# Resolver-to-Digital Converter

**Libraries:**

Simscape /
Electrical /
Control /
Observers

## Description

The Resolver-to-Digital Converter block models a transducer that converts the angular position or velocity of a rotating shaft to an electrical signal. Resolver-to-digital converters are commonly used in harsh, rugged environments, such as in fully electric vehicles.

The converted signal is proportional to the sine or cosine of the shaft angle.

A resolver sensor has one rotor winding with the exciter sine wave that is AC-coupled to two stator windings. The stator windings, a sine coil and a cosine coil, are mechanically positioned 90-degrees out-of-phase. As the rotor spins, the rotor position angle changes with respect to the stator windings. The resulting amplitude-modulated signals must then be gained, demodulated and post processed to extract angle and velocity information ([1] and [2]).

### Equations

The block uses a phase-locked loop (PLL) to extract the angle and the velocity of the rotating shaft. The error voltage used by the PI controller is obtained as:

$${V}_{e}={V}_{y}{V}_{p}\mathrm{cos}(N\theta )-{V}_{x}{V}_{p}\mathrm{sin}(N\theta ),$$

where:

`V`

is the excitation voltage._{p}`V`

is the_{x}`x`

voltage for the secondary winding of the resolver.`V`

is the_{y}`y`

voltage for the secondary winding of the resolver.`N`

is the number of pole pairs for the resolver.`θ`

is the angle.

Therefore, the velocity is obtained as:

$$\omega ={K}_{p}{V}_{e}+{K}_{i}{\displaystyle \int {V}_{e}},$$

and the angle is computed from the velocity using:

$$\frac{d\theta}{dt}=\omega .$$

## Examples

## Ports

### Input

### Output

## Parameters

## References

[1] Santanu Sarma, V.K. Agrawal,
Subramanya Udupa. *Software-Based Resolver-to-Digital Conversion Using a
DSP*. IEEE Transactions on Industrial Electronics, 55, 371-379. February
2008. (https://www.researchgate.net/publication/3219673_Software-Based_Resolver-to-Digital_Conversion_Using_a_DSP)

[2] Ankur Verma, Anand Chellamuthu.
*Design considerations for resolver-to-digital converters in electric
vehicles*. Texas Instruments, Analog Applications Journal.
2016.

## Extended Capabilities

## Version History

**Introduced in R2019b**