18.2.1 Resolver-to-Digital Converter (RDC)

The primary purpose of the Resolver-to-Digital Converter (RDC) module is to provide excitation input signals and process output signals from an electrical resolver or other position sensors with sinusoidally varying output, such as an LVDT. It can also be used to demodulate other signals with square wave carriers.

Figure 18-1 shows a typical block diagram of the RDC.

The RDC provides the excitation signal to the resolver and demodulates the sine and cosine outputs to generate a digital representation of angular position and velocity.

A resolver is an electromagnetic transducer that converts mechanical angular position into electrical signals. It consists of a stationary part (stator) and a rotating part (rotor). The stator typically contains one primary winding and two secondary windings. The primary winding is driven by an excitation signal of specified frequency and amplitude that must be resolved. The two secondary windings are positioned 90° out of phase with each other. They resolve the resulting magnetic field into two orthogonal components: “sine” and “cosine.” An example of a resolver as a rotary transformer is shown in Figure 18-4.

Resolvers are typically excited with a sinusoidal signal. The sinusoidal excitation waveform and the demodulated outputs are shown in Figure 18-2.

Consider the excitation voltage applied to the rotor as follows:

$V_E=V\sin \left(\omega \tau \right)$

The voltage induced in the sine winding of the stator is given as:

$V_S=K{V}_E\sin \left(\theta \right)=KV\sin \left(\omega \tau \right)\sin \left(\theta \right)$

Where,

K = transformation ratio

θ = rotor's mechanical angle

Similarly, the voltage induced in the cosine winding of the stator is given as:

$V_C=K{V}_E\cos \left(\theta \right)=KV\sin \left(\omega \tau \right)\cos \left(\theta \right)$

In the voltage equations of the sine (Equation 18-2) and cosine windings (Equation 18-3), except for the θ, which changes with the shaft, the remaining parameters are fixed.

The dsPIC33AK256MPS306 Resolver-to-Digital converter uses square waves as the excitation signal, in contrast to the conventional approach that employs sinusoidal signals. These square waves drive the stator’s primary winding at a fixed frequency and amplitude, producing sine and cosine outputs at the secondary windings. These output signals are then sensed and digitized by the ADC. Demodulation can be performed by multiplying these digitized samples with the excitation signal; for a square wave signal, this can be accomplished by conditionally inverting the resolver outputs when the excitation signal output is at low polarity. This will heterodyne the signals, creating one signal with the excitation frequency components removed, and one signal with components at multiples of the excitation frequency. A low-pass filter can then remove the higher-frequency components, leaving only the sine and cosine signal envelopes. The square wave excitation signal and its typical demodulated output are as shown in Figure 18-3.

Once the demodulated sine and cosine values are recovered, a single angle value can be recovered with an arctangent calculation, or a series of values can be recovered with a ratiometric tracking loop.

Using Equation 18-2 and Equation 18-3:

$$\begin{gathered} e_S/e_C=K{V}_E\sin \left(\theta \right)/K{V}_E\cos \left(\theta \right) \\ =\tan \left(\theta \right) \end{gathered}$$

$\theta =a\tan 2(e_S,e_S)$

The RDC provides an optional CORDIC block, which can be used to calculate an error signal for use in the tracking loop.