LINEAR VARIABLE DIFFERENTIALTRANSFORMERS

WHITE PAPER BYKAVLICO CORPORATION

KAVLICO PROPRIETARY

June 1997Revised: May 2000

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DESCRIPTION ........................................................................................................................... 2Excitation ................................................................................................................................... 2Output ....................................................................................................................................... 3Resolution .................................................................................................................................. 3Repeatability ............................................................................................................................... 3Construction ............................................................................................................................... 3Temperature Range ....................................................................................................................... 3Mechanical Design ....................................................................................................................... 4Length ....................................................................................................................................... 4Typical Armature Length ............................................................................................................... 4

Diameter ................................................................................................................................. 4Measurement Range ..................................................................................................................... 5Configurations ............................................................................................................................ 5LVDT CHARACTERISTICS ........................................................................................................ 6FAULT DETECTION ................................................................................................................ 11DIFFERENCE OVER SUM OUTPUT .......................................................................................... 12

NOMINAL VALUES .............................................................................................................. 13LVDT ENVELOPE REQUIREMENTS ......................................................................................... 14COST CONSIDERATIONS ........................................................................................................ 14

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DESCRIPTION

The Linear Variable Differential Transformer (LVDT) is a Displacement Transducer thatproduces an electrical signal proportional to the displacement of a moveable core (armature)within a cylindrical transformer.

The transformer consists of a primary and two secondary windings, coaxial wound, with eachsecondary located on opposite ends. The nickel-iron armature is positioned within the coilassembly providing a path for magnetic flux linking the primary coil to the secondary coils.When the primary coil is energized with an alternating current, a cylindrical flux field isproduced over the length of the armature. This flux field produces a voltage in each of the twosecondary coils as a function of the armature position.

For the longer strokes, the primary winding is designed to maintain a flux field that is aconstant magnitude for any position within the linear range. A change in the position of thearmature will then move the flux field into one secondary and out of the other. This results inan increase in the voltage induced in one secondary and a corresponding decrease in the other.

The secondary coils are normally connected in series with opposing phase. The net output ofthe LVDT is the difference between the two secondary voltages. When the armature issymmetrically positioned relative to the two secondary coils the differential output isapproximately zero, since the voltage in each secondary is equal but opposite in their phaserelationship (see Null Voltage).

There are several coil configurations that are used for LVDT’s. The very short strokes requirea high sensitivity to produce a reasonable output. They are normally wound with the primarycoil located between the secondary coils with the armature extending into each secondary(commonly known as three coils design). This configuration has the highest sensitivity, thelowest phase shift, and a low temperature coefficient of the sensitivity. It should be pointedout that the individual secondary voltages of this configuration contain an X2 term, where Xis the displacement, and they are inherently non-linear. The differential output is very linear(the squared terms subtract out) but the sum is not linear. For three coil designs, if the strokeis larger than ±0.025 inches a difference over sum output is not recommended. The coilconfiguration used on older four-wire LVDT designs with strokes longer than 0.25 incheshave a primary winding which is wound across the entire length with each secondary startingin the center and ramping up to the end. This produced a linear differential output but if thecenter tap was brought out, it was usually obvious that the sum was not linear. The computercontrolled winding machines allowed ramping the secondary coils from one end to the otherwith a linear output that provides a constant sum.

Excitation

An LVDT requires an AC voltage for operation. Aircraft power or low impedance AC sourcespecifically designed for the LVDT normally supplies this excitation. In today’s aerospaceand aircraft industry, multi-channels with individual excitation sources are often used toobtain the highest possible system reliability.

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Output

The output voltage of an LVDT is proportional to the voltage applied to the primary. Toavoid problems of excitation tolerances the output should always be stated in volts/volt.System accuracy will depend on providing a constant input voltage to the primary orcompensating for variations of the input by using ratio techniques. The output can be takenas the differential voltage, or with a center tap, as two separate secondary voltages whosedifference is a function of the displacement. If the Sum of the secondary voltages is designedto be a specific ratio of the difference voltage, overall accuracy can be significantly improvedusing the (V1-V2)/(V1+V2) ratio as the output. (See Difference Over Sum Output). Figure 1shows the AC input; and Figure 2 the two secondary output voltage waveforms as seen on anoscilloscope. The Va secondary phase is shown referenced to the center of the coil and Vbshown referenced to the end of the two secondary coils with the phase shift of Va at 2.5o andVb at 2.7o.

Resolution

Resolution of an LVDT is the smallest change in armature position that can be detected as achange in the output. Sub-micro-inch resolution is not uncommon with LVDT’s. In practice,the resolution is usually less than the noise threshold of external circuitry or resolution of theequipment used to measure the output.

Repeatability

Repeatability of an LVDT is defined as the ability to reproduce the same output for repeatedexact positioning of the armature under the same operating conditions. The armaturedisplacement mechanism and test equipment normally limits the ability to measure therepeatability of an LVDT.

Construction

Nearly all LVDT’s designed for aircraft or missile applications are wound on an insulatedstainless steel spool, magnetically shielded, and enclosed in a stainless steel housing usingwelded construction. The armature is normally made from a 50% Nickel Iron alloy and brazedto a stainless steel extension. Secondary leads are usually shielded to minimize channel tochannel crosstalk for multi channel units (See Crosstalk) and to keep RF energy from gettinginto the signal conditioner. An LVDT does not contain electronic components and it isunaffected by RF energy, making the LVDT nearly immune to EMI, EMP and lighting.

Temperature Range

The operating temperature range determines processes and materials used for construction.LVDTs have been designed for operation from cryogenic temperatures of -440°F and tooperation submerged in liquefied metal (+1100°F). Construction and assembly for theseextreme conditions require very special materials and processes that assure complimentarycoefficients of expansion while maintaining good electrical and magnetic properties. Kavlico’sstandard construction provides operational temperature ranges from -65°F to +350°F. High

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temperature solder and special potting materials can extend this range from less than -80°F toover 450°F.

Mechanical Design

The length and diameter of an LVDT must be sufficient to mechanically allow adequatewinding space to achieve the electrical performance:

To meet pressure requirements

To withstand the shock, vibration and static acceleration environments.

Where physical size is limited, electrical performance must be flexible. Although the LVDT isbasically a simple device, the operating characteristics and electrical parameters are complexand depend to a large extent on the physical limitations.

Length

The minimum length of a coil housing for most aerospace applications can be estimated asfollows:

It will require approximately 0.5 to l.5 inches for the sum of the front and rear weld washersplus possible lead connections. Small housing diameters (less than 0.5 inches), large lead wires(larger than 26 AWG) or high pressures may require the longer length for lead connectionand/or support of a high pressure. Add the total electrical stroke and the length of thearmature and you have the housing length.

The length of the armature ranges from 0.6 inches, to up to twice the length of the electricalstroke, depending on the frequency of the excitation and the actual stroke. Table 1 gives atypical armature length for good performance at an excitation between 1800 to 3500 Hertz.Additional housing length may be needed for mounting flanges, connectors, fluid passages,cable routing or seal grooves which limit the coil length.

Typical Armature Length

Electrical Armature Stroke Length (Inches) (Inches)

0.10 (+0.05) 0.67 0.50 (+0.25) 1.00 1.00 (+0.50) 1.50 2.00 (+1.00) 2.20 3.00 (+1.50) 2.60 4.00 (+2.00) 3.00 5.00 (+2.50) 3.20 7.00 (+3.50) 3.50 10.00 (+5.00) 3.75 14.00 (+7.00) 4.00

Table 1

Diameter

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The minimum diameter of the transformer housing will depend on electrical performancecriteria for the excitation frequency being used and housing wall thickness required to supporta pressure requirement.

Armature diameters less than 0.110 inches are easily damaged and are not recommended. Thearmature extension should be slightly larger than the armature in diameter to protect thearmature from rubbing the bore. Ideally, the armature should have a short guide on the freeend that is the same diameter as the extension.

To determine the inside diameter of the spool tube, add the extension diameter and theclearance to the tube. This diametrical clearance should be 0.010 inches minimum to 0.025inches maximum. The wall of the spool tube should be at least 0.006 inches thick but must bethick enough to contain any pressure requirement. It should be kept in mind that the tubematerial and wall thickness does affect the performance.

The finished coil assembly diameter is determined by adding insulation to the spool tube,winding the primary coil, insulating the coil, winding the secondary coils, insulating thesecondary, routing the magnet wire for lead connections, insulating the entire coil andinstalling the shields. Typical coil assembly diameters for operating frequencies between 1800and 3500 Hertz are 0.420 inches. A typical assembly for 400 Hertz would be 0.625 diameter.

This coil assembly must be installed in the housing that could have a wall thickness from0.015 to 0.070 inches depending on the physical length, pressure and environment.

Measurement Range

The Full Scale or span is the displacement range of the LVDT’s armature for which theelectrical performance is required and is referred to as the Electrical Stroke. Since an LVDTis inherently a center null device (zero output occurs at mid-stroke), the range or stroke isnormally specified as a plus and minus displacement from the null position. This does notyield a 200% stroke or a 200% output. The Full Scale (100% of the stroke) being the totalend to end stroke and the Full Scale Output (100% of the output) the total end to end outputvoltage. It is a common error to use the output at the end of the stroke as the Full ScaleOutput.

Special winding placement of each secondary or the addition of a bias winding can repositionthe null to an off-center position. A bias winding is wound to produce a constant voltage overthe stroke and is added in series with the secondary coils to produce the required offset. Thefull scale (span) is still the end to end stroke and full scale output is still the end to endoutput. The null output of an LVDT has no sensitivity error and is the point in the strokewith the highest overall accuracy. Sensitivity errors due to frequency variations, load effectsand temperature, have little effect on the null position.

Configurations

The Four Wire LVDT or Two Wire Output. A differential output only requires twosecondary wires and can be used directly in AC servo systems or synchronouslydemodulated to a ±DC voltage.

The Five Wire LVDT or Three Wire Output. More elaborate signal conditioners use athree wire secondary connection and use the two secondary voltages relative to a common

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connection. This arrangement facilitates fault detection and/or a difference over sum ratio.(See Fault Detection or Difference over Sum Output)

The Six Wire LVDT. Performs the same as the five-wire unit but allows a differentialinterface to each secondary to avoid shielding by using the common mode rejection.

Multiple LVDT’s. Where system reliability requires more than one output signal forredundancy, up to four independent LVDT’s can be packaged in a single transducerassembly. Coil placement may be in series (Tandem), or grouped side by side as a (Parallel)cluster, see Figure 4. Multiple LVDT’s in one housing require less space, weight, andinstallation time and are lower cost than purchasing quantities of single LVDT’s. Multiplechannels do present several new problems that must be considered. (See Tracking, NullDifference and Crosstalk)

LVDT CHARACTERISTICS

Due to the principle of operation and the application of an LVDT, the parameters canbecome very complex. The following requirements should be defined in a specification topermit an optimum design for coil size and housing dimensions.

Electrical Stroke is the displacement range over which the specified performance and allelectrical parameters will be valid.

Mechanical Stroke is the guaranteed minimum physical stroke. Many LVDT’s will havephysical limitations for the actual Mechanical Stroke. When the displacement exceeds theelectrical stroke, the performance will be degraded. If specific output requirements for anover-stroke are needed, these requirements should be specified to insure proper design sincethese requirements could affect the physical length of the LVDT.

Excitation Voltage is the electrical potential intended to excite the transformer. Thisvoltage requires definition of amplitude, function, and frequency. An LVDT can be designedfor operation at less than 1 volt RMS to over l00 volts RMS. Normal excitation voltages formissile or aircraft applications range from 3 to 26 volts RMS. Kavlico does not recommendmixing RMS, Peak, or Peak to Peak specification requirements.

Excitation Frequency The best overall size and performance is obtained using excitationfrequencies in the range of 1800 to 3500 hertz. An LVDT can be designed for operation atany frequency between 50 and l0, 000 hertz, but physical size or performance may becompromised at the extremes.

The primary impedance of an LVDT is quite complex and must be designed for a specificfrequency when low phase shift and high accuracy are desired. The range of frequencies overwhich an LVDT will operate with low phase shift and good accuracy is highly dependent onits physical size, coil geometry, displacement range and sensitivity. To achieve the bestoverall performance, it is recommended that the range of the excitation frequency be kept aslow as possible. When multiple channels are used with different frequencies, a specificfrequency with a reasonable tolerance should be assigned to each channel.

Excitation Waveform It is recommended that only sine excitation is used for LVDT’s.Both triangular and square waves contain several odd harmonics of significant magnitude.

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Phase shift of harmonics through an LVDT will be a similar multiple of the phase shift for thefundamental frequency.

The geometry necessary for an LVDT design can produce significant primary to secondarycapacitance and the high harmonics of a square wave will produce large leading and trailingspikes on the output signal. The secondary circuit of an LVDT is slightly inductive and whenusing square wave excitation, shunt capacitance across the secondary, both inter-winding aswell as load capacitance, will lower the self resonance of the secondary circuit, which willcause severe ringing of the output signal. The primary current with square wave excitation is atriangular waveform and the IR drop across the primary resistance will cause the secondaryvoltage to have a dropping slope.

Both triangular and square waves have been used successfully for LVDT excitation butaccurate calibration is difficult and severe limitations on impedance, sensitivity and load arerequired for good performance. These waveforms often cause calibration correlationproblems using commercial test equipment and may require using the actual circuit todetermine the proper sensitivity. It is recommended that after the proper sensitivity isestablished, sine excitation be used for calibration using the standard commercial testequipment.

Input Power describes the real power in watts, or apparent power in volt-amperes, requiredfor the excitation of the LVDT. Since the input impedance of an LVDT is not purelyresistive, input power is generally given in Volt-Amps. This limits the input current ratherthan actual power dissipated. It is recommended that the maximum volt-amperes be specified.Practical limits for lower frequencies (26 VRMS, 400 Hz.) could be as high as l.5 VA down to0.1 VA when using 7.0 VRMS at 3500 Hz.

Power Factor describes the ratio of the real power in watts, to the apparent power in voltamps. This ratio is normally computed from the complex impedance. The Rs/Z (See InputImpedance) will yield the power factor. Typical power factors for an LVDT are in the rangeof 0.4 to 0.9.

Input Impedance will define the load the primary coil of the LVDT will present to theexcitation source. The input impedance of an LVDT is complex and is best described withboth the resistive and reactive components (Rs +jXL). It should be noted that the Rs term isnot just the DC resistance but includes the equivalent series real part of a complex impedance.Eddy current losses and shunt capacitance across the inductance will add an AC resistance tothe DC resistance to produce the Rs term of the complex impedance. The vector sum of Rsand XL, (impedance Z), is normally specified as a minimum value for design purposes. Themaximum volt-amperes will limit the minimum input impedance - both requirements need notbe specified. Quality assurance requirements normally require a specific value with atolerance for the impedance. It is recommended that if the specific impedance value isrequired, it should be taken from the actual measurement when the design iscompleted. A +20% tolerance is practical for primary impedance.

Output Impedance describes the maximum source impedance of the secondary voltage.The source impedance of the LVDT secondary will depend on input power limitations,sensitivity requirements and the constraints on the wire size due to physical space available.

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It is extremely difficult to predict the actual output impedance of an LVDT and this value isnormally taken from the actual coil design.

The output impedance will form a voltage divider with the load (see Load). The open circuitvoltage of the secondary will be reduced by the ratio of the load impedance divided by theload impedance plus the output impedance of the LVDT. Errors due to loading are minimizedby calibrating with the equivalent of the actual interface load. A tolerance of +15% ispractical for secondary impedance.

Load. The load is the impedance of the circuit that the secondary of the LVDT is connectedto. The equivalent of the actual in-service load should be specified for proper calibration. Iflong cable connections or RF filters are used, the shunt capacitance should be included withthe description of the load. When a center tap secondary is used, the load across each coil andany additional differential load should be specified.

The load on the output of an LVDT will affect the sensitivity, phase shift and temperatureerror. If the correct load is used for calibration, all performance requirements will be met withthe service load. To minimize load errors, tolerances should be kept as small as possible andthe load impedance should not be less than l0, 000 ohms. Shunt capacitance of the load circuitshould be kept under 7500 pF when using excitation frequencies over 1000 hertz.

Sensitivity, gain and scale factor are the same requirement. They are the slope of the outputvoltage Vs displacement. Kavlico prefers to define sensitivity as the slope of a best-fitstraight line drawn through the output data. An LVDT is a ratiometric device and thesensitivity should be expressed as the ratio of the volts out, per volt in, per Inch ofdisplacement (V/V/Inch).

A practical upper limit for the sensitivity of short stroke units (less than 0.065 inches) thatoperate at frequencies less than 500 hertz would be in the range of 3.0 V/V/Inch. Up to 6.5V/V/Inch can be achieved for short stroke units that operate at frequencies around 3500 hertz.This limit will decrease with longer strokes and should not exceed 0.5 Volts/Volt at the end ofstroke for the lower frequencies or 0.85 Volts/Volt at the higher frequencies.

Synchronous type demodulators will only produce a DC output for the in-phase componentof it’s input signal. A simplified way of looking at a phase shifted signal is that it contains thesum of two sine waves, one that is in-phase with the reference and one that is at 90°(quadrature). When a synchronous type demodulator is used, phase shift errors are eliminatedif the LVDT output is measured using an analyzing (phase sensitive) voltmeter that canmeasure the component of the output that is inphase (0 or 180 degrees) with the excitation.Looking at the waveforms of this type of demodulator it is not obvious but it does rectify thein-phase component. Non-synchronous (rectifier) type demodulators are used on some fiveor six wire LVDTs and the LVDT output is measured using the total voltage ratio (withoutregard to phase). A requirement for Sensitivity should include a statement for the ratio of thein-phase component or the total voltage.

Temperature Coefficient Temperature error for the sensitivity is normally specified as acoefficient of the sensitivity. The temperature coefficient of the sensitivity of an LVDT isnot linear over wide temperature ranges. It should be expressed as the maximum allowedchange in sensitivity, as a percentage of the nominal sensitivity, averaged over 100° oftemperature change. Typical coefficients range from +0.5% to -3.0% per 100°F.

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Accuracy is a term that has no specific definition and requires the user to provideone. This term is often incorrectly used as being synonymous with linearity. Accuracyshould be used when a group of independent errors, such as linearity, sensitivity andtemperature effects, are combined. For many applications only the total error is importantand not the individual error sources.

Once components of accuracy are defined, it becomes useful to state the minimum andmaximum deviations allowed from a specified reference (usually the nominal output) as apercent of Full Scale output. These bounds are called Accuracy or the Error Band and are thebounds of uncertainty for any measurement point under defined conditions. Acceptancetesting of the LVDT is conducted at room temperature and both room temperature limits andenvironmental limits should be stated. Room temperature accuracy is very useful forcalibration, since it establishes specific limits for acceptance and the individual error sourcesneed not be computed.

Linearity describes the maximum deviation of any calibration point from a specified straightline. The error is usually expressed as a percentage of Full Scale output. Unless linearityerrors are to be included in an “Accuracy” definition, the type of straight line used for thereference must be stated. The most commonly used line is the “Best Fit Straight Line”(BSFL).

Null Voltage is the minimum differential output voltage of an LVDT that can be obtainedwith the armature position. For most LVDTs this is at a balanced center where an equalnumber of secondary turns are engaged for both secondary coils. The null position isnormally defined as the position where the inphase components of the differential output arezero (this is 0 VDC for a synchronous demodulator). The null voltage is primarily due toslight differences in phase shift of one secondary to the other at the null position. Whentaking the difference of two voltages with different phase, the in-phase components beingequal, the quadrature is not and this difference is the null voltage. Figure 5 shows the nullquadrature that results from taking the difference in two secondary voltages with only 0.2degrees of phase difference. It is possible to bias the null position with an additional coil thatwill have a constant output over the stroke.

The only known purpose of a low null voltage is for rigging the stroke to a zero position(adjusting the physical position of the LVDT housing with respect to the armatureextension). This is often done using the null output measured with a non-phase-sensitivevoltmeter. If the null voltage is low, a more precise zero position can be achieved for the in-phase component.

Imperfections in the core material, high flux densities and non-uniform hardness of metal inthe flux path will generate harmonic distortion, which, if not equal in the two secondary coils,could also contribute to the null voltage.

Offset Null. The Null with a biased offset winding is not at a balanced position of thesecondary coils and larger phase differences in the secondary voltages will produce a largernull voltage. For a biased null position, three voltages produce the in-phase zero and willnever have the same phase shift. This will result in a higher than normal null voltage. NullVoltage for a biased offset could be as high as 5.0% of the maximum output. For most

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applications, only the Inphase Component is used and the null voltage will have little or nosignificance on the accuracy.

Null Shift. Kavlico defines null shift as the change in null position that cannot be attributedto material growth. Temperature error of the null position of an LVDT may result from anumber of sources but for most applications is negligible. The most significant null positionerrors are from different linear expansions of the materials that close the loop from themounting point of the housing to the mounting point of the armature extension. Whenpossible, linear expansions can be matched to minimize null shift. Most aircraft or aerospaceLVDT are constructed from 300 series stainless steel and the change in length from themounting point of the housing to the mounting point of the armature extension will be about9.3 to 9.6 PPM/oF.

Phasing. As noted in LVDT description, the differential output voltage will be in phase orl80o out of phase with the primary voltage as the armature is displaced through the nullposition. Phasing is used to determine in which direction the armature is displaced from thenull position. When specifying the phase for a specific direction of core displacement, thecommon elements (low side of both primary and secondary) must be specified.

Phasing for a three-wire secondary can be specified by indicating the desired phase of eachsecondary with the low side of the primary connected to the center tap and specifying whichsecondary voltage is to increase for a specific direction of the armature displacement.

Phase Shift for an LVDT normally refers to the difference in angular degrees between theprimary excitation voltage and the secondary output voltage when the output is takendifferentially.

For LVDTs that use three wire or split secondary, the phase shift requirement shouldindicate the specific output voltage for which the requirement applies (the differential voltageor each individual secondary voltage).

Limiting the phase shift will limit the quadrature voltage. In some applications a limit onquadrature is necessary since it appears as quadrature on the output of an error amplifier in aservo system or as a reverse voltage across the switch of a synchronous demodulator.

Phase Difference is used to describe the maximum allowed difference in the phase shift ofthe two secondary voltages when using a three wire or split secondary. It should be pointedout that this is NOT the differential phase shift. Both magnitude and phase shift of eachsecondary must be considered when computing differential phase shift. Typical phasedifference for the two secondary voltages, at the end of the stroke, is 3 to 8 degrees. At theend of the LVDT stroke, one secondary will be at its highest voltage and have its lowestphase shift when the other secondary will be at its lowest voltage with its highest phase shift(See Figure 6).

Tracking is used to define the uniformity of performance between channels of multiplechannel LVDTs. Calibration data is taken from a single reference point (normally the firstchannel null position). Each channel’s output is compared and the maximum differencebetween any two channels is termed “tracking.” This is normally expressed as a percent ofFull Scale.

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Null Difference tracking at the null position is sometimes specified as a maximum “NullDifference” and may have a different requirement than at other stroke positions. The smallestpractical Null Difference is 0.001 inch or 0.15% of the stroke whichever is larger. Nulldifferences less than 0.010 inches will require trimming the extension prior to final calibration.

Crosstalk is a term used for multiple channel units to describe the voltage produced in thesecondary of one channel by the primary excitation of another channel. When separate driversare used for different channels they may not be synchronous and slight differences infrequency will produce a beat frequency (difference frequency), which may produce anapparent oscillation of the system. Frequencies for different channels are sometimesseparated such that the beat frequency is above the system response. Typical crosstalk fortandem construction is less than 0.0010 V/V and for parallel construction 0.0010 to 0.0025V/V.

FAULT DETECTION

Many technological advances in the design, construction and use of the Linear VariableDifferential Transformer (LVDT) have been made in the last 15 years. Utilizing computeraided winding machines, the state of the art in LVDT performance has made significantadvances.

Much of the progress that has been made is due to achieving the ability to produce an LVDTwhere the two secondary windings provide not only the normal differential signal, but also aconstant sum. Add to this, the ability to adjust the sum for a specific differential output, anda whole new dimension for the LVDT is opened.

The first benefit one can realize is the ability to fault detect the signal on a real time basiswithout affecting performance or placing the signals in jeopardy should the fault detection cir-cuit fail. Using the LVDT output as two discrete signals relative to the center tap of thesecondary can do this. From this point of reference, (assume the center tap is the signalground) the two secondary voltages will both be linear with armature displacement and bothwill have the same phase relationship relative to the excitation. They may be either in-phaseor out-of-phase (should be specified for the application) and neither will have a zero voltageoutput. At this point, two approaches are possible.

The first approach would be to either actively rectify or synchronously demodulate eachsecondary voltage and then use the DC voltages to produce a difference and sum. Accuratecalibration can be accomplished using a total voltage ratio for active rectification or calibratingusing only the in-phase component of the output voltage (See Figure 7) when synchronousdemodulation will be used. No phase shift correction is required when the proper calibrationis performed.

A second approach would be to use the AC signals, Va and Vb, directly to produce both adifference and a sum voltage (See Figure 8) using both a differential and summing amplifier,then demodulating these voltages. It should be pointed out that this approach, when usedon the AC signals, must be used with caution.

The individual secondary voltages have differences in phase (see Phase Difference) and theoutput of a differential amplifier will not be the exact algebraic difference of the secondaryvoltages. When only the inphase components are used, this phase difference is not significant.

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When using the total component, the LVDT can be calibrated using the differential outputthat will yield the same voltage as the output from a differential amplifier.

A differential amplifier can cause a not so obvious error in that it does not present a fixed loadto its inverting input due to the common mode voltage generated by the non-inverting side.This will cause the Va secondary to be loaded differently than Vb. The input resistors for adifferential amplifier should be 20K ohms or larger to minimize load errors.

Also an open circuit fault in the LVDT on the inverting side will result in the differentialamplifier producing a false signal to the summing amplifier due to the common mode signalproduced on the non-inverting side.

When using a differential and summing amplifier the ideal configuration would have a non-inverting buffer for each secondary signal with the summing resistors on its input. This willpresent a fixed load to each half of the secondary of the LVDT and act as a pull down and notallow the input to float in the event of an open circuit in the secondary of the LVDT. Thebuffer will also isolate the common mode voltage from the differential amplifier since the sumis taken in front of the buffer (see Figure 9)

When using a flight or engine control computer the best configuration would be to simplydemodulate the Va and Vb to DC signals, digitize them and then let the computer do the rest.

In any case, by establishing a minimum value for the sum voltage, any value below this wouldindicate a fault in the signal. The total loss of the sum would most likely indicate an open inthe primary side if the excitation were still present. All significant fault conditions (opens orshorts), which could occur in the LVDT, would be detected.

DIFFERENCE OVER SUM OUTPUT

In addition to fault detection, a constant sum provides another possible advantage when usingan LVDT. Nearly everything that affects the differential output voltage also affects thesum voltage. If the output of an LVDT is taken as the difference over sum ratio, nearly allexcitation changes, temperature effects, frequency effects, loading and long term gain loss donot produce an error.

(Va/Ex. - Vb/Ex.) / (Va/Ex. + Vb/Ex.) = (Va-Vb)/(Va+Vb)

[The Excitation Voltage drops out]

This five/six-wire configuration presents many possible alternatives for the signalconditioning of an LVDT, but also presents a few new specification clarifications that mustbe addressed.

Definition of the difference over sum gain with its tolerance and the sum with itstolerance, describe the requirements for this use. The limits of the individual secondaryvoltages can be determined working from these requirements.

A typical requirement might be as follows:

1. Excitation: 7.07 VRMS with a +5% tolerance.2. Stroke: +3.000 inch.3. Sum: 0.6000 V/Vex. (4.242 VRMS) with a +10% tolerance.4. A difference over sum Gain: 0.16667 V/V/Inch (0.5000 V/V at each end of the stroke).

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5. And the total accuracy: +1.0% F.S. (+2%) of the reading at either end of the stroke.

The nominal differential gain is the sum ratio multiplied by the difference over sum gain =0.6000 V/Vex * 0.16667 V/V/Inch = 0.1000 V/Vex/Inch and this times 3.000 inches = 0.3000V/Vex

NOMINAL VALUESStrokePosition Va Vb Va-Vb Va+Vb (Va-Vb)/(Va+Vb)Inches V/Vex V/Vex V/Vex V/Vex V/V

3.000 0.1500 0.4500 -0.3000 0.6000 -0.5000-0- 0.3000 0.3000 0.0000 0.6000 -0-

+3.000 0.4500 0.1500 0.3000 0.6000 +0.5000

See Figure 10

The worst case for secondary values is:

1. For the sum tolerance, 0.6000 V/V +10% = 0.5400/0.6600 V/V and each secondary is0.2700/0.3300 V/V.

2. When the sum is 0.5400 V/V the nominal differential must be 0.5400*0.5000 or0.2700 V/V. Adding +2% tolerance to the gain and calculating the outputs at the endsof stroke yields 0.2754 V/V and for each secondary the change to the end of thestroke=0.1377 V/V;

3. When the sum is 0.6600 V/V the nominal differential must 0.6600*0.5000 or 0.3300V/V. With the ±2% this is 0.3366 V/V and for each secondary =0.1683 V/V

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A. For the minimum low voltage;0.2700 V/V minimum at the zero position -0.1377 V/V maximum change = 0.1323 V/Vand the lowest excitation = 6.7165 Volts, therefore the minimum value = 0.8886 volts.

B. For the maximum high voltage;0.3300 + 0.1683 = 0.4983 V/V and the highest excitation is 7.4235 Volts, and themaximum value = 3.6991 volts.

These values do not allow for rigging errors or mechanical over stroke.

Practical accuracy for a difference over sum unit is +0.5% of full scale at 75oF. This accuracywill include errors due to sensitivity, non-linearity, input voltage variations, frequencyvariations and load tolerances for the service life of the unit. The temperature coefficient ofsensitivity is normally less than +0.25% per 100°F. For strokes over 2 inches, frequenciesbetween 1500 and 2500 hertz will produce the highest accuracy.

The classic use of an LVDT was the differential connection, using only a four-wireconfiguration. There is only one possible connection for the load, phase shift referred to thedifferential signal at the end of the stroke, there was only one possible output impedance tocontend with and normally a null voltage occurred at mid-stroke. For nearly all applications,only the in-phase component was used for calibration. For the five and six wireconfigurations it gets more complicated.

The load for each secondary and any additional differential loading must be specified.

Phase shift for the Va or Vb outputs will change over the entire stroke with the highestphase shift at the low voltage end. The highest quadrature will occur at the high voltage end ofthe stroke and the phase shift for Va or Vb should be measured at that end of the stroke.

The output impedance of the Va or Vb coils changes over the stroke. The output impedanceis normally measured for quality purposes at the high voltage end for each secondary.

When the secondary center tap is to be the signal reference, the Null Position (ZeroPosition) is normally defined as the place in the displacement where Va is equal to Vb (thereis no “Null” voltage). A Null voltage is only obtained from an LVDT when connected suchthat the differential output is obtained. (see Null Voltage).

Calibration of the output can be done using the in-phase or total component.

Using the secondary sum for the switching circuit of a demodulator, phase shifting networksor scaling sensitivity to correct for phase shift is not recommended.

LVDT ENVELOPE REQUIREMENTS

Once the electrical, mechanical and performance parameters have been determined, severalfactors must be considered in packaging. Kavlico’s design team can provide the length anddiameter necessary to meet both the environmental and electrical performance.

COST CONSIDERATIONS

Boilerplate and over specifying performance attributes becomes costly in production. Designoptions and cost savings are available when specific requirements and system performanceare analyzed and practical limits placed on all requirements.

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