# Resolver Decoder

Compute electrical angular position of resolver

• Library:
• Motor Control Blockset / Sensor Decoders

• ## Description

The Resolver Decoder block calculates the electrical angular position of the resolver from the resolver sine and cosine output signals.

The resolver uses a primary sinusoidal excitation input signal to generate the modulated secondary sine and cosine waveforms.

You must normalize these waveforms (within the range of [-1,1] and centered at 0) and sample them to obtain the secondary sine and cosine input signals of the Resolver Decoder block.

The block computes and outputs the resolver position in [0, 2π] radians. The block can also add a phase delay to the sampled sine and cosine signals with respect to the excitation signal. ### Note

The block inputs should have identical amplitude and data types (either signed fixed or floating point).

### Equations

The block computes the average, peak amplitude values, and the sign of the peak amplitude of a signal cycle as

`${Å}_{average}=\frac{1}{n}\sum _{i=0}^{n-1}\left(|{Å}_{i}|\right)$`
`${Å}_{peak}={Å}_{average}×\frac{\pi }{2}$`

where:

• ${Å}_{average}$ is the average amplitude value of a signal cycle

• $n$ is the number of samples per excitation cycle

• ${Å}_{peak}$ is the peak amplitude value of a signal cycle

The block computes the electrical angular position of the resolver as

where:

• ${u}_{\text{sin}_peak}$ is the ${Å}_{peak}$ of the secondary sine signal

• ${u}_{\text{cos}_peak}$ is the ${Å}_{peak}$ of the secondary cosine signal

• $\theta$ is the electrical angular position of the resolver

## Ports

### Input

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Secondary sine waveform output from the resolver that is sampled and normalized within the range of [-1, 1] and centered at 0.

Data Types: `single` | `double` | `fixed point`

Secondary cosine waveform output from the resolver that is sampled and normalized within the range of [-1, 1] and centered at 0.

Data Types: `single` | `double` | `fixed point`

### Output

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Electrical angular position of the resolver (and the rotor) in [0, 2π] radians.

Data Types: `single` | `double` | `fixed point`

## Parameters

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The phase delay that the block must add to the `Sin` and `Cos` input port signals.

Number of samples available in one cycle of the `Sin` and `Cos` input port signals.

The data type of the resolver position output `θ`.