CERN. Geneva-Switzerland OCR OutputSeptember 1994

potential of an important performance increase.measurements on several units. Strategies will be presented which have thethe C loaded monitor. Computed performances will be confronted with a set of(resolution!) will be addressed. This leads to a set of optimum design values forvery important problem of perturbations both coherent and incoherentdone both for the bare monitor and for the monitor with capacitive loading. Theexpression for the transfer impedance of the device. The computation will bemagnetic torus is computed based on measurable quantities. This will lead to an

After a brief recall of the principle of the monitor an electric model of athis has important consequences as will be shown.absence of signal (magnetic field) is lost in the case of the current monitor andleast) two parts for the DC current monitor. As a result the perfect balance in thethat in the flux gate a single ring is used while this ring had to be split up into (atthe principle of enhancement of the second harmonic. This difference is the factbetween a DC current transformer and a flux gate of the ring type. Both work onthe flux gates is without question. However, there exists a basic differencecalculate their performance have been made [9-11]. The interest of the reports onThese devices are well documented in the literature [5,7-ll]. Attempts tocalled second harmonic flux gate sensors introduced in the early l930’s[8].

The DC monitors used in accelerators are direct descendants of the so

that direction.performance in mind. The ambition of this report is to make a definite step inthese reports it is not possible to design a DC monitor with a specificno indication is given on the recipe used to build the monitors. Clearly, fromresults obtained with regards to stability, precision, resolution and dynamic rangethe subject of several papers already[l,2]. While they generally report on the

The DC monitor used for intensity measurement in accelerators has been

Abstract

L. Vos

TRANSFORMER FOR DC INTENSITY

THE SECOND HARMONIC BEAM CURRENT

-sr-94-74

CERN SL/94-74 BI ‘ IIIIIIQyllllllllllllllllllllllllllCERN LIBRARIES, GENEVA

CERN — SL DIVISION

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

QC

18References OCR Output

17Acknowledgements

167.2 Objective

7.1.2 Enhancement of resolution with special processing 16157.1.1 Torus matching procedure

157.1 Future development strategies

15Conclusions, future development and objective

146.2 Observed and computed performance figures136.1 Input data of a set of different DC monitors

13Confrontation between analysis and observations

125.2.2 Toms shunted with capacitor125.2.1 Bare magnetic torus

115.2 Incoherent perturbations (noise)

115.1.2 Offset105.l.l Common mode

105.1 Coherent perturbations

Perturbations

4.2 Magnetic torus with capacitive shunt4.1 Magnetic torus

Transfer impedance of double magnetic torus

3.4 Equivalent circuit for torus3.3 Time constants3.2 Resistance R3.1 Inductance L

Electric model of a magnetic torus

Principle of the DC monitor

Introduction

OCR OutputCONTENTS

-1OCR Output

noise level that is as low as possible to achieve the best possible resolution.harmonic is as large as possible within the constraints of the material and athe DC monitor is related to the choice of parameters such that the secondharmonic and multiples thereof of the magnetisation signal. The problem oflinear process of the magnetisation itself creates a signal at the secondfollows that the combination of the common mode magnetisation and the nonThe process repeats for every alternance of the magnetisation cycle. Itcommon mode magnetisation which is the quantity that has to be measured.difference flux will no longer be zero. ln fact, it will be a function of theentry into saturation on one ring while it delays it in the other one. Hence thethe symmetry. Indeed, the common mode signal will advance the moment ofcurrent which creates two fluxes in the same sense (common mode) destroyszero at all times in the ideal case. The presence of an extra magnetisingThe difference flux that is detected by a common detector winding will beinto saturation. The magnetic fields in the two rings are in opposite direction.

Consider two identical magnetic tori that are periodically magnetised

2. Principle of the DC monitor

presented which have the potential of an important performance increase.confronted with a set of measurements on several units. Strategies will bedesign values for the C loaded monitor. Computed performances will beincoherent (resolution!) will be addressed. This leads to a set of optimumloading. The very important problem of perturbations both coherent andbe done both for the bare monitor and for the monitor with capacitivean expression for the transfer impedance of the device. The computation willmagnetic toms is computed based on measurable quantities. This will lead to

After a brief recall of the principle of the monitor an electric model of a

and this has important consequences as will be shown.absence of signal (magnetic field) is lost in the case of the current monitortwo parts for the DC current monitor. As a result the perfect balance in theflux gate a single ring is used while this ring had to be split up into (at least)enhancement of the second harmonic. This difference is the fact that in thetransformer and a flux gate of the ring type. Both work on the principle ofquestion. However, there exists a basic difference between a DC currentto this point later. The interest of the reports on the flux gates is withoutquestion on performance related to resolution is still open. I will come backcalculate their performance have been made [9-l 1]. Nevertheless, theThese devices are well documented in the literature [5,7-ll]. Attempts tocalled second harmonic flux gate sensors introduced in the early l930’s[8].

The DC monitors used in accelerators are direct descendants of the so

make a definite step in that direction.monitor with a specific performance in mind. The ambition of this report is tomonitors. Clearly, from these reports it is not possible to design a DCdynamic range no indication is given on the recipe used to build theon the results obtained with regards to stability, precision, resolution andbeen the subject of several papers already[l,2]. While they generally report

OCR OutputThe DC monitor used for intensity measurement in accelerators has

-2OCR Output

of the tape can be expressed in terms of the skin depth:

and - = 1 — e, where 5 is the skindepth. The half thickness t5%{—E}é§dT2;,

R Z R°

will be less then t/2. If this ejfecrive thickness is called teff, then :The available thickness for the conduction current at higher frequencies

R° _ p nd:4wm

The low frequency resistance is called R0 :

3.2 Resistance R

1+wgL = -—l2

The frequency dependant inductance is :

Lo = HOMRO Engr

The low frequency inductance is called Lg .·

3.1 Inductance L

the equivalent circuit elements will be computed.the resistance varies with frequency due to the skin effect. In what followsparallel with a resistance R. The inductance depends on frequency via it}; and

The equivalent circuit diagram of a torus consists of an inductance L in

while the diameter is d.magnetic torus consists of m windings which have a width w , a thickness rmaterial is p. No frequency dependence is assumed for this parameter. A

The parameters um; and Tn can be measured. The resistivity of the

= MR 1+ wrUno

dependence:convenience the following function was chosen to model the frequencygeneral law for this dependence has been established long ago [3,4,6]. Forincreasing frequency leading to an apparent decrease in permeability. Thethis case the induced current provides increased magnetic shielding forsame physical process that is at the origin of the well known skin effect. Intapes. The permeability decreases as a function of frequency. It is due to

The magnetic tori of DC monitors are made of thin high permeability

wr varies from 2 to 3.16. It is important to note that this variation of wr is OCR OutputParameter s varies with frequency from O to a maximum value of 1 and

(1 + wru)S _ { }!

wr

The expression for s simplifies and becomes

This relation is surprisingly well verified by magnetic measurements.

To = No -= 2%z gf(E)Tu and ro:

This expression is very important since it relates the two time constants

.. T”_ 1 _ 2 #120 I 2nf ` ¢¤10°_ E I p

The relation between fg and qi is simply:where fg is the frequency that halves the low frequency permeability.

UnotP 6 f =———-10 g z

the so called Eddy ciurent limit:discussion it may be interesting to refer back to Wolman,s law [3] concerninginteresting to appreciate its frequency dependence. At this point of the

The factor wr plays an important role in what follows. Therefore it is

- R <1+wr#)s(1-e") (l—e")`wr - Qi I L; .. L

2(1 + mtu)It follows that s = [ii- and also :

L = :a R0 p 2

The low frequency time constant is called 10 :

3.3 Time constants

R = R0s(l — e").

The final expression for the resistance becomes

25 2 2pS Z _f__ = L lirliow `

from negative saturation to positive saturation in a time which is determined OCR Outputdrives the toms into saturation. The magnetisation of the torus will changeparagraph. Suppose that the current value A/2 corresponds to the current thatcomponent is the positive pulse which has been introduced in previouscomponents. The first component is a negative DC current A/2. The second

Consider first a single torus. The basic excitation consists of two

1* as :-4i-. ’"'( ) 1+ iwrmagnetisation current. Hence :

We shall be interested in the spectrum of the time derivative of the

[Mw) = ·—t—· 1+ mrcA/jw

magnetisation current. Its spectrum follows from Vs(w) :The part of the current that flows through the inductance is the

(0 = 4-M;-. ‘< ) 1+ iwt

and the response of the torus will be :

I.(w)=

with amplitude A is :The basic excitation is a step stimulus. The spectrum of a current step

4.1 Magnetic torus

and LEP, a capacitive shunt is added in parallel with the torus.current it, is computed. In the second case, which is the one used in the SPSconfronted with a current modulation at rotational frequency S2 and a beam

Two cases are considered. In the first case the response of a torus

4. Transfer impedance of double magnetic torus

parameter s.

All the elements are known or measurable and are a function of the

1+ your 1+ jwrZ = ·——= RJCL{L jar:

_ straightforward way:The expression of the equivalent parallel circuit can be written in a

3.4 Equivalent circuit for torus

getting increasingly smaller with frequency.very small for a very large variation of eo. Hence the time constant r is

-5OCR Output

domain shape is sketched in following figure.

limit is reached for w >—i. The spectrum of F and its corresponding time

The spectrum of F spans from 1 to (wr),_° = 3.16 . The high frequency

iw) =

1 Hmp = _13_ = AF .,.(w) (wl

computed before :The spectrum of the time derivative of the magnetising current was

kind of amplitude to phase modulation.interesting to note in passing that the double excited saturating tori perform atorus, hence the relation between ib and 9 is equally known. It may be

The spectrum of % is known from the properties of the magnetic9 dr

ib _ dim9 and ib can be approximated with :

The value of 6 is estimated in the following way. The relation between

rc 1+ ]2nQ‘r ibt

Z(2nQ) = ?..LR

voltage and the current to be measured. This then yields :The transfer impedance of a monitor is the ratio between the output

T l+]2nQ‘r rr l+j2nQ1.‘X/(2,19) = 4AR j2izQr A 2QAR j2nQr

modulator frequency. This yields for the periodic spectrum :This process is repeated every T/2 seconds where T is the period of the

1+ year1+ your

A£“vos): vb, - VH, : £—;—sin(w9)= ZARJLQ.

are combined:indeed. This point is important to consider if the two delayed step responsesof the 2 tori would simply be 29. As will be shown later 9 is very smallmagnetisation ahead in time. The total time difference between the responsesubjected to the opposite magnetisation except for ib, would shift itsthe presence of ib is called 6. A second torus identical to the first one andtake place but it will slightly be displaced in time. The time delay caused byassume that il, is much smaller than A. The same magnetisation change willelement is introduced, that is ib, the current to be measured. It is reasonable toby the spectral value of I,(co) calculated before. Now a third magnetisation

-6.

l+j2Qr OCR Output815 j2Qr Z 2Q = —E—2Qsl— " —-—-—‘( )R°- ( e )

For later comparison reasons the value at the second harmonic is selected:The spectrum of this transfer impedance rises steadily with frequency.

`r(2nQ) = 717 1+ 12nQr169 R ‘

The final expression for the transfer impedance becomes :

calculations give rm = 81:,,where 1,,, is defined by the properties of the magnetic toms. Computer

f(r) = I FLF(w)dw = i?

simplified form :covers the low frequency part. The result of the integral can be written in a

f (t)= }FLF(w)dw where it is understood that the integration only

be calculated as follows:The maximum value of the low frequency response in time domain can

present calculation with respect to the low frequency part.theoretically over a time which is infinitely short it can be neglected in thewhich yields a Dirac pulse at zero time. Since its activity extendsparticular dependence of wr on frequency. There is the high frequency part

The spectrum F ( co) is composed of two distinct parts due to the

Figure 1

Spectrum and shape of time derivative of magnetisation current

<m>

Jr)

f(t>Ftw) X

-7OCR Output

bandwidth. The value for the second harmonic is :The spectrum of this impedance is very peaked with a relatively small

]2nQt'i ' = ‘° ~ ...1% thm J. i2nQRC

4QRr

been introduced. The transfer impedance becomes:A new time constant rc = ROC related to the retarding capacitor has

m Cr= = 2r

L C

The magnetisation time follows:

rm 2n___ RC(wr)A = L =

This yields for the time derivative at t=O :

jwr(1 + jwRC)I ' = "”(w)

for the spectrum of the time derivative of the magnetising current is found:Following the same reasoning as in previous paragraph the expression

]2nQ1:1 V = ·* — rC . ” .;lff2"”’ + iznruec ‘»

The transfer impedance follows immediately :

Jwr

l+jCL)T . 1+.10JT+z = R-Ji 2 = R :>

parallel capacitor C:expression of the parallel circuit impedance is modified by the presence of aprocess. The same calculation as in previous paragraph is repeated. Thefrequencies so that the low frequencies are enhanced in the magnetisingcapacitor is added in parallel with the tori. It effectively shunts the hightime of magnetisation. To increase the low frequency part of the spectrum ain the order of several A. The presence or not of a few mA will not alter thephysical interpretation is very simple. Consider an infinitely fast current riseis dominated by the low frequency content of the magnetising current. The

In the analysis of previous paragraph it appears clearly that the response

4.2 Magnetic torus with capacitive shunt

second (n= 1) contribute to the useful signal.where s is a function of 2Q . Note that also harmonics higher than the

Figure 2 OCR Output

Monitor transfer impedance for a given modulator frequency Q

w/1000

010 20 30 40 50 60 70 80 90100

no ccpccitg;O-l

0.2

0.3

0.4

0.5

0.6

with capacitor

0.7

0.8

x 10

superiority in the lower frequency range.band nature of the capacitive arrangement appears clearly as well as itsimpedance at the second harmonic frequency 2Q exclusively. The narrow(Q = 2rc/T) as a function of radial frequency w. Figure 3 shows the transferFigure 2 shows the transfer impedance for a given modulator frequencyC is optimised experimentally to obtain the best resolution for 9:211500.set up for SPS lab monitor was assumed. It should be noted that the value ofrelated to the magnetic material Vitrovac for both cases while the capacitiveand without capacitor) in the following figures. The assumed parameters are

As an illustration a comparison is made between the two cases (with

toms without capacitive shunt.This valuc is much larger than thc second harmonic impedance for the

j2Qr

Z‘C(2Q)=i€T?m?;_.. z R0£;7T J + 7T 1 +25£€£&

-9OCR Output

error is caused by a difference in the two modulating tori with the result thatmode type and a perturbation caused by phase errors. The common mode

The first family can be subdivided into a perturbation of the common

of incoherent perturbations.families. The first one is the family of coherent perturbations and the second

The perturbations in a DC current monitor can be classified in two

S. Perturbations

frequency.resolution was the experimental criterion for selecting C for a fixedof C it yields the best resolution. as will be shown below, After all, bestcorrespond with the maximum impedance but in combination with the value

It is interesting to note that the chosen frequency is 2Q=2000tt does not,/1*,, TC

2Q =

can easily be computed with the following result:In order that the second harmonic frequency falls at the impedance peak

Monitor transfer impedance at second harmonic of modulator frequency

Figure3

20/1000

010 20 30 40 50 60 70 80 90100

0.1

0.2

O_3 no capacitor

0.4

0.5

0.6

O.7

_ weth ccpccitor0.8

O.9

-10OCR Output

z.<2¤>i = VCH! I

This signal level can be expressed in terms of measured intensity :

The common mode response at frequency Q is simply :

is called Aph.called Am, and the relative difference that is responsible for the phase errorsdifference that will be responsible for the generation of common mode ison the relative difference between the modulating tori. The relative

All the perturbations that will be considered in this paragraph depend

5.1 Coherent perturbations

excluded that phase switching errors also contribute.harmonic of the modulation frequency and its multiples. It is not totallyat the output. The perturbing frequency band is situated around the secondunavoidable differences in the tori (see common mode) this noise will appearsensor output which carries the difference signal. However due to theFor a perfectly matched pair of magnetic tori this noise would cancel in thefound in the excitation source following the principle of Occam’s razor [13].[7,12]. Therefore, the noise source for the monitor under scrutiny is to befor flux gates it has been argued that Barkhausen is an unlikely sourcethe passive monitor by classical noise sources in resistive material[l4]. Evenidentically the same. On top of that it is possible to explain the resolution ofthe DC monitor. Hence it is difficult to imagine that the origin of this noise isnoise level in practice which is at least an order of magnitude lower than inindication is that a passive transformer using exactly the same tori shows aThere are indications that the first source can be neglected. The maingenerated in the tori (Barkhausen) and noise coming from the modulator.case of flux gates [7]. Two sources can be considered: magnetic noiseThe origin of this noise is a matter for discussion. This is also true for thedefines the performance of the monitor from the point of view of resolution.

The family of the incoherent perturbations is caused by noise and

generated at the same frequency by a current flowing through the toroids.the second harmonic is not necessarily the same as the phase of the signalequivalent current. This is due to the fact that the phase of the offset signal atboth amusing and annoying that this offset cannot be compensated by itsthe modulation frequency and causes an offset in the monitor response. lt isdifferent delays. This perturbation is at the origin of a static response at twicedifference in the modulating tori. Here the two responses do not cancel due torejection are needed to eliminate them. The phase error is also caused by amay cause problems for the processing electronics and filters with goodproduces a signal at the modulation frequency. The amplitude of this signalthe amplitude responses of the two tori are not identical. This perturbation

-11OCR Output

The quadratic sum of the two terms yields:

. 5lph = ·iqAAph.(Ar)

the modulator switching circuit:The second contribution is related with random phase errors caused by

az} = §§(AmAiA)

delivered:modulator which is expressed as a fraction A5 of the current A/2 that is

The first estimation is related to the stability of the current source of the

monitor assembly.estimations concerning 5if, the noise current density at the input of the

In order to quantify the resolution it is necessary to make some

5.2 Incoherent perturbations (noise)

I _ bojf _·cuAAp,,

For the case with retarding capacitor the static off set becomes :

bof 4

}[ : :.5 °tori:

an expression for the off set current can be found for the case with bare

fb = -;-9

Since :

A9 = A ph T0.

error A8. This delay stems from a difference in 10 between the toroids:The relative tore matching error Ap}, is the major contributor to the delay

5 .1 .2 OfsetRoto

ibm 2 AMA E $(1- e")AmA.2Z Q r ( ) "

and the case with capacitive shunt gives:

Ms12,,s2¢uS(1- e *) ampbm[E AA E 92

For the bare tori case this yields:

-12OCR Output

will be at the expense of more power in the magnetisation circuit. TheThis limit is not absolute. The value of C can be chosen larger but this

TC _; ROC S2.5

hence for the maximum value of s (§ =1).This yields:magnetisation has to be fulfilled for the maximum value of the time constant,a rising function of frequency up to some maximum. The condition of fullquite large. As was pointed out before, the time constant of magnetisation ismodulator period. The frequency spectrum of the magnetisation process isimposing the condition that full excitation is guaranteed within half aexcitation frequency increases. The upper limit for C can be found bythis capacitor decreases more and more the current in the tori when theC. However, this will cause rapidly a problem for the magnetisation sinceapparently can be achieved by increasing rc, hence the value of the capacitorthe best performance the noise current should be as low as possible which

The last formula may lead to an erroneous conclusion. Indeed, to obtain

291;:0 4QrCif 5. =—-i—y{6`2 E-———y[5`2. lb" *L" L"

7IT

The result on the output noise is:Z rr

Z,_ _ 4QrCThe impedance ratio is:

5 ,2,2 Tcrus shuntcd with capacitor

6` = —;L- S`2. lbf! ln

_ The result on the output noise is:Z rc

Z! _ 16QrMThe impedance ratio is:

5,2,1 Bare magnetic tara

Z!5i,fn = 6i,f

current density 6ib,,2 in units of intensity to be measured:impedance This value divided by the transfer impedance yields the noise

The noise current 5if produces a voltage in the monitor assembly

. /F-/`l - 51E — (ACMAJ +·Ah2 2 (AT)2 {Tp.

-13OCR Output

Table 1 : Hardware data concerning DC monitors

Hzmodulation freouenc 500 I 7000 I 7000 I 500C (for 1 tum) 0.0087 I 0.0043 I 0.0043 I 0.0144

nFshunt capacitor 300 I 220 I 220 I 500optimum tc 250 I 250 I 250 I 250optimum modulation frequency Hz 1100 I 1600 I 1600 I 1600

14 I 10 I 10 I 10tums modulator coil 120 I 99 I 99 I 120turns (m) so I so I 80 I 20

mmtape width (w) 1010 I 10 I 5

monitor Hs s1>s I 158 LEP I 142 LEP I Lab unit

Table 1 summarises the other teclmical characteristics:

diameter (d)=O.215 mresistivity (p) =1.35u.Qmthickness (t) =25 am

common parameters are :one unit that has been tested extensively in the laboratory (Lab unit). Theirmonitor installed in the SPS (HS SPS i.e. high sensitivity SPS monitor) and

The data presented in this paragraph concern 2 monitors in LEP, one

6.1 Input data of a set of dyferent DC monitors

the material presented in the report.observations on the performance and finally the performance computed usingVitrovac 6025. Here follows a list of values of several parameters, a set ofare of interest contain toroids made of the same magnetic material, i.e.

Several DC monitors are installed in the SPS and LEP. The units that

6. Confrontation between analysis and observations

1OrM

rc = 25 rll

frequency Q follow:The optimum values for retarding time constant rc and modulator

,/ru rc29 =

transfer impedance. This value was computed before :It will clearly be an advantage to work at the maximum value of the

6zbn E 0.2,/6zf.lowest value for 5i;,,, :obtained value for C can be considered as an optimum and it will result in the

-14OCR Output

Table 3: Computed performance of SPS and LEP DC monitors

(*) computed for optimum value of C since real value C is an order of magnitude too large.ibm; (off SCI CUIYEHI) 7.5 I7.5 I 7.5 I 7.5i bm, (common mode) 120120 I96i;,,,(noise current density) 11A/v Hz 0.35 I0.35 I5Z, (transfer impedance) Q 0.001 I 0.029 I 0.015 I 0.00028no capacitive shan!ibm (off set current) 0.5 I 0.5 I 0.5 I 0.55i bm (common mode) 8.8 I 8,8 I 16ib,,(noise current density) ;1.A/ V Hz 0.24 I 0.24(*) I 0.24(*) I 0.24C ( maximum) 0.0021 I0.00022 I0.00046 |0.012stg (maximum) 800 I60 I60 I800rc (transfer impedance) Q 0.06 I 0.16 I 0.08 I 0.007

wgiacamcitive shun

s(2Q) 0.2 I 0.63 I 0.63 I 0.182200 I 1100 I550 I900

0.256 I 0.256 I0.l28 I0.064

monitor HS SPS I158LEP I142 LEP ILab unit

was added for the sake of comparison.are in following Table. The expected performance for the bare toroid case

The computed values based on the known or estimated input parameters

Table 2: Observed performance of DC monitors

0.2ibm ( off set current)0.6i bm (common mode)

noise current I 0•y0•4 I I 0•5 I0-007transfer impedance Z,C(1 turn) QI 0.037

monitor HS SPS I 158 LEP I 142 LEP ILab unit

summarised in next Table:A number of observations concerning capacitive loaded monitors are

6.2 Observed and computed performance figures

an estimation of the input noise density is derived : 6if = 0.8yA/~/IE.the magnetisation source in 1 kHz was taken to be Ai=0.001 [15]. From this

The excitation current was estimated at A=6 A p-p while the stability of

confirmed in [2].Am_=Ap,,=0.005 was a reasonable thing to do. These figures are alsothe test unit toroid of 0.008 was measured. It was concluded that putting

By injecting a perturbation inthe modulator a global mismatch between

values of ru between 7 ps and 14 ys. The average value of 10 ps is retained.the Lab unit. Measurements on toroids similar to the ones used for LEP gave

The magnetic time constant ru was measured for the HS SPS and for

-16OCR Output

double of that of ferrite.for similar permeability amorphous material has a resistivity that is nearly the

Amorphous soft material is preferred above ferrite. The reason is that

chosen at the theoretical maximum of the expectations.within the strategy of future work. Mixing interest and excitement a goal is

In the light of the preceding material it is worthwhile to tix an objective

7.2 Objective

regularly.measurement record a stored zero current reading which can be refreshedis also straightforward to eliminate the static offset by subtracting from eacheasy to do the synchronous detection in a dedicated DSP after the filtering. ltresolution of the ADC. Since the signal is already digitised it will be quiteamplifier that lifts the noise level of the monitor assembly above theThe digitalisation will have to be preceded by a low pass filtered (lOOkHz)bandwidth would yield a linear gain in resolution of more than a factor 3.keeps the even ones. Modern 16 bit ADC's with in the order of lOO kHzfilter characteristic is a cosine function which rejects the odd harmonics andpath before additive recombination with the second signal path. The resultantacquisition. A delay of half a modulator period is introduced in one signalharmonics. This can be performed as follows. The signal is split after digitalcan be done in a digital filter combined with the rejection of the odd

The combination of the even harmonics of the modulation frequency

linearly.with the root of the number of harmonics while the signal will increaseobviously the signal but also the noise. However the latter will only increase

Combining the signals of a number of even harmonics increases

of the performance.impedance. This observation may pave the way for a possible enhancementoptimum value, i.e. the second harmonic is at the maximum of the transferare present. It is assumed that frequency and retarding capacitor C are at theirloaded monitor is narrow banded but a number of higher (useful) harmonics

By examining Figure 2 it can be noticed that the response of the C

cs0luri0n with special processin

impossible that the obtained improvement lies between a factor 2 and 5.magnetic properties with more than two selected tori should be less. It is notmode of the composite toroid set are reduced. In general the dispersion of thecan be merged into a single one such that both the offset and the commonmodulator signal. A number of toroid pairs can be measured. Several pairshas to be determined with a transfer function measurement based on thedetermined in a straightforward fashion. The polarity of the common modemeasured on a spectrum analyser. The polarity of the offset can bepair of tori in the classical way both the offset and common mode can bealso the resultant noise current density will be diminished. After matching aOCR Outputmode and offset. lf their magnitude can be reduced it is to be expected that

-17OCR Output

set up. Thanks to them all.(Protvino). He also performed the measurements on the simplified bare tomsmeasurements on toroids at various frequencies were done by A. Loguinovmeasurements were given by B. Halvarsson and H. Jakob. MagneticJakob. The data on the SPS and LEP monitors including the noiseL. Disdier performed the measurements on the Lab unit with the help of H.

Many persons have contributed to the material presented in this report.

8. Acknowledgements.

requirement for this machine[17].loss of 109 particles in one LHC turn which has been a long standingLHC. This resolution and the available rise time makes it possible to detect acurrent for full bandwidth is then O.8,uA,or 0.45 109 particles in the fururefactor of 10 lowering the noise current density to 20nA/ ~/-171; . The noisemaximum bandwidth of 1500Hz. The resolution increase is expected to be aalready some experience is Vitrovac 6025 F with t‘,i== 10 us. This yields abandwidth a fast (small ru) is required. A typical material where we havewhich in tum is related to the magnetic property characterised by 1*,,. For high

The bandwidth of the device is determined by the modulation frequency

-13OCR Output

L. Burnod and D. Leroy, LHC Note 65, December 1987.17. Influence of beam losses on the LHC magnets,16. G. Gelato in DC transformers, February 1990.15. H. Jakob, private communication.

L. Vos, CERN SL/94»18, June 1994.14. The LEP monitor for the measurement of bunch intensity,13. B. Montague quoted by E. Keil in LEP note 257, August 1980.

R.M. Bozorth, D. Van Nostrand Co, 1951.

12. Ferromagnetism,J.R. Burger, IEEE Transactions on Magnetics, December 1972.

11. The Theoretical Output of a Ring Core Fluxgate Sensor,1984.B.B. Narod and R.D. Russell, IEEE Transactions on Magnetics, JulySensor,

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