A resolver is an electromagnetic sensor that measures the rotational position of a shaft by converting mechanical angle into electrical signals. It works like a specialized transformer: an AC voltage is fed into a primary winding, and two secondary windings output signals whose amplitudes change depending on how far the shaft has turned. Resolvers are widely used in electric vehicles, industrial motors, and aerospace systems because they’re rugged enough to handle extreme heat, vibration, and electromagnetic interference.
The Basic Principle
A resolver operates on electromagnetic induction, the same principle behind any transformer. An AC excitation signal (typically 1 kHz to 20 kHz at 3 to 7 volts RMS) is applied to a primary winding on the rotor. This primary winding is sometimes called the reference winding. As current flows through it, the winding creates a changing magnetic field that couples energy into two secondary windings mounted on the stator.
The key design feature is that these two secondary windings are physically offset by 90 degrees from each other. One is called the sine winding and the other the cosine winding. As the rotor turns, the magnetic coupling between the primary and each secondary changes. At any given shaft angle, one secondary picks up more of the signal and the other picks up less, in a pattern that traces out sine and cosine curves. This is what makes it possible to determine exact angular position from the output signals.
Physical Construction
Resolvers are built by winding copper wire through slots in steel rotor and stator cores. Physically, they look like a small AC motor, with diameters typically ranging from 10 to 100 mm. The stator (the stationary part) houses the two output windings at right angles. The rotor (attached to the spinning shaft) carries the primary winding plus a reference winding that helps couple signals between rotor and stator.
Because the rotor spins, getting an electrical signal onto it requires a rotary transformer. This is a contactless coupling that transfers the AC excitation from the stationary electronics to the spinning rotor without any brushes or slip rings. The absence of physical contact points is one reason resolvers last so long and tolerate harsh conditions.
How the Output Signals Encode Position
The two output voltages from the sine and cosine windings carry the same AC carrier frequency as the excitation signal, but their amplitudes are modulated by the shaft angle. If the shaft angle is θ, the sine winding output amplitude is proportional to sin(θ) and the cosine winding output amplitude is proportional to cos(θ). More precisely, each output is the excitation signal multiplied by either the sine or cosine of the shaft angle.
This means the outputs are AC waveforms that swell and shrink as the shaft rotates. When the shaft is at 0 degrees, the cosine output is at maximum and the sine output is at zero. At 45 degrees, both are equal. At 90 degrees, the sine output is at maximum and the cosine is at zero. By measuring the ratio of these two signals, you can calculate the shaft’s exact angular position anywhere through a full 360-degree rotation.
Converting Signals to a Digital Angle
The raw sine and cosine outputs are analog AC signals. To turn them into a usable digital angle reading, a dedicated chip called a resolver-to-digital converter (RDC) processes them through several stages.
First, the analog front end cleans up the signals by filtering noise, adjusting the DC bias, and amplifying the AC waveforms to a consistent level. Then the converter uses a clever feedback loop: it assumes a digital angle, generates its own internal sine and cosine values for that assumed angle using lookup tables, and multiplies those against the actual resolver outputs. The math works out so that the result is an error signal proportional to the difference between the assumed angle and the real shaft angle.
A synchronous detection circuit strips away the AC carrier frequency, leaving just the error value. This error feeds into a digital tracking loop that continuously adjusts the assumed angle to drive the error toward zero. When the error reaches zero, the converter’s assumed angle matches the shaft’s true position. The loop runs constantly, so the digital output tracks the shaft in real time, providing both angular position and rotational speed.
Single-Speed vs. Multi-Speed Resolvers
A single-speed resolver has one pair of sine and cosine windings in the stator. It produces one complete sine cycle and one complete cosine cycle per full shaft revolution, giving a unique position reading across all 360 degrees.
A multi-speed resolver integrates multiple pairs of sine and cosine windings. A resolver with, say, four pole pairs will produce four complete sine and cosine cycles per revolution. This effectively divides the rotation into four identical electrical cycles, which improves measurement resolution within each segment. The trade-off is that a multi-speed resolver alone can’t distinguish between segments, so it’s often paired with a single-speed resolver. The single-speed unit identifies which segment the shaft is in, and the multi-speed unit pinpoints the exact position within that segment.
Accuracy and Precision
A conventional variable-reluctance resolver typically achieves accuracy around 15 arcminutes in simulation and roughly 30 arcminutes in practice (one arcminute is 1/60th of a degree). More advanced designs push accuracy down to about 8 arcminutes, which approaches the performance of commercial magnetic encoders used in space applications (around 1.5 arcminutes). For context, 8 arcminutes is about 0.13 degrees, so even a standard resolver can pinpoint shaft position to a fraction of a degree.
The actual precision you get depends on the quality of the resolver, the RDC processing, and how well the system filters noise. In many motor control applications, especially electric vehicle traction motors, this level of accuracy is more than sufficient for smooth, efficient operation.
Why Resolvers Survive Harsh Environments
Resolvers are built entirely from copper wire and steel. There are no LEDs, no glass discs, no semiconductors inside the sensor itself. This gives them a major durability advantage over optical encoders, which use light sources and photodetectors that degrade under extreme conditions.
Resolvers can operate at temperatures exceeding 200°C. Optical encoders, by comparison, typically work within -20°C to 85°C, with extended-range versions reaching about 120°C. The encapsulated, all-metal construction also makes resolvers highly tolerant of shock, vibration, radiation, and electromagnetic interference. In environments where particulates, moisture, or temperature swings would damage an optical encoder, a resolver keeps working reliably.
This durability is exactly why resolvers are the dominant position sensor in electric vehicle traction motors. The sensor sits close to the motor, exposed to heat from both the motor windings and the power electronics, plus constant vibration from the drivetrain. A resolver handles all of that without degradation. It feeds precise rotor position and speed data to the motor controller, which needs that information to time the current pulses that drive the motor efficiently.
Common Applications
Electric vehicles are the highest-volume application today. The resolver mounted on the traction motor measures rotor position, speed, and direction of rotation, then sends those signals to the vehicle’s electronic control unit. Without accurate, real-time position data, the controller can’t synchronize the rotating magnetic field properly, and motor efficiency drops.
Beyond EVs, resolvers are standard equipment in aerospace actuators (flight control surfaces, landing gear), industrial servo motors, CNC machines, and military systems. Any application where precise rotational measurement must happen reliably in tough conditions is a natural fit. Their combination of contactless operation, environmental resilience, and straightforward analog output makes them one of the longest-lived sensor technologies still in widespread use.