Resolver Vs Encoder
by Donald Barnett
Resolvers and Encoders are vastly different though they serve the same purpose in many applications. In rotary applications, both of them are used to sense the speed, direction and position of a rotating shaft. They function as transducers by transforming mechanical motion into electronic information. This electronic information is feedback to electronic devices controlling the mechanical motion. Feedback is the vital link that closes the control system loop to improve the system performance.
The fundamental technologies of resolvers and encoders can be packaged in a variety of ways to better function in specific applications. The discussion here will be narrowed to the more common technologies and constructions in use today to sense rotary motion. By better understanding the differences between resolvers and encoders, system designers can easily decide between them when choosing a feedback device for a given application.
For many years now, the dominant trend in feedback devices has been away from contacting toward non-contacting methods. The wear associated with contacting brushes and wipers reduces longevity and reliability. A brushless resolver uses a second set of rotor and stator coils called the transformer to induce rotor voltage across an air gap. Optical encoders use a rotating shutter to interrupt a beam of light across an air gap between a light source and a photodetector.
It is important for the designer to understand the critical nature of the air gap in resolvers and encoders. Of course the gap must be maintained under all circumstances otherwise damage to the feedback device will likely occur. Additionally, variations in the gap can translate into variation in the accuracy of the device. Tolerance to variation in gap is an important figure of merit when choosing the feedback device. Resolver gap is parallel with respect to the rotating axis and optical encoder gap is perpendicular to the axis of rotation. The design of the feedback device will dictate the optimal gap dimension and tolerance to deviations from optimum.
Resolvers use magnetic flux between windings on iron cores much like transformers. The typical resolver has two stator output coils at 90 degrees mechanical from each other. An AC voltage (6 VAC to 60 VAC, 400 Hz to 10,000 Hz) applied to the rotating coil (rotor) induces a voltage across the gap in the stationary coil (stator). In a brushless resolver, a second set of stator and rotor coils is used to apply voltage to the resolver rotor coil across the air gap. A transformer stator coil induces the input voltage across the gap to the transformer rotor on the rotating member of the resolver. The current in the transformer rotor flows through the resolver rotor creating the magnetic field of the rotor coil. Again the voltage is induced back across the gap to the resolver stator coils. The amplitude of the induced stator voltage is proportional to the relative angular positions of the rotor and stator coils. Since there are two stator windings at 90º, the output voltages are at 90º electrical phase. These voltages are called sine and cosine as given by the equations:
Vs = K E * SINq
Vc = K E * COSq
K, transform ratio (max output voltage / input voltage)
E, excitation voltage (E = Vo SIN wt)
q, rotor angle with respect to the stator
The output of a resolver is therefore an analog AC voltage equivalent to the absolute angle between the rotor and the stator. The absolute position is calculated by:
ARCTAN (SINq /
Optical Encoder technology
Optical encoders rely on optoelectronic components to detect rotary motion. A light source emits a beam across a gap onto a photodetector. A codewheel with graduated patterns of opaque and clear spaces rotates between the source and detector. The clear areas allow light to pass through the codewheel to the photodetector. The photodetector produces an electrical current proportional to the intensity of the illumination reaching it. Opaque areas in the codewheel interrupt the light beam allowing little or no light to reach the photodetector.
The codewheel pattern is usually a large number of evenly spaced lines at the optical radius around the axis of rotation. The output of the photodetector is a DC level rising and falling as the lines on the codewheel pass through the light path. Each change in state between high and low levels represents an incremental angle of rotation of the codewheel as given by:
qinc = 360 / lines on the codewheel
The position angle of the codewheel is obtained by digitally counting the incremental pulses:
q = count * qinc
Differences in construction between resolvers and optical encoders account for differences in longevity and environmental robustness. Resolvers are made of tough materials that withstand harsh environments over extended periods of time. Encoders use less robust materials that are sometimes fragile and environmentally sensitive. A simple listing of the materials in each device illustrates the obvious differences. Resolvers are made of copper wire, iron laminations, steel housings, and high temperature coatings. Encoders employ optoelectronics, glass optics, plastic housings, and epoxy adhesives.
Environmentally demanding applications eliminate encoders as an option. An encoder is more sensitive to shock and vibration than a resolver. With few exceptions, resolvers can operate at higher temperatures. Since encoders rely on a transparent optical path for reliable operation, they are much more sensitive to contamination. However, much can be done to improve the robustness of optical encoders. Metal or plastic can replace fragile components such as glass. Temperature sensitive components can be thermally isolated or upgraded to higher rated components. Mechanical isolation can be used to dampen shock and vibration. Sealed enclosures significantly reduce contamination effects.
Conversely, the materials that make resolvers robust also make them less desirable in applications where mass and inertia are critical design factors. Encoders offer much lower weight and considerably less revolving inertia. The higher mass of a resolver rotor could make it unsuitable for the control of high acceleration and deceleration motion profiles. Resolvers are much heavier than equivalent encoders. The designer should opt for encoder feedback where reducing system weight is important.
A variety of packaging options is available. Resolvers and encoders can be packaged as self-contained units. The feedback device is mounted on a shaft inside a protective housing. The shaft may extend from one end of the package or hollow shaft models are available. The housing may be less expensive light duty construction or a heavy duty sealed design. More economical and smaller packaging eliminates the housed construction, bearings and shaft. A frameless resolver is supplied as a rotor and a stator as separate parts. The installer is required to mount and align the resolver components on a shaft and its base plate. Modular encoders are similarly supplied without the rotating shaft. This type of encoder is installed and aligned on a shaft by the customer.
No discussion of motion control feedback is complete without defining accuracy. There are three components to the accuracy of a feedback device: precision, resolution, and repeatability. Precision is the ability of the device to measure a given angle relative to a theoretical standard. Resolver and encoder specifications list the limits of measurement precision as “Accuracy.” Resolution is the extent to which the device can detect small changes in angles. The resolution of a resolver is infinite because the output is analog. In practical terms however, the resolution of a resolver is limited by the interpolation of the resolver-to-digital converter electronics. The resolution of an encoder is determined by the lines per revolution (counts) in the codewheel pattern. Repeatability is the capacity of the device to consistently measure the same angle. Brushless resolvers and optical encoders are repeatable well within their precision and resolution. For this reason, repeatability is seldom specified.
For both resolvers and encoders, precision is predominately a function of the manufacturing process variability for a given design. Absolute precision is a design goal and statistically possible but variability in the manufacturing process results in measurement output errors. Improved designs can reduce manufacturing variability or null the effects of variability but ultimately errors in precision are process related.
For example, it was found that constructing resolver cores of stamped sheet metal laminations in place of machined cores could reduce costs. However, the stamped lamination assembly process introduced geometric variability that affected accuracy.
In an encoder, precision is closely related to the concentricity of the code pattern with the axis of rotation. Control of manufacturing tolerances alone will not produce precise encoders. An assembly process called “centering” will null out most of the manufacturing variability to greatly improve the encoder precision. In the centering process, a highly skilled assembler taps the code disk into a position where the codewheel pattern is concentric with the axis of rotation before the code wheel is bonded to its hub.
A similar process known as “accuracy grinding” is used to improve the precision of resolvers. A skilled operator grinds away small sections of the resolver stator while measuring the resultant precision after each trial. This operation would not be done on a production basis but is used to adjust the precision of a particular unit by up to 50% when manufacturing processes fail to produce a unit within specification.
As stated earlier, specifications for precision are given as accuracy in fractions of an angle. For a resolver, accuracy is given as the limits of variation from the absolute position of the detected angle. A typical brushless resolver specification for accuracy is 10 arc minutes. With improvements in design and process, the accuracy of resolvers could be increased to 3 arc minutes. Encoders comparable in size and price (code disk centered as described above) are routinely accurate within 20 arc seconds. Encoder accuracy within 3 arc seconds is economically obtainable.
In general we have been discussing the single-speed resolver. Such a resolver has only one coil and thus only one North Pole and one South Pole per revolution. More coils and thus more poles can be added. Resolvers with multiple poles are called multi-speed resolvers. The absolute angular position is not available from a multi-speed resolver because the detectable angle is no longer 360 degrees mechanical. The detectable angular position of a multi-speed resolver is 360 degrees mechanical divided by the number of pole pairs. However, the detecting error for each pole is the same as a single pole. Therefore, the number of poles reduces the angular error of a multi-speed resolver (qerror = qdetecting error / pole pairs). Multi-speed resolvers are used when resolver accuracy must be significantly improved.
Where feedback device precision is primarily process related, resolution is strictly a design factor. Maximum design resolution for a feedback device may be limited by the outer limits of process capabilities. However, within the design limit, process has no effect on resolution. Theoretically the resolution of a resolver is infinite but the interpolation electronics processing the resolver signal is not. By design, the resolver-to-digital conversion divides the smooth analog resolver signal into finite detectable levels. Encoder resolution is determined at design time by the number of lines dividing the circumference of the coded disk at its optical radius.
Resolution of continuous angles into finite divisions results in an ambiguity known as quantization error. Quantization error (round off error) occurs whenever analog data is changed into digital data. Since shaft rotation is essentially a smoothly variable analog function and resolver interpolation or encoder output resolution is a subdivision of shaft rotation into a finite number of increments, there is an inherent error of 1/2 the value of the last division. That is, a 10-bit feedback device can resolve no more than 360/1024 degrees of rotation and the quantization error is therefore approximately 0.18 degrees. Stated another way, the shaft must rotate 0.36 degrees before an output transition occurs and during that angle, the last count is 1023.5 0.5. Quantizing error is fixed error and can only be reduced by increasing the feedback resolution.
It is useful to compare precision and resolution and their respective error components, detection error and quantization error. If the detection error of a resolver is 10 arc minutes then the quantization error will be the same at roughly 10 bits of resolution (1024). The resolver-to-digital conversion electronics adds another 2 to 8 arc minutes of uncertainty. As a measuring device, the least significant bit of such a system is useless since the sum of the errors exceeds the smallest detectable angle.
The precision of encoders is much higher than resolvers therefore by the same analysis encoders can be used to resolve much smaller angles. If the precision of an encoder is 20 arc seconds then 20 arc seconds of quantization error occurs when the resolution is approximately 15 bits (32768).
Encoder resolution needs some further clarification. Incremental optical encoders have two digital output signals labeled A and B. The B signal is 90 degrees electrical phase from the A signal. This phase shift results in four unique states of the A and B signals known as quadrature output. They are A high – B low, A high – B high, A low – B high, and A low – B low. Since these four detectable states occur for every line on the codewheel, the resolution of the graduated lines can be multiplied by four. The smallest resolvable angle is then ¼ the angle between the coded lines (q = 360° / 4 * n). A 10 bit encoder (1024 lines) can be used to resolve 12 bits (4096 counts).
Tuning and bandwidth
Since resolvers are infinitely tunable feedback devices, a number of parameters must be considered when selecting components for a specific application. The resolver input frequency, winding impedances and input transformer ratio must be carefully considered in conjunction with system tracking rate, bandwidth, filtering, phase compensation and desired accuracy.
The maximum RPM of a resolver is limited by the conversion rate of the system resolver-to-digital converter. If the resolver is directly coupled to a shaft, this is then the maximum RPM of the shaft. The maximum RPM is calculated by dividing the conversion resolution in bits by the conversion rate. For example, a 10 bit converter has a resolution of 1024 bits per revolution. At a conversion rate of 10 µS, the maximum RPM is 6000. It is apparent that an increase in resolution must be accompanied by a proportional increase in conversion rate to result in the same maximum RPM.
The same limitation applies to an optical encoder. The incremental digital output frequency is limited by internal sensor electronics. As in the above example, an encoder with 1024 pulses per revolution and a maximum output frequency of 100 KHz (10 µS) also has a maximum RPM of 6000. Resolution and output frequency must increase proportionately to retain the same maximum RPM.
This is not to say that a stable control loop can be obtained at the maximum RPM. The excitation frequency of a brushless resolver is limited by electrical parameters of the windings such as winding resistance and the capacitance between the windings. The typical maximum excitation frequency is 10 KHz.
By contrast, encoder resolution and maximum output frequency are the only systemic considerations. Resolution of optical encoders is limited by the size of the rotating code wheel. Output frequency is limited by sensor electronics. High resolution encoder bandwidth is limited by output pulse frequency.
Resolvers are insensitive to reasonable amounts of contamination. Optical encoders are extremely sensitive to contamination. If the encoder code wheel becomes contaminated, the resulting output will have errors or cease to function all together. Typically encoders are housed to protect them from contamination in harsh environments.
Resolvers are heavy and have high inertia. The nature of their materials is primarily heavy metal cores and windings. Encoders are generally smaller electronic devices and the code wheel has comparatively low inertia.
Both resolvers and encoders constructed with internal shafts require only coupling to the motor shaft. Frameless resolvers and modular or kit encoders require alignments during installation.
Frameless resolvers require both radial and axial alignments of the rotor and stator. There must be a non-contacting gap between the rotor and stator. Misalignment of the concentricity between the stator and rotor effects detecting accuracy. Axially, the rotor and stator laminations should be in the same plane for best reliability.
Modular encoders also have alignments in both radial and axial directions. The code wheel pattern must be concentric with the axis of rotation for best accuracy. Also the optical path of the stationary member must be at the same radius as the pattern on the code wheel. The non-contacting gap is aligned in the axial direction. A close and consistent gap is necessary for both accuracy and reliability.
The mating shaft is of concern for both devices. Shaft concentricity, perpendicularity and axial runout are important for resolver function and reliability. Encoders are affected by thermal differential expansion between motor housing and shaft and motor shaft axial endplay and axial runout. Poor shaft tolerances can result in poor accuracy and in the worst case catastrophic failure.
Resolvers have an analog output with theoretically infinite resolution. Practical limitations are due to signal noise and analog-to-digital conversion electronics. A resolver-to-digital converter is required to digitize resolver signals for the controller. The position data is most often absolute.
Encoders can have analog or digital and incremental or absolute outputs. The electronics required to digitize encoder signals are simple and generally supplied as part of the encoder. Electrical noise immunity is another advantages feature of encoders.
The following is a checklist of parameters that should be known before specifying the feedback device of choice:
Speed (number of poles)
Transformer ratio (K)
Electrical error (detecting error)
BLDC commutation (6 state absolute)
Accuracy (arc minutes)
4 to 40
absolute or incremental
.25 to 6
analog or digital
The motion control application dictates the choice between resolver and encoder feedback. Because they are more accurate and easier to implement, the system designer should consider using encoder feedback first. However, if environmental or longevity requirements exceed the limits of optical encoders, then the obvious choice is resolver feedback. Cost has not been discussed because resolver and encoder feedback systems can now compete on price alone.
Copyright © 2013 Donald E. Barnett
Last Updated: 05-10-13