High-loop-delay 6 th -order band-pass continuous-time sigma-delta modulators M. Javidan, J. Juillard and P. Benabes

This paper focuses on the design of high loop delay modulators for parallel sigma-delta conversion. Parallel converters, allowing a global low oversampling ratio, consist of several bandpass modulators with adjacent central frequencies. To ensure the global performance, the noise transfer function of each modulator must be adjusted regarding its central frequency. In this thematic a new topology of 6 th -order modulators based on weightedfeedforward techniques is developed. This topology offers an adequate control of the noise transfer function at each central frequency by simple means.

Additive signal paths are moreover proposed to obtain an auto-filtering signal transfer function. An optimization method is also developed to calculate the optimized coefficients of the modulators at different central frequencies.

The main concerns are improving the stability and reducing the sensitivity of the continuous-time circuit to analog imperfections. This is essential for parallel conversion since, in each channel, the modulator works at a central frequency which differs from the fourth of the sampling frequency. The performance of the optimized modulator is compared with its discrete-time counterpart with good argument.

Introduction

In broad band applications, many new approaches to achieve both highresolution and large-band converters have been proposed. One is parallel sigma-delta (Σ∆) conversion, which performs the required signal-to-noiseratio (SNR) in a wide frequency band without increasing the sample frequency (f s ) [START_REF] Eshraghi | A comparative analysis of parallel deltasigma ADC architectures[END_REF]. We explore, in the context of the VERSANUM project funded by the FRENCH ANR AFRU program, a novel technique to design parallel Σ∆ converters based on frequency-band-decomposition (FBD) technique [START_REF] Benabes | Extended frequency-bandsigma-delta A/D converter[END_REF]. The global oversampling ratio (OSR: defined as half the sample frequency divided by the converter bandwidth (∆f )) is decreased by putting in parallel high-order (≥ 4) modulators. Thus, each modulator passes one M th of the signal frequency band when there are M modulators. In this project the normalized frequency band of interest is between 0.2f s and 0.3f s resulting in an equivalent OSR equal to 5. For example, with 8 modulators in parallel, the OSR of each modulator must be equal to 40, resulting in a global precision of about 12 bits. Higher precision can be theoretically reached by increasing the OSR of each modulator but the power consumption and the complexity of signal re-composition algorithms increase. Here an OSR equal to 64 is chosen resulting theoretically into 14 bits of resolution by 13 parallel modulators.

6 th -order continuous-time (CT) band-pass single-stage Σ∆ modulators are good candidates in this thematic since they are high resolution converters, quite immune to coefficient errors and capable of working at high frequencies [START_REF] Candy | Oversampling delta-sigma data converters : theory, design, and simulations, Handbook[END_REF]. However, the sensitivity of the performance of CT circuits to analog imperfections (such as the excess loop delay) and the signaldependent stability of high-order modulators are the main obstacles to overcome [START_REF] Reddy | Fundamental limitations of continuous-time delta-sigma modulators due to clock jitter[END_REF], [START_REF] Oliaei | Design of continuous-time sigma-delta modulators with arbitrary feedback waveform[END_REF], [START_REF] Fischer | Alternative topologies for sigma-delta modulators-A comparative study[END_REF].

For high loop delay CT Σ∆ modulators, a methodology to calculate the CT loop filter (G * (s)) through its discrete-time (DT) counterpart (F (z)) is presented in [START_REF] Yahia | Bandpass sigma-delta modulators synthesis with high loop delay[END_REF]. Indeed there exist various methods and toolboxes to find the discrete-time transfer function corresponding to demands and the design of CT modulators may lean to this progress [START_REF] Hamoui | High-order multibit modulators and pseudo data-weighted-averaging in low-oversampling ∆Σ ADCs for broad-band applications[END_REF]. In [START_REF] Yahia | Bandpass sigma-delta modulators synthesis with high loop delay[END_REF] It is shown that G * (s) and F (z) can be linked by: Because of practical issues widely discussed in [START_REF] Javidan | A new method to synthesize and optimize band-pass delta-sigma modulators[END_REF], the implementation of the terms of D(z) which have a delay less than the DAC delay faces several problems and in most of cases they are neglected (Fig. 1.b). In (1) these terms correspond to a 1 z -1 , a 2 z -2 , ... and a m-1 z -(m-1) . As a result, the noise transfer function (NTF) and the signal transfer function (STF) of this design (Fig. 1.b), called all over the paper the initial design, do not match the original DT modulator. This results in resolution loss and stability issues.

F (z) = (1 -z -1 )Z T {L -1 [ G * (s)B(s) s ]} - m k=1 a k z -k D(z) , (1)
In recent studies, single-stage topologies are based on multi-feedback techniques [START_REF] Maghari | Single-loop Σ∆ modulator with extended dynamic range[END_REF], [START_REF] Van Engelen | A sixth-order continuous-time bandpass sigma-delta modulator for digital radio IF[END_REF], [START_REF] Yu | sigma-delta modulator employing SAW resonator as loop filter[END_REF], [START_REF] Ashry | Simple architecture for subsampling LCbased Σ∆ modulators[END_REF] inspired from [START_REF] Cherry | Excess Loop Delay in Continuous-Time Delta-Sigma Modulators[END_REF]. The deteriorated performance of the initial design (because of the neglected terms of D(Z)) is matched to the DT counterpart by tuning separately the pulses of two DACs in the feedback controlling the position of the poles of the NTF. The drawback is the sensitivity of the performance of high-order (≥ 4) modulators to nonlinearity of DACs. Although DAC linearity is achievable by correction methods such as dynamic element matching (DEM) [START_REF] Rakulijic | Tree-structured DEM DACs with arbitrary numbers of levels[END_REF], these methods result in increasing the size and the power consumption of the circuit as well as the loop delay. Moreover, at low OSR, DEM algorithm must be modified to prevent the occurrence of in-band signal-dependent tones in the modulator output spectrum [START_REF] Rakulijic | Tree-structured DEM DACs with arbitrary numbers of levels[END_REF]. The disadvantages of the linearization methods are doubled for multi-feedback topologies since two DACs are used.

Feedforward topologies with only one DAC are an alternative although their main inconvenient is a loop delay which is not a multiple of the clock period. We propose a new topology of 6 th -order modulators based on weighted feedforward techniques with only one DAC. An optimisation method employing the pulses of the DAC together with the modifiable gain stages is also developed to control the position of the poles of the NTF. Extra signal paths are moreover added to obtain a filtering STF without missing the advantage of implicit anti-aliasing filtering of CT Σ∆ modulators. Indeed, in real applications, the input signal of the converter consists of both the desired frequency band and a wide spectrum interferer. Non-filtering STF results in reducing the dynamic range of the modulator.

In section II the proposed topology is described and the governing equations of the NTF and the STF are given. It is shown that the performance of the initial design, obtained through [START_REF] Eshraghi | A comparative analysis of parallel deltasigma ADC architectures[END_REF], is deteriorated for central frequencies other than 0.25f s because of the absence of the neglected terms of D(z). This design is optimized by the developed method in section III to recover the performance. In section IV a design example is given for f s equal to 400 MHz. The scope of silicon implementation of the full system is also discussed. Finally conclusions are presented in section V.

The proposed topology for 6 th -order CT single-stage Σ∆ modulators is shown in Fig. 2. g i is the feedforward coefficient, H i is the resonator transfer function, k i is the additional signal path coefficient and a m , the last term of 1), compensates the excess loop delay. The main differences between this topology and other feedforward topologies are g 1 which increases significantly the flexibility to control the poles of the NTF without modifying the zeros and k i that modifies the STF without modifying the NTF.

D(z) in (

Noise transfer function

The loop filter transfer function (G(s)) of the proposed topology illustrated in Fig. 2 is governed by:

G(s) = H 1 (s) ((g 3 (s) + H 3 (s)) H 2 (s) + g 2 (s) + g 1 (s)H 3 (s)) , (2)
in which each function can be replaced by the behavioral model of the corresponding analog component. In the ideal case g i (s) is simple gain and

H i (s) is governed by b i s 2 + ω ri Q i
s+ω ri 2 (the transfer function of an ideal 2 th -order resonator with a finite quality factor (Q)), in which ω ri = 2πf ri and f ri is the resonance frequency of the resonator, and b i denotes the gain of the resonator.

For central frequencies (f c ) in the frequency band of interest (0.2f s < f c < 0.3f s ), loop delay between T s and 2T s and Q = 75, the analytically calculated parameters of G(s) to fit G * (s) are shown in Fig. 3.

D(z) = a 1 z -1 + a 2 z -2 . ( 3
)
The variation of a 1 , the non-implemented term of D(z), is given in Table 1.

M M = min {(1 + N T F (jω))} = S -1 (jω) , (4)
The interested reader can refer to [START_REF] Banyasz | A new gap metric for robustness measure and regulator design[END_REF]. As it is shown in Fig. 4, the resolution of the initial design corresponds to that of the DT modulator whereas the modulus margin does not. Indeed the absence of a 1 modifies the poles of the NTF while the zeros of the NTF are maintained fixed.

A small modulus margin indicates that the initial design is highly sensitive to imperfections for f c other than 0.25f s . As it is mentioned in the introduction, in many studies an extra feedback is used to compensate the performance loss of the initial design while in section 3 it is shown that the provided degrees of freedom by the proposed topology are sufficient to recover the performance.

Signal transfer function

The expression of the STF cannot be directly governed in the s or the z domains since the input of the STF is CT while its output is DT. In order to calculate analytically the STF, the signal filter (G x (s)) and the noise filter (F l (z)) must be separated (Fig. 5). A sampler is placed after G x (s)

Figure 5: System modifications to calculate the STF.

to ensure the DT behavior of the model. The modifications are done in the sense that an input signal at pulsation ω gives, after a possible aliasing, an output component at pulsation ω -2kπf s where -πf s < ω -2kπf s < πf s .

The expression of the STF can be then governed by:

ST F (jω) = G x (jω) 1 -F l (e jωT ) . (5)
For the topology of Fig. 2, G x (s) is as follows:

G x (s) = g x0 (s) + g x1 (s) + g x2 (s), (6)
in which g x0 (s) is the main signal path and g x1 (s) and g x2 (s) are the extra signal paths. The expression of g i (x) is governed by:

               g x0 (s) = H 1 (s) (g 2 + g 1 H 3 (s) + H 2 (s) (g 3 + H 3 (s))) , g x1 (s) = k 1 (H 2 (s) (g 3 + H 3 (s))) , g x2 (s) = k 2 H 3 (s). (7)
For f c = 0.25f s , Fig. 6 shows the STF when k 1 and k 2 are set to 0. The other parameters of the topology corresponds to the initial design (Fig. 3). The STF of feedforward topologies contains unwanted overshoots close to f c . Indeed the design of feedforward Σ∆ modulators has traditionally been focused on increasing the order of the NTF to obtain a high SNR without destabilizing the modulator and most of conventional modulators containing only the main signal path (g x0 (s)) presents STF overshoots close to f c . This results in decreasing the input dynamic range of the modulator.

The proposed topology presents the advantage of STF shaping by tuning k 1 and k 2 to reduce the overshoots. The developed method to increase the modulus margin while maintaining the resolution and to shape the STF is described in the next section.

Optimisation method

As it was mentioned in section 2.1, the absence of a 1 modifies the poles of the NTF which may leads to performance degradation and even instability (Fig. 4). To answer the requirements of FBD converters (in which several modulators work at different central frequencies [START_REF] Benabes | Extended frequency-bandsigma-delta A/D converter[END_REF]), the stability margin at f c other than 0.25f s must be improved considering analog imperfections.

In this regard the NTF and the STF are calculated by introducing in the loop filter transfer function (2) the system-level behavioral model of the analog components obtained from post-layout simulations. An optimisation method is developed to increase the modulus margin while maintaining the resolution and to shape the STF. This method can be used for other structures by calculating the proper NTF and STF.

NTF optimization

The vector of the modifiable parameters to optimize the modulus margin

(M M ) is: µ = [d, a m , g 1 , g 2 , g 3 , b 2 ] , (8)
in which d corresponds to the loop delay and g i and b 2 denote the DC gain of the feedforward coefficients and H 2 (s) respectively. It should be noted that b 1 and b 3 are not independent degrees of freedom. The starting point of the iterations, at each f c , is the parameters of the initial design (Fig. 3). The optimization has to ensure a sufficient resolution (SNR) while maintaining certain immunity to analog mismatches (large modulus margin). We introduce the optimization criterion (κ) as :

κ = (1 -M M CT ) + λ 1 N B DT -N B CT 2 + ζ, (9)
in which N B DT and N B CT are the bit resolution of the original DT and the CT modulator respectively. M M CT corresponds to the modulus margin of the CT modulator. Theoretically the modulus margin cannot exceed one. ζ is a regularization term given by:

ζ = λ 2 i ∂((1 -M M CT ) + λ 1 N B DT -N B CT 2 ) ∂µ i . (10)
Although the exact partial derivatives cannot be calculated, a finite differ-

STF optimization

The second objective of the optimisation method consists in shaping the STF by adjusting the additive signal paths coefficients (k 1 and k 2 ). The proposed solution in this work (Fig. 7) consists in optimizing k 1 and k 2 to minimize the error between the ideal form and the real form of the STF.

The error function to minimize in order to obtain a unity-gain STF can be governed by:

EF = 3 i=1 ef i , (11)
in which ef 1 , ef 2 and ef 3 are given by:

             ef 1 = fc+ ∆f 2 fc-∆f 2 ( 1 -Gx(jω) 1-F l (e jω )
df ),

ef 2 = fs fc+ ∆f 2 ( Gx(jω) 1-F l (e jω )
df ),

ef 3 = fc-∆f 2 0 ( Gx(jω) 1-F l (e jω ) df ). ( 12
)
and ∆f is equal to f s /OSR. Once this objective is attained, the modulator is an auto-filtering system and it is less dependent on the input filter of the modulator to reduce interferer. Another possibility is to use a constrained optimization. In this case, the function to minimize is the maximum of the modulus of the STF out of band (∆f )). The constraint is the minimum of the modulus of the STF in band which must be higher than one. Both methods give almost identical results.

4 Design example

Behavioral models

In [START_REF] Benabes | Extended frequency-bandsigma-delta A/D converter[END_REF] it is shown that for broadband applications with low OSR, a large Q-factor (higher than 75 ) is necessary to achieve the required SNR. A large Q-factor can be obtained using piezo-electric resonators such as surface acoustic wave (SAW) [START_REF] Yu | sigma-delta modulator employing SAW resonator as loop filter[END_REF] or lamb wave resonators (LWR) [START_REF] Desvergne | Intermediate frequency lamb wave resonators and filters for RF receiver architectures[END_REF]. Their resonant frequency is also less sensitive to process and temperature variations. However they have their own disadvantages such as harmonic content and the anti-resonance frequency (Fig. 8.c). In [START_REF] Yu | sigma-delta modulator employing SAW resonator as loop filter[END_REF], a differential struc-

Simulation results

Let us consider a 6 th -order Σ∆ modulator with OSR = 64. The sample frequency (f s ) is equal to 400MHz. In the context of VERSANUM project we intend to employ LWRs performing a Q-factor equal to 75 [START_REF] Desvergne | Intermediate frequency lamb wave resonators and filters for RF receiver architectures[END_REF]. Although a large Q-factor is considered, it is not a fundamental requirement of the proposed approach. The parameters of the equivalent model of the electronic control circuit (Fig. 8.b) are extracted from post-layout simulation presented in [START_REF] Javidan | Design of electronic control circuit of piezo-electric resonators for Σ∆ modulator loop in AMS Bi-CMOS 0.35µm[END_REF] containing the electrical response of the LWR [START_REF] Desvergne | Intermediate frequency lamb wave resonators and filters for RF receiver architectures[END_REF]. Through the worst cases simulations, in AMS Bi-CMOS 0.35µm technology, the maximum error on C c is up to 6%, the cut-off frequency of gain stages (ω p ) is down to 3f s , the real part of Z I and Z O is up to 40Ω and finally the error on the DC gain of the gain stages (γ) is up to 20%.

The parameters of the initial design and the optimized design are presented in Table 2. The initial design is unstable with analog imperfections while the stability is recovered for the optimized design with the same imperfections.

However the resolution is reduced by 2-bits compared with the original DT modulator. The calculated values of k i to achieve a filtering STF across the frequency band of interest (0.2f s < f c < 0.3f s ) is also shown in Fig. 9.a.

For f c = 0.25f s , the optimized STF (k 1 = 4.95, k 2 = -8) is compared with the initial one (k 1 &k 2 = 0). The amplitude axis is in logarithmic mode to prove that the additive paths have no influence on the implicit antialiasing filtering characteristic of the modulator.

The SNR of the optimized modulator and the output signal spectrum are shown in Fig. 10.a and Fig. 10.b respectively for f c = 0.25f s considering the imperfections. To prove the reliability of this approach, the sensitivity of the optimized design to imperfections is compared to that of the initial design.

The position of the critical poles of the NTF are compared in Fig. 11.a, for f c = 0.25f s before and after the optimisation. As it is shown, some poles of the initial NTF lie outside the unit circle. So the modulator is unstable Here we have no intention to compare the proposed methodology with others since the results are obtained from a behavioral simulation. However it is shown that the proposed methodology is theoretically able to find the optimal parameters ensuring the performance of the modulator despite of

Converter Implementation

Although the results are interesting in terms of stability and resolution, implementation issues must be overcome. The values of the optimized k 1 and k 2 are large. This complicates the design of the corresponding analog circuits. Moreover, the design of a tunable DAC delay is difficult since the linearity of the DAC is a critical parameter of high-order Σ∆ modulators.

The digital part of the project has been studied along the VERSANUM project [START_REF] Benabes | Extended frequency-bandsigma-delta A/D converter[END_REF]. It was shown that in a 0.35µm technology, the area of the digital part is around 0.8mm 2 for each modulator, resulting in 6mm 2 for 8 modulators. Using more recent technologies (0.65 nm), this area could be reduced 0.2mm 2 for the whole converter. Several techniques, specially lamb wave resonators or BST filters (based on Ba x Sr 1-x T iO3 materials), are studied to implement the resonators. However all of them are off-chip components increasing the circuit size (upto 1mm 2 ) and the sensitivity to the environment noise.

All modulators plus the digital part could be integrated in a single chip although the resonators are for the moment off-chip. This integration is in the scope of the European ARTEMOS project [19].

Conclusion

A new topology for 6 th -order CT single-stage sigma-delta modulators based on weighted-feedforward techniques was proposed. This topology offers an adequate control of the NTF by feedforward coefficients. Another advantage of this topology is its filtering STF thanks to the additive signal paths. It was shown that for high loop delay structures, the required system modifications due practical obstacles results in stability issues specially for f c other than 0.25f s . Moreover it was shown that the CT modulator is highly sensitive to analog imperfections. A numerical optimisation method was developed to reduce the sensitivity to imperfections while maintaining the resolution. Major analog circuit imperfections such as the anti-resonance frequency of the piezo-electric resonators are modeled and are introduced in the optmisation algorithm. Then, the modifiable parameters of the modulator were determined through the optimisation method. The results of similations prove the reliability of this approach.

in which L - 1

 1 denotes the inverse Laplace transform, B(s) denotes the Laplace transform of the impulse response of the digital to analog converter (DAC) including the ADC delay and Z T is the Z-transform with sampling period equal to T s . D(z) is introduced to ensure the existence of a solution for (1) i.e. finding an identification in z -k term. It can be considered as additive feedback terms between the modulator output and the ADC input (Fig.1.a).

Figure 1 :

 1 Figure 1: Continuous-time modulator with DAC delay: a possible implementation of D(z) (a) and the simplified topology (b).

Figure 2 :

 2 Figure 2: Proposed filtering STF weighted-feedforward topology.

Figure 3 :

 3 Figure 3: Parameters of the initial design (Fig.1.b) to fit G * (s).

b 1

 1 and b 3 are chosen arbitrarily equal to 1 and 0.2 respectively since they are not independent degrees of freedom. a 2 is the last term of D(z) governed by[START_REF] Candy | Oversampling delta-sigma data converters : theory, design, and simulations, Handbook[END_REF] for a loop delay between T s and 2T s .

a 1 Figure 4 :

 14 Figure 4: Comparison between the performance of the initial design and the original DT modulator.

Figure 6 :

 6 Figure 6: STF for k 1 = k 2 = 0 at f c = 0.25f s , the frequency axes is normalized by f s .

  ence scheme is used to approximate ζ. Without ζ, the optimisation criterion (κ) has several local minima and a global minimum. Some of them are not reasonable answers since the derivative of κ versus some parameters of µ may be large. In such a case, there is a strong chance for performance degradation because of analog imperfections. It is important to study the global behavior of κ around the minima in function of modifiable parameters to obtain the reasonable ones. ζ is introduced to meet this goal. λ 1 and λ 2 are hyper parameters the values of which must be set by the user who must trade large modulus margin against resolution. Practical values are given in the design example. A gridding method in association with the "Fmin search" function of MATLAB can be used to find the answers.

Figure 7 :

 7 Figure 7: principle of k i optimization.

Figure 8 :

 8 Figure 8: (a): Electronic control circuit to remove the anti-resonance frequency. (b): Equivalent electrical model. (c) Frequency response of a typical LWR.

Figure 9 :

 9 Figure 9: (a): Calculated k 1 and k 2 across the frequency band of interest. (b): STF of the modulator before and after optimisation.

Figure 10 :

 10 Figure 10: (a): SNR of the optimized design. (b): Output signal spectrum of the optimized design.

Figure 11 :

 11 Figure 11: (a): Position of the critical poles of the NTF of the optimized and initial design. (b): Influence of g 1 and g 3 on the modulus margin of the optimized modulator. (c): Sensitivity of the STF to k 1 and k 2 variation. (d): Sensitivity of the optimized and the initial design to C c errors. .

Table 2 :

 2 The modifiable parameters, the modulus margin (MM) and the bit

	resolution (NB) before (Int.) and after (Opt.) optimisation
	f c	0.21f s	0.25f s	0.29f s
		Int. Opt. Int. Opt. Int. Opt.
	b 2	0.68 0.48 0.71 0.28 0.75 0.32
	g 1	1.10 0.75 0.68 1.24 0.15 0.17
	g 2	1.71 2.16 1.62 1.43 1.58 1.43
	g 3	0.80 0.78 0.88 0.96 1.00 1.11
	d * T s	1.8	1.1	1.4	1.0	1.1	1.0
	a m	0.95 1.00 0.58 0.51 0.21 0.22
	M M	-	0.58	-	0.62	-	0.61
	N B	-	16.4	-	16.2	-	15.9

Acknowledgements

This work was supported in part by the ANR (National French Research Agency)within the VERSANUM project. M. Javidan (LIP6 Lab, Pierre and Marie Curie University, 4 place Jussieu, Paris, France) J. Juillard (SSE Lab, Supelec, Gif/Yvette, France) P. Benabes (SSE Lab, Supelec, Gif/Yvette, France) E-mail: mohammad.javidan@lip6.fr


Mohamed Lehsaini
email: m_lehsaini@mail.univ-tlemcen.dz

Herve Guyennet
email: herve.guyennet@femto-st.fr

Improvement of LEACH for fault tolerance in sensor networks

Keywords: LEACH, FT1-LEACH, FT2-LEACH, Fault-tolerance, Checkpoint, WSN

In wireless sensor networks, failures occur due to energy depletion, environmental hazards, hardware failure, communication link errors, etc. These failures could prevent them to accomplish their tasks. Moreover, most routing protocols are designed for ideal environment such as LEACH. Hence, if nodes fail the performance of these protocols degrade. In this context, we propose two improved versions of LEACH so that it becomes a fault-tolerant protocol. In the first version, we propose a clustered architecture for LEACH in which there are two cluster-heads in each cluster: one is primary (CHp) and the other is secondary (CHs). In the second version, we propose to use the checkpoint technique. Finally, we conducted several simulations to illustrate the performance our contribution and compared obtained results to LEACH protocol in a realistic environment.

Introduction

Wireless sensor networks (WSN) consist of a large number of low-cost and lowpowered sensor devices, communicating with each other through wireless links and collaborating to accomplish a common task. Sensors can be deployed over a geographical area for monitoring physical phenomena like temperature, humidity, vibrations, seismic events, and so on [START_REF] Akyildiz | Wireless sensor networks: a survey[END_REF]. Now, WSN are permeating a variety of application domains such as avionics, environmental monitoring, structural sensing, telemedicine, space exploration, and command and control. WSN should have a long lifetime to accomplish the application requirements. However, In addition to resource constraints in WSN, the failure of sensor nodes is almost unavoidable due to energy depletion since they have been usually deployed in hostile environments and their batteries cannot be recharged or replaced, hardware failure, communication link errors, and so on [START_REF] Woo | Taming the underlying challenges of reliable multihop routing in sensor networks[END_REF][START_REF] Paradis | A Survey of Fault Management inWireless Sensor Networks[END_REF][START_REF] Ammari | Fault tolerance measures for large-scale wireless sensor networks[END_REF]. Therefore, in WSN, fault tolerance has become as important as other performance metrics such as energy efficiency, latency and accuracy.

In general, the consequence of these failures is that a node becomes unreachable, violates certain conditions that are essential for providing a service or returns false readings which could cause a disaster especially in critical applications. Furthermore, the above fault scenarios are worsened by the multihop communication nature of WSN. It often takes several hops to deliver data from a source node to the remote base station; therefore, failure of a single node or link may lead to missing reports from the entire region of WSN.

Therefore, since sensors are prone to failure, fault tolerance should be seriously considered in many sensing applications which are generally required to be faulttolerant, where any pair of sensors is usually connected by multiple communication paths. Recently, several studies have dealt with fault tolerance in WSN, particularly in the routing process. Moreover, these works focus on the detection and recovery of failures in WSN.

We evaluate LEACH in a realistic environment in which sensor nodes can fail and links may be lost. Then, we propose two improved versions FT1-LEACH and FT2-LEACH of LEACH so it is fault tolerant. FT1-LEACH involves two cluster-heads in each cluster one is primary and the other secondary and FT2-LEACH use the checkpoint technique. Moreover, cluster-heads are elected based on their capabilities. Furthermore, in clusters, main cluster-heads and their vice cooperate with each other to reduce extra costs by sending only one copy of sensed data to the sink.

FT1-LEACH and FT2-LEACH could tolerate links failures and therefore guarantee routing reliability in WSN while dissipating less extra energy and time. Finally, we conducted several simulations to demonstrate the performance of our contribution and we compared obtained results with those of LEACH [START_REF] Heinzelman | Energy-efficient communication protocol for wireless microsensor networks[END_REF] in a realist environment.

The rest of this paper is organized as follows: Section 2 presents briefly the protocol LEACH; in Section 3, we propose two improved versions of LEACH; Section 4 illustrates performance analysis of LEACH and the proposed schemes in a realistic environment. Finally, we conclude our paper and discuss future research work in Section 5.

Presentation of LEACH

LEACH (Low Energy Adaptive Clustering Hierarchy) is a hierarchical cluster-based routing protocol for wireless sensor networks which partitions the nodes into clusters.

In each cluster a dedicated node called Cluster-head (CH) and other nodes are cluster members. CH is responsible for creating and manipulating a TDMA schedule and sending aggregated data from nodes to the base station using CDMA technique. Moreover, this protocol is divided into rounds and each round consists of two phases:

Setup Phase

During this phase, cluster formation takes place. In which, each sensor node decides independently of other nodes if it will become a CH or not. This decision takes into account when the node served as a CH for the last time i.e. the node that has not been a CH for long time is more likely to elect itself as a CH.

Once CHs are elected, they inform their neighborhood with an advertisement packet that they become CHs. Each non-CH node picks the advertisement packet with the strongest received signal strength and it sends the message "Join Packet" to request to join its corresponding CH.

After this process, the CH knows the number of member nodes and their IDs. Based on all messages received within the cluster, the CH creates a TDMA schedule and broadcast it to its cluster members. Then, it picks a CSMA code randomly to avoid interference when transmitting data to the base station.

Steady-state phase

During this phase, data transmission begins. Sensor nodes send their data collected during their allocated TDMA slot to their respective CHs. The radio of each non-CH node can be turned off until the nodes allocated TDMA slot, thus minimizing energy dissipation in these nodes. When all the data has been received, the corresponding CH aggregates these data and sends them to the remote base station as presented by Fig. 1.

Fig. 1. Cluster formation in LEACH

LEACH is able to perform local aggregation of data in each cluster to reduce the amount of data that transmitted to the base station. Although LEACH protocol acts in a good manner, it suffers from many drawbacks such like;

• CH selection is randomly, that does not take into account energy consumption and CHs can quickly deplete their batteries and hence they stop working and cause holes in the target area. • It cannot cover a large area when some sensor nodes fail.

Since LEACH has many drawbacks, many works have been done to make this protocol performs better but to the best our knowledge there is no work dealing with faulttolerance in LEACH.

Contribution

In most routing protocols, fault-tolerance was not considered particularly in LEACH.

In this context, we propose two improved versions of LEACH protocol so that it becomes a fault-tolerant protocol. In the first version called FT1-LEACH, we propose a clustered architecture for LEACH in which there are two cluster-heads in each cluster: one is primary (CHp) and the other is secondary (CHs). In the second version, we propose to use the checkpoint technique to make LEACH as a fault-tolerant protocol.

Contribution 1: FT1-LEACH

FT1-LEACH is performed in three consecutive phases:

Cluster formation. This phase is performed in two steps:

Election of primary cluster-heads (CHp).

The election of primary cluster-heads is made in the same way as in LEACH based on the probability of being cluster-heads during this period.

Election of secondary cluster-heads (CHs).

After the election of CHp, this step begins wherein each sensor calculates its weight which is a combination of 2-density and residual energy as presented in Eq. ( 1) We involve 2-density factor in the purpose to generate clusters whose members are linked with cluster-heads and remaining energy parameter to select the nodes with more energy in their 2-neighborhood. Then, each cluster member generates a 'Hello' message including two extra fields addition to other regular contents: Weight and CHp and broadcast it as well as it eavesdrops its neighbor's 'Hello' message. The node with the largest weight in each cluster is elected as secondary cluster-head (CHs).

ℎ = * + * ∧ + = 1 (1)
The values of α and β are chosen depending on the application. For example if we want to favor the node that has more energy as cluster-head we would attribute great value to β.

Routing paths.

When a node detects a relevant event, it sends it to its corresponding cluster-heads (CHp and CHs). If the primary cluster-head does not send to the remote base station within a threshold time interval, the secondary cluster-head considers it that is down and it sends data to the base station.

There are two kinds of routing:

Intra-cluster.
Cluster members do not transmit data collected directly to the base station but they send them to their respective Cluster-heads (CHp and CHv).

CH-to-BS .

In each cluster, primary cluster-head is responsible to transmit the aggregated data to the remote base station and if they do not perform this task within a defined time interval the secondary cluster-head considers that the primary cluster-head is down and it sends information to the base station.

Contribution 2: FT2-LEACH

Our second contribution is based on the checkpoint technique which is considered the most typical approach to tolerate failures in parallel and distributed systems. By writing checkpoints into stable storage periodically, the checkpoint approach is able to tolerate the failure of the whole network. The advantage of this approach is that it is very general and is able to tolerate the failure of the whole network. However, the limitations of checkpoint approach are that it generally needs stable storage to save a global consistent state periodically and that it aborts all survival processes even if only one of many processes failed.

In this context, we use the base station to store availability information about cluster-heads. Each cluster-head sends periodically a message to the base station. If during a period, the base station does not receive a message from a clusterhead, it is considered as defective. As a result, the base station transmits a message to the cluster concerned to elect a cluster-head among its members. The member which has the greatest weight based on its remaining energy and its density parameter as presented in Equation ( 2), becomes cluster-head.

ℎ = +

(2)

Evaluation and simulation results

In our experiments, we conducted extensive simulations to evaluate FT1-LEACH and FT2-LEACH performance and compare them with LEACH in terms respectively of the ratio of successful reception at the base station during the network's lifetime and energy consumption. To achieve these goals, the simulations have been performed in NS-2 [START_REF]Network Simulator, World Wide Web[END_REF] using the MIT_uAMPS [7]. We have carried out these simulations with the same scenario presented in LEACH in order to illustrate the performance of our contribution. Hence, we considered a network topology with 100 non-mobile sensor nodes with a sensing range of 25 meters. Sensor nodes are placed randomly in a 100 m×100 m square area by using an uniform distribution function, and the remote base station is located at position x = 50, y = 125, i.e. the base station was placed 75 meters outside the area where the sensor nodes were deployed. At the beginning of the simulation, all the sensor nodes had an equal amount of energy i.e. the sensor nodes started with 2 Joules of energy. We note that system lifetime is defined as the time when last sensor dies in the sensor network.

The simulations were performed until all the sensors in the network consumed their energy and the average values were calculated after each round whose duration is 20 seconds. This duration represents the cluster timeout. It is used to prolong network lifetime and balance energy deviation among all its sensors. On expiry of this period, FT-LEACH1 and FT-LEACH2 triggered the cluster-head's election process again. Moreover, we used the same energy parameters and radio model as discussed in [START_REF] Heinzelman | An application-specific protocol architecture for wireless microsensor networks[END_REF], wherein energy consumption is mainly divided into two parts: receiving and transmitting messages. The transmission energy consumption requires additional energy to amplify the signal according to the distance from the destination. Thus, to transmit a k-bit message to a distance d, the radio expends energy (E Tx ) as described by the formula (3), where ε elec is the energy consumed for radio electronics, ε friss-amp and ε two- ray-amp for an amplifier. The reception energy consumption is E Rx = ε elec × k. Fig. 3 shows that the ratio of successfully received packets to the base station is higher than in LEACH because in LEACH, if a cluster-head stops working information will not be forwarded to the base station while in LEACH-FT1 if the main cluster-head is down its vice transmits the information to the base station. However, in LEACH-FT2, a cluster-head may fail before the end of the warning period the base station. 4 illustrates that in FT1-LEACH and FT2-LEACH, the amount of packets received at the base station during network lifetime is higher than in LEACH because in LEACH, if a cluster-head stops working information will not be forwarded to the base station and hence the energy will be lost without sending information. Furthermore, in FT1-LEACH and FT2-LEACH if the main cluster-head is down its vice transmits the information to the base station and hence the energy consumed reflects a transmission.

Conclusion

The evaluation of LEACH in a realistic environment showed that LEACH loses performance when some nodes fail. In this context, we have proposed two improved versions of LEACH so it becomes a fault-tolerant protocol. Simulation results showed that our contributions have improved the performance of LEACH in terms of number of packets successfully received at the base station and the energy to send these packets to the base station.

Fig. 2 .

 2 Fig. 2. Cluster formation in FT1-LEACH

=!( 3 )

 3 "!# * $ + %&'(()*+, * $ * -< /&0((01!& !"!# * $ + 230)&*4)*+, * $ * 5 -≥ /&0((01!& 7 Simulated model parameters are set as shown in

Fig. 3 .

 3 Fig. 3. Ratio of successful reception with different failure rates

Fig. 4 .

 4 Fig. 4. Amount of packets received at the sink during network lifetime

Table 2 .

 2 The data size were 500 bytes/message plus a header of 25 bytes. The message size to be transmitted was:

	$ = 500 :	+ 25 :	× 8 = 4 200 :

Table 1 .

 1 Model Parameters

	Parameter	Value
	Network grid	(0,0) x (100,100)
	Base Station	(50,125)
	ε elec	50 nJ/bit
	ε friss-amp	10 pJ/bit
	ε two-ray-amp	0.0013 pJ/bit
	d Crossover	87 m
	Data packet size	500 bytes
	Packet Header size	25 bytes
	Intial energy per node	2 J
	Number of nodes (N)


D Märk

C Teyssier

R Fillol

H Abdoul-Carime

B Farizon

M Farizon

T D Märk

A novel "COrrelated Ion and Neutral Time OfFlight" Method: event-by-event detection of neutral and charged fragments in Collision Induced Dissociation (CID) of mass selected ions

    A novel "Correlated Ion and Neutral Time Of Flight" Method: event-by-event detection of neutral and charged fragments in Collision Induced Dissociation (CID) of mass selected ions C.

I. Introduction

Mass spectrometry is nowadays a standard technique used in many fundamental and applied areas of science. As an analytical technique, it is used in diverse fields such as for the detection of drugs 1 in forensic applications, for the controllingof processes 2 in food production, or for the analysis during microchips manufacturing processes 3 in the field of nanotechnology.One analytical method in mass spectrometry involves Collision Induced Dissociation (CID) where a primary molecular ion dissociates into secondary fragments after collision with a gas target. Indeed, the CID technique isalso a powerful tool in physics and chemistry to shed light onthe nature of ion collision reactions present in many fundamental and technical phenomena (e.g., interstellar media, planetary ionospheres, plasmas). Moreover, it is widely applied in analytical chemistry to elucidate the identity and the nature of molecular and cluster ions via MS/MS spectrometry 4 . Although so far limited to the detection and identification of the produced ion fragments in recent studies it has been extended to the analysis of ions formed in single events 5 or to the detection of neutrals species 6 . Nevertheless directly monitoring all ionized and neutral fragments produced and their correlations within a single fragmentation eventas will be described in the following-is a major step towards the complete description of the physics and chemistry of the reaction.

Here a new type of mass spectrometry technique, namedCOINTOF (COrrelatedIon and Neutral Time OfFlights) mass spectrometry developed in our laboratory [START_REF] Farizon | Method for tandem time of flight analysis and analysis appliance using said method (EN). / Procédé d'analyse à temps de vol en tandem et appareil d'analyse en faisant application (FR)[END_REF] is presented.This method allows the exploration offragmentationprocesses by recording all ionized and neutral productsin a single dissociation event of an individual precursor ion. Detailed information on the physics of the dissociation process is obtained by a statistical analysis of an ensemble of recorded events. This new method is illustrated in the following forthe case of CID of protonated water cluster ions.

II. Principle of the COINTOF method

The principle of the method is presented in Figure 1. As the COINTOF technique is a part of an MS-MS technique, a prerequisite to COINTOF is the production of a mass and energy selected beam of parent (precursor) ions. This production of an intense mass and energy selected ion beam has been thoroughly described elsewhere 8 . Briefly, protonated water clusters are produced by electron impact in a supersonic nozzle expansion of water vapor.

They are accelerated to an energy between 2 to 8 keVand mass selected by a double focusing sector field mass spectrometer 9 . For the present CID experiment, the energy and massselected H + (H 2 O) n beam crosses an effusive argon gas jet whose density is controlled in such a way as to insure single collision conditions in the CID region. It is noteworthy however, that the precursor ions can collide with other type of particles (protons, ions, electrons or photons) at the collision point.The newly designed time of flight COINTOF apparatus is mounted right after the collisionregion along the direction of the incident beam as shown in Fig. 1. A single dissociative collision of a H + (H 2 O) n parent ion with an Ar atom will in general produce a daughter ion and one or more neutral fragments. This daughter ionis then extracted from the collision area and accelerated through 1.8kV before reaching a field free time of flight TOF zone.Neutral fragments emerging from the collision zone however will not be affected by this acceleration field and remain after the collision close tothe initial velocity of the parent ion (except for small changes due to additional kinetic energy released in the collision process itself, see below). All the fragments (ionized and neutral) are then detected by the one Micro Channel Plate detector (MCP, Hamamatsu) with the charged fragment arriving significantly earlier than the neutral species. The MCP set-up is designed to ensure the collection/detection of all the fragments by this detector. The signals produced are sampled by a fast Analog to Digital Converter (ADC8 GHW/10bits fromAcqiris®, Agilent) and it is recorded without dead time during a given arrival time window. The intensity of the initial parent ion beam is controlled in such a way as to ensure that only the fragments of one single parent ion can reach the detector during the acquisitiontime window. Therefore, the correlation between the arrival times of the charged and neutral fragments resulting from the dissociation of one single parent ion can be recorded. This correlation is determined consecutively for a large number of dissociation events.

III. Description of the COINTOF detector

The COINTOF detector is based on theWiley-McLarentype 10 timeofflight principle.Itconsistsofthreeseparatezoneswith different values of electric fields(see Figure 1).Thefirstzoneis theextractionzone andthesecondthe acceleration zone.Thecollision induced dissociation takes placeatthecenteroftheextraction zonethat is the crossing point between the cluster ion beam and the neutral target beam. In the present CID experiments argon or helium is used as a neutral target gas and theneutral gas jet has a maximum extent of 2mm at the crossing point 11 .Since all fragments (neutral and ionized) produced after dissociation have a velocity close to the velocity of the parent ion, the use of an extraction voltage is a priori not a mandatory requirement. Nevertheless the charged products are extracted by an electric field applied and after reaching the acceleration zone accelerated further by an acceleration field produced bya series of electrodes which provide ahomogenous electric field in this zone.

Therefore any charged specieswill be accelerated by the same electric field and thus acquire on top of the initial velocity an additional velocity characteristic of its mass/charge ratio.

After this acceleration zone, all species travel through afield free time of flight zone before reaching the MCP detector.This TOF zoneconsists of a drift tube of 150 mm length held at the acceleration potential.Detection is carried out with a MCP detector operated with a difference voltage of 1700 V and positioned 40 mm behind this field free zone. In the present casewe used a pair of MicroChannel Plates(MCP-F4293-07-Hamamatsu) with an effective area of 20mm in diameter and with channel diameters of 12µm mounted in a Chevronlike fashion. The MCP signal is collected on a single anode. It should be noted that this anode can be replaced by wire anodes, to determine the exact position of impact of the collision products on the detector.

One of the key points in the COINTOF technique is that the parent ions, in the present case protonated water cluster ions,have an energy prior to collision of 2 keV up to 8 keVand this high energy ensures that after fragmentation both ionized and neutral products are detectable on the detector because both will lead upon collision at the entrance plate of the MCP to the emission of secondary electrons which are then amplified by the channel plates. It must be underlined though that neutral products are notaccelerated after the interaction zone while the charged species receive an additional energy due to acceleration in the electric field applied. The velocity of the neutral products is close to the velocity of the parent ion.

Neverthelessthe neutral products from the parent ion reach the detector with sufficient energy (at least 2 keV) to be detected and they are well separated in their arrival time from the ionized fragments which are arriving much earlier due to the additional energy drawn from the accelerating field. It is clear that the present technique is limited to studies where the initial collision energy is at least 2 keV, because below this energy the efficiency for emission of secondary electrons at the entrance plate of the MCP is too small.

IV. Simulation of the COINTOF geometry

Thenecessary geometryofthepresent timeofflight set-upand the corresponding trajectoriesofthe particles has been calculatedusing the charged particleoptics simulationsoftware,SIMION® [START_REF] Dahl | SIMION® 3D Version 7.0[END_REF] .Figure 2showsthepresent COINTOF detector simulated bySIMION®showingtheequipotentiallines(inblue)in the three different zones and voltages applied.As mentioned above the produced ions and neutrals will have after the collision the velocity of the parent ion that is they will have a kinetic energy in proportion of their mass to the mass of the parent ion. These fragment kinetic energies will be modified in case of ionized fragments by the accelerating field and in addition by the kinetic energy released (KER)during the fragmentation process.This KER may amount to up to several 100 meV [START_REF] Laskin | [END_REF] (i.e., typical H bond energies). This energy ishowever negligibleto a first approximationin comparison to thekineticenergyofthefragments(fractionofkeV) and the energy gained by the accelerating field (1.8 keV). Nevertheless,this additional KER will lead to an additional broadening of the measured distribution of the time difference between the arrival times of the ionized and the neutral products. On the other hand, the mean time difference between ionized fragment and the neutral fragments is directly related to the mass of the ionized(and accelerated) fragment.

V. The acquisition set up

The output signal generated by the impact of neutral and ionized fragments on the MCP detector is connected to an acquisition devicevia preamplifiers (FAMPS8, HandelsRoentdek GmbH). During the measurements carried out to validate the present method, two acquisition chains are installed in parallel as shown in Figure 3 andH + from left to right respectively.

-The "ADC-signal SID" acquisition line uses a 10-bit analog to digital converter, coupled to a memory 8GHz Quick Access 1.2 MB (Acqiris map). The PCI card is connected to a standard PC computer.Recording of the detected signal is performed on an event by event basis. Within a single event, in contrast to the TDC line, there is no dead time.For each dissociationthe signal is recorded individually as shown in Fig. 3.

By summing up these individual signals this acquisition linecan also produce a

COINTOFmass spectrum of charged fragments as in case of using the TDCmultihitacquisition line but in this mode more information can be deduced from the data. By choosing an appropriate time window,it is possible to record onlyspecificdissociation events.

From these data we can immediately deduce the number of products for a given precursor ion. The precursor ions arriveone after the other in the interaction zone at a rate of typically one ion per 1ms (i.e., 1000 cps). On the other hand, the acquisition time window is about two to four microseconds. Therefore on average there is no overlap between successive dissociation events and the number of peaks can be directly related to the reaction under study. In the example shown in Figure 3, three products are detected for the tetramer parent ion, i.e., a charged product and two neutral fragments. Indeed, thecharged product from the precursor, which has been accelerated,hitsthe detector before the two neutral products from the same precursor. Moreover, the acquisition set upincludes a series of signal triggering modulesthus allowing us to select a specific (adjustable) acquisition timeafter the first (neutral) product of interaction hits the detector. Moreover the duration of the acquisition window is adjustable. This allows making specific measurements, for example, using acquisition strategies reducing the acquisition time.

The present acquisition set-up also allows the recording of the amplitude of the detected signal as shown in Figure 4foran example utilizingthe ADC converter line.The amplitude of the detected signal is digitized into 10 bits at a rate of 8 gigahertz (125ps). For each event, the shape of the detection pulse is also recorded. The acquisition device is organised in such a way as to label the set of numbers obtained for a given precursor as an event associated with the interaction of this one precursorwith the target. This labelling step allows to distinguish information acquired (arrival time and magnitude of the peaks) between different precursors, thereby preserving the correlation between information obtained for eachevent. It should be noted that without an external time reference, this approach enables us to work with a continuous beam of precursor ions of strong intensity and to have a highrate of repetition. Typically, we carry out experiments with MCP intensities of 500counts/s. The acquisition time window is about a couple ofµs thus allowing us to record event after event.

VI. CID of protonated water cluster ions explored bythe COINTOF Method: a test case

The COINTOF method can be applied to a wide range of molecular ions. As a test case, we present here results obtained for collision induced dissociation of protonated water cluster (H 2 O) n=2-5 H + withan argon target beam. All parent cluster ions studied here are accelerated to energies corresponding to the velocity of 130. In Figure 5A, ΔT is characteristic of the H + (H 2 O) ion and by comparison with the ion trajectory simulations the underlying dissociation event corresponds to

H + (H 2 O) 2 → H + (H 2 O) + H 2 O (1)
In contrast, three peaks are observed in the time arrival window shown in Figure 5B, corresponding to one charged fragment and two neutral fragments. The difference in arrival times between the charged and neutral fragments is characteristic of the H + ion. Thus this arrival time spectrum indicates the dissociation of the protonated dimer in three fragments, the proton and two neutral water molecules via reaction

H + (H 2 O) 2 → H + + H 2 O + H 2 O (2)
Note that thearrival time difference between the two neutral fragments (caused by different KER values of the two fragments) may besmaller than the typical dead time of discriminators used in standard arrival time measurements with a time to digital converter.Nevertheless, in the present case it is accessible by the useof a fast ADC.

The examplepresented in Figure 6involving CID of the protonated water pentamerillustratesvarious steps in a particular analysis. In the left upper insert we show thespectrum of the charged fragments forCID of 8keV (H 2 O) 5 H + with argon as target gas.

Each ΔT (ns) peak is associated to a given mass to charge ratio(s) for aspecific charged fragment produced in the collision event (see Table 1), corresponding to the detection of

H + (H 2 O) (19amu -ΔT≈490ns) , H + (H 2 O) 2 (37amu -ΔT≈312ns), H + (H 2 O) 3 (55amu -ΔT≈230ns)
and H + (H 2 O) 4 (73amu -ΔT≈182ns)fragments. In the lower insert right hand side, a single event for the dissociation channel of (H 2 O) 5 H + into (H 2 O) 3 H + + 2(H 2 O) is reported; three peaks are observed, the first one corresponding to the ionized fragment and the two close peaks at higher arrival times corresponding to the twoneutral water units. Figure 6 shows also the most stable protonated water pentamer structure from theoretical calculations of Miyazaki et al. 14 . After collision the excess energy can lead to various dissociation channels with two neutralsubunitsthat can arise from any site of the H + (H 2 O) central ion. Nevertheless, the measurement of the time differencebetween the two neutral water subunits (≈31.3 ns) will be a key information regarding the structure of the decaying parent ion.

In addition CID experiments have been performed here with protonated water cluster ions H + (H 2 O) n for sizes n from 1 up to 5 all at a velocity of 130.10 3 m/s. In Figure 7 we show the mass spectra of the respective charged fragmentsobtained by the COINTOF method. The arrival time of the first neutral fragment is used as a time reference to identify the charged fragments for each dissociating precursor ion H + (H 2 O) n using the results obtained with the SIMION simulation (Table 1). The red asterisksin Figure 7 14 (see Figure 6).

VII. Conclusion

In conclusion, the novel CID mass spectrometry technique, COINTOF, presented here provides compared to earlier studies a more detailed description of a collision induced dissociation process by directly probing not only all ionized and neutral fragments produced but also their correlations in time within each single dissociative event. This COINTOF method is implemented on DIAM 1). All the parent ions are initially accelerated to the same velocity of 1.3 10 7 cm/s (130.10 3 m/s). The various dissociation channelsobserved are given on the right hand side.

TABLES

  SIMION®simulations were carried outforvariousion massesanda range of energies.Thesesimulationsprovide the arrivaltimesonthe MCP detectorforeachionandcorresponding neutralfragmentseparately.Table1presentsresultsforfragmentsfrom different parent ionsall at the sameparentvelocityof 130x10 3 m/s.As mentioned above thetimeofflightsfortheneutralfragmentsareindependentoftheirmass since the applied electric fields have no influence on their flight times, in contrast to that of the ions.Thedifferencesintimesbetweenchargedandneutral(lastcolumn)depend onthemassofthecharged fragment and thus allowtheidentificationofthe chargedfragment for each dissociation event.

3 (

 3 :-The"TDC multihit" acquisition line consists of a constant fraction discriminator, a TDC (Time Digital Converter) module and a fast bus (ECL) for transferring the time values in a memory. The unit is managed by standard CAMAC. The TDC module allows multi-hits to record with a time resolution of 0.5ns, however with a dead time of 15ns between successive pulses. It is programmed inthe "common stop" mode. In this mode the time of arrival of the various fragments produced by the dissociation of a given precursor is savedand labeled as the arrival times corresponding to the dissociation of the corresponding precursor ion. This acquisition line provides a directCOINTOF mass spectrum of the charged fragments obtained in continuous operation without an external trigger (CID-recorded COINTOF spectrum). Figure parent ions interacting with argon target gas. It is noteworthy that the COINTOF mass spectrum differs from that obtained traditionally, where the charged species are plotted as a function of the mass to charge ratio. In the COINTOF mass spectrum, the ions are plotted as a function of the difference between the arrival instant of the neutral and the ion,T. Since the neutral species remain at the velocity of the precursor (to a first approximation), they can be used as an intrinsic time reference within a single dissociation event. Thus the lighter the ion species, the larger is T, as shown in fig.lowerright side) where the four mass peaks refer toH + (H 2 O) 3, H + (H 2 O) 2, H + (H 2 O) 3

  Fig. 5 for CID of the protonated dimer. Each arrival time window is associated with the dissociation of one single H + (H 2 O) 2 . Due to the acceleration zone after the collision, the first

FIGURESFigure 1 :

 1 FIGURES

Figure 3 :

 3 Figure 3: Principle of the acquisition set-ups used. Two acquisition lines have been used in parallel. The TDC-multihit chain providesthe COINTOFmass spectra (right hand side). The ADC (10bits/8GHz)acquisition chain is used to record an arrival time spectrum for a single dissociation event in a specific dissociation channel (left hand side).

Figure 4 :

 4 Figure 4: Signal produced from the impact of one particle on the detector by the fast ADC (8GHz/10bits) acquisition line.

Figure 5 :

 5 Figure 5:COINTOF arrival time spectra for8keVH + (H 2 O) 2 ions interacting with anArtarget beam: (A) Detection of a H + (H 2 O)fragment ion and one neutral fragment (B) Detection of a H + fragment ion and two neutral fragments The time differences between the ion and the neutral(s)are in accordance with those obtained from ion trajectory simulation.

Figure 6 :

 6 Figure 6:CID of the protonated water pentamer cluster ion

Figure 7 :

 7 Figure 7:COINTOFmass spectraof the charged fragmentsfor H + (H 2 O) n . parent ions with n from 1 to 5 The arrival time of the first neutral fragment is used as a time reference to identify the charged fragments for each of the dissociating precursor ions H + (H 2 O) n . The red asterisks correspond to the predictions fromSIMION calculations (Table1). All the parent ions are initially accelerated to the same velocity of 1.3 10 7 cm/s (130.10 3 m/s). The various dissociation channelsobserved are given on the right hand side.

  correspond to the values obtained with the SIMION calculations. On the right hand sideof Figure7the various dissociation channelspresent in the mass spectra are listedfor each incident precursor ion H + (H 2 O) n .As expected the charged fragments observed correspond to the loss of one up to n H 2 O molecules. Nevertheless differences are observed concerning the abundance of the variousH + (H 2 O) p productions formed by these collisions. The most surprising result is the therelative large abundance of the H 3 O + fragment ion among the fragment ions produced in the protonated water pentamer case. This may be understood however by the important role ofthe H 3 O + ion (Eigen ion) as the central core of protonated water clusters as discussed in numerous papers and shown experimentally by Headricks et al. 15 in infrared spectra of H + (H 2 O) n clustersfor specific small cluster sizes. The present results on the water pentamer ionssuggest that the parention structure seems in accordance with a H 3 O + ion (Eigen) core surrounded by H 2 O molecules as calculated by Miyazaki et al.

  1 , a recentlydesigned experimental setup at University Lyon 1 to investigate processes resulting from the irradiation of various molecular nanosystems. This new MS/MS spectrometer detects neutral and charged fragments arising from the dissociation of a single precursor ion. The set up does not need any prior external time reference and can be operatedin a continuous mode. The "event by event" recording allows to analyzeCID reactions beyond the sole average production rate of charged fragments. This technique allows the correlated measurements of the time of flights of charged and neutral fragments produced within the same dissociation event of a mass and energy pre-selected molecular parent ion. The power of this COINTOF technique is illustrated here showing examples from collision induced dissociation of protonated water cluster ions with atomic gas targets (e.g. argon).

Table 1 :

 1 Arrival time differencebetween the charged fragment ionanda neutralfragmentfor different initial kinetic energies (amounting to the same initial velocity of 130.10 3 m/s for all parent ions studied).

	Parent mass ofprotonated water cluster ions(amu)	Parent energy (eV)	Fragment charged mass (amu)	Charged fragment KE (eV)	Charged fragment arrival time (μs)	Neutral fragment arrival time (μs)	Arrival time difference Δ T (μs)
	19	1670.33	1	87.91210	0.522104	1.90407	1.381966
			19	1670.329	1.41434		0.48973
	37	3252.747				1.90407
			1	87.91208	0.522104		1.381966
			37	3252.747	1.59219		0.31188
	55	4835.165				1.90407
			19	1670.329	1.41434		0.48973
			1	87.91209	0.522104		1.381966
			55	4835.164	1.67453		0.22954
	73	6417.582	37	3252.747	1.59219	1.90407	0.31188
			19	1670.329	1.41434		0.48973
			1	87.91208	0.522104		1.381966
			73	6417.582	1.72225		0.18182
			55	4835.164	1.67453		0.22954
	91	8000				1.90407
			37	3252.747	1.59219		0.31188
			19	1670.329	1.41434		0.48973
			1	87.91208	0.522104		1.381966