How does a Resolver-to-digital converter work?

Question

I am currently taking a class on sensors and sensor design and I came across this homework problem:

In a commercial resolver to digital converter the digital angle Φ is determined to be 20 degrees. The output of the summing amplifier is resolver signal A sin (2πft), where frequency f is 60 hz, A = 0.7 volts and the input voltage V to the resolver is 10 volts. What is the rotor angle in the resolver in degrees at time t = .07 seconds?

I am having a hard time figuring this out. I've read through our assigned textbook and came across this block diagram of the Resolver to Digital Converter that we are going over.

Based on my understanding, the converter will start with a Digital Angle (Φ) and combine it with the input signals from the two secondary transformers in the resolver. Then the detector will use the reference voltage in conjunction with the output of the summing amplifier in order to find the Error signal: Ksin(θ-Φ). It then uses this error signal in some way to determine how far off the digital angle (Φ) is from the true angle of the resolver.

How does this detector work? What is it doing exactly? How does the integrator work? Is there some information or equation I'm missing? I don't need the answer to the homework problem, I am only looking for some guidance.

As a side note, I would greatly appreciate any recommendations for some good textbooks on sensors.

Answer 1

The detector is a phase detector. It tells you on the diagram that its output is Ksin(theta-phi), the sine of the angle error, which for small errors is more or less the error itself.

This is used to complete the phase locked loop, which drives the angle estimate to be equal to the input angle. The integrator is used so that any small error does not persist, but builds up until it gets corrected. It effectively gives it infinite gain at DC.