Stepper Motors for GATE RA 2027: Types, Step Angle, Modes & Torque-Speed Characteristics

Stepper motors are the digital actuator of choice for open-loop positioning, and they are a high-yield topic in the “Actuators” line of the GATE Robotics and Automation (RA) 2027 syllabus. A stepper motor converts each electrical pulse into a precise, fixed angular step, so the shaft position is set simply by counting pulses — no feedback sensor required. This makes stepper motors ideal for 3D printers, CNC tables, camera and telescope drives, printers and pick-and-place machines. This guide explains the principle of operation, types, step angle, modes, performance and the torque-speed characteristics of stepper motors, with diagrams, governing equations, worked examples and the mistakes that trip up exam candidates.

Principle of operation

A stepper motor is a synchronous, doubly-salient machine driven in discrete steps rather than continuous rotation. Its stator has several pairs of electromagnet poles wound as separate phases; its rotor is a toothed iron piece (or a permanent magnet). When one phase is energised, the rotor turns until its teeth line up with the excited stator poles, at the position of minimum reluctance (or, for a permanent-magnet rotor, of magnetic alignment). Energising the phases in a fixed sequence “drags” the rotor round one precise step at a time. Because each pulse produces exactly one step, the total rotation equals the step angle multiplied by the number of pulses — the shaft position is inherently digital and repeatable.

Types of stepper motors

• Variable-reluctance (VR) stepper: a soft-iron toothed rotor with no magnet. The rotor moves to the minimum-reluctance position when a phase is energised. It has no detent (holding) torque when unpowered, small step angles and low inertia, giving fast response but modest torque.
• Permanent-magnet (PM) stepper: a magnetised rotor that aligns with the energised poles. It has detent torque even when de-energised (the magnet holds position), larger step angles (typically 7.5° or 15°) and higher torque than VR.
• Hybrid stepper: combines a magnetised, axially-toothed rotor with VR-style teeth. It offers the best of both — small step angles (commonly 1.8°, i.e. 200 steps/rev), high torque and good detent torque. Hybrids dominate industrial and 3D-printer use.

Step angle and resolution

The step angle β is the angle the shaft turns for one input pulse. It is set by the number of stator phases and the number of rotor teeth (poles):

where N_ph is the number of stator phases (or the number of energisation states per rotor-tooth pitch) and N_r is the number of rotor teeth. A smaller step angle means finer resolution: a 1.8° motor makes 200 steps per revolution, while a 0.9° motor makes 400. The resolution (positioning fineness) is simply the step angle, and it can be improved electronically by microstepping, described below. Since the controller knows the step angle and counts the pulses, it always knows the shaft angle — the essence of open-loop position control.

Modes: full-step, half-step, microstepping

• Full-step (one-phase-on or two-phase-on): phases are energised in the basic sequence, giving the rated step angle. Two-phase-on full-stepping gives more torque than one-phase-on because two poles pull the rotor together.
• Half-step: alternates between one-phase-on and two-phase-on states, halving the step angle (e.g. 1.8° → 0.9°) and doubling the resolution, at the cost of an uneven torque between steps.
• Microstepping: the drive supplies sinusoidally-graded currents to the two phases, positioning the rotor at many intermediate points between full steps. It multiplies resolution (often ×16, ×32 or more) and gives very smooth, quiet, low-vibration motion — the standard in modern 3D printers and CNC.

Torque-speed characteristics

The torque behaviour of a stepper motor is described by several distinct quantities that the exam loves to separate:

• Holding torque: the maximum torque the motor resists when a phase is energised and the rotor is stationary. It is the highest torque figure quoted.
• Detent (residual) torque: the small torque that holds a PM or hybrid rotor in place when no phase is energised, due to the permanent magnet.
• Pull-in torque curve: the maximum load torque with which the motor can start, stop or reverse without losing a step, at a given step rate. The region inside it is the start-stop (self-start) region.
• Pull-out torque curve: the maximum load torque the motor can carry while running (already slewing) without losing synchronism. The band between pull-in and pull-out is the slew region, which can only be entered by ramping (accelerating) the pulse rate gradually.

Both torque curves fall as step rate rises, because at high stepping frequency the winding inductance limits how fast current can build in each phase, so less torque is developed. This is why steppers are excellent at low speed (very high torque, precise holding) but weaken at high speed, and why a motion profile must ramp the pulse rate up and down rather than jump straight to top speed.

Drive circuits

A stepper needs a drive that switches current through the phases in the correct sequence in response to STEP and DIRECTION signals from a controller. Unipolar drives use a centre-tapped winding and simple single-transistor switches per half-coil, but use only half the copper. Bipolar drives reverse the full winding current using an H-bridge per phase, giving more torque for the same size. Modern chopper (constant-current) drives rapidly switch the supply to regulate phase current, allowing higher voltages that push current in quickly and so extend the usable high-speed torque. Because the whole scheme runs open-loop, no encoder is needed — though if the motor is overloaded it silently “loses steps” and the position error goes undetected, the main limitation of stepper drives.

Performance parameters

• Resolution / step angle: smaller is finer; improved by half- and microstepping.
• Positional accuracy: typically ±3–5% of a step, and importantly non-cumulative — the error does not add up over many steps.
• Maximum stepping rate: the highest pulse frequency the motor can follow, limited by winding inductance.
• Response and settling: a single step is fast but the rotor rings (oscillates) about the new position before settling; damping or microstepping reduces this.
• Torque density: high holding torque at low speed, falling with speed.

Worked examples

Key formulas

Applications

Stepper motors excel wherever accurate, repeatable open-loop positioning at low-to-moderate speed is needed without the cost of a feedback encoder. Typical uses include 3D printers and CNC machines (axis drives), printers, scanners and plotters (paper and carriage feed), camera, telescope and antenna drives, medical pumps and dosing systems, and pick-and-place and indexing tables in automation. Their digital, pulse-counting nature makes them a natural match for microcontroller control, which is why they appear in almost every hobby and industrial motion project — and reliably in the GATE RA exam.

Resonance, damping and stepper vs servo

Because each step ends with the rotor springing into its new position, a stepper motor behaves like a lightly-damped spring–mass system and tends to oscillate (ring) about every step before settling. If the stepping frequency happens to coincide with this natural frequency — typically a few hundred pulses per second — the motor can hit mid-frequency resonance, lose torque and stall even though it is well inside its torque curve. Designers avoid this by adding mechanical or electronic damping, by microstepping (which softens each transition into many tiny ones), or by ramping quickly through the resonant band. This ringing is also why a stepper’s settling time, not just its raw step rate, matters in precise motion systems.

It is worth contrasting the stepper with the servo motor covered next in this series. A stepper runs open-loop: it is cheap, simple and gives excellent low-speed holding torque and repeatable positioning, but it wastes power holding position, loses torque at speed, and can silently lose steps if overloaded. A servo runs closed-loop with an encoder: it delivers full torque across a wide speed range, never loses position (the loop corrects any error), and is far more efficient at high speed, but it is more expensive and complex. As a rule of thumb, engineers pick a stepper for low-cost, low-speed, high-holding-torque positioning where an occasional missed step is tolerable, and a servo for high-speed, high-dynamic, high-accuracy motion where guaranteed positioning justifies the cost.

Common mistakes to avoid

• Confusing holding torque (powered, stationary) with detent torque (unpowered magnet torque) — they are very different in size.
• Believing a stepper can jump straight into the slew region — you must ramp the pulse rate; otherwise it stalls and loses steps.
• Assuming positional error accumulates — stepper error is non-cumulative as long as no steps are lost.
• Thinking VR steppers have detent torque — they do not; only PM and hybrid types do.
• Forgetting that torque falls with step rate because winding inductance limits current rise at high frequency.

Frequently asked questions

How does a stepper motor position without feedback?

Each input pulse moves the shaft by exactly one fixed step angle. The controller therefore knows the shaft position simply by counting the pulses it has sent, so no encoder is required — this is open-loop position control. The only risk is losing steps if the motor is overloaded.

What is the difference between pull-in and pull-out torque?

Pull-in torque is the maximum load with which the motor can start, stop or reverse instantly at a given step rate (the start-stop region). Pull-out torque is the higher load it can carry once already running and synchronised (the slew region). The slew region can only be reached by gradually ramping the pulse rate.

What is microstepping and why is it used?

Microstepping drives the two phases with graded sinusoidal currents so the rotor settles at many intermediate points between full steps. It multiplies resolution and gives smooth, quiet, low-vibration motion, which is why it is standard in 3D printers and CNC machines.

Why does stepper torque fall at high speed?

At high stepping frequency there is less time for current to build up in each phase against the winding inductance, so less magnetic force and torque are developed. Chopper (constant-current) drives with higher supply voltage push current in faster and extend the usable high-speed torque.

Which stepper type has the smallest step angle and highest torque?

The hybrid stepper. It combines a magnetised, finely-toothed rotor with variable-reluctance geometry, giving small step angles (commonly 1.8°), high torque and useful detent torque — which is why hybrids dominate industrial and 3D-printer applications.

This guide is part of the Actuators series in the complete GATE RA 2027 Syllabus overview. Continue with Servo Motors, or review DC Motors and Hydraulic & Pneumatic Actuators.