IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 1, FEBRUARY 2008 67

LVDT Conditioning on the LHC CollimatorsAlessandro Masi, Arnaud Brielmann, Roberto Losito, and Michele Martino

Abstract—The Position Readout and Survey system of the LHCcollimators has to monitor in real time (RT), at a frequency closeto 100 Hz, the position of the 555 synchronized axes with anaccuracy of 20 m. Radiation hard Linear Variable DifferentialTransformers (LVDT) are used as absolute position sensors fortheir ruggedness, intrinsic accuracy and infinite resolution. Be-cause of the radioactive environment the conditioning electronicsis located in safe zones up to 800 m away from the sensors. Underthese conditions, standard conditioning techniques cannot guar-antee the accuracy requested by this application because of cableimpedance, noise immunity, crosstalk between signals of differentsensors passing within the same multiwire cable and temperaturestability. A fully digital approach based on a sine-fit algorithmhas been followed and will be described showing the excellentresults measured up to now. Particular attention is devoted to theRT implementation of the algorithm on the PXI platform fromNational Instruments.

Index Terms—Digital signal processing (DSP), linear variabledifferential transformers (LVDT), PXI, sine fit.

I. INTRODUCTION

THE high luminosity performance of the LHC relies onstoring, accelerating, and colliding beams with unprece-

dented intensities. The energy density of the nominal beam is1000 times higher than previously achieved in proton storagerings. Tiny fractions of the stored beam suffice to quench asuper-conducting LHC magnet or even to destroy parts of the ac-celerator. More than 100 collimators will therefore be installedto protect the machine from uncontrolled particle losses, and toabsorb energetic particles outside the nominal beam core [1].

An LHC collimator consists of two 1-meter long blocks thatcan be made of different materials (graphite, copper, tungsten)depending on their position in the lattice.

Each jaw can be moved on both ends by stepping motors thatcan position it at a well defined angle and distance with respectto the nominal beam trajectory. The required accuracy of posi-tioning is one tenth of the beam core diameter, which at nominalenergy will be of the order of 200 m. We therefore assumed asproject parameter for the accuracy 20 m.

The stepping motors are controlled in open loop, in the sensethat they follow predefined trajectories without feedback froma position sensor. The trajectories are sent to the low level con-trol system by a Central Supervisory System (CSS) applicationcoordinating all the collimators [2]. The concept of open loopcontrol is based on the precision of the cinematic chain that hasbeen designed to be free of mechanical play. Every collimator is

Manuscript received May 10, 2007; revised November 20, 2007.A. Masi, A. Brielmann, and R. Losito are with CERN, Geneva 1211, Switzer-

land (e-mail: alessandro.masi@cern.ch).M. Martino is with the Dipartimento di Scienze Fisiche, Universita di Napoli

Federico II, 80126 Napoli, Italy.Digital Object Identifier 10.1109/TNS.2007.913473

tested before installation to verify that the mechanical play andthe non linearity of positioning remain below 20 m on everyaxis.

However in order to ensure the level of machine safetyrequired by the LHC, an independent Position Readout andSurvey (PRS) module has been defined in the low level controlsystem to verify in real time the actual position of the jaws.Depending on the type and energy of the circulating beams,the PRS will be enabled to trigger a beam abort in case ofdiscrepancy between the desired and the measured position ofthe jaw.

The PRS is based on radiation tolerant linear LVDTs specif-ically designed and built for this project by Measurement Spe-cialties Inc. On each collimator up to seven LVDTs have to bemonitored, four of which will measure the absolute position ofeach jaw’s end, one the collimator’s vertical position. The tworemaining sensors will measure the distance between the jawsto build a certain level of redundancy and fault tolerance in thesystem.

Each PRS will control up to three collimators. Overall, thePRS systems will have to monitor in real time more than 700LVDTs. All the PRS systems have to be synchronized to atrigger coming from the supervisory collimator control systemat the start of a motion profile.

With the nominal motor speed of 400 steps per second, anda reduction factor of 2 mm/revolution, a survey frequency of100 Hz is required to detect position errors not exceeding 20 m.

The most challenging problem in ensuring the required accu-racy is given by the environmental conditions of the LHC. Dueto the high level of radiation expected in the proximity of thecollimators (several MGrays/year), no electronics can be em-bedded in the sensors or in the motors. On top of that, radiationsafe alcoves for the installation of the driving electronics canbe up to 1 km far from the collimator itself, generating a com-plex matching problem for the conditioning electronics. Theimpedance of the cable can in fact transform on long distancesthe impedance of the sensor from inductive to capacitive. Stan-dard off the shelf conditioners do not generally provide a widerange of tuning to cover cable distances from 20 m up to 800 mas required for the LHC collimators, while preserving a satis-factory stability and accuracy of positioning. In Sections II–Vwe will review the state of the art in LVDT conditioning tech-niques, and put in evidence the pros and cons of the differentapproaches.

I will then detail our original approach that allowed us at thesame time to cope with long cables and to feed up to seven sen-sors with a single multiwire cable without interference from onesensor to the other, allowing considerable savings on cabling. Iwill show then the implementation of the algorithm on a realtime platform, and provide figures about accuracy and time re-sponse of the measurements.

0018-9499/$25.00 © 2008 IEEE

68 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 1, FEBRUARY 2008

Fig. 1. Working principle of the LVDT.

II. THE LINEAR VARIABLE DIFFERENTIAL TRANSFORMER:CONDITIONING TECHNIQUES

A. The LVDT Working Principle

The linear variable differential transformer (LVDT) has beenchosen as displacement sensor for the LHC collimator jaws be-cause of its good characteristics in terms of linearity, resolution,repeatability, and reliability. Special radiation hard (50 MGrays)LVDTs have been designed to have a linearity error below 0.2%.Being based on a contactless construction, they will provide alonger lifetime and a high repeatability. The LVDT principle isshown in Fig. 1. By applying a voltage sinewave to the primarywinding, a voltage will be induced in the secondaries. The dif-ference between the two secondary voltages will depend linearlyon the displacement of the central moveable core.

If we call the LVDT feeding signal at frequency :

(1)

The two secondary signals can be expressed as:

(2)

Where the amplitudes of and depend on the LVDT sensi-tivity and on the position of the LVDT core.

B. State of the Art in Conditioning Techniques

The LVDT is generally used either in a 4-wire or in a 5-wireconfiguration.

In the 4-wire configuration the signal at the output terminalsis the difference of the secondary windings. The 4-wire LVDTdoes not have a center tap available. As the magnetically per-meable core is moved from the center position, the magneticcoupling between the primary and one secondary coil increases,while the other simultaneously decreases. Therefore, the differ-ence between the two output signals is a non-zero sine wavewith amplitude proportional to the core position.

The 5-wire configuration includes an additional wire whichrepresents the connection point (center tap) for both secondarywindings, allowing the individual measurement of the voltageat each secondary winding with respect to the center tap.

The traditional technique of LVDT signal processing consistsin a synchronous demodulation of the differential secondaryvoltage with respect to the primary [3]. The effect of noise withfrequency components far from the frequency of the sinewavesent to the primary is reduced. Fluctuations of the primary signalamplitude are also eliminated at the first order. Nevertheless,most LVDTs present a phase difference between the signal ap-plied to the primary and the signal resulting from the differencebetween the two secondaries. The angle depends on the oper-ating point.

The differential secondary voltage can be expressed as:

(3)

where depends on the LVDT core position.The synchronous demodulation is obtained by multiplying a

signal synchronous with the carrier and low pass filtering:

(4)

As a result the LVDT position depends on the phase differ-ence which in turn depends on the cable length used to drivethe sensor. A manual tuning is therefore needed at installationto compensate the phase error related to different cable lengths.This is the case for instance of the integrated circuit AD698 fromAnalog Device [4].

Some digital techniques have been developed to estimate witha PLL the phase error in order to correct it automatically [5].This approach provides a greater accuracy, but they maintain thesame original dependence on . Near the null point, say formeasurement below 5% of the Full Scale (FS), the variabilityof increases and moreover, since the differential secondarysignal is very low, it will be heavily affected by noise, at thepoint that phase recovery may become impossible. In addition inour application the long cables between sensors and electronicstransform the impedance seen by the conditioner from inductiveto capacitive. In this situation phase recovery would require avery sophisticated algorithm.

The AD598 IC performs an asynchronous demodulation tocorrect the effect of uncertainty in the null position [6]. It workswith a 5-wire configuration and is based on ratiometric condi-tioning dividing the difference of the LVDT secondary voltagesby their sum. This ensures a compensation of the amplitude drifton the excitation signal. The noise immunity of this solution isnot better than that obtained with a synchronous demodulationespecially if it is used in a 4-wire configuration [7]. Ratiometricconditioning however implies that the sum of the two secon-daries has to be independent of the position of the LVDT coreto not affect the measurement linearity.

MASI et al.: LVDT CONDITIONING ON THE LHC COLLIMATORS 69

Spectral techniques, for instance the one based on Goertzelalgorithm [8], are characterized by a higher noise immunity butsuffer of the spectral leakage problem. A window on the sam-pled signal has to be applied in the frequency domain to reducethis error.

III. THE NEWLY PROPOSED CONDITIONING TECHNIQUE

None of the techniques mentioned above were fully satisfac-tory for our purposes. The requirements on accuracy and speedof acquisition imposed to adopt a technique highly immune toexternal noise. Moreover, the wide range of cable lengths fromthe sensor to the electronics (25 m up to 800 m) imposed to havea technique that allows a wide range of tuning without the needof local intervention. We proposed to use a SineFit algorithm[9] to reconstruct the response from the LVDT secondaries andthen use the ratiometric formula (5) to compute the absolute po-sition. The details are below.

A. Ratiometric Conditioning

The position reading of the LVDT is based on a ratiometricdecoding of the two secondary voltages. The ratio is given by:

(5)

The design of the LHC collimator LVDTs guarantees a con-stant sum over the useful positions range mm .

The amplitude demodulation has been performed with a sinefit algorithm [9] because it is an asynchronous demodulation soit does not suffer of the phase error problem. As we will see inthe following, no filtering or windowing is required to eliminatethe spectral leakage. This algorithm is characterized by highnoise immunity and a frequency response that can significantlyreduce the crosstalk due to the proximity of different LVDTs.

B. Sine Fit Algorithm Formalization

The best estimate of the amplitude , the phase , and theoffset of a sine wave signal of frequency from of itssamples acquired at the time instants isobtained minimizing the following error quantity

(6)where , , are given by:

(7)

The square of the error can alternatively be expressed by thematrix equation:

(8)

where:

...

......

...(9)

It can be demonstrated that the minimum of the error functionis given by the following equation [9], [10], [11]:

(10)

where

(11)

Estimating the amplitude, phase and offset of a sine wavestarting from samples reduces to computing the elements ofthe matrix , computing the matrix (11) and then multiplyingby the vector of the samples.

C. Algorithm Characterization

Since one of the biggest concerns is noise immunity, intensivesimulations have been carried on with Matlab, to fully charac-terize the SineFit algorithm in terms of its immunity to differentkind of perturbations expected in the operating environment ofthe LVDT in the LHC.

1) Immunity to White Noise: We first combined a whitegaussian noise to the sinusoidal signal. We evaluated the un-certainty on the amplitude estimate for different values of theSignal to Noise Ratio and number of samples acquired at thesampling frequency .

In Fig. 2 the standard deviation on 500 repetitions is shownas a function of the SNR and at a different number of acquiredsamples is shown.

An exponential model has been used to fit the standard devi-ations on the SNR:

(12)

Then the values of the parameters and have been fittedon the number of samples with the following model:

(13)

Fig. 3 shows that, for the case , increasingfrom 500 to 2500 the coefficient is reduced only by a

factor of two. Increasing even more substantially the number ofpoints will be less and less beneficial to the noise figure of thealgorithm.

on the contrary stays more or less constant.

70 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 1, FEBRUARY 2008

Fig. 2. Amplitude estimate uncertainty on 500 repetitions of a sinusoidal signalwith white noise. The simulations refer to different SNR values and number ofsamples acquired N .

Fig. 3. Fit of the model introduced in (13) to describe the amplitude estimateuncertainty with the sine-fit algorithm on a sinusoidal signal at f = 2500 Hz,f = 250 kS/s with superimposed white noise.

The simulation results can be summarized by the followingapproximated formulas:

(14)

Taking into account the previous simulations, we decided toimplement the algorithm with 2000 samples. This number guar-antees an uncertainty of less than 10 ppm on the estimate of theamplitude even with the unrealistic case of 15 dB of SNR. With250 kS/s the samples are acquired in 8 ms. This value is com-patible both with the survey frequency requirement and with theposition signal dynamics.

2) Immunity to Crosstalk: In order to save on cablings (morethan 200 km of cables have already been pulled in the LHC

Fig. 4. Frequency response of the Sine Fit algorithm calculated with f =

2500 Hz, N = 2000, f = 250 kS/s SineFit algorithm.

for the collimation project), the seven LVDTs of a single colli-mator are all connected to the conditioning electronics throughthe same multiwire cable. A cross talk between different chan-nels can be expected. The frequency response of the SineFit al-gorithm has been characterized in order to evaluate the influenceof a sinusoidal perturbing signal on the amplitude estimate.

The algorithm performs an average of the instantaneous am-plitude over the acquisition period (i.e., the time needed to ac-quire the samples of the signal, 8 ms in our case). Let bethe generic sine tone with variable amplitude described by

(15)

Under the assumption that varies slowly with respect to, at the survey time the algorithm will return the value ex-

pressed in (16):

(16)

The frequency response has been determined evaluating the am-plitude estimated by the SineFit algorithm of a unity sine waveinput signal at an arbitrary frequency expressedas:

(17)

By means of (16) it follows:

(18)

A direct simulation with Matlab matches very well the ex-pression obtained analytically.

Fig. 4 shows clearly that it is possible to find a set of frequen-cies that do not interfere to each other. Let’s introduce

(19)

MASI et al.: LVDT CONDITIONING ON THE LHC COLLIMATORS 71

A tone centered on a frequency spaced by an integer numberof from the design frequency will not perturb theestimate of the tone amplitude. In order to ensure an a prioriorthogonality of the LVDTs channels, 7 non-interfering (i.e.,orthogonal) frequencies have been chosen to excite the LVDTsof the same collimator and 7 different SineFit demodulations areperformed.

IV. THE POSITION READOUT AND SURVEY SYSTEM

A. General Description

The PRS is responsible for checking the coherence of actualjaws’ positions of up to three collimators with those expectedby the CSS. To increase the overall reliability of the controlsystem, the PRS is required to be independent from the MDC(Motor Drive Control), the low level control module that di-rectly controls the movement of the stepping motors by sendingthe STEP and DIRECTION signals to their power drivers, andby reading the angular position of the motors from resolversmounted on their axes, in order to quickly detect lost steps. Tomake it independent, the PRS runs on a different machine thanthe MDC.

Two National Instruments PXI chassis with two different con-trollers are therefore attached to one, two or three collimatorsand host one the MDC and the other the PRS. The two PXIchassis are completely independent, and do not directly commu-nicate with each other. DIM servers installed on each of themprovide connectivity to the CERN middleware CMW and ex-change commands and data with the CSS through the CERNframework FESA (Front End Software Architecture).

The PRS monitors the position of the jaws through the upto seven LVDTs installed on each collimator at a rate of up to100 Hz. Such a high rate is necessary to ensure that the relativeposition of two jaws in different collimators remains unchangedduring the execution of a movement function within a toleranceof 20 m. The maximum speed of the motor will in fact beof one revolution per second, for a linear movement of 2 mm/revolution.

Measurements in a laboratory with metrology palmers haveshown that the reading from the PRS, once each LVDT has beenproperly calibrated, is accurate to within less than 10 m atnormal pressure and temperature even with cable lengths up to800 m. In addition, the sensors themselves have been designedto have a negligible thermal sensitivity. Temperature changes upto 30 K (well above what is expected on a LVDT in the LHC)produce a measurement drift below 10 m.

The PRS fulfills then the requirements on accuracy as a re-sult of the excellent noise rejection and independence from thesensor non linearity of the sine fit algorithm combined to ra-tiometric conditioning, as well as of the careful design of thesensor and of the collimator mechanical parts. The fulfillmentof the requirements on the time response is the merit of the realtime architecture used and of the RT optimization of the con-ditioning algorithm combined with the performance of the realtime platform chosen for the implementation, the National In-struments PXI.

Fig. 5. Hardware Architecture of a PRS.

B. The Hardware Architecture

The hardware architecture of a PRS for 3 collimators has al-ready been described in details in [2]. The description is heresummarized for convenience, and shown in Fig. 5.

A National Instruments PXI chassis is equipped with an RTcontroller NI-PXI 8106 based on an Intel® Core 2 Duo Processorat 2.16 GHz.

For each collimator controlled by the specific chassis, twoDAQ cards NI PXI 6143 with 8 simultaneous differential analoginputs sampled at 16 bit and 250 kS/s are used to acquire the14 signals coming from the secondary coils of the 7 LVDTsinstalled on each collimator.

Data acquired are transferred to the CPU via DMA using cir-cular buffers as shown in Fig. 5. In this way the acquisition of thesignals coming from the LVDT secondaries is decoupled fromtheir processing, releasing CPU resources.

Furthermore, an FPGA card NI PXI 7831R having 8 analogoutputs is used to generate the feeding signals for the 21 LVDTs.Seven outputs are used to generate sinewaves of different fre-quencies, orthogonal with respect to the frequency response ofthe sine-fit algorithm used.

All the signals sent to or coming from the LVDTs are inter-faced through custom PCB in Europe format1 to ensure at thesame time reliability and modularity.

1CEI 60297-3-101, CEI 60297-3-102, CEI 60297-3-103/IEEE 1101.1, IEEE1101.10/11

72 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 1, FEBRUARY 2008

Fig. 6. Software Architecture.

Every signal coming from the analog outputs of the 7831card is split on three different lines in the Europe cards, andthen amplified individually through buffer amplifiers to prop-erly drive each sensor over the long cables. In case of fault ona power stage of one of the collimators, the two others will notbe affected.

The same FPGA card is also responsible for the synchroniza-tion of all the DAQ cards on the precise 10 MHz clock dis-tributed to all the PXI chassis as well as for the synchronizationof the motion survey process for each collimator on the triggersignal sent by the CSS.

A 250 kHz clock for all the DAQ cards is generated by theFPGA from the CLK/10 on the RTSI bus used as referenceclock. The start of the readout and survey loops for each colli-mator is triggered respectively by the signals TRG0, TRG1 andTRG2 on the RTSI bus generated by the FPGA at reception ofa trigger from the CSS.

C. Software Architecture

1) RT Tasks Architecture: The following functionalities areimplemented in the PRS:

• pre-processing the commands received from the CSS: co-herence check, protocol check;

• preparation of the upper and lower threshold profiles forthe collimator axes and the two gaps;

• feeding the up to 21 LVDTs with signals at proper frequen-cies;

• reading up to 21 LVDTs with 20 accuracy at a rate ofup to 100 Hz;

• synchronization of the motion profiles survey process onthe trigger received by the CSS.

Most of these functions are executed by RT tasks running onthe PXI controller NI-PXI 8106, apart from the excitation ofthe sinusoidal waves to feed the LVDTs and the synchronizationtask, which are entirely implemented in the FPGA of the NI-PXI7831 card.

The architecture of the RT tasks executed on the PRS for thereadout and survey of three collimators is shown in Fig. 6, wheregrey tasks are executed on the CPU and light-colored tasks onthe FPGA.

The CPU command listener waits for commands or settingssent by the CSS on the related DIM services. The event recogni-tion loop has 1 ms cycle time and the highest priority to ensurenegligible reaction time. At reception of the request of motion

profile survey, it prepares upper and lower limit arrays for eachaxis according to the boundary function sent by the CSS. Thelimits represent thresholds for triggering a beam abort. A linearinterpolation is applied to update the threshold value each 10 ms.An acknowledge is then sent to the CSS to inform it that the PRSis ready for the profile survey and is waiting for the hardwaretrigger.

The synchronization of the reading and survey process onthe CPU is performed by the FPGA card (task LVDTs exci-tation reading and synchronization). As soon as the triggeris received from the CSS a 100 Hz clock is generated on theRTSI trigger line related to the collimator to survey. This accu-rate timing signal synchronizes the CPU task that performs theLVDTs reading and the comparison with the associated thresh-olds. This approach guarantees that the time jitter on the LVDTsreading will not exceed 100 microseconds, the error on positionreading will therefore remain well within specifications.

The position readout and survey task on the CPU performsthe processing of the signals of the 7 LVDTs installed on thecollimator using a ratiometric conditioning. The time needed toexecute a full reading cycle for all the 21 LVDTs of one colli-mator using 2000 samples for each signal has been measured tobe 1 ms with a jitter below 50 s.

2) Optimization for RT Implementation: The frequencyis known therefore the matrix in (9) can be calculated justonce per sensor. Furthermore as only the amplitudes of the sec-ondaries are needed to evaluate the sensor reading we do notneed to calculate the offset and the matrix can be furthersimplified to an instead of an . For a single sec-ondary channel we have:

......

(20)

For LVDTs an matrix has to be created and pseudo-inverted:

(21)

where

...... (22)

The data coming from the acquisition boards and sampled at afrequency , are stored in an matrix and then multipliedwith the matrix , the pseudo-inverse of the matrix in (21),so at each survey cycle a simple matrix product is performed toproduce a coefficients’ matrix estimate. sinusoidalsignals can be in fact expressed by the following equation:

(23)

MASI et al.: LVDT CONDITIONING ON THE LHC COLLIMATORS 73

Fig. 7. The Positioning Readout and Survey Task.

in which the amplitudes are:

(24)

(25)

Equation (23) relates ideal sinusoidal signals to their ampli-tudes, decomposed in cosine and sine components, while (24)describes the diagonal structure of the amplitudes’ matrix inwhich each block, described by (25), gives contributions onlyfor its own frequency. The , superscripts refer to the firstand the second secondary respectively.

Finally the best amplitudes’ matrix estimate is given by:

(26)

Two acquisition boards are needed to sample all the LVDTsof a same collimator, respectively 8 channels on board A and6 channels on board B. The demodulation scheme specifiedin (21) to (25) has therefore been split: two SineFit matricesare generated at startup pseudo-inverting one matrix for the 4LVDTs connected to the board A, and one for the 3 LVDTs con-nected to the board B. At each reading cycle two matrices comefrom the DMA to be multiplied with the fit matrices. Fig. 7 de-scribes the reading and survey task for a single collimator.

V. EXPERIMENTAL RESULTS

A. Software Performances

Fig. 8 shows the statistics for the parallel readout of 3 colli-mators’ LVDTs running on the same CPU. The execution timewith 2000 samples acquired for each channel and at each cycleis around 1 ms per collimator with a negligible jitter.

B. Single LVDT Reading Characterization

Some measurements have been carried out to characterize thesingle LVDT reading performances. The nominal configurationis with samples and no motor driver running during

Fig. 8. Each reading task runs in parallel and is completed in approximately 1ms. No significant differences exist between them and the time jitter is negli-gible. The statistics are evaluated on 5000 readings each one coming from 2000samples per channel.

Fig. 9. Typical performance of the channel amplitude estimate. On the left,histogram of the first secondary of LVDT A of Collimator 2 (short cable); onthe right the second secondary. f = 2125 Hz. The statistics are evaluated on5000 readings.

the test. The nominal gain of 100 mm/ratiometric unit is as-sumed for all the LVDTs. Fig. 9 shows the typical amplitudeestimate, in the lab setup, for the two secondaries of a singleLVDT connected to the PRS by a short cable. The SNR mea-sured on the signals is close to 30 db. The standard deviationevaluated on 5000 readings is about 10 ppm of the amplitude.This value is in reasonable agreement with the approximatedformulas (14) obtained as simulations result.

To take into account the possibility of noise generated bythe stepping motor drivers power electronics we added noiseon one secondary of the LVDT using the experimental setup ofFig. 10. We applied square wave noise at 9 kHz and 18 kHz,since the LHC motor drivers work at a chopping frequency of18 kHz and sub-harmonics may be present due to the PWMcontrol; the main sub-harmonic involved is the half order [12].The square waves have been generated with a SRS DS-360 fre-quency generator; to add the “noise” to the useful channel a

74 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 1, FEBRUARY 2008

Fig. 10. Measurement setup for motor driver noise immunity test.

Fig. 11. The position reading � have been normalized to the nominal value� with no square wave noise applied in order to highlight the effect of thenoise applied. Each value plotted is the average of two different measurements,in which the � is evaluated on N = 5000 readings.

Single Ended-Differential mixer has been built, since the outputof the DS-360 is single ended while the LVDT’s signals are dif-ferential. The ratio between the standard deviation of the po-sition reading at various SNR level and the standard deviationwhen no noise is applied has been evaluated. The reference stan-dard deviation is measured with the mixer connected andthe generator switched off.

The experimental results are summarized in Fig. 11. The im-munity is very good for all the reasonably expected values ofthe SNR.

C. Multiple LVDTs Reading Characterization

Finally the performance of the overall system has been mea-sured in the nominal conditions. A multiwire 500 m long cablehas been used to connect the 21 LVDTs of 3 collimators to thePRS. Fig. 12 shows the amplitude spectrum of a LVDT sec-ondary channel measured with an Agilent E7405 EMC Ana-lyzer. As expected all the other LVDT’s frequencies were de-tected. The amplitude of the tones is 60 dB below the main tone,however the effect of these spurious tones is negligible since thefrequencies are chosen to be orthogonal.

Fig. 13 shows statistics for some LVDTs connected both withshort cable and 500 m long cable. The difference between the

Fig. 12. Typical spectrum of a LVDT secondary channel.

Fig. 13. Position reading performance with the lab setup.Upper. Standard devi-ations of two LVDTs on 5000 readings with 500 m long cable.Lower. Standarddeviations of two LVDTs on 5000 readings with short cable.

standard deviations can be explained mainly by the different ex-citation frequencies and, in second place, by the different be-havior of the front end channels.

Anyway the standard deviations of the readings are all below1 m with the laboratory setup and no dramatic degradation canbe foreseen in normal operation.

ACKNOWLEDGMENT

The authors would like to thank J. Lendaro, B. Simon, C. Mi-tifiot, and C. Serpico for their support on the technical realiza-tion of prototypes and measurements. They would also like tothank Prof. F. Cennamo and Prof. V. G. Vaccaro for their usefuldiscussions and suggestions.

MASI et al.: LVDT CONDITIONING ON THE LHC COLLIMATORS 75

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