How Stator-Rotor Electromagnetic Coupling Enables Position Sensing

A resolver, also known as a synchronous resolver, is an electromagnetic sensor designed to measure rotational angles with high precision. Its operation hinges on the principle of electromagnetic induction, where the interaction between a stator (fixed component) and a rotor (rotating component) generates position-dependent electrical signals. Below is a detailed explanation of how this electromagnetic coupling translates mechanical rotation into measurable electrical outputs.

1. Core Structure and Excitation
The resolver consists of two main parts: the stator and the rotor. The stator contains primary windings energized by an alternating current (AC) excitation voltage, typically at frequencies like 400 Hz, 3 kHz, or 5 kHz. This excitation creates a rotating magnetic field within the stator. The rotor, mechanically linked to the shaft whose position is to be measured, features secondary windings that rotate within this magnetic field.

2. Electromagnetic Coupling Mechanism
As the rotor rotates, the relative position between the stator's rotating magnetic field and the rotor's windings changes. The rotor windings, often arranged orthogonally (e.g., sine and cosine windings), experience varying magnetic fluxes. According to Faraday's Law of Induction, these changing fluxes induce sinusoidal voltages in the rotor windings. The amplitudes of these induced voltages depend on the angular displacement between the stator and rotor, typically following sine and cosine functions of the rotor angle.

3. Signal Characteristics
The output signals from the rotor windings are analog voltages. For a single-speed resolver, the outputs are:

• Sine Output (E_sin): Proportional to sinθ, where θ is the rotor angle.

• Cosine Output (E_cos): Proportional to cosθ.

In multi-speed resolvers (e.g., dual-channel systems), additional pole pairs generate higher-frequency signals, enhancing resolution and enabling finer angle detection.

4. Signal Processing and Position Extraction
To convert the sine/cosine outputs into usable position data, external circuitry or algorithms are required. Common methods include:

• Analog Division: Using tan−1(Esin/Ecos) to compute θ, though this is sensitive to noise.

• Resolver-to-Digital Converters (RDCs): Integrated circuits that employ tracking loops (e.g., Type II servo loops) to decode the resolver signals. These devices compare the resolver outputs to internally generated references, adjusting until the phase error is minimized, thereby recovering the rotor angle.

5. Design Advantages and Applications
Resolvers excel in harsh environments due to their rugged construction (no optical components or contacts) and immunity to electromagnetic interference. They are widely used in:

• Motor Control Systems: Providing real-time feedback for servo motors in robotics, aerospace, and automation.

• Aerospace and Defense: Critical for applications requiring high reliability and tolerance to vibration/temperature extremes.

• Industrial Equipment: In precision machining tools, where resolver-based systems enable sub-arcminute resolution.

6. Key Parameters Influencing Performance

• Excitation Frequency: Affects signal-to-noise ratio and system bandwidth.

• Number of Pole Pairs: Determines resolution and measurement range.

• Winding Configuration: Optimized for linear or nonlinear (e.g., sinusoidal) output relationships.

In summary, the resolver's ability to transform mechanical rotation into electrical signals via electromagnetic coupling makes it a vital component in systems demanding precise angular measurement. Its design balance between simplicity, robustness, and accuracy ensures its continued relevance in modern engineering applications.