Resolver Model

A resolver is a rotary transformer where the magnitude of the signal through the resolver windings varies sinusoidally as the shaft rotates.

Resolver Cross Section

Single excitation resover

The equations of the resolver can be expressed as follows:

where is the resolver angle, is the mechanical angle of the machine, is the angle offset, is the number of pole pairs of the resolver, , , , and are the resolver sine cosine gains and is the direction of the sensor rotation (0 = clockwise, 1 = counterclockwise).

Note: does not have an effect to the resolver angle, but change the resolver sine sign to match the counterclockwise convention.

When the gains are set to its default values (, , , and ), the sensor rotation is clockwise, and the excitation is a sinusoidal wave (, where is the excitation frequency), the outputs are given by the following expressions:

which means the excitaition signals are modulated by the sinus and the cosinus of the rotor position angle.

Excitation source

The excitation signal can be selected among one of the following options:

DC: a continuos signal is used as excitation, so the outputs are and ;
AC: a constant-frequency sinusoidal, unitary amplitude waveform is used as excitation , so the outputs are those expressed in the previous section.
External: a external signal, coming from one of the analog inputs, is used as excitation. This incoming signal may be rescaled by the Analog Input Differential Rescaling module (AIR).

Resolver gains

The resolver gains can be used to simulate non-ideal conditions of the sensor, occuring due to manufacturing imperfections.

Amplitude imbalance

Output phases have unequal inductances. Assuming the coupling between the rotor excitation winding and the cosine winding as the reference:

where .

Imperfect quadrature

Output phases are not in perfect spatial quadrature. Assuming the angle when the rotor excitation winding is aligned with the cosine winding:

where is the angle between the cosine winding and the sine winding (for there is a perfect quadrature, so one retrives the default gain values).

Faults

One of the windings is not connected due to a fault. In this case, the corresponding gain is equal to zero.

Excitation time shift

When the excitation signal comes from an external source (one of the analog input channels) the signal can be shifted by a given amount of time.