Page 129 - Electric Drives and Electromechanical Systems

122 Electric Drives and Electromechanical Systems

power to the rotating primary winding. The stator consists of the two output windings
spaced 90 electrical degrees apart and the primary of a rotary transformer. The rotor also
carries the secondary of the rotary transformer that is used to excite the rotor of the
resolver. In the construction of resolvers, considerable care is taken to ensure that the
cores, windings, and the air gap are constructed to an accuracy which ensures that non-
linearity does not occur. In practice, errors can be caused by a number of factors
including: a difference in the primary/secondary transformation ratio, an electrical
phase shift, or a zero-shift error between the two secondary windings and unequal
loading of the windings by the external decoder. If the input to the resolver is,
V ¼ A sin ut (4.13)
the two outputs signals will be
V out1 ¼ Ak 1 sin q sinðut þ aÞ (4.14a)

V out1 ¼ Ak 1 cos q sinðut þ aÞ (4.14b)
where A is the amplitude of the excitation voltage, and k 1 and k 2 are the transformation
ratios between the primary and the two secondary windings (which ideally should be
equal), u equals 2pf where f is the carrier frequency, and a is the rotor/stator phase shift
(including any zeroing error) which ideally should be zero.
The output from the resolver can be used either directly as an analogue signal or after
conversion to a digital signal. The advent of resolve-to-digital converters (RDC) has
allowed digital data to be easily produced from resolvers. A modern RDC uses a ratio-
metric method, thus the system is not affected by changes to the absolute values of the
signal to and from the resolver. This is of considerable importance if the transmission
distance between the resolver and the RDC is large. It is current practice to provide a
complete RDC as integrated circuits or as hybrid packages. This ensures that the best
possible performance is obtained, with the packages’ components optimised for tem-
perature drift and other external sources of inaccuracy. A number of manufacturers
provide devices that determine the resolver’s velocity and position in a number of
different formats: as a bipolar analogue signal or as a digital clock proportional to the
speed, together with a logical direction signal. It is not uncommon for a device to have
1
12-bit resolution up to speeds of 375 rev s .
In this type of tracking converter shown in Fig. 4.14, the two inputs (assuming a
perfect resolver where a ¼ 0 and k ¼ k 1 ¼ k 2 ) are multiplied by the value held in a
counter; if the output of the counter is assumed to be equivalent to an angle 4, then,

0
V ¼ Ak sin q cos 4 sin ut (4.15a)
1
V ¼ Ak cos q sin 4 sin ut (4.15b)
0
1
and the difference from the error amplifier is,