver setup/hold limits cap usable count frequency |
Common Errors
- Treating microstep count as position accuracy.
- Confusing PPR with decoded CPR.
- Applying x4 quadrature twice.
- Using total poles instead of pole pairs.
- Calling ERPM mechanical RPM.
- Omitting the factor of 60 between RPM and hertz.
- Reversing gearbox ratio direction.
- Ignoring encoder location relative to gearbox.
- Ignoring backlash and missed steps.
- Using pulse frequency without an acceleration profile.
- Treating six-step sector rate as PWM frequency.
- Ignoring controller and driver timing limits.
Support reference
FAQ
How many full steps per revolution does a 1.8 degree stepper have?
360 divided by 1.8 gives 200 full steps per mechanical revolution.
How do microsteps change counts per revolution?
Multiply full steps per revolution by the selected microstep divisor. A 200-step motor at 16 microsteps has 3200 command counts per motor revolution.
Does 16x microstepping provide 16x position accuracy?
No. It increases command resolution and smoothness, but torque nonlinearity, load, friction, current regulation and detent effects limit actual positional accuracy.
What is the difference between encoder PPR and CPR?
Terminology varies. PPR may describe base pulses or cycles, while decoded CPR may include x1, x2 or x4 edge counting. Always state the convention.
How is encoder RPM calculated?
RPM = edge frequency × 60 / effective counts per revolution, using a CPR that matches the actual decoder convention.
How are BLDC mechanical and electrical RPM related?
Electrical RPM equals mechanical RPM multiplied by pole pairs. Electrical frequency is ERPM divided by 60.
Are pole count and pole pairs the same?
No. A motor with 14 magnetic poles has 7 pole pairs.
How many commutation sectors are in one BLDC electrical cycle?
Ideal six-step commutation has six 60-electrical-degree sectors per electrical cycle.
How does a gearbox affect encoder counts?
An encoder on the motor side produces motor counts multiplied by the reduction ratio per output revolution, subject to ratio convention and backlash.
Does pulse frequency guarantee stepper speed?
No. The motor must have enough torque and acceleration margin to follow commands without missed steps.
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