2026-06-19
A resolver is a rotary transformer that reports shaft angle as the ratio of two analog signals. Unlike optical encoders, resolvers have no electronics in the rotating assembly — just copper windings on a laminated steel rotor and stator. That's why they survive in jet engines, missile actuators, EV traction motors, and steel mills where temperatures hit 200°C and vibration would shake an encoder to death.
How it works: The rotor carries a primary winding excited with a sinusoidal reference, typically 4–10 kHz at 2–7 VRMS. Two stator windings sit 90° apart mechanically. As the rotor turns through angle θ, the stator outputs are:
The carrier ωt is identical in both; only the envelope encodes θ. Take the arctangent of the demodulated envelopes and you have absolute angle — no homing required at power-up. A synchro is the older three-phase cousin (S1/S2/S3 at 120°); a Scott-T transformer pair converts synchro outputs to resolver-format sin/cos for modern processing.
The RDC (Resolver-to-Digital Converter): Chips like the AD2S1210 or AD2S1205 perform the demodulation and arctangent in hardware using a Type-II tracking loop. The loop drives an internal angle counter until sin(φ̂)·cos(θ) − cos(φ̂)·sin(θ) = sin(θ − φ̂) ≈ 0. Output is a parallel digital word (10–16 bits) plus a velocity signal — useful for closing motor control loops without a separate tachometer.
Real-world example: A Toyota Prius traction motor uses a brushless resolver on the rotor shaft. The inverter excites it at 10 kHz, an AD2S1210 produces 12-bit angle (4096 counts/rev) at update rates above 200 kHz, and the field-oriented control algorithm uses that angle to commutate the IPM motor. The resolver tolerates the 150°C oil bath that would melt an optical encoder's LED.
Design rule of thumb: Pick your excitation frequency at least 10× your maximum mechanical rotation frequency to avoid envelope aliasing. For a 12,000 RPM motor (200 Hz), 4 kHz excitation works; for 30,000 RPM aerospace actuators, push to 10 kHz. Drive the rotor through a low-impedance buffer (≤10 Ω) — resolver primary impedance is typically 50–500 Ω, and any source impedance creates a phase shift that masquerades as angle error.
Watch out for: Quadrature error (sin and cos amplitudes mismatched) causes angle-dependent error that looks like a 2× harmonic. Most modern RDCs include automatic gain calibration to null this out.