## 248 – Analysis of a Variable Reluctance Resolver

### Overview

To measure the angular position / speed of a rotating element there are different available devices. Encoder (incremental, absolute) or Resolvers.
Since the resolver is composed only of iron cores and coils, it is more robust than the rotary encoder about environmental resistance. So, it is used for power system motors and EPS which require high environmental resistance.
In this example, we introduce the case study that evaluates the output voltages and angle error of the variable reluctance resolver.

### Principle of resolver

Fig. 1 shows the principle of resolver. The resolver feeds a source signal at a pulsation Ï‰, and obtains two sinusoidal signals Va and Vb as shown in Fig. 1. Those two signal will then allow us to obtain the position of the rotor.
But in the case of the variable reluctance (VR), the exported signal Va and Vb are different as they are created due to combination of the saliency of the rotor with X poles, the pulsation Ï‰ of the source and the position Î¸ of the rotor.

### VR Resolver

The output signals of the VR Resolver is created using reluctant rotor with a X number of poles and a n number of teeth. In Fig. 2, we have an example layout of a VR Resolver with X=4 and n=10.
To obtain the signals Va and Vb from Fig. 1, we will need to adapt the winding of the two signals so that Va follows a sine function and Vb a cosine function.
Feeding the system with a 10 kHz source signal and rotating the machine at 500 r/min, we obtained the output signals shown in Fig. 3.
The signals have an envelope that corresponds to the rotational speed. We can see that the two signals are not exactly the one we hoped to obtain in Fig. 1, but the resulting signals can easily be converted and extract from the cosine and sine signals for the resolver.
Fig. 4 shows that the output signal are modulated by the source signal of 10 kHz.
If we do not take in account any delays or error in the demodulation of the signal we can find that the VR resolver has an angular error of maximum 70 ÂµDeg, as shown in Fig. 5.