A typical linear encoder consists of a scanning unit and a scale. The scale is generally glass and is cemented to a support, usually an aluminum extrusion. The scanning unit contains a light source, photocells, and a second graduated piece of glass called the scanning reticle. This scanning reticle sits a short distance from the scale.

In operation, a parallel beam of light produced by the light source and lens passes through four windows on the scanning reticle, through the glass scale, and onto a set of photosensors. When the scanning unit moves, the scale modulates the light beam, creating sinusoidal outputs from the photosensor.

The four windows in the scanning reticle are each phase shifted 90° apart. The system combines the phase-shifted signals to produce two symmetrical sinusoidal outputs phase shifted by 90°. A fifth pattern on the scanning reticle has a random graduation that, when aligned with an identical pattern on the scale, creates a reference signal.

To obtain high resolution, a fine-scale pitch is used. Because of the diffraction effects of the scale grating, spacing between the fixed scale and scanning reticle must be extremely narrow and constant. Consequently, the entire scanning unit mounts on a carriage that runs on ball bearings along the glass scale. The scanning unit connects to the machine slide via a coupling that compensates for alignment errors between the scale and the machine guideways.

In linear encoders for NC applications, external electronics interpolate sinusoidal signals from the encoder head. The effect is to subdivide the basic line spacing on the scale to gauge smaller increments of motion. Standard encoders using this principle come in a variety of form factors. Some have small exterior dimensions while others fasten along the length of the scale with screws, permitting higher accuracy (up to ±2 ∝m/m). These encoders may incorporate a mechanical corrective device, which contains correction points at 100-mm (4-in.) intervals. This feature allows compensation for errors caused by imperfections in the guideways.

Encoders described above are limited to measuring lengths of about 3 m or so. Encoders that measure longer distances contain scales made from steel tape. A typical tape is about 0.3 mm thick and contains a grating of highly reflective gold lines with a pitch of about 100 ∝m.

In operation, a small carriage runs along the tape and holds a photoelectric scanning unit. The unit also contains error compensation devices every 300 mm (8 in.). Additional compensation is possible through appropriate tensioning of the steel tape. The steel tape can be made in lengths of 100 m and can be rolled into a coil. The scale housing is assembled in segments. After the housing is assembled, the tape scale and sealing lips are inserted in one piece.

To provide a resolution of 1 ∝m from a pitch of 100 ∝m, the signals must be interpolated by a factor of 25. The maximum traversing speed of the encoder is set by the maximum scanning frequency (in scanned signal cycles per second). This, in turn, depends on the interpolation factor. Also important is the minimum pulse edge distance that the controller can process. The maximum speed is 30 to 90 m/min, or about 100 to 300 fpm.

New systems have been developed to allow smaller measuring steps. These use circuits that provide 10, 25, or 50interpolation. When used with counters that count rising and falling edges of quadrature square waves, these systems can measure steps of 0.5 ∝m or 0.1 ∝m when used with a 20-∝m pitch.

One instrument in this category uses a 25interpolation in conjunction with a 10-∝m pitch to provide a 0.2-∝m (4-∝in.) measuring step. Such encoders are needed for machine tools with extremely high precision. Typical applications include diamond lathes for manufacturing concave mirrors or magnetic disks. Other uses are on accurate milling or grinding machines that produce precision prismatic parts such as polygons for scanners. The controls for such machines are usually equipped with electronic error correction, allowing electronic compensation for scale errors. Thus, mechanical error correction is generally not needed.

High-resolution encoders can be either sealed from contamination or exposed. Exposed linear encoders have been used for several years on precision jig borers, grinding machines, and stages. These encoders consist of a glass scale and a noncontacting scanning head. In this way, coupling error and other mechanical errors are eliminated and a resolution to 0.05 ∝m (about 2 ∝in.) is possible.

Naturally, exposed instruments must be protected from environmental contaminants. Designers must also align encoders optimally so accuracy is transmitted to the workpiece. A final concern is to provide easy accessibility for assembly.

Encoders based on magnetic sensing frequently use a scale consisting of a thin ferromagnetic bar or rod of magnetic material fastened at both ends. The bar is imprinted with magnetic domains. A read head senses magnetic fields as the bar moves to measure position.

Ferromagnetic bars are typically magnetized with a period of 0.2 mm (0.008 in.). Sensing electronics basically consist of two magnetic heads spaced so that signals are 90°apart. Each head contains a low-reluctance magnetic yoke wound with primary and secondary coils.

Primary coils are powered with alternating current. As the magnetic bar moves past the sensing unit, it changes the magnetic flux through each yoke. This modulates the electrical coupling between the coils because of the nonlinear magnetic qualities of the yoke material. Thus, the amplitude of the output signals changes as the scale bar moves.

A resulting signal is derived from the two output signals. Its phase changes with the relative movement of the bar and reading head. Interpolation circuits can detect this change to gauge position. However, these types of systems have seen only limited use because of the necessary high interpolation factor, high cost of the electronics, and because of speed and acceleration errors.

A different method is used in linear Inductosyn systems. These devices contain a scanning plate (slider) and a scale. The scale is a meander pattern that is supplied with a carrier frequency. The slider contains two coils spaced 90° apart. The coils inductively pick up the signal and produce an alternating voltage amplitude that is proportional to the sine and cosine of the slider position within a scale pitch.

Tracking electronics count signals received from the slider coils to gauge motion. These systems also incorporate interpolation so that a scale pattern with a 2-mm pitch produces a 1-∝m linear resolution. However, Inductosyns are not as widely used as other systems. The mounting and adjusting of the scales can be tedious; and the system must be protected from contaminants.

Magnetic encoders are a viable alternative to optical types because they are inherently rugged and operate reliably under shock and vibration, at high temperature, and in contaminated and humid areas. Hall-effect and magnetoresistive devices are two sensors commonly used for these conditions, and motor speed and position accuracy dictate which of the two is better suited for an application.

The magnetic encoder wheel in these devices is usually made from an injection-molded ferrite with an array of poles embedded near the surface. A 15-mm encoder contains a 7.6-mm-diameter wheel, magnetized with 32 poles (16 north and 16 south) using a static fixture. Fixture size typically limits the number of poles that can be embedded. The pole pitch for a 32-pole motor is about 0.75 mm, the smallest practical size a fixture can handle.

Hall-effect encoders usually switch with an output characterized by hysteresis. They switch when the magnetic field from the rotating encoder wheel reaches a flux density sufficient to overcome a critical threshold level.

Likewise, when the detected field reaches a flux density below a lower threshold level, it switches back to the previous state. Consequently, Hall sensors containing 32-pole encoder wheels generate 16 pulses per revolution. Today, however, higher resolution is needed from miniature encoders.

The need for higher resolution is being met by encoders using magnetoresistive material that lowers its bulk resistance by about 1.6% in the presence of a saturating magnetic field. Magnetoresistive sensors differ from Hall-effect sensors in two important ways. First, the saturating field is in the range of 0.003 to 0.005 T, an order of magnitude smaller than typical switching fields for digital Hall sensors. This makes magnetoresistors more sensitive measuring devices.

Second, the change in resistance is independent of magnetic field polarity, so the 32-pole wheel generates 32 pulses per revolution, twice the resolution of previous sensors.

A magnetoresistive sensor assembly comprises an array of thin nickel-iron permalloy strips. Strip width is much larger than thickness. The sensor is located above the magnetic track of the encoder wheel with the strips parallel to the wheel axis.

One channel of a magnetoresistive sensor consists of two strips displaced one-half pole pitch from each other. They are connected differentially to double the sensor's output voltage. As the encoder wheel rotates past one pole (two sensor strips), the output voltage completes one cycle, generating a 40-mV peak-to-peak signal from a 5-Vdc power supply.

Resolvers and synchros: Resolvers and synchros perform well where small size, long-term reliability, absolute position measurement, and high accuracy are required. Typical synchros and resolvers resemble small cylindrical ac motors. Diameters vary from 0.5 to 3.7 in. One end of the body contains an insulated terminal block; the other a mounting flange. Rotor shafts are normally threaded and splined.

The simplest devices employ single-winding rotors that revolve inside fixed stators. Synchros contain a stator with three windings located 120° apart and electrically connected in a Y-configuration. Resolvers differ from synchros in that their stators contain only two windings mounted 90° apart.

Synchros and resolvers resemble rotating transformers during operation. The rotor winding is typically excited by an ac reference voltage at frequencies ranging up to a few kilohertz. The magnitude of the voltage induced in any stator winding is proportional to the cosine of the angle between the rotor-coil axis and the stator-coil axis.

In synchros, the voltage induced across a pair of stator terminals is the vector sum of the voltages across the two connected coils. For example, if a reference voltage Vsin(wt) excites the rotor of a synchro, then the stator voltage will be

V(S1 to S3) = Vsin(wt)sin(θ)
V(S3 to S2) = Vsin(wt)sin(θ + 120°)
V(S2 to S1) = Vsin(wt)sin(θ + 240°)
where θ is the shaft angle.

Resolvers, on the other hand, will have stator terminal voltages of

V(S1 to S3) = Vsin(wt)sin(θ)
V(S4 to S2) = Vsin(wt)cos(θ)

Resolver-to-digital converters transform these voltages into digital representations of the actual angle θ>.

When combined with such converters, synchros and resolvers can provide 12-bit resolutions of 5.3 arc-minutes. Absolute accuracies approach more than 20 arc-seconds for higher resolution models. Attaching a resolver to a 0.1-in. pitch lead screw and using a 12-bit converter provides 25-∝in. linear resolution.

Synchros and resolvers can also perform linear position measurements by employing lead screws. Alternatively, Inductosyns measure linear position directly, and because Inductosyns offer high accuracy and ruggedness, they are often used in severe industrial environments.

Inductosyns operate somewhat like resolvers. When the scale is energized with ac, the voltage couples into the two slider windings and induces voltages proportional to the sine and cosine of the slider spacing within a cyclic pitch. If S is the distance between pitches, X is the slider displacement within a pitch, and the voltage Vsin (wt) energizes the scale, then the slider windings will see terminal voltages of

V(S1 to S3) = Vsin(wt)sin(2πX / X)
V(S4 to S2) = Vsin(wt)cos(2πX / X)

Since slider output signals arise from an average of several spatial cycles, small residual errors in conductor spacing have little effect. When combined with 12-bit digital interface modules, 0.1-in. pitch linear Inductosyns readily provide 25-∝in. resolutions.

Rotary Inductosyns are made by forming the scale and slider in a loop. These devices have high resolutions. A typical rotary Inductosyn may have 360 cyclic pitches/rotation and might use a 12-bit Inductosyn-to-digital converter. The converter effectively divides each pitch into 212 or 4,096 sectors. With 360 pitches, rotary Inductosyns resolve a total of 1,474,560 sectors for each rotation. This corresponds to an angular resolution of less than 0.9 arc-second.

LVDTs: An LVDT provides position feedback using mutual inductance between primary and secondary windings. A moveable core couples the excitation voltage in the primary to the two secondaries. Phase and amplitude of the secondary output voltage vary with the position of the magnetic core. The amplitude of the secondary voltage is proportional to the magnitude of position. The phase indicates the position of the core relative to the null.

With the core centered between the two secondaries, at the null position, secondary voltages have equal amplitudes and are 180° out of phase. The net voltage across the secondaries is zero. As the core moves toward positive full scale, the amplitude of the in-phase sine wave increases. As the core moves toward negative full scale, the amplitude of the 180° out-of-phase sine wave increases.

LVDTs used in applications such as aviation have either dual or quadruple redundancy. Some units have a mean time between failure of almost 3 million hours; over 300 years. LVDT manufacturers often use Inconel or stainless-steel housings, electron-beam welding, and spherical bearings to reduce rod misalignment. And because coils are wound by computer control, unit interchangeability is high.

The primary limitation is the full-scale displacement. This is the maximum distance the core travels without a serious decrease in linearity. The linear operating range is twice the full-scale displacement since the core can travel in either direction from the null position. The actual linear range will always equal or exceed the nominal value.

Linearity is the deviation from an ideal straight-line response. The output voltage of an LVDT is a function of the core displacement and is a straight line within a specified range. Beyond the nominal range, the output deviates from a straight line in a gentle curve. Linearity is a percentage of reading. It is inherent in the transducer and largely determines absolute accuracy.

LVDT nonlinearities are typically 0.25%. Precision units have maximum nonlinearities of 0.05%. An LVDT with a 0.25% nonlinearity and output of 0.39 mV/V/mil, with a 1.0 Vrms excitation and 390 mVrms full-scale output, will exhibit a maximum nonlinearity of 2.5 mil.

Linearity can be improved by using an LVDT at less than the nominal range. Conversely, an LVDT can be used beyond the nominal range where linearity is not important. The range sets the full-scale output of the LVDT. This is matched to the full-scale output range of the LVDT-to-digital converter.

LVDTs require signal-conditioning circuitry that includes a stable sine-wave oscillator to excite the primary winding, precision demodulators to convert secondary ac voltage signals to dc, and amplifiers to buffer the dc output signal. Such complex electronics, when synthesized with discrete components, requires manual trimming and calibration to obtain accuracy commensurate with that of the LVDT. Furthermore, circuits must often be recalibrated if the transducer is replaced.

LVDT signal-conditioning chips, however, solve these problems. These ICs measure displacement to within 0.63% of the LVDT's full travel. Except for a few resistors and capacitors, the devices need no additional circuitry to produce dc voltages proportional to core displacement.