Posted on 09 December 2013

Angular Position Sensors (Shaft Angle Transducer)


Almost every machine or industrial process contains one or more rotating shafts. It is therefore important in most instrumentation systems or control systems to be able to measure the exact shaft angle of a mechanical shaft. This angular data can be used to control position, speed or acceleration of a mechanism.

Standard shaft angle transducers include:

  • potmeters
  • encoders (optical or magnetic)
  • resolver

Since control systems operate digitally it is necessary to have the data in digital form. Potentiometers need to be followed by an A/D converter while resolvers require an RDC (resolver to digital converter).

The sensors discussed here may be implemented with a linear or angular displacement. Linear displacements are usually obtained via a motor and worm wheel (figure 1) so that a shaft angle transducer which is coupled to the motor can give an indication of linear displacement.

Use of shaft angle transducers to control linear movement

Figure 1. Use of shaft angle transducers to control linear movement

Per revolution of B, sensor A produces 100 revolutions. Sensor B is the coarse and sensor A the fine shaft angle transducer. Sensor A could be a resolver and sensor B a low resolution sensor such as an absolute encoder or potentiometer. In the case of a revolver the associated A/D converter is an RDC.

In certain applications in order to accurately measure a linear displacement it may be safer to monitor the linear displacement rather than the angular position of a motor.


The wiper of the potmeter is connected with the mechanical shaft of which we want to know the position. A stabilised voltage is connected across the potmeter. The voltage between wiper and one end of the potmeter is an electrical indication of the angular position. To be useful in a digital control system the output voltage has to be digitised. Due to the presence of the connection terminals the pot meter has only a useful rotation angle of between 300 and 340°. Typical resistor values lie between 5 and 50 kΩ. By turning the wiper the output impedance is changed (of our signal source) between zero and maximum. This can affect the accuracy of the conversion. The most accurate potmeters are wire wound and the maximum resolution is normally 12 bit. By moving the wiper over the wire wound potmeter body noise is produced which cannot be completely filtered out. Wear and tear reduces the total number of movements of the wiper.

The most important advantages of potmeter sensors are:

  • suitable for use with high temperatures (up-to several hundred degrees Celsius)
  • can handle vibrations and shocks

Optical encoders

We distinguish between:

  • incremental optical encoder
  • absolute optical encoder

The incremental encoder gives a specific number of impulses per revolution (e.g. 500 impulses ) while the absolute encoder only gives a unique code which corresponds to a specific angular position. Figure 2 shows the principle configuration of an optical encoder.

Principal configuration of an optical encoder

Figure 2. Principal configuration of an optical encoder

The encoder is comprised of:

  • a light source (e.g. LED)
  • code disc, with fields that are darkened and allow light through.
  • light detector, mostly comprised of photo-transistors.

Incremental encoders

 Incremental encoders have three output signals as standard:

a signal A consisting of n pulses per revolution (this signal can be a block or sine-wave)

a signal B, identical to A but 90° displaced

a signal Z (= zero marker output)

From the combination A,B and Z we can:

  1. determine the shaft position. For this the Z pulse, the initialisation pulse, is used and there after the pulses A or B are counted.
  2. determine the direction of rotation (comparing A with B!)

Code disc of incremental encoder together with the resulting waveforms

Figure 3. Code disc of incremental encoder together with the resulting waveforms

The rotating code disc of an incremental encoder consists of a disc that allows light through and which has a number of darkened strips to prevent light shining through. Figure 3 shows what this involves. Notice also how A and B channels and the Z pulse is formed with the transparent parts. The code disc can be made of glass, metal or plastic.

If the resolution has to be increased (more pulses per revolution) then the diameter of the disc (and thus the encoder) must by necessity be larger.

A standard “trick” to increase the number of pulses per revolution involves differentiating the block wave. Take an encoder with 500 pulses per rev. Differentiation of the positive flank of the block wave in figure 3 results in 1000 pulses per rev, and differentiation of the positive and negative flanks results in 2000 pulses per rev.

The encoder is usually specified as : n pulses per rev with the options x2 and x4.

The photo below from the firm Heidenhain shows once again the transparent principle of an optical encoder.

Principle configuration optical encoder

Photo Heidenhain: Principle configuration optical encoder

The light beam emitted by L (e.g. a LED) is concentrated by a lens K and thereafter split by a detection plate into five fields. If a glass ruler M with an incremental scale C (e.g. 20μm) comprised of chrome strips (C/2 wide) moves with respect to the detection plate A the light which shines through is sinusoidally modulated (due to the special construction of the detection plate). Four of the five fields produce via photo-transistors sinusoidal signals displaced by 90° with respect to each other. Since the four sinusoids are not symmetrical with respect to the zero line two resulting symmetrical sinusoids S1 and S2 are produced via a push pull circuit which are 90° out of phase with each other. This is the SIN/COS output. A typical amplitude is 1 V peak to peak. The sinusoids can also be converted internally to block waves (as in figure 3) which then appear on the output at TTL or HTL level. The fifth field serves as a reference R (one per revolution of the shaft). Encoders may be single turn and multi turn types. Single turn systems provide the actual position within one revolution. Multi-turn pulse sensors operate with multiple revolutions.

Absolute encoder

If the stripe code disc of figure 3 is replaced by a code disc as shown in figure 4 then we have an absolute encoder. The sixteen positions of the disc correspond with a specific code. Usual are Gray, BDC and natural digital codes to form the 4 bit word that indicates the disc position.

Code disc of an absolute encoder

Figure 4. Code disc of an absolute encoder

The advantage of the absolute encoder is amongst others its “memory”. In this way a short or long duration power outage will not interfere with the output signal. Indeed for every position of the encoder disc there is only one unique binary word. With an incremental encoder you have to wait every time for the Z pulse for initialisation.

If we look at figure 4 it is clear that an absolute encoder does not have 500 different “positions” as did the strip code of the incremental encoder. Therefore, the absolute encoder can serve as a course sensor while the incremental encoder can serve as the fine sensor.

Magnetic encoder

We discuss the case of absolute encoder GEL235 from Lenord&Bauer. The most important parts are:

  • ferromagnetic code disc
  • magneto-resistive elements
  • electronic circuit, including an ASIC
  • gearbox for the multiturn operation


On a ferro-metal disc via a lithographic process a trace of “increments”or steps is etched, for example 64 for the entire circumference. As seen earlier per step we produce one period of an electrical signal. We now produce 64 periods if the disc completes one revolution.

The etch process is similar to that which produces the optical glass code disc, but now we use a complete ferro-magnetic disc.

With the GEL235 three concentric tracks are etched on the disc, with respectively 64, 63 and 56 periods.

Between three permanent magnets and the code disc three magneto-resistive sensors are placed, one between every magnet and trace of the code disc. The electrical resistance of the sensors changes with the changing magnetic flux as a result of the passing increments on the code disc. This flux change is sinusoidal which results in a sinusoidal resistance change. Electronic circuits see to it that three sinusoidal voltages are derived from this.

Magnetic encoder

Photo Lenord & Bauer (Multiprox): Magnetic encoder GEL235

One revolution of the code disc produces respectively 64, 63 and 56 sinusoidal voltages. With a trace of 64 increments we obviously have only 64 pulses/rev, but by applying the nonius-principle to our three traces we obtain an accurate angular position for the position of the code disc. With the GEL235 the resolution is 16 bit. In addition it is clear that the phase delay between the three signals allows (after processing in an ASIC) the angular position of the code disc to be uniquely determined, it is in fact an absolute encoder.

Multiturn operation

The GEL235 is available as single turn or multiturn model. With the multiturn model the code disc determines the single turn position and with a mechanical gearbox we determine the number of revolutions of the shaft. A gearbox with three reductions of 1:16 gives us 16×16×16 = 4096, which corresponds with the resulting 12 bit for the multiturn operation. The total maximum resolution is 16 + 12 = 28 bit.


The principle of the ferro-magnetic code disc is per definition immune to dirt, oil, shocks, vibrations, temperature differences and moisture level. The encoder produces SIN/COS signals as standard. The GEL235 is available in SSI or BISS versions with Gray code or binary code.



A resolver is in fact a transformer in which the coupling between the coils can be changed by turning a coil. The rotor consists of a coil, wound on a laminated iron core. The stator winding consists of two coils displaced by 90° with respect to each other. The rotor is supplied with a sinusoidal voltage v_i = \hat{v_i}\cdot sin(\omega t).

If the rotor coil is at an angle \theta with the stator coil S1, then the stator voltages are respectively proportional with the SIN and COS of the rotor angle \theta. This is indicated in figure 5. Originally (in the 50’s of the twentieth century) the resolver was used to solve trigonometric relationships, hence the name “resolver”.


Figure 5. Resolver

Applications of resolvers

A modern application is for example a robot for which the angular positions (of the various degrees of freedom) are determined with resolvers. Other applications: the angular position of a radar antenna or remotely controlling the course of a ship (gyro-compass), CNC machines, etc.

Synchro converters

Synchros are small machines which were developed during the second world war. The resolver is a derivative type which is practically as old as the synchro. These devices were used in analogue servo systems. Due to their excellent properties resolvers continue to be widely used.

Control systems have become completely digital so that a converter is required between resolver and micro-controller. These converters are available hybrid micro-electronic modules. It is referred to as an RDC (resolver-to-digital converter).

Brushless resolvers

In most cases “brushless” resolvers are used. At one end of the rotor the secondary of a transformer is wound which delivers the reference voltage for the rotor.

The primary of this supply transformer is wound on the stator. In this way no brushes are required to supply the rotor.

The output coils of the resolver are on the stator and with an angle \alpha of the rotor we obtain the voltages v_i \cdot sin(\alpha) and v_i \cdot cos(\alpha) across the stator coils S1 and S2.

Resolver configuration followed by a converter

Figure 6. Resolver configuration followed by a converter

Observing the ratio \frac{v_i \cdot sin(\alpha)}{v_i \cdot cos(\alpha)} = tan(\alpha), we notice supply voltage variation has no influence on the measured angular position \alpha. The distance between resolver and converter (RDC- or RD-converter) may be tens of meters.

Linear measuring systems

In addition to rotating encoders linear encoders also exist. We distinguish between closed and open linear measuring systems. The closed systems are resistant to the penetration of dust, moisture and shavings and are predominately used for machine tools.

There are also closed linear encoders which can measure linear distance from cm to for example 30m. Accuracy classes of for example ± 3μm/m to ± 5μm/m are possible. This means that within 1 m of the ruler the error is maximum 3 to 5μm. Typical measurement increments are 0.1μm / 0.5μm / 1μm / 10μm.

Both optical and magnetic measurement systems are in operation. Also here we see the distinction between absolute and incremental encoders.

The top photo below shows an optical linear encoder from the firm Heidenhain. The ruler has a Diadur-scale. Measurement spans may be from 140 to 4240 mm. Accuracy is  ± 3μm to ± 5μm. Sinusoidal signal is 1V p-p. Frequency limit is 150 kHz.

Linear encoder TC183

Photo Heidenhain: Linear encoder TC183

DIADUR and AURODUR scales on different carriers

Photo Heidenhain: DIADUR and AURODUR scales on different carriers

The most important parts of the measuring systems from Heidenhain are the scale carriers, mostly in the form of a strip scale. These precision divisions are implemented according to their DIADUR- or AURODUR-process. The photo above shows carriers for both linear and rotating encoders. DIADUR-graduations are created by a very thin chrome layer on a carrier of glass or glass-ceramic. The accuracy of the graduation structure is in the micrometer region (10 to 40μm per graduation).

Angular position transmitters with large diameters, as is the case with linear measurement systems longer than 3040 mm, use AURODUR. Here use is made of the mirror principle. The graduations consists of well reflecting gold strips and etched matt openings. AURODUR-graduations are predominantly placed on steel carriers.

An example of a magnetic system from MTS is shown in the photo below.

MTS-sensor for linear positioning

Photo MTS (Multiprox): MTS-sensor for linear positioning

Some ferromagnetic materials change their length under the influence of a magnetic field and conversely there magnetic state can change under the influence of mechanical force. This is called the magnetostrictive property of the material. Central in the MTS-sensor is such a magnetostrictive waveguide.

A movable position magnet which is connected to the position to be determined produces a magnetic field in the longitudinal direction of the waveguide. A current impulse through the waveguide creates a radial magnetic field around the waveguide. At the instant that both magnetic fields coincide, a torsion impulse is produced in the waveguide. This impulse flows as a sound wave with the constant speed of the sound from the measurement point to the end of the waveguide and is converted in the sensor head to a distance proportional output signal.

Comparison of the various angular position sensors

Operating environment

Dirt, oil, salt atmosphere, high temperature, shocks and vibrations have only a small effect on resolvers and magnetic encoders. Optical encoders are sensitive to vibration and shocks. Potmeters can display “bounce “ as the wiper vibrates as a result of shocks or movement. Resolvers can operate in ambient temperatures up to 200°C and higher. The weak point of an optical encoder can be that a part of the accompanying electronics is placed close to the sensor so that temperature influence can be important. By contrast a resolver can have its electronics tens of meters away. High temperatures will also result in oxidation and wear of moving parts of a potmeter.

Accuracy and resolution

The resolution of an angular position sensor is the weight of the smallest movement in the digital scale or expressed another way, the least significant bit (LSB): LSB = \frac{\text{full angular range}}{2^N}. Resolvers have an infinite resolution and it is mainly the converter (RDC) that determines the resolution of the measurement. An RDC typically delivers 10, 12, 14 or 16 bit output depending on the type of converter. A 14-bit RDC has a positional resolution of \frac{360^{\circ}}{2^{14}} = 1.32 arc minutes. The resolution of an optical encoder is determined by the amount of transparent windows. The measurements of optical encoders are smaller when a laser light source is used.

Accuracy is the maximum error of the digital code with respect to the original value. Optical encoders have the best accuracy. Resolvers have an accuracy of about 10 arc minutes. Here of course we need to include the accuracy of the RDC in the calculation with its accuracy of a few arc minutes.


In the case of a resolver we usually obtain one output period per revolution resulting in an absolute position measurement. With an encoder, the maximum speed is mainly limited by the frequency response of the encoder input of the positioning system.

An encoder has 2000 pulses/rev and the maximum encoder input of the drive train is 150 kHz. The motor can then have a maximum speed of 4500 rev/min in order not to miss a pulse.
Indeed: \frac{2000\times 4500}{60} = 150kHz.


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This post was written by:

- who has written 7 posts on PowerGuru – Power Electronics Information Portal.

Professor Dr. Jean Pollefliet is the author of several best-selling textbooks in Flanders and the Netherlands

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