Comment by MisterTea

Not at all unusual. They are called resolvers which are rotary transformers which output a sine and cosine signal. You input an AC sine wave and compare the phase offsets of the outputs to determine the rotor angle. Another type is called the Inductosyn which uses a flat coil. My Beckhoff 500W 400V brush-less servos have them as do older brushed Electrocraft servos in a CNC machine at work. https://en.wikipedia.org/wiki/Resolver_(electrical)

Quadrature encoders don't skip counts unless your output is single ended and your wiring is poor leading to interference of the signal. PWM drives tend to make a lot of noise and single ended encoders will see lots of problems unless you take great care. I always use differential signal encoders in our machines here at work. They use an RS485 driver to achieve this in the encoder itself. Aerotech, the main vendor we use for motion control, uses differential signal by default. Never had positioning or counting problems unless the encoder was physically damaged.