# Resolvers Working Principle & Applications

Resolver

Resolver is a synchro whose rotor is mechanically driven to translate rotor angle into electrical information corresponding to the sine and cosine of rotor angle. It can interchange rectangular and polar coordinates. It is also called a sine-cosine generator and synchro-resolver.

It is an analog device. A resolver is a special type of rotary transformer that couples voltage from an primary (input) winding into two secondary (output) windings with a magnitude that varies as a function of angular position.

Working Principle of Resolver

• The resolver consist of stator and rotor. Stator is the stationary part and rotor is revolving part. A shaft is attached to the rotor.
• The rotor carries the primary winding. The stator carry the two secondary winding displaced angularly offset with respect to one another by 90°. These secondary windings are designated as the sine winding and the cosine winding.
• The basic function of a resolver is to resolve a vector into its sine and cosine components.
• An AC voltage applied to the reference winding in the rotor.
• This inductively couples to the sine and cosine windings, and hence generating an output voltage with a magnitude that varies as the sine or cosine, respectively, of the angular position of the input shaft relative to some zero point.

Consider a right triangle defined by the points (x1,y1), (x2,y1), and (x2,y2) as shown in fig.2. For the angle θ, we can define the side opposite θ as y2-y1, the side adjacent to θ as x2-x1, and the hypotenuse as R. Therefore, we can write as

We can define a circle with radius of R in Cartesian coordinates as R2 = X2 + Y2 as shown in fig.3. Using identities in equations 1 and 2, we can express any point (X,Y) on a unit circle (R = 1) as:

Hence to determine the angle with a resolver, we have to take the arctan of the ratio of the two voltages supplied by the secondary (output) windings of the resolver.
Electrical zero (EZ) is defined as the position of the rotor w.r.t. the stator during excitation of the primary winding at which there is minimum voltage amplitude across the sine winding and the maximum voltage amplitude across the cosine winding as shown in fig.4. This ratio-metric format provides an inherent noise-reduction feature for any injected noise whose magnitude is approximately equivalent on both windings, and it compensates for thermal swings.

Classification of Resolvers

1. Computing resolver

It is used for generating cosine, sine and tangent functions. It also solves geometric relationships.

2. Synchro resolver

It is used for data transmission. It has same functions as synchro transmitter, receiver and control transformer but with a better accuracy.

Applications of Resolvers

1. Phase shifting
2. Vector composition
3. Vector resolution
4. Vector angle & component resolution
5. pulse amplitude control & pulse resolution

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