In a single-speed resolver, a complete voltage signal sine wave and a complete cosine wave are generated from the output windings. Single-speed resolvers are simple and economical. They are the most common type of resolver deployed in the field today. They are good fits for use with servo-motors, actuators, robotics, etc.
The historical method for building these types of resolvers was to monitor the additional turns mechanically using a gearbox mounted between the motor and the resolver. A more economical method is to monitor the additional turns electrically by modifying the windings.
In a multi-speed resolver, the windings are wound to generate a higher number of electrical cycles. A three-speed resolver, for example, is wound to generate three complete sine waves and three complete cosine waves per mechanical rotation. The higher ratio of electrical cycles to mechanical rotation helps minimize the effects of mechanical error sources in the system. Although multi-speed resolvers are effective, the more complex winding pattern adds to cost.
As a result, it should only be used if the performance improvement is required for the application. Position-measuring applications require single-speed resolvers. Recall that a single rotation of the shaft corresponds to one complete sine or cosine wave.
A resolver can be thought of as a special transformer. On the primary side, as expressed in Equation 1, EXC is the excitation sinusoidal input signal. In a real resolver system with amplitude mismatch, phase shift, imperfect quadrature, excitation harmonic, and inductive harmonic, any of these five nonideal conditions may happen and contribute error. To determine the position error created by amplitude mismatch, Equation 3 can be rewritten as Equation 5.
Where a represents the amount of mismatch between SIN and COS signals, the remaining envelope signal after demodulation can readily be shown, as in Equation 6. Then we can receive error information, as shown in Equation 7.
So, Equation 7 becomes Equation 8, and the error term is expressed in radians. Assume the amplitude mismatch is 0. Phase shift refers to both differential phase shift and common phase shift. To determine the position error created by differential phase shift, Equation 3 can be rewritten as Equation Then we can get error information as shown in Equation So, Equation 13 becomes Equation 14 with the error term expressed in radians.
Assume the differential phase shift is 4. Speed voltages, which only occur at speed and not at static angles, are in quadrature to the signal of interest.
As shown in Equation 19, the error is proportional to the resolver speed and phase shift. Thus, in general, it is beneficial to use a high resolver excitation frequency. This occurs when the two resolver phases are not machined or assembled in perfect spatial quadrature.
As before, the envelop signal remaining after demodulation can readily be shown as Equation Then we can receive error information, as shown in Equation Compared to the error due to amplitude mismatch, in this case, the mean error is nonzero and the peak error is equal to the quadrature error. In all the preceding analysis, it was assumed that the excitation signal was an ideal sinusoid and contained no additional harmonics.
In a real-world system, the excitation signal does contain harmonics. So, Equation 2 and Equation 3 can be rewritten as Equation 24 and Equation The envelope signal remaining after demodulation can readily be shown, as in Equation Driving this signal to zero in Type II tracking loop.
If the resolver excitation has identical harmonics, the numerator of Equation 27 is zero and no position error is incurred. That means the common excitation harmonic has negligible effect on the RDC, even at very large values. However, if the harmonic content is different in SIN or COS, the position error incurred has the same functional shape as the amplitude mismatch shown in Equation 8. Rev: 6 Pages, KB. Rev: 7 Pages, KB.
Rev: 8 Pages, KB. Rev: 9 Pages, Rev: 16 2 Pages, 1. Rev: 19 Pages, 3. In practical resolvers, rotor windings include both reactive and resistive components.
The resistive component produces a nonzero phase shift in the reference excitation that is present when the rotor is both at speed and static. Together with the speed voltages , the nonzero phase shift of the excitation produces a tracking error that can be approximated as. A block diagram of the synthetic reference block is shown in Figure 7. The advantage of Type-II tracking loops over Type-I loops is that no positional error occurs with constant velocity.
Even in a perfectly balanced system, however, acceleration will create an error term. The amount of error due to acceleration is determined by the control-loop response. Figure 8 shows the loop response for the AD2S This is not always feasible, however. Figure 10 shows a typical interface circuit between the resolver and the AD2S The series resistors and the diodes provide adequate protection to reduce the energy of external events such as ESD or shorts to supply or ground.
These resistors and the capacitor implement a low-pass filter that reduces high-frequency noise that couples onto the resolver inputs as a result of driving the motor. This can be accomplished by the addition of resistor R A. This weak bias can be easily overdriven. This excitation buffer can be implemented in many ways, two of which are shown here. The first circuit is commonly used in automotive and industrial designs, while the second simplifies design by replacing the standard push-pull architecture with a high output current amplifier.
The high-current driver shown in Figure 11 amplifies and level shifts the reference oscillator output. The driver uses an AD dual, low-noise, precision op amp and a discrete emitter follower output stage. This high-current buffer offers drive capability, gain range, and bandwidth optimized for a standard resolver, and it can be adjusted to meet specific requirements of the application and sensor, but the complex design has a number of disadvantages in terms of component count, PCB size, cost, and engineering time needed to alter it to application-specific needs.
The design can be optimized by replacing the AD with an amplifier that provides the high output current required for driving resolvers directly, simplifying the design and eliminating the need for a push-pull stage. The high-current driver shown in Figure 12 uses the AD high-current dual op amp with rail-to-rail outputs to amplify and level shift the reference oscillator output, optimizing the interface to the resolver. The AD achieves low-distortion, high output current, and wide dynamic range, making it ideal for use with resolvers.
A duplicate circuit provides a fully differential signal to drive the primary winding. The capacitor should be chosen to minimize phase shift of the carrier. The total phase shift between the excitation output and the sine and cosine inputs should not exceed the phase-lock range of the RDC. The capacitor is optional, as classical resolvers filter out high-frequency components exceptionally well.
Figure 13 shows the AD reference buffer compared with a traditional push-pull circuit. The power of each fundamental shows little discrepancy between both configurations, but the AD buffer has reduced harmonics. Although the AD circuit offers slightly lower distortion, both buffers provide adequate performance.
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