Sofiane Ghenna

Member, IEEE Fr Éd Éric Giraud

Member, IEEE Christophe Giraud-Audine

Michel Amberg

Vector Control Of Piezoelectric Transducers and Ultrasonic Actuators

Keywords: digital synthesis, energetic macroscopic representation (EMR), piezoelectric transducers (PTs), resonance tracking, ultrasonic transducer, vector control

This paper presents the implementation of a novel vibration amplitude control and resonant frequency tracking for piezoelectric transducers (PTs) and ultrasonic motors (USMs). It is based on a generalization of the vector control method to the PT and the USM, which is explained in the first part. We show that two independent controllers with a similar structure are required: one tracks the resonant frequency and the second controls the amplitude. We then present the implementation into a low-cost digital signal processing controller with a sampling period of 200 µs. Experimental results on a Langevin transducer achieved a time response of 20 ms approximately, and the generality of the method is further demonstrated on a 2-D tactile stimulator at the end of this paper.

I. INTRODUCTION

Piezoelectric transducers (PT) are found in a growing range of applications, where a tool vibrating at high frequency is used. Examples include local heating as in ultrasonic welding [START_REF] Wang | Design of high-frequency ultrasonic transducers with flexure decoupling flanges[END_REF] or surgery [2], generation of acoustic waves in a fluid as in cleaning [START_REF] Mason | Ultrasonic cleaning: An historical perspective[END_REF] or acoustic levitation [START_REF] Thomas | Development of an acoustic levitation linear transportation system based on a ring-type structure[END_REF], ultrasonic motors [START_REF] Zhao | Ultrasonic motors: technologies and applications[END_REF], or active lubrication as in tactile feedback systems [START_REF] Vezzoli | Physical and perceptual independence of ultrasonic vibration and electrovibration for friction modulation[END_REF]. All these application requires large oscillations and therefore, in order to minimize the power consumption of the system, the PT should be operated at its resonance frequency, where the vibration to voltage amplitude ratio is higher. However, this optimal frequency strongly depends on several factors, e.g the dimensions of the transducer, the properties of the materials composing it, or the temperature. More importantly, the acoustic load coupled with the transducer can modify both the resonant frequency and the damping [START_REF] Bai | Effect of different standoff distance and driving current on transducer during ultrasonic cavitation peening[END_REF]. Finally, due to the non linear nature of the piezoelectric material, the resonance frequency may shift as the vibration amplitude increases [START_REF] Lim | A preliminary investigation into optimising the response of vibrating systems used for ultrasonic cutting[END_REF]. Therefore, using PT often requires a control which acts both on the frequency and the amplitude of the excitation.

Since, for highly coupled PTs, the voltage and the current are virtually in phase at resonance [START_REF] Hayashi | On the tracking of resonance and antiresonance of a piezoelectric resonator[END_REF], a tracking method consists in adjusting the excitation frequency until this condition is verified. This can be achieved with a Phase Locked Loop (PLL) [START_REF] Kuang | Resonance tracking and vibration stablilization for high power ultrasonic transducers[END_REF] for example, and many authors have proposed different practical implementations of this principle [START_REF] Cheng | A resonant frequency tracking circuit for a low-coupling-coefficient piezoelectric transducer[END_REF],

The authors are with the Laboratoire d'Electrotechnique et d'Electronique de Puissance, EA 2697, HEI, Arts et M étiers Paris-Tech, École Centrale de Lille, Universit é de Lille, F-59000 Lille, France [START_REF] Gui | Automatic frequency tracking system for needle actuating device[END_REF]. However, these methods can not maintain a constant vibration amplitude when the load changes, and, since the voltage amplitude is not controlled, the power delivered to the transducer can not be increased in order to compensate the acoustical load impedance variation. To address this issue, some authors control the current amplitude at resonance [START_REF] Kuang | Resonance tracking and vibration stablilization for high power ultrasonic transducers[END_REF], which is proportional to the vibration amplitude, by adjusting the voltage amplitude. This is done with a boost converter as in [2].

In general, the performances of these controls are measured only in steady state, i.e for constant or slowly varying reference values of the vibration setpoint. However, some applications require high dynamics, either to ensure a large bandwidth of the variation of the vibratory amplitude [START_REF] Ben Messaoud | Textile Fabrics' Texture: From Multi-level Feature Extraction to Tactile Simulation[END_REF], or to reject perturbation induced by the high dynamic of the load [START_REF] Mathieson | Ultrasonic needles for bone biopsy[END_REF]. In order to simultaneously address the resonant frequency tracking, and the high dynamic amplitude control, the concept of Vector Control Method (VCM) is generalized to piezoelectric actuators. The VCM has been successfully applied on a wide range of electromagnetic actuators [START_REF] Shinnaka | New sensorless vector control using minimum-order flux state observer in a stationary reference frame for permanent-magnet synchronous motors[END_REF] to reach outstanding performances in transitory operations or to realize sensorless drives. In the case of PT, the VCM allows both resonance fequency tracking and vibration amplitude control using two loops operating in parallel [START_REF] Messaoud | Amplitude control of an ultrasonic vibration for a tactile stimulator[END_REF]. The VCM can also be used to synchronize ultrasonic transducers, in order to generate a traveling wave [START_REF] Ghenna | Modelling and control of a travelling wave in a finite beam, using multi-modal approach and vector control method[END_REF] for instance.

This paper presents the practical implementation of the VCM for PT, and typical performances obtained on experimental test bench, within the field of tactile stimulation although the exxtension to other application is straightforward. The paper is therefore organized as follows: we first present the modelling of a PT in a rotating reference frame, which is the core of the VCM. Then, we present the control in the rotating reference frame. We will show that the tracking of the resonant frequency and the amplitude control is deduced naturally by application of VCM. Its implementation on a DSP is then discussed and experimental results on a Langevin transducer are given. We will then conclude with the presentation of an application which requires the synchronization of several PTs to operate.

II. MODELING IN A ROTATING REFERENCE FRAME

A. Energy Conversion in a PT

A PT exploits the inverse piezoelectric effect to create internal stresses in the piezoelectric material when a voltage v is applied. The stresses deforms the matter, generating and propagating a wave. A longitudinal wave is used in the case of a Langevin transducers, however transverse waves (Lamb or Rayleigh wave) can also be also used e.g in ultrasonic motors. Considering a specific point of the transducer, the vibration is only a function of time and denoted w(t) hereafter. A Spring-Mass-Damper Model is presented figure 1 which describes the behavior of PTs near resonance. In this model, the inverse piezoelectric effect produces a force named f p which is proportional to the voltage v, i.e f p = N v where N is the conversion factor. Due to f p the mass m is put in motion, while a visco elastic force f e = cw + d s w counteract on it. The environment of the transducer is taken into account through the reaction force f r . According to Newton's second law, one can write:

m ẅ + d s ẇ + cw = f p -f r (1)
On the electrical side, a PT has a capacitive behavior, so the voltage v is deduced from the current. In this paper, however, we assume that the voltage is perfectly controlled and imposed by the power supply. Hence, v is an input of the system. Moreover, the vibration induces a motional current on the electrical part i m , which is proportional to the vibration speed and we write:

i m = N ẇ (2)
note that conversion factor N is the same for the piezoelectric force and the motional current, which results from the assumption that the conversion is lossless.

This model is useful for describing the instantaneous evolution of the vibration. However, in many applications, describing the amplitude is more of interest than the vibration itself. Therefore, we present the model in a rotating reference frame.

B. Definition of the rotating reference frame

Since PT are mechanical resonators, the vibration w is a sinusoidal function of time, and one can use the complex notation w(t) = (w) with:

w = W (t)e jωt ( 3
)
where W is the complex vibration amplitude which conveys simultaneously the amplitude of the vibration and its phase with respect to some arbitrary reference that will be defined later. (.) denotes the real part and ω is the pulsation of the vibration. This representation can be extended to the other variables, and we define V as a complex number relative to the voltage. Figure 2 shows the positions of the aforementioned complex variables at a given time t.

I m R e d q ωt φ W V ψ W d W q V d V q Fig. 2

. Representation of the voltage and vibration amplitude in a rotating reference frame

During operation, the vectors affixed to the complex amplitudes are rotating. It is then convenient to project them in a rotating reference frame to obtain fixed vector in steady state. For that purpose, we denote:

w = (W d + jW q ) e jωt v = (V d + jV q ) e jωt f r = (F rd + jF rq ) e jωt (4)
We define a rotating reference frame (d, q), where the axis d is by convention aligned with e jωt . The objective of the VCM is then to give the evolution of the complex amplitudes, which is equivalent to the modeling in the rotating reference frame.

C. Modeling in the rotating reference frame

The equation 1 is supposed to be also valid for the complex vectors, and we write:

m ẅ + d s ẇ + cw = f p -f r (5)
The problem stated by equation ( 5) is general. However, to yield a less general, yet implementable model, we assume at this stage several simplifying hypotheses:

• The frequency is slowly varying, so the derivatives of ω are negligible, • The dynamic of W , that is the closed-loop bandwidth, is smaller than ω. From the equation (4), we can calculate the derivative of w, which is simplified by neglecting ω as stated in the first assumption:

ẇ = Ẇd + j Ẇq + jω (W d + jW q ) e jωt (6)
It is convenient to calculate the dynamic of the amplitude of the vibrating speed, rather than the amplitude of the vibration, hence, let:

u(t) = ẇ = (U d + jU q ) e jωt (7)
leading to

U d = Ẇd -ωW q and U q = Ẇq + ωW d (8)
and ẅ = Ud -ωU q + j Uq + ωU d e jωt (9)

Using the equations 8, leads to

W d = U q ω + Ud ω 2 - Ẅd ω 2 (10)
Since the dynamic of W d is limited by ω, it is reasonable to neglect Ẅd ω 2 compared to W d for a non-zero amplitude vibration. According to this assumption, and following a similar process with W q ,one can write:

w = U q ω + Ud ω 2 + j - U d ω + Uq ω 2 e jωt (11)
Introducing ( 11), ( 9) and ( 7) into ( 5), and identifying the real and imaginary part, we obtain two new equations, describing the dynamic of the vibration speed in the rotating reference frame:

m + c ω 2 Ud + d s U d + c ω -mω U q = F pd -F rd (12) m + c ω 2 Uq + d s U q - c ω -mω U d = F pq -F rq (13)
This model in a rotating reference frame shows that the forces in axis d control the dynamic of the vibration velocity U d , the environment acts as a perturbation (through F rd ) and there is a coupling between the axis. Same conclusion applies on axis q which is controlled by F q with perturbation and coupling from the other axis.

PTs have high quality factor. It is,therefore, admitted that the pulsation of the vibration is close to the pulsation of resonance ω 0 . We name δω the deviation of ω from ω 0 such that ω = ω 0 + δω with δω ω 0 . We consider then that m + c ω 2 2m and c ω -mω -2mδω. The equation 13 simplifies then to:

2m Ud + d s U d -2m.δω.U q = F pd -F rd (14) 2m Uq + d s U q + 2m.δω.U d = F pq -F rq (15)
We introduce two forces as follows:

F d = F pd + 2m.δω.U q and F q = F pq -2m.δω.U d ( 16
)
The Energetic Macroscopic Representation (EMR, [START_REF] Allegre | Energy storage system with supercapacitor for an innovative subway[END_REF]), represents the system, highlighting the energy conversion (circles) and the energy storage (dashed rectangles) and therefore respects the causality. The EMR of a PT is given figure 3 in the rotating reference frame. It shows two coupled kinetic energy storage: one for the axis d the other for the axis q. A coupling, which depends on the pulsation deviation with the resonance, shows that the two axis interact with each other. Such a coupling exists in electromagnetic machines, and the fact that this coupling depends on pulsation is a common feature that PTs share with them. This coupling is exploited in the next section, in order to implement original controls: control of the vibration speed, and tracking of the resonance frequency. In this section, the pulsation ω is fixed, and it is not necessarily the resonance frequency of the transducer. To fully control its vibration, the two outputs of the system namely U d and U q must be controlled. The step-by-step inversion of the EMR is given figure 4, and results in:

MS

MS ES V d V q v i F d F q I d I q δω 𝑒 -𝑗ω𝑡 U d F rq
• two vibration controllers (which will be discussed later) represented as dashed blue boxes; • the compensation of the couplings represented by the interlaced blue boxes; • the inversion of the electromechanical coupling;

• the modulation at frequency ω realized by rotation of the vector V in order to obtain v(t). Hence, U d and U q can be controlled by two independent loops in the rotating reference frame. These two loops can be implemented using similar structures. For instance, consider the control along the q axis, represented by the block diagram depicted on figure 5. The motor is represented by its transfer function which derives from the equation 15:

δω U q_ref δω F pq_ref F pd_ref V q_ref V d_ref F d_ref MS MS V d V q v i I d I q δω Control path Tuning path ES 𝑣 𝑟𝑒𝑓 𝑒 -𝑗ω𝑡 U d U q F pd F pq F d F q U d U q U d U q 𝑒 𝑗ω𝑡 U d_ref F rq F rd [1] [2] [3] F q_ref
U q F q = 1 d s + 2ms (17)
Since this transfer function is a first order, a simple PI is used to control the force F q , and its parameters can be adjusted in order to obtain a predefined response time, without overshoot [START_REF] Giraud | Design and control of a haptic knob[END_REF]. Moreover, since the dynamic in axis d and q are equal, the two PI controllers are the same. Finally, it is recommended to compensate for the effect of the external forces or the coupling in the other axis, but they can be omitted provided that the controllers are designed to reject these perturbations.

E. Frequency tracking

Considering δω as an additional input of the system, the system has three inputs (V d , V q and δω) to achieve two criteria (U d = U dref , U q = U qref ): the problem is underdetermined. Therefore, one input is arbitrarily set, and we choose to have let V d = 0. Moreover, it is generally admitted that for an efficient operation of the PT, it is necessary for the motional current to be in phase with the voltage. Since V d = 0, this leads to

U dref = 0 (18)
These aforementioned considerations lead to the EMR of the control depicted in figure 6; it shows two loops, operating in parallel:

• the vibration speed controller controls V q in order to obtain U q = U qref , and has been presented in the previous section • the resonance tracking controller, which adjusts the value of δω in order to d 0 The implementation of the control loop of U d is presented figure 7. It looks very similar to that of Figure 5, and it also features an optional compensation of the force related to the environment (F rd and F rq ). However, the inversion of the coupling yields a variable gain 1 2mU d in the block [2] of figure 7(as opposed to the constant gain 1 N in the previous controller). Hence, the frequency tracking controller can be the same as the velocity controller in axis q.

MS MS V d V q v i I d I q δω 𝑒 -𝑗ω𝑡 U d U q F pd F pq F d F q U d U q U d U q F rq F rd δω F pq_ref V q_ref V d_ref F q_ref = 0 F d_ref Control path Tuning path ES 𝑣 𝑟𝑒𝑓 𝑒 𝑗ω𝑡 U q_ref U d_ref=0 U d U q [1] [2]
Unfortunately, this control is not suitable at low vibration amplitudei.e U q small. Indeed, inverting the relation 16 with small value of U q leads to large values of δω. To avoid this, the control is activated only when U q is above a threshold.

III. EXPERIMENTAL RESULTS IN DIFFERENT EXAMPLES

If the control of the piezoelectric transducers resembles that of the electromagnetic motors, its implementation is different because the pulsation of the supply voltage is much larger than the bandwidth of the vibration amplitude control. Moreover, the measured variables represent only the real parts of the corresponding complex vectors in the fixed frame (i.e the projections on the real axis on fig 2). It is therefore necessary to estimate in the vector in the rotating frame {d, q}. This implies to transport the real measurement in the rotating frame and reconstruct the missing imaginary parts of the various vectors. The practical implementation on a low cost DSP (STMicroelectronics STM32F4) is discussed below, as well as two experimental results on two applications, one requiring a resonance frequency tracking, the second operating at constant frequency.

A. Practical implementation of the VCM

The control scheme proposed in this paper involves two processes working at different sampling frequencies. A high speed process (T e = 1µs) that handles the {d, q} transformation and is driven by a Digital Direct Synthesis (DDS) as shown in the dashed box of figure 8. The VCM, that defines the voltages and the frequency, and is updated at a slower frequency (T s = 200µs).

Direct Digital Synthesis (DDS):

The DDS produces the two sampled signals of cos(ωt) and sin(ωt), named c and s respectively. It consists in a N = 32 bit accumulator named R DDS . At each rising edge of a 1Mhz timer (providing a signal with a period T e = 1µs), the register is increased by a quantity named ∆θ. Therefore, the DDS needs T = 2 32 ∆θ T e to overflow, which is also the period of the voltage v(t). The only 9 highest bits of R DDS are used as an input of a read-out table, where the values of cos and sin are stored in a memory coded on two 8 bits numbers, ranging from -128 to +127.

These settings of the DDS allows us to fine tune the frequency of the voltage, with a resolution of 1 2 32 Te = 0.2mHz, which is enough for this application.

Inverse rotation: According to (4), one can write

v(t) = V d cos(ωt) -V q sin(ωt) (19)
Hence, the Inverse Rotation consists in 2 multiplications and one addition. The values of V d and V q are given with signed 8 bits numbers. Therefore, the result is truncated to the 12 most significant bits, and sent to the Digital to Analog Converter Register.

Figure 9 shows the output voltage of the DSP when V d = 0 with ∆θ = 121762322 leading to ω = 2π × 28350Hz. The waveform evolves by steps as a result of discretization and digitalization. Rotation: The rotation block computes the values U d and U q from the measurement u(t), and we propose to use a Discrete Fast Fourier Transform. Using (4), one can write

u(t) = U d cos(ωt) -U q sin(ωt) (20)
Considering that

1 T T 0 u(t) cos(ωt)dt = 1 2 U d ( 21
)
1 T T 0 u(t) sin(ωt)dt = - 1 2 U q (22)
The principle of the Rotation block is illustrated in figure 10. It consists in sampling u(t) at each step kT e and multiplying this value by the signals c and s obtained from the DDS block. Then, the two resulting values are stored in 2 rotating buffers with equal length denoted by N b . At the beginning of a period of the VCM nT s , the N b elements of each buffer are summed in order to calculate the discrete integral of ( 21) and ( 22) and consequently U d and U q .

The length N b of the buffers must be chosen so that it contains a number of samples spanning a duration as close as possible to an integer number of period, that is: Where E(x) is the integer part of x. Because the calculation of U d and U q is done on a large number of samples, this method is robust in the presence of noise and harmonic in the signal, and was found to give satisfactory results.

N b = E T s T E T T e (23)

B. Vibration amplitude and frequency tracking of a Langevin Transducer with VCM

The proposed Vector Control Method (VCM) is illustrated for a Langevin transducer (FBL28252SSF-FC, Fuji Ceramics Corp, Japan) depicted in figure [START_REF] Cheng | A resonant frequency tracking circuit for a low-coupling-coefficient piezoelectric transducer[END_REF]. This transducer is used in an experiment on diminished haptics [START_REF] Yamaguchi | Driving System of Diminished Haptics: Transformation of Real-World Textures[END_REF]. This involves vibrating a textured surface to several tens of kilohertz at about 2 µm of amplitude. When the finger touches the vibrating surface, it is felt less rough than without vibration.

It is essential that the actuator always operates at the resonant frequency to ensure the lowest supply voltage and the best system efficiency. Indeed, to minimize the bulk of the power supply, it has little power reserve. These consideration allow us to use a linear amplifier (LM675 -Texas Instrument) mounted in non-inverting amplifier with a gain of 9, as presented figure 12. Because a DSP is used to supply the reference voltage to the amplifier, an input capacitor C e anf the resistor R e are added in order to cancel its mean value. Moreover, R s and C s are added to stabilize the amplifier. The vibration velocity can be measured indirectly by measuring the current supplied to the to the piezoactuators if the latest is highly coupled and operating near the resonance frequency. Nonetheless, in this study, we preferred to directly measure the deformation of the vibrating mass of the transducer by gluing a piezoelectric patch on it. A resistor with a small value is then connected in parallel, so that the output voltage of the patch is directly proportional to the vibration speed of the PT corresponding to u(t) in the equation [START_REF] Bai | Effect of different standoff distance and driving current on transducer during ultrasonic cavitation peening[END_REF]. This way, a current sensing circuit is not necessary. The sensor has been calibrated by comparing the signal's output with the vibration amplitude measurement from a laser interferometer. The sensor's voltage shows a good linearity with the vibration velocity u(t).

The frequency response of the transducer is given figure 13. This response is highly non linear, and the resonance frequency shifts due to variations of the stiffness with the vibration amplitude; this non linear behavior justifies the necessity to track the resonant frequency, while controlling the vibration speed. At t < 0.02 s the frequency controller is not activated, and the PT operates below the resonance, as a consequence U d = 0. At t = 0.02 s, the frequency tracker is switched on: the frequency increases in order to reach the value where U d = 0 is verified. Since the PT operates closer to the resonance, the supply voltage V q decreases in order to maintain U q to its reference setpoint. To reach the final value, the controller requires only 0.020 s. Figure 15 presents the transient response of the PT when a step variation of U q is applied. The two controllers on each axis were activated. During this test , due to the non-linear amplitude vs frequency response presented in figure 13, the resonance frequency of the system shifts by 50 Hz, which is large compared with the bandwidth of the system (aproximately 100 Hz). Figure 15 clearly shows that first, the voltage U q increases to reach the reference setpoint. Doing so, the PT shifts away from its resonance and U q decreases. Consequently, δω decreases by the action of the corrector in axis d. At t = 0.05 s, the value of U d is stabilized, but U q is positive, meaning that the PT now operates below its resonance. Therefore, the frequency tracker increases ω to reach the resonance frequency, as previously shown in figure 14.

C. Application to the synchronization of two Piezoelectric Transducers

In some applications, two or more actuators are coupled to excite several modes. For instance, Traveling Wave Ultrasonic Motors (TWUM) use two vibration modes in quadrature to propel by friction a rotor pressed on it. A pure progressive wave is then obtained when the two modes vibrate with a temporal phase shift of 90 deg [START_REF] Shi | An optimum-frequency tracking scheme for ultrasonic motor[END_REF], [START_REF] Mashimo | Micro ultrasonic motor using a cube with a side length of 0.5mm[END_REF]. In some cases, the two modes are of different nature [START_REF] Zhou | Novel 2-dof planar ultrasonic motor with characteristic of variable mode excitation[END_REF], and therefore do not necessarily have the same resonant frequency. In [START_REF] Oberti | Manipulation of micrometer sized particles within a micromachined fluidic device to form two-dimensional patterns using ultrasound[END_REF], the authors use a vibrating plate to manipulate cells according to patterns produced by the vibration of two orthogonal modes.

All these examples have in common the necessity to control the phase and amplitude of the two modes which, in practice, do not have the same resonance frequency. For the best performance, precise adjustment of the amplitude, phase and frequency of the supply voltages is required [START_REF] Minikes | On the sensing and tuning of progressive structural vibration waves[END_REF]. In this paper, we apply the Vector Control Method on a 2-fingers tactile stimulator. By combining two vibration modes with particular amplitudes, it is possible to produce tactile stimuli on two fingers independently [START_REF] Ghenna | Control and evaluation of a 2-d multimodal controlled-friction display[END_REF]. With the proposed closed loop control, we can control the vibration amplitude under two fingers located anywhere on the plate.

The device is a 140 × 140 × 4 mm 3 plate made with aluminum. Two pairs of piezoelectric actuators glued on the plate excite two bending modes, one along axis x the other along axis y, which are denoted by Mode X and Mode Y hereafter. The two deformation mode shapes Φ X (x, y) and Φ Y (x, y) are depicted figure 16. Two more patches are glued in order to measure the vibration velocity of each mode by the direct piezoelectric effect. When the two modes are vibrating at the same frequency, the vibration amplitude depends on the position on the plate, and we write:

w(x, y, t) = (W X Φ X + W Y Φ Y ) e jωt (24)
Where W X and W Y are the vibration amplitudes of the two modes. Hence, by setting the two modes with different amplitude, several vibration patterns can be obtained.However, the two modes are not at the same frequency, and their frequency response depicted figure 17 shows that mode X is at 33 011 Hz, while mode Y is at 33 065 Hz. The difference is small (less than 0.02%); however, we can see that the resonance of one mode falls outside the bandwidth of the other mode, and setting the frequency at one mode's resonance would lead to high voltage requirement for the other. Operating in the middle of the two modes is a trade-off, which would lead to control the amplitude and the phase directly with the voltage of each mode. In practice however, this condition is difficult to attain, because the resonance frequencies shift due to temperature rise and/or the environment. Therefore in openloop, synchronizing the two modes needs a fine tuning of the voltages, in amplitude and phase [START_REF] Minikes | On the sensing and tuning of progressive structural vibration waves[END_REF]. In the rotating reference frame, synchronizing the two modes is achieved by setting U dXref = U dY ref , and U qXref = U qY ref . We then implemented two VCM, one for each mode, leading to four control loops, working at a constant frequency chosen approximately in the middle of the two modes. Hence, the frequency tracking is not activated. The response time of the control is about 20 ms as can be seen in figure [START_REF] Allegre | Energy storage system with supercapacitor for an innovative subway[END_REF]. The result of this superimposition is given in figure [START_REF] Giraud | Design and control of a haptic knob[END_REF]. Compared with the measurements of the figure 16 the nodal line (where w(x, t) = 0) are straight lines oriented at 45 0 , demonstrating the good synchronization of the two modes.

IV. CONCLUSION

This paper presents the implementation of the Vector Control Method on Ultrasonic Transducers. We show that the VCM of a PT is very similar to the VCM of an Electromagnetic machine. However, since the couplings between the axis d and q strongly depend on the frequency of the supply voltage, we show how they can be either compensated in a fixed frequency control, or inverted in order to achieve a resonant frequency tracking. The originality of the proposed method is that the vibration amplitude controller and the frequency controller are identical, with the same parameters. The real-time implementation achieved with a low-cost DSP is based on a DDS for the matrices inversion. Good performances are obtained with simple PI controllers, since in steady state, the variables in the rotating reference frame are constant. The performances of the control are measured on a non-linear PT, and on a 2 DoF Tactile display where the synchronization of two vibration modes is critical.

Compared with other closed loop controls, the advantage of the VCM are the synchronization of several PTs, the possibility to operate the frequency tracking in parallel with the vibration amplitude controller, and the generality of the approach which can be applied to several types of PT's. Future work will focus on the extension of the proposed method to more than 2 modes.

Fig. 1 .

 1 Fig. 1. Equivalent Mass-Spring-Damper model of the PT

Fig. 3 .

 3 Fig. 3. EMR of the actuator in rotating frame

Fig. 4 .

 4 Fig. 4. EMR of the actuator in rotating frame and inversion-based control

Fig. 5 .

 5 Fig. 5. Block diagram of the Control along the q-axis in the rotating reference frame; the labels refer to the block in the EMR of figure 4.

Fig. 6 .

 6 Fig. 6. EMR and the control for resonance frequency tracking

Fig. 7 .

 7 Fig. 7. Block diagram of the Control of the axis d for the tracking of the resonance frequency; the labels refer to the block in the EMR of figure 6.

Fig. 8 .

 8 Fig. 8. Real-Time implementation of the VCM in a STM32F4.

Fig. 9 .

 9 Fig. 9. Output voltage of the DSP; each step is Ts = 1µsec long.

Fig. 10 .

 10 Fig. 10. Principle of the inversion block for U d , with Ts = 7Te, T < 5Te and N b = 5; • are sampled values of c(t) and u(t). The rotating buffer is named B.

Fig. 11 .

 11 Fig. 11. The Langevin Transducer and its control and power electronics

Fig. 12 .

 12 Fig. 12. The linear Amplifier.

Fig. 16 .

 16 Fig. 16. Measured deformation mode shapes at resonance frequency of Mode X at 33011Hz and Mode Y at 33065 Hz

Fig. 17 .

 17 Fig. 17. Frequency response of the tactile plate

Fig. 18 .

 18 Fig. 18. Experimental measurement of the vibration amplitude control of mode X and mode Y in a rotating frame.

Fig. 19 .

 19 Fig. 19. Experimental measurement of superimposition of two vibration modes X and Y with W X = W Y .

  Figure14shows the behavior of the controller when reaching the resonance frequency.

								0.1
								Ud
								0	Uq
								-0.1
								0	0.02	0.04	0.06	0.08	0.1	0.12
								20
								Faq
								10
								0
								0	0.02	0.04	0.06	0.08	0.1	0.12
								4
								2.83
								Freq
								2.82
								2.81
								0	0.02	0.04	0.06	0.08	0.1	0.12
								Fig. 14. Resonance Frequency Tracking
	Normalized vibration amplitude	0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1					20 V 40 V 60 V 80 V 100 V 120 V 140 V
		0
		2.8	2.81	2.82	2.83	2.84	2.85	2.86
					Frequency [Hz]		x 10 4

Fig. 13. Measured vibration amplitude curves for different driving signals according to up and down (plain line) frequency (dashed line)


Juan Antonio Clemente
email: ja.clemente@fdi.ucm.es

Guillaume Hubert
email: guillaume.hubert@onera.fr.

Francisco J Franco
email: fjfranco@fis.ucm.es.

Francesca Villa
email: francesca.villa@lpsc.in2p3.fr

Maud Baylac
email: baylac@lpsc.in2p3.fr.

Hortensia Mecha

Helmut Puchner

Raoul Velazco
email: raoul.velazco@imag.fr.

Sensitivity Characterization of a COTS 90-nm SRAM at Ultra Low Bias Voltage

Keywords: COTS, SRAM, neutron tests, radiation hardness, reliability, soft error, low-bias voltage

This paper presents the characterization of the sensitivity to 14-MeV neutrons of a Commercial Off-The-Shelf (COTS) 90-nm Static Random Access Memories (SRAMs) manufactured by Cypress Semiconductor, when biased at ultra low voltage. Firstly, experiments exposing this memory at 14-MeV neutrons, when powering it up at bias voltages ranging from 0.5V to 3.3V, are presented and discussed. These results are in good concordance with theoretical predictions issued by the modeling tool MUSCA-SEP 3 (MUlti-SCAles Single Event Phenomena Predictive Platform). Then, this tool has been used to obtain Soft Error Rate (SER) predictions at different altitudes above the Earth's surface of this device vs. its bias voltage. Finally, the effect of contamination by α particles has also been estimated at said range of bias voltages.

I. INTRODUCTION

C Ommercial CMOS SRAMs have recently drawn the attention of researchers and manufacturers of complex electronic systems in fields such as avionics and aerospace. The reason is their affordable cost and that many modern devices implement error detection and protection mechanisms, such as the well-known Error Correcting Codes (ECCs) [START_REF] Abraham | Memory System Design for Tolerating Single Event Upsets[END_REF], [START_REF] Maestro | Reliability of Single-Error Correction Protected Memories[END_REF], which make them very reliable to the so-called Single Event Effects (SEEs) [START_REF] Velazco | Single Event Effects on Digital Integrated Circuits: Origins and Mitigation Techniques[END_REF].

Hence, these SRAMs can potentially be used in environments where energy efficiency is a real concern [START_REF] Baumann | Radiation-Induced Soft Errors in Advanced Semiconductor Technologies[END_REF]. It has been reported that modern SRAMs can keep the information even if the bias voltage falls down to 15-20% of the nominal value, which can be used to effectively reduce the power dissipation [START_REF] King | Electron-Induced Single-Event Upsets in Static Random Access Memory[END_REF]. However, as the bias voltage decreases, the critical charge to trigger a SEE decreases as well [START_REF] Kumar | SRAM supply voltage scaling: A reliability perspective[END_REF], [START_REF] Galib | Supply Voltage Decision Methodology to Minimize SRAM Standby Power Under Radiation Environment[END_REF]. Thus, bitflips are much more likely to occur when the circuit operates at ultra-low bias voltage, not far above from the minimum power supply that allows retention of data. This fact is valid for Single Event Upsets (SEUs) -in particular for Single Bit Upsets (SBUs), and for Multiple Cell Upsets (MCUs)-and even for Multiple Bit Upsets (MBUs) with the possible exception of the Single Event Latch-ups (SELs). Even electrons, which constitute the lightest charged particles, can provoke bitflips in 45-nm CMOS SRAMs at ultra-low bias voltage [START_REF] King | Electron-Induced Single-Event Upsets in Static Random Access Memory[END_REF].

Previous studies have pointed out the relationship between the bias voltage reduction and the sensitivity against SEEs in different technologies of SRAMs [START_REF] Hazucha | Neutron Soft Error Rate Measurements in a 90nm CMOS Process and Scaling Trends in SRAM from 0.25-/spl mu/m to 90-nm Generation[END_REF], [START_REF] Fuketa | Neutron-Induced Soft Errors and Multiple Cell Upsets in 65-nm 10T Subthreshold SRAM[END_REF]. In [START_REF] Clemente | Single Events in a COTS Soft-Error Free SRAM at Low Bias Voltage Induced by 15 MeV Neutrons[END_REF], the authors studied the sensitivity against 15-MeV neutrons of a COTS Advanced Low Power SRAMs (A-LPSRAM), manufactured in 150-nm CMOS technology, at 0.5V -3.3V. However, to the authors' knowledge, little work has been carried out on COTS SRAMs at ultra-low bias voltages under natural radiation: cosmic rays or α emitter impurities. This paper presents the characterization of the sensitivity of a CMOS SRAM manufactured by Cypress Semiconductor with 90-nm technology, when powered up at voltages ranging from 0.5V to 3.3V. Radiation ground tests were performed with 14-MeV neutrons at the GENEPI2 neutron source (GEnerator of NEutrons Pulsed and Intense) [START_REF] Villa | Accelerator-Based Neutron Irradiation of Integrated Circuits at GENEPI2 (France)[END_REF], [START_REF] Villa | Multipurpose applications of the acceleratorbased neutron source[1pt] GENEPI2[END_REF]. These results were in concordance with theoretical neutron crosssection predictions issued by the MUSCA-SEP 3 modeling approach, developed at the French Aerospace Lab (ONERA), in Toulouse, France [START_REF] Hubert | Operational SER Calculations on the SAC-C Orbit Using the Multi-Scales Single Event Phenomena Predictive Platform (MUSCA-SEP3)[END_REF]. SER predictions at different bias voltages for a spectra including protons, neutrons and muons, as well as for α-particles contamination have been also performed with MUSCA-SEP 3 and discussed in the paper.

The performed tests issued up to several thousands of bitflips per round, especially for the lowest power supplies. Very interesting conclusions could be drawn, including a clear trend in the SBU/MCU sensitivity increase at lower bias voltages. The main contributions of this paper with respect to the previous conference version presented at RADECS (RADiation Effects on Components & Systems) [START_REF] Clemente | Evaluation of the Sensitivity of a COTS 90-nm SRAM Memory at Low Bias Voltage[END_REF] are:

• The utilization of the proprietary unscrambling information of Cypress to accurately discern SBUs/MCUs instead of the probabilistic methodology presented in [START_REF] Clemente | Statistical Anomalies of Bitflips in SRAMs to Discriminate SBUs From MCUs[END_REF]. • Novel SER predictions obtained with MUSCA-SEP 3 at different low-bias voltages for different environments: ground, avionics and space. • A significant extension of the results regarding the SER predictions for the protons, neutrons and muons spectra, and for the α-particles contamination.

+ -

Volt meter

+ -

V L + - 3.3 V SRAM P 50 cm PC RS232 USB 40 cm 20 m

Shielded pipe

Figure 1. Schematic of connections and length of the cables. A 100-µF capacitor was placed between the power supply and ground in the microcontroller board, and a smaller one (100 nF) in the SRAM board. The cable shield was connected to the ground output of the 3.3 V power supply.

II. EXPERIMENTAL SETUP

Tests were carried out on one sample of the CY62167EV30LL-45ZXI CMOS SRAM manufactured by Cypress, which has a capacity of 16 Mbits. It was configured as 2M×8 bits. Due to a bug in the software that performed the read/write operations on the SRAM, the most significant bit of the address port was permanently set to '0' and hence, only half of the memory was examined. However, according to the manufacturer, this memory comprises two 8-Mbit independent blocks, so only one of them was examined. In any case, the number of events that were observed in the memory were significant enough to extract statistical conclusions. The nominal bias voltage of this memory ranges from 2.7V to 3.6V. However, we verified that even with a bias voltage of 0.45V, it retained information.

Static tests were carried out: the memory was initially written with the checkerboard pattern (0 × 55), then it was radiated in rounds of 5 minutes each, and examined after irradiation. Tests were performed at the GENEPI2 facility, which is located at the LPSC (Laboratoire de Physique Subatomique et Cosmologie) in Grenoble, France [START_REF] Villa | Accelerator-Based Neutron Irradiation of Integrated Circuits at GENEPI2 (France)[END_REF]. Neutrons were produced with an average energy of 14.2 MeV. The target memory was placed 39 mm away from the neutron source.

The test system comprised a motherboard with a PIC18F85J90 microcontroller, which run the test software. This device worked with a 20-MHz quartz clock and, experimentally, we observed that it could operate correctly even with a bias voltage of 1.9V. An extension board with the SRAM under test was attached to it. Both the microcontroller and the SRAM were biased by two independent power supplies, which made possible to tune that of the SRAM from 0V to 3.3V (Figure 1).

The SRAM bias voltage was measured with a Keithley 2001 multimeter directly at the memory board. The three grounds (two for the power supplies, and one for the multimeter) were connected near the extension board for an accurate measurement. That means that six shielded cables, with a length of 20-m each, were necessary to build the test system.

In order to effectively tune the voltage of the SRAM to levels below 2.7V, it was necessary to manually set the address and data buses, as well as the enable signals of the SRAM, to ground. This prevented the activation of the over-voltage protection structures present in this SRAM, which otherwise kept its bias voltage to levels above 2.7V. Therefore, in each experiment, a 0 × 00 word was always written in the first address in the memory, 0 × 00000, whichever the pattern was.

In any case, let us bear in mind that only 1 byte was sacrificed in a memory with 8 Mbits and, also, this allowed testing and debugging the test software.

III. EXPERIMENTAL RESULTS WITH 14-MEV NEUTRONS

Table I shows the successive tests that were performed. The initial voltage supply was 0.5V and the last one, 1.2V. At 1.4V, the memory was no longer functional. These tests were included in a larger campaign of experiments. Thus, due to logistic reasons, we could not perform more experiments at voltages above 1.2V.

A. Sensitivity vs. Bias Voltage

Results at nominal voltage (3.3V, Round H), which were carried out in previous tests in 2013 for a sample of the same batch [START_REF] Clemente | Statistical Anomalies of Bitflips in SRAMs to Discriminate SBUs From MCUs[END_REF], have also been included in Table I as reference. In that occasion, SRAMs were set at a fairly large distance from the target (40 cm), to limit the neutron flux to approximately 3 × 10 4 n•cm -2 •s -1 . Under those conditions, the memories were exposed to a fluence of 1.08×10 8 n•cm -2 within 1 hour. It must be taken into account that, after that test, the facility was upgraded so the flux neutron value used in the low-power tests presented in this paper was significantly higher (4.5×10 7 n • cm -2 • s -1 ).

In rows A-H of Table I, one can roughly observe that, under identical conditions, the number of observed events increases as the power supply decreases. However, those data "as is" cannot be used to estimate the sensitivity of the device because MCUs need to be extracted from the bulk set of errors. In order to discern SBUs/MCUs from the bulk set of errors, proprietary unscrambling information from Cypress was used, which allowed relating addresses involved in the same multiple event. Affected addresses located at a Manhattan distance lower than 5 were grouped in the same MCU. This threshold distance was chosen to detect cells placed in opposite coins of a 3x3 square. Table II shows the MCUs that were detected, and classifies them by their multiplicity. The largest event that was observed was a 10-bit MCU, which occurred at 0.5V. Finally, Figure 2 shows the cross section of this device for SBUs to 4-bit MCUs, and for different voltage levels. This graph also includes error bars for the experimental crosssection calculations, which have been calculated with 95%confidence intervals, as explained in [START_REF] Velazco | Evidence of the Robustness of a COTS Soft-Error Free SRAM to Neutron Radiation[END_REF]. Those of 5-bit to 10-bit MCU cross sections were so wide that it was impractical to include them in the figure. In any case, all the values have also been tabulated in Table III. In this case, it is easy to hint Bias Voltage (V) 3.5 the cross sections for 7-bit to 10-bit MCUs, given the very few number of such events that were observed (not included in Table III for the sake of clarity).

Figure 2 also includes predictions issued from the modeling approach MUSCA-SEP 3 . The calculations of this tool consider a dynamic neutron spectrum issued from a spectrometer and a technological model (i.e. elementary cell topology), determined through a technical analysis and technological parameters, based on the International Technology Roadmap for Semiconductors (ITRS) [START_REF]International Technology Roadmap for Semiconductors (ITRS)[END_REF].

B. Discussion

From the obtained experimental results, it can be easily deduced that the device sensitivity increases as the bias voltage decreases. This sensitivity seems to decrease significantly for the range 0.5V-1V, but for higher voltage values, it clearly flattens (see Figure 2).

As Figure 2 shows, the predictions for SBUs are in very good concordance with the experimental results. However, there are some problems with the interpretation of MCUs. Apparently, there is a soft increase as the power supply approaches 0.5V followed by saturation. This saturation is not predicted by MUSCA-SEP 3 . This discrepancy can be attributed to two factors: First, the lack of specific information about the physical layout of the SRAM under test. Second, MUSCA-SEP 3 is a Monte-Carlo tool exposed to randomness in such a way that unusual events occur few times, so the uncertainty in the calculation of unusual events is not negligible.

In any case, the predictions match fairly well the experimental results, with the possible exception of the SBU one at 3.3V. We believe that the reason of such small disagreement is that the experiment with 3.3V (Round H in Table I) was carried out at completely different environmental conditions: On the one hand, the neutron fluence was not the same as in Rounds A-G (let us remember that this experiment was made in 2013), and the uncertainty in that fluence value was higher. On the other hand, obviously the physical chip that was tested was different as well. In any case, they can still be considered acceptable since they are very similar. For 4-bit to 10-bit MCUs (not shown in the figure), error margins in the experimental cross sections are so high that it is impossible to reach any sound conclusions. Maybe the main point of disagreements between predictions and experimental results is the fact that MUSCA-SEP 3 did not predict events with multiplicity greater than 5, but experimentally, MCUs with larger multiplicities were observed. Thus, 2 6-bit MCUs were observed at 0.7V and 1.0V, respectively; a 7-bit MCU was observed at 1.0V; and a 10-bit MCU was observed at 0.5V (Table II). This is due to the fact that MUSCA-SEP 3 does not use exact data about the topology and internal organization of the memory cells, because this is proprietary information of the manufacturer. Approximations must be used instead and, as a consequence, the provided absolute values might disagree. However, the changes observed in the sensitivity of the memory at different voltages match quite accurately the experimental values (Figure 2). Hence, we can postulate MUSCA-SEP 3 as a good tool to make SRAM cross-section predictions at low bias voltages.

In these experiments, no microlatchups were observed. However, other authors, such as Hands et al. in 2012 [START_REF] Hands | Large-Scale Multiple Cell Upsets in 90 nm Commercial SRAMs During Neutron Irradiation[END_REF] did report events with multiplicity up to 150 (which they attributed to microlatchups) in very similar 90-nm Cypress SRAMs. In that case, two samples of Cypress CY62148ELL and CY62148EV30LL were irradiated with fusion-produced neutrons at 14 MeV, at the ASP facility at the Atomic Weapons Establishment (AWE), Berkshire, U.K. [START_REF]AWE Radiation Sciende homepage[END_REF]. In that case, the tested samples belonged to a different batch as the one that was tested in this paper, which clearly indicates that the manufacturer solved this problem in the release of further batches of the CY62148EV30LL SRAM. In addition, Samaras By checking the sensitivity trends in Figure 2, it can also be observed that the SBU sensitivity significantly increases at very low voltages, especially at near-threshold ones, contrarily to that of MCUs. This trend is consistent with the results presented by Pawlowski et al. [START_REF] Pawlowski | Characterization of Radiation-Induced SRAM and Logic Soft Errors from 0.33V to 1.0V in 65nm CMOS[END_REF], where it can observed that the sensitivity for all types of MCUs barely increased in the range of 0.3V-1.0V.

The shape of the observed MCUs has also been analyzed. These results are presented in Figure 3, which is a physical representation of the SRAM bitcell topology. The memory that was examined implements bit interleaving, and we obtained the physical location of the observed bitflips by using proprietary unscrambling information from the manufacturer. The 2-bit MCUs were firstly studied in greater detail, since they were numerous enough to extract some conclusions. The types of the observed 2-bit MCUs are described in Figure 3a.

The percentages of observed events of each type are described in Table IV. In all the cases, the most often 2-bit MCU was H1, followed by V1. Diagonal ones were also representative, whereas other types of horizontal and vertical ones, as well as the knight-jump ones occurred very few times. In addition it seems that, as the bias voltage decreases, the H1 type of event is less likely to occur. We believe that this is due to any technological and proprietary parameters of the memory to which, as users, we do not have access.

The shapes of large MCUs were also studied (Figure 3b). It can be observed that they were linear or almost linear (following a horizontal, vertical or diagonal distribution). This is clearly due to a ionizing particle displaced as a consequence of the interaction with the impinging neutron, which flips cells along its track until it loses all its energy. If microlatchups had occurred, a complete block of information would have been affected completely, and this is not the case. This figure also shows the bit values of the affected cells before the bitflips occurred. There are distributed roughly 50%-50%, hence there is no dependency in the value (0 or 1). However, an additional interesting fact can be observed: all the bit values belonging to the same MCU are the same. Since the experiments were carried out with the checkerboard pattern (0x55), this means that all the affected cells were placed in the same logical column. The reason being, in our opinion, that the power lines of the memory cells are distributed vertically. 3 MODELING TOOL This section discusses the impact of ultra low bias voltage for the 90-nm SRAM for an atmospheric environment. Results are based on MUSCA-SEP 3 predictions thanks to 90-nm SRAM sensitivity model deduced from experiments analysed in Section III. Two radiation fields have been discussed: ground and avionic, which have been issued from the modeling tools ATMORAD (ATMOspheric RADiation) [START_REF] Hubert | Radiation Effects Investigations Based on Atmospheric Radiation Model (ATMORAD) Considering GEANT4 Simulations of Extensive Air Showers and Solar Modulation Potential[END_REF].

IV. SER PREDICTIONS ISSUED BY THE MUSCA-SEP

A. Cross section calculation based on MUSCA-SEP 3

MUSCA-SEP 3 is a soft error prediction platform based on a Monte-Carlo approach that allows obtaining a complete simulation, ranging from the interaction of radiation particles with the matter to the occurrence of a SEE in the integrated circuit. The principle of the modeling is discussed in previous works [START_REF] Hubert | Operational SER Calculations on the SAC-C Orbit Using the Multi-Scales Single Event Phenomena Predictive Platform (MUSCA-SEP3)[END_REF], [START_REF] Artola | SEU Prediction From SET Modeling Using Multi-Node Collection in Bulk Transistors and SRAMs Down to the 65 nm Technology Node[END_REF].

To model the 90 nm SRAM (planar bulk technology) devices, it is necessary to describe the active zones (drains and sources) and the Shallow-Trench Isolation (STI) topology. The methodology includes a General Design Specification (GDS) extractor, which allows deducing these details from GDSII files. Concerning the 90 nm SRAM studied in this paper, a reverse analysis was performed to deduce the elementary cell topology and the organization between adjacent cells (MCU investigation). The results of this analysis were presented in a previous work [START_REF] Artola | In Flight SEU/MCU Sensitivity of Commercial Nanometric SRAMs: Operational Estimations[END_REF].

Concerning interactions, GEANT4 was used to develop and to integrate databases containing electron-hole pair densities induced by nuclear and ionization physical processes. Electron-hole pair's depositions occurring close to the sensitive areas were modeled from the 3D morphology database as a function of the ion energy, type and incidence angle [START_REF] Raine | Impact of the Radial Ionization Profile on SEE Prediction for SOI Transistors and SRAMs Beyond the 32-nm Technological Node[END_REF].

Transport and collection mechanisms in the active area are crucial to evaluate the impact at semiconductor level (charge or transient). Indeed, 3D carrier morphology evolves according to mechanisms as well as drift (electric field), diffusion (carrier concentration gradient), collection and recombination processes. Bipolar amplifications can also be considered. Analytical models describing the transport and collection mechanisms were mainly issued from Technology Computer Aided Design (TCAD) simulations, and calibrated for investigated technological nodes.

Thus, MUSCA-SEP 3 aims at calculating SEE cross sections, including neutron, proton, muon, alpha and heavy ion contributions. It is important to note that nuclear and coulomb processes were simultaneously considered, which is crucial for protons. Conventional methods to calculate the cross section consist in calculating the ratio between the number of events the particles fluence. Therefore, a more realistic approach in defining the probability of obtaining a given number of SEEs during a given time and for a given flux level [START_REF] Hubert | Operational Impact of Statistical Properties of Single Event Phenomena for On-Orbit Measurements and Predictions Improvement[END_REF].

B. Methodology to calculate the atmospheric SER

The sensitivity against SEEs of advanced nano-scale electronic devices is expected to increase, and recent studies have demonstrated the occurrence of SEEs due to cosmicray showers, which are composed by neutrons, protons and muons [START_REF] Sierawski | Impact of Low-Energy Proton Induced Upsets on Test Methods and Rate Predictions[END_REF]- [START_REF] Hubert | Effect of Radial Ionization Profile of Proton on SEU Sensitivity of Nanoscale SRAMs[END_REF]. The type of secondary radiations and their intensity depend on the altitude, the geomagnetic latitude and the Sun's activity. For example, at sea level, muons are the most numerous terrestrial species. Thus, it is necessary to take into account the neutron, proton, and muon spectrum in order to assess the SER, particularly for ultra low bias voltage conditions, for which the critical charge is very low.

In order to study the effects of SEEs, it is also necessary to take into account the emitter alpha problematic induced by the contamination of the materials (wafer, package and radioactive specific materials in passivation and metallization layers).

The methodology that allows calculating the atmospheric SER is based on Equation 1.

SER = p=n,p,µ σ SEE (E, p)• dΦ p (E, p) dE •dE +SER α (1)
where

dΦp(E,p) dE
, σ SEE (E, p) and SER α stand for the differential spectrum, the SEE cross section and the Alpha SER, respectively. The p index designates the particle type; i.e., neutron, proton or muon. SEE cross sections were calculated thanks to MUSCA-SEP 3 . In this work, the atmospheric radiation fields (ground and avionic) were deduced by means of an atmospheric radiation model named ATMORAD [START_REF] Hubert | Radiation Effects Investigations Based on Atmospheric Radiation Model (ATMORAD) Considering GEANT4 Simulations of Extensive Air Showers and Solar Modulation Potential[END_REF], which is based on GEANT4 simulations of extensive Air Showers according to primary spectra which only depend on the solar modulation potential (Force-Field Approximation [START_REF] Gleeson | Solar Modulation of Galactic Cosmic Rays[END_REF], [START_REF] Cheminet | Cosmic Ray Solar Modulation and Forbush Decrease Analyses Based on Atmospheric Neutron Spectrometry at Mountain Altitude and GEANT4 Simulations of Extensive Air Showers[END_REF]). Moreover, the solar potential is deduced from measurements issued from the neutron spectrometer operated by ONERA [START_REF] Hubert | Long and short-term atmospheric radiation analyses based on coupled measurements at high altitude remote stations and extensive air shower modeling[END_REF], [START_REF] Hubert | Analyses of cosmic ray induced-neutron based on spectrometers operated simultaneously at mid-latitude and antarctica high-altitude stations during quiet solar activity[END_REF] in the Pic-du-Midi (France, +2880 m above sea and the Concordia scientific station (Antarctica). The ground environment has been characterized by the geomagnetic location and altitude of the city Toulouse (France, 141 meters above sea level), whereas a Paris -Los Angeles flight has been considered to investigate the avionic conditions.

Concerning Alpha radiation impurities, they can be found in some packaging materials and chemicals used in the fabrication process of the chip. The emission can range widely depending on the quantity and purification grade of the materials. MUSCA-SEP 3 can be adapted to investigate and quantify the α-SER contribution. However, the material properties required to define the α-emissivity types and their locations are rarely available. The alpha emitter contamination effect is considered as the sum of the package and wafer contributions (Equation 2). In this first approach, we have considered a constant value for ε waf er of 5 × 10 -4 α • cm -2 • hr -1 . This value was selected because it is typically considered for wafer emissivity [START_REF] Heald | How Cosmic Rays Cause Computer Downtime[END_REF]- [START_REF] Baumann | Call for improved ultra-low background alpha-particle emission metrology for the semiconductor industry[END_REF] and because it corresponds to a Hyper-Low-Alpha (H.L.A. [START_REF] Zhu | Logic SER characterization, Tutorial[END_REF]) grade for package contamination. In fact, four alpha emission categories can be considered for ε package :

• Hyper-Low-Alpha (H.L.A., ε package < 5×10 -4 α•cm -2 • hr -1 ). • Ultra-Low-Alpha (U.L.A., ε package < 10 -3 α • cm -2 • hr -1 ). • Low-Alpha (L.A., ε package < 10 -2 α • cm -2 • hr -1 ). • Standard (S., ε package ∼ 0.01 -10 α • cm -2 • hr -1 ).
In order to simplify the calculations, the alpha energy is considered equal to 6.5 MeV. This approach constitutes a very first step for determining the order of magnitude to be compared with the other contributions of concern (neutrons, protons and muons).

C. SER experimental results

Figure 4 presents the ground and avionic radiation fields including the neutrons, protons and muons spectrum. Although it was mentioned that a Paris -Los Angeles flight was considered to study the avionic conditions, Figure 4b shows the spectrum of the instantaneous geomagnetic position: Latitude = 61.35 SER calculations discussed in Subsection IV-C2 consider the total flight. 1) SER for Ground radiation field: SER predictions at ground level were firstly carried out with MUSCA-SEP 3 . Figure 5 shows the calculated SER due to particles, which was obtained considering U.L.A., H.L.A., L.A. and Standard emission categories. Note that, for the sake of clarity, the curves for H.L.A. and U.L.A. have been multiplied by 100, and that of L.A. has been multiplied by 10. Besides, the SERs attributed to neutrons, protons and muons are presented in Figure 6 as a function of the bias voltage. In Figure 6a, different types of events multiplicity are categorized, from SBU to 6-bit. In this case, the curves for 4-bit, 5-bit and 6-bit have also been multiplied by 10. Both results allow evaluating the global SER for ground environment. As both figures show, the voltage decrease induces an increase in the SEU susceptibility against radiation, especially below 1.3V. For this technology, α-SER is the main contribution if the emission category is L.A. (Figure 5). Besides, the orders of magnitude issued from calculations are consistent with underground experiments [START_REF] Hubert | Radiation Effects Investigations Based on Atmospheric Radiation Model (ATMORAD) Considering GEANT4 Simulations of Extensive Air Showers and Solar Modulation Potential[END_REF], [START_REF] Lesea | Qualification Methodology for Sub-Micron ICs at the Low Noise Underground Laboratory of Rustrel[END_REF].

It is also interesting to investigate the separate neutrons, protons, and muons contributions to the SER, particularly at ultra low bias voltages. Thus, for the SER corresponding to SBUs in Figure 6a, these separate contributions have been calculated and presented in Figure 6b. The results suggest that muon-induced upsets start affecting the SER when the SRAM memory operates at bias voltages below 1.2V.

2) SER for Avionic radiation field: This subsection presents a similar analysis, but applied to the avionic environment (in particular, for heights at which commercial flights operate, ∼12 km). The results are presented in Figure 7. Figure 7a shows the SER vs. bias voltage, categorizing the events by multiplicity (from SBUs to 6-bit MCUs). As in the ground environment results, the SER increases as the bias voltage decreases, and it skyrockets when the SRAM is powered up at 1.2V or below. The contributions of neutron, proton and muon are presented in Figure 7b, and demonstrate that the main contribution is due to neutrons, regardless of the bias voltage. The contribution of muons start to become significant 2V, but it is still lower than that of the protons in all of the cases (note that Figure 6b shows the opposite for ground level, as expected). It would be interesting to conduct a similar analysis on more integrated technologies, mainly to investigate the contribution of direct ionization of protons.

Another interesting analysis that has been performed consisted in evaluating the total number of SEUs observed during commercial flights. Figure 8 presents predictions issued by MUSCA-SEP 3 for SEUs; in particular, for a Paris -Los Angeles flight, and distinguishing the contributions of SBUs and MCUs separately. These predictions have also been crosschecked with actual results. In 2009, an experimental platform developed by the authors including 1 Gigabit memory built with 64 16-Mbit 90-nm Cypress CY62167EV30LL-45ZXI SRAMs was used for SEU detection during said flights [START_REF] Peronnard | Real-Life SEU Experiments on 90 nm SRAMs in Atmospheric Environment: Measures Versus Predictions Done by Means of MUSCA SEP3 Platform[END_REF]. These memories belonged to a different batch than the ones tested at low voltage (Table I). Among them, it is remarkable to mention a Paris -Los Angeles flight, during which 15 bitflips detected (6 SBUs, 1 double MBU, 2 double MCUs and 1 triple MCU). These data (6 bitflips due to SBUs and 9 bitflips due to MBUs/MCUs) were in agreement with the estimations. They are also displayed in Figure 8. In that case, the SRAMs were powered up at nominal bias voltage. This paper has presented the sensitivity characterization of the COTS CMOS 16-Mbit SRAM CY62167EV30LL-45ZXI manufactured by Cypress Semiconductor, when powered up at ultra-low bias voltage. Firstly, experimental results carried out with 14-MeV neutrons at GENEPI2 facility have shown a clear evidence of the increase in the neutron cross section at ultra-low bias voltages, especially below 1.3V. These results were mostly in concordance with theoretical cross-section predictions issued by the modeling tool MUSCA-SEP 3 . However, discrepancies on MCUs at lower voltages were found, which have been attributed to the statistical error made in the predictions with few data. Finally, MUSCA-SEP 3 also issued SER predictions that allowed characterizing the sensitivity of this memory at different radiation fields (ground and avionics); for neutrons, protons, muons and α particles.

Figure 2 .

 2 Figure 2. Cross sections of the 90-nm memory studied, for different voltage levels. Dots indicate experimental measurements, whereas the dashed line indicates the predictions issued from MUSCA-SEP3.

Figure 3 .

 3 Figure 3. Shapes of the observed MCUs. (a) 2-bit MCUs. There are two types of horizontal ones (H1 and H2), two vertical ones (V1 and V2), two diagonal ones (D45 and D135), and 4 types of events disposed in chess-like knight-jump move (K1, K2, K3 and K4). (b) 5-bit to 10-bit MCUs. Values stored in the cell before the bitflip are shown.

α 2 )Figure 4 .

 24 Figure 4. Characterization of the neutrons, protons and muons spectrum for (a) ground and (b) avionic radiation fields

Figure 6 .

 6 Figure 6. Calculated SER vs. bias voltage at ground level. (a) SBU to 6-bit MCU SER. (b) SER distinguishing the contributions of protons, neutrons and muons

Figure 7 .Figure 8 .

 78 Figure 7. Calculated SER vs. bias voltage at the avionic level. (a) SBU to 6bit MCU SER. (b) SER distinguishing the contributions of protons, neutrons and muons

  Table III EXPERIMENTAL CROSS SECTIONS (NORMAL INCIDENCE), IN cm 2 /bit

			Table II
	EVENTS CLASSIFICATION (NORMAL INCIDENCE)
	Bias voltage (V)	SBU	2-bit	3-bit	4-bit	5-bit
	0.50	1645	96	12	8	2
	0.60	1385	89	10	3	0
	0.70	1215	96	13	3	1
	0.80	1065	97	15	4	0
	0.90	876	99	12	4	0
	1.00	734	79	16	5	0
	1.20	623	69	7	0	0
	3.30	86	12	2	1	0
	Bias voltage (V)	6-bit	7-bit	8-bit	9-bit	10-bit
	0.50	0	0	0	0	1
	0.60	0	0	0	0	0
	0.70	1	0	0	0	0
	0.80	0	0	0	0	0
	0.90	0	0	0	0	0
	1.00	1	1	0	0	0
	1.20	0	0	0	0	0
	3.30	0	0	0	0	0
	Bias voltage (V)	SBU		2-bit		3-bit
	0.50	8.73 -9.62	4.33 -6.53	3.45 -11.70
	0.60	7.31 -8.13	3.98 -6.10	2.67 -10.20
	0.70	6.39 -7.16	4.33 -6.53	3.86 -12.40
	0.80	5.58 -6.30	4.38 -6.59	4.68 -13.80
	0.90	4.56 -5.21	4.48 -6.71	3.45 -11.70
	1.00	3.80 -4.40	3.48 -5.48	5.09 -14.50
	1.20	3.20 -3.75	2.99 -4.86	1.57 -8.03
	3.30	3.79 -5.86	3.42 -11.60	1.34 -40.00
		×10 -14		×10 -15		×10 -16
	Bias voltage (V)	4-bit		5-bit		6-bit
	0.50	1.92 -8.78	0.14 -4.02		0 -2.05
	0.60	0.35 -4.88	0 -2.05		0 -2.05
	0.70	0.35 -4.88	0.01 -3.10	0.01 -3.10
	0.80	0.61 -5.71	0 -2.05		0 -2.05
	0.90	0.61 -5.71	0 -2.05		0 -2.05
	1.00	0.90 -6.50	0 -2.05	0.01 -3.10
	1.20	0 -2.05		0 -2.05		0 -2.05
	3.30	0.14 -30.80	0 -20.40		0 -20.40
		×10 -16		×10 -16		×10 -16

Table IV OCCURRENCE

 IV DISTRIBUTION OF THE MOST OFTEN 2-BIT MCUS: H1, V1, D45 AND D135 al.[START_REF] Samaras | Single Event Upset cross section dose dependence on 90nm SRAM, ESA/ESTEC[END_REF] also reported a very high susceptibility of the CY62148EV30LL45ZSXI and CY62167EV30LL45ZXA 90nm Cypress SRAMs to suffer microlatchups when exposed to heavy ions at nominal bias voltage. Although the work in this paper does not target radiation effects caused by heavy ions, in the future it would be interesting to carry out similar tests at ultra-low bias voltage, too.

	Round	H1	V1	D45	D135	Others
	A (0.50V)	60.42% 10.42%	7.29%	9.38%	12.49%
	B (0.60V)	65.17% 19.10%	4.49%	3.37%	7.87%
	C (0.70V)	66.67% 22.92%	3.13%	2.08%	5.2%
	D (0.80V)	62.89% 23.71%	4.12%	4.12%	5.16%
	E (0.90V)	74.75% 14.14%	2.02%	3.03%	7.06%
	F (1.00V)	75.32% 14.29%	2.60%	3.90%	3.89%
	G (1.20V)	79.71%	7.25%	0%	7.25%	5.79%

et

  • , Longitude = -64.18 • and Altitude = 11.58 km. Nevertheless,

	Soft Error Rate (S.E.R.) (FIT/Mbit)	4.0×10 5 6.0×10 5 8.0×10 5 1.2×10 6 1.4×10 6 1.0×10 6				PREDICTIONS Alpha impurities U.L.A. (x100) H.L.A. (x100) L.A. (x10) Standard
		0	0.5	1	1.5	2	2.5	3	3.5
				Bias Voltage (V)
	Figure 5. Calculated SER vs. bias voltage due to alpha emission categories
	(U.L.A., H.L.A., L.A. and Standard)

  Soft Error Rate (S.E.R.) (FIT/Mbit)

		7×10 6 8×10 6			(a)	SBU PREDICTIONS Avionics
							2-bit MCU
		6×10 6					3-bit MCU 4-bit MCU (x10)
							5-bit MCU (x10)
		5×10 6					6-bit MCU (x10)
							TOTAL SER
		4×10 6
		3×10 6
		2×10 6
		10 6
		0
		0	0.5	1	1.5	2	2.5	3	3.5
					Bias Voltage (V)
	Soft Error Rate (S.E.R.) (FIT/Mbit)	0 10 6 2×10 6 3×10 6 4×10 6 5×10 6 6×10 6 7×10 6

IEEE TRANSACTIONS ON NUCLEAR SCIENCE -PEER REVIEW -DRAFT COMPILED ONMarch 14, 2017-12:33

This work was supported in part by the Spanish MCINN project TIN2013-40968-P and by the mobility grant "José Castillejo" for professors and researchers.

J. A. Clemente and H.


Remy Vauche
email: remy.vauche@im2np.fr

Sylvain Bourdel

Nicolas Dehaese

Jean Gaubert

Oswaldo Ramos Sparrow

Eloi Muhr

Herve Barthelemy

High Efficiency UWB Pulse Generator for Ultra Low Power Applications

This paper presents the design of a fully integrated ultra low power Ultra Wide Band (UWB) pulse generator. The circuit is designed and optimized for low rate and localization applications. This UWB transmitter is based on the impulse response filter method in order to achieve high energy sub-nanosecond pulses. The circuit has been integrated in a ST-Microelectronics CMOS 0.13µm technology with a supply voltage of 1.2V on a die area of 0.56mm 2 . A power manager is used to reduce the power leakages to 3.91µW which gives a power consumption of 3.98µW@10kbs -1 . The measured dynamic energy consumed per pulse is 68pJ and the measured energy of the emitted pulse is 2.15pJ.

I INTRODUCTION

Thanks to the gated nature of the signal, Ultra Wide Band Impulse Radio (IR-UWB) is a promising technology for ultra low power application. When efficient power gating techniques are used, the power consumption between two consecutive pulses can be highly reduced and the overall power consumption is scalable with the bit rate. Consequently, IR-UWB is a good candidate for ultra low power applications such as Radio Frequency Identification (RFID), or autonomous Wireless Sensor Network (WSN) in particular when localization capabilities are needed. For these applications, the need for (low cost) self or remotely powered communication systems is very high. The design of an ultra low power communication system is a very challenging issue, especially concerning the radio-frequency front-end which generally consumes the greatest part of the power budget. For example, in a remotely powered RFID UHF transmitters commonly named passive TAGs, the available power is only about few micro-watts at 10 meters from the reader and has to supply the TAG [START_REF] Karthaus | Fully integrated passive UHF RFID transponder IC with 16.7W minimum RF input power[END_REF]. In the case of a 10cm 2 photovoltaic harvesting system, the available power is around 100µW under 100lm (lumen) lighting which corresponds to a typical indoor environment. In both cases, the energy must be stored which is a major drawback. First, the use of an energy tank such as external capacitors or micro-battery (cell) increases the manufacturing cost. Second, the communication is turned off when the battery is charging which reduces the instantaneous bit rate. IR-UWB can resolve these issues since previous published works present fully integrated transmitters having a power consumption of few micro-watts [START_REF] Crepaldi | An Ultra-Low-Power interference-robust IR-UWB transceiver chipset using self-synchronizing OOK modulation[END_REF]. Such power consumption allows the system to be always powered and lower than the constraint on the storage. Since it reduces the storage constraints and can be fully integrated, IR-UWB appears to be a good low cost solution for ultra low power applications. Moreover, IR-UWB is also a promising technology for localization systems due to the high temporal resolution of the signal. Both localization and low cost are interesting properties for ultra low power applications such as RFID or WSN, but they need high energy pulses to be efficiently exploited. Indeed, high energy pulses increase the localization precision [START_REF] Guidi | Backscatter Communication Using Ultrawide Bandwidth Signals for RFID Applications[END_REF] and enable the use of a low cost non-coherent receiver [START_REF] Dehaese | Lowpower CMOS energy detector for noncoherent impulse-radio UWB receivers[END_REF]. Finally, to meet these application requirements, the transmitted energy must be increased while the energy consumed by pulse must be reduced. In other words, the energy efficiency of the transmitter must be increased as much as possible. Consequently, this energy efficiency appears to be the most significant Figure Of Merit (FOM) in order to evaluate performance in such a context. In this paper, we present the design of an ultra low power pulse generator providing high energy pulses. The power consumption and the energy efficiency have been optimized for ultra low power and low cost systems. In the first part, starting from the analysis of the FOM presented in the literature dedicated to pulse generators, a design strategy which optimizes the energy efficiency for a given low power application is presented. Then the proposed architecture, based on an integrated filter excitation technique, is described in section III. Particular attention is paid to the power management and to the output dynamic. The last section presents measurement results of the pulse generator realized in a standard 130nm CMOS technology.

II POWER EFFICIENT TOPOLOGY A) Figure of Merit

For pulse generator design, the most often used FOM is the consumed energy per bit E C which is easily derived from the power measurement as follows:

E C = P DC @P RF P RF (1)
where P RF is the pulse repetition frequency and P DC @P RF the power consumption measured at a given P RF . In a practical implementation, due to leakage or biasing, some energy is consumed between the emission of two consecutive pulses and E C varies with P RF as shown in Fig. 1. It is therefore difficult to extrapolate from E C , the power consumption at any P RF and then to compare different architectures designed for different bit rates.

To overcome this limitation, [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF] gives the power consumed at a P RF equal to 0Hz (P 0Hz ) which represents the leakage power and the energy dynamically consumed by the generator (E AC ). As shown in Fig. 1, these metrics give the power consumption as a function of the P RF as follows :

P DC (P RF ) = P 0Hz + E AC • P RF (2)
These FOM are interesting since they give the power consumption at any bit rate. Moreover, these FOM can be easily extracted from measurements since P DC linearly varies with P RF . However, this FOM has some limitations. Since it does not take the emitted power P E into account, it is not possible to compare pulse generators that produce pulses with different energies. It is then relevant to evaluate the power efficiency which is finally equal to the energy efficiency shown as follows :

η (P RF ) = P E P DC = E P • P RF E C • P RF = E P P 0Hz /P RF + E AC (3)
where E P is the energy of the emitted pulse. This FOM can also be obtained from measurement data (E P = P E /P RF ). Due to the frequency limitation of some topologies, E P can decrease with the P RF . This FOM enables this effect to be taken into account.

B) Design strategies

Fig. 2 presents the power consumption of different published pulse generators. [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF] and [START_REF] Dokania | An Ultralow-Power Dual-Band UWB Impulse Radio[END_REF] principally use CMOS digital circuits which have no DC power consumption. This leads to a low P 0Hz which is mainly due to leakage current (96µW and 5µW for [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF] and [START_REF] Dokania | An Ultralow-Power Dual-Band UWB Impulse Radio[END_REF] respectively). It appears that a low P 0Hz performs best at low rate and leakage is one of the main issues in this context. In [START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF], differential MOS Current Mode Logic cells are used. This gives a high DC power consumption (3.2mW@0Hz) and a small E AC (6.4pJ/pulse) compared to other works (47 and 30pJ/Pulse for [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF] and [START_REF] Dokania | An Ultralow-Power Dual-Band UWB Impulse Radio[END_REF] respectively) since differential structures do not consume dynamic current. Fig. 2 clearly shows that this topology performs better for P RF higher than 100MHz and that reducing E AC is the main issue for the design of high speed pulse generators. The efficiency is given by ( 3) and shows relevant information. In Fig. 3 the efficiency is plotted as a function of the bit rate for the same generators as in Fig. 2. Since E P is rarely given, it has been approximated using ( 6) and [START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF]. For a better approximation, the effect of the pulse envelope on the energy is taken into account. Depending on the pulse shape, the pulse is modeled by a sine wave modulated by square function [START_REF] Dehaese | Lowpower CMOS energy detector for noncoherent impulse-radio UWB receivers[END_REF] or by a Gaussian pulse transposed at the center frequency f M of the pulse [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF].

p S (t) = A sin (2πf M t) π τ (t) (4) p G (t) = A exp -at 2 cos (2πf M t) (5)
The energy of the pulse can then be easily derived from the maximum value of the pulse A and its width τ as follows:

E P S = A 2 Z L τ 2 - sin (2πf M τ ) 4πf M (6)
E P G = A 2 2Z L π 2a 1 + exp - |4πf M | 2 8a with a = π 2 BW 2 -XdB 2 ln (10 XdB/10 ) (7)
where Z L is the load impedance of the pulse generator and BW -XdB the -XdB bandwidth. An analysis of the efficiency gives interesting information for the design strategies. [START_REF] Wentzloff | A 47pJ/pulse 3.1-to-5GHz All-Digital UWB Transmitter in 90nm CMOS[END_REF] achieves a higher output dynamic A than [START_REF] Dokania | An Ultralow-Power Dual-Band UWB Impulse Radio[END_REF] which consequently increases the dynamic consumed energy E AC . It is a drawback when only the power consumption is considered but, as shown in Fig. 3, the efficiency is finally higher for bit rates higher than a few MHz. It also appears that maximizing the output dynamic is an important issue when high efficiency is needed, even if it is at the cost of an increased E AC . Based on these observations, the presented design will first focus on leakage current reduction methods to address ultra low power and low rate applications. Secondly, the output dynamic will be maximized (at the cost of an increased E AC ) to improve the efficiency and also to optimize the power budget which is an important issue in low power applications.

C) Architecture Choice

Among the different techniques used for pulse generation, ON/OFF Local Oscillator (LO) and filter excitation are the most promising topologies to reduce power consumption. To maximize the output dynamic and the bandwidth in ON/OFF LO, the LO start time must be as small as possible and an inverter based ring oscillator should be preferred [START_REF] Sim | A CMOS UWB Pulse Generator for 6-10 GHz Applications[END_REF].

With such topology, CMOS technology can be used which reduces the P 0Hz . ON/OFF LO technique highly reduces the P 0Hz since the LO is turned on only during the pulse duration. To be fully efficient, the power amplifier or the antenna driver must be power managed [START_REF] Phan | Energy-Efficient Low-Complexity CMOS Pulse Generator for Multiband UWB Impulse Radio[END_REF][START_REF] Barras | Low-power ultra-wideband wavelets generator with fast start-up circuit[END_REF]. To reduce further the time conduction of the active cells, it is possible to use filter excitation. With such a technique, a very short baseband pulse is used to excite a filter to produce its impulse response. Here, the conduction time of the active cells is around 100ps [START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF] and is independent of the pulse bandwidth BW whereas in ON/OFF LO it depends on 1/BW . A short time conduction of the active cells limits E AC and improves the efficiency. Moreover, the filter excitation technique can achieve large amplitude pulses which lead to high E P . It also facilitates the integration and the packaging process [START_REF] Bourdel | CMOS UWB pulse generator co-designed with package transition[END_REF]. At last, the filter excitation well suits the generation of sub-nanosecond duration pulses needed to reach high localization precision [START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF].

The proposed architecture is based on an integrated filter excitation technique and the principle is given in Fig. 4. The baseband pulse used to excite the filter is generated by a Low-Vt Digital Edge Combiner implemented with CMOS logic cells. To reduce the leakages, a high-Vt Managed Power Supply (MPS) which control managed power lines (V-VDDX and V-GNDX) is used. The filter is a passive fully integrated circuit and is driven by a C class amplifier to reduce P 0Hz consumption.

III PULSE GENERATOR DESIGN

The pulse s(t) produced by the excitation filter technique is the response of the filter to a baseband pulse π τ (t). The expression of s(t) and its Fourier transform are given by :

s (t) = B √ l • π τ (t) * h E (t) (8)
S (f ) = Bτ sinc (πτ f ) • H E (f ) √ l (9)
where l represents the power loss of the filter, H E (f ) the normalized transfer function of the filter, B the magnitude of the basesband pulse and τ its time duration. The main characteristics of the pulse are given by the baseband pulse (through B and τ ) and by the filter impulse response. This technique has been widely presented and a detailed sizing method is given in [START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF]. In this design, we use a third order Bessel-Thompson filter driven by a 1.2V magnitude and 75ps width baseband pulse. A standard CMOS 130nm technology is used.

A) Power Management System

The aim of the power manager is to reduce the leakage current when no pulses are generated. Several techniques have been proposed to reduce leakage current of CMOS logic circuits. A first technique named VTCMOS consists in applying different bias voltages to the substrate depending on the operating mode of the cell [START_REF] Keshavarzi | Effectiveness of reverse body bias for leakage control in scaled dual Vt CMOS ICs[END_REF]. When the cell is off, the substrates of the NMOS transistor (resp. PMOS) can be for example connected to VDD (resp. GND) in order to increase (resp. decrease) the threshold voltage V t and thus limiting the leakages. A second technique (DTCMOS) consists in dynamically changing the threshold voltage when the circuit is commuted [START_REF] Assaderaghi | A dynamic threshold voltage MOSFET (DTMOS) for very low voltage operation[END_REF]. In the CMOS inverter case, the gates of the PMOS and NMOS are connected to the substrate. For both VTCMOS and DTCMOS, an isolated substrate is needed and triple-well or SOI technologies must be used which increase the manufacturing cost. A third solution is to use a multi-Vt CMOS technology [START_REF] Wei | Design and optimization of dual-threshold circuits for low-voltage low-power applications[END_REF] which provides transistors having different threshold voltages. Most of the standard CMOS technologies offer Low Leakage (LL) transistors having high-Vt and High Speed (HS) transistors having low V t. The proposed power manager uses a multi-Vt-CMOS approach where Low Leakage (LL) transistors are used to power supply the High Speed (HS) transistors which are used to implement the Low-Vt Digital Edge Combiner.

The elementary inverter used in the design of the Digital Edge Combiner is presented in Fig. 5. The NMOS and PMOS HS transistors have respectively their bulks connected to GND and VDD whereas their sources are respectively connected to the managed power line V-GNDX and V-VDDX provided by the MPS. The MPS is based on LL inverters which are sized in order to deliver the same drain source current I DS than the HS transistors. Since I DS is a linear function of the saturation current density J SAT (A.m-1) and of the MOS width W [START_REF] Sakurai | Alpha-power law MOSFET model and its applications to CMOS inverter delay and other formulas[END_REF], the required size of the LL is given by :

W LL = J SAT -HS J SAT -LL • W HS ( 10
)
where the NMOS, or the PMOS transistors of the HS and LL inverters can be considered. The idle state of the HS inverter output defines the signal to be connected at the input of the LL inverter of the MPS. When the idle state is 0, the LL inverter input which provides V-GNDX is connected to VDD and the LL inverter input which provides V-VDDX is connected to PM since it is the power management signal active on the high state provided by MPS. When the idle state is 1, the LL inverter input which provides V-GNDX is connected to PM\ and V-VDDX is connected to GND. Thus, when power management is active (PM = 1), HS inverter is short-circuited since its V-GNDX, V-VDDX and also OUT are equal to the same voltage. In this case, the total leakage depends only on twice the sum of leakage current of the LL inverter which is much lower than the HS inverter leakage for an equivalent saturated current. The gain g OF F on the leakage power P 0Hz achieved by this power management technic only depends on the saturation current density J SAT of the LL and HS transistor and is given by :

g OF F = J OF F -HS • W HS 2 • J OF F -LL • W LL = J OF F -HS • J SAT -LL 2 • J OF F -LL • J SAT -HS (11)
where J OF F is the linear leakage current density (A.m -1 ) of the considered MOS transistor. It clearly appears that the proposed power management technic has benefits only when the ratio between J SAT and J OF F of the LL inverters is greater than twice the one of the HS. In the case of a more complex logic function such as the inverter chains used in the edge combiner or in the power manager, a particular focus has to be done on the chosen idle state of each stage which composes the function. Here the idle states have to be alternatively 0 and 1 in order to keep coherent logic states with the realized logic function inside each HS stage as shown on Fig. 6 where an inverter chain with a growth factor of h is represented. To reduce the complexity, LL inverters with an identical input signal can be merged in order to simplify the final circuit. To limit the current driven by each inverter and to improve the decoupling, the LL inverters are split into several parts which are distributed all along the power line.

B) Edge combiner

The edge combiner used has to generate the baseband pulse required by the filter excitation technique when a rising edge appears on CK. Then, CK is used to set PM and PM\ to GND and VDD respectively and then to control the MPS. As shown in Fig. 7, CK is delayed (CKd) before being provided to the edge combiner in order to ensure that the circuits are turned on when the signal is applied to the input. CKd is propagated through a delay line. Two consecutive edges (A and B\) are combined to produce the baseband pulse needed to excite the filter. CKd is further delayed to produce the signal (CKend) which is used by the power manager to shut down the power lines. The edge combiner uses only CMOS logic gates implemented with HS transistors and driven by the MPS. The baseband pulse is produced by using a simple CMOS NOR gate based on inverters designed as described above. A driver based on an inverter string is inserted at the output to match the small transistors (W=10µm) used in the NOR gate with the large ones used in the filter driver.

C) Band pass filter and filter driver

The band pass filter is a Bessel-Thompson filter. This filter is chosen because a third order is sufficient to match the FCC mask. Low order reduces the number of inductors needed and then reduces the loss in the filter which finally maximizes the E P . The filter must be carefully designed and the interconnected wires must be shortened during the layout realization to limit loss. The parasitic capacitances of the inductors must be compensated to avoid the degradation of the filter impulse response and to ensure that the pulse complies with the FCC mask. Among the different possible filter structures, the one chosen offers many advantages. The first resonator (L-C1) can be used to bias the filter driver. Cs achieves a DC isolation and C2 can be used to compensate the pad capacitance. Moreover, Cp can be reduced to compensate the parasitic capacitance of Lp.

Cp and Cs can be reduced to compensate that one of Ls and C1 can be reduced to compensate both the output capacitance of the filter driver and the parasitic capacitance of L. The filter is driven in a current mode in order to achieve a pulse magnitude greater than the supply voltage on the 50Ω input impedance of the filter. The driver is a class C amplifier to avoid power consumption when no pulse is generated. To further reduce the leakage, a LL transistor is used. The width of the transistor M1 is tuned to maximize the energy efficiency given by ( 3) which leads to a value of 560µm. The main parameters of the filter design are summarized in Table 1.

IV MEASUREMENT RESULTS

The pulse generator has been designed with a 0.13µm standard CMOS technology from ST Microelectronics. The die is shown in Fig. 8 and its area is 0.56mm 2 . The measured time and normalized frequency responses of the generated pulse are given in Fig. 9. The -10dB bandwidth (BW -10dB ) is 5.22GHz and is centred on 6.25GHz. The very wide bandwidth of the pulse leads to a very short time duration equal to 0.6ns which is a large benefit for localization precision but a major drawback for the emitted energy. The pulse magnitude is 2Vpp and produces high pulse energy although the duration of the pulse is short. The measured energy of the emitted pulse is 2.15pJ whereas the approximation given by ( 7) is 2.37pJ which confirm the accuracy of this approximation. The static leakage current is equal to 3.26µA which leads to a power leakage P 0Hz of 3.91µW for a voltage supply of 1.2V. Half of the power leakage is due to the filter driver. The measured power consumption is plotted for different PRF in Fig. 10 and is identical to the one obtained [START_REF] Crepaldi | An Ultra-Low-Power interference-robust IR-UWB transceiver chipset using self-synchronizing OOK modulation[END_REF]. The performances are compared with previous works in Fig. 10. The power consumption is only 3.98µW@1kbs -1 and 10.7µW@100kbs -1 which is well suited for ultra low powered applications. The value of E AC is extracted from this measurement and is 68pJ. Most of the consumed dynamic energy is due to the inverter string needed to match the edge combiner with the filter driver. In Fig. 11, the efficiency is plotted as a function of the PRF as introduced in (3) and is compared to previously published works which are summarized in Table 2. The pulse generator also exhibits good efficiency at low rates (0.06%@1kbs -1 and 2.22%@100kbs -1 ).

V CONCLUSION

The design of an ultra low power and high efficient pulse generator has been presented. The topology has been carefully chosen to achieve good performances at low rates. It is demonstrated that the filter excitation technique can generate very short 2.15pJ pulses which can be helpful for high precision location applications. Associated to a power management technique which reduces leakage current, this topology demonstrates also low power capabilities (3.98µW@10kbs -1 ) and could be used in ultra low power systems.

to 2000 he was an Assistant Professor at the Institut Supérieur dElectronique de la Méditerranée (ISEN) in Toulon, France. In 2000 he joined the University of Provence where is has been a full Professor since 2005. In 2007 He joined the University of Sud-Toulon-Var. Since 2005 he headed the Integrated Circuits Design Team at the IM2NP. The team has 12 researchers and Ph.D. students involved in several research projects with industry. His research interests are mainly in the design of radiofrequency analog integrated circuits. He authored and co-authored multiple publications in international journals and conference proceeding. Table 1. Main design parameters summary. Table 2. Performance summary of the proposed pulse generator and comparison with previous works.

List of figures and tables

Figure 1 :

 1 Figure 1: Instantaneous consumed power.

Figure 2 :

 2 Figure 2: Power consumption of several published pulse generators.

Figure 3 :

 3 Figure 3: Energy efficiency of several published pulse generators.

Figure 4 :

 4 Figure 4: Proposed pulse generator principle.

Figure 5 :

 5 Figure 5: Inverter set to 0 (a) and set to 1 (b) in the idle state with its associated Managed Power Supply (MPS).

Figure 6 :

 6 Figure 6: Inverter chain with MPS.

Figure 7 :

 7 Figure 7: Main signal chronograms.

Figure 8 :Figure 9 :

 89 Figure 8: Die photograph of the proposed pulse generator.

Figure 10 :

 10 Figure 10: Measured power consumption as a function of the PRF.

Figure 11 :

 11 Figure 11: Estimated efficiency as a function of the PRF.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .

 12345 Instantaneous consumed power. Power consumption of several published pulse generators. Energy efficiency of several published pulse generators. Proposed pulse generator principle. Inverter set to 0 (a) and set to 1 (b) in the idle state with its associated Managed Power Supply (MPS). Fig. 6. Inverter chain with MPS. Fig. 7. Main signal chronograms. Fig. 8. Die photograph of the proposed pulse generator. Fig. 9. Measurement of the time response (a) and the frequency response (b). Fig. 10. Measured power consumption as a function of the PRF. Fig. 11. Estimated efficiency as a function of the PRF.

Table 1 :

 1 Main design parameters summary.

	L	C1	Cs	Lp	Cp	Ls	C2	WM1
	(pH) (fF) (fF) (nH) (fF) (nH) (fF) (µm)
	326	486	584	1.08	338	1.05	32	560

Table 2 :

 2 Performance summary of the proposed pulse generator and comparison with previous works.

	Ref.	Vpp VDD Width BW	fM	P0Hz	EAC EP	Area	CMOS
		(V)	(V)	(ns)	(-10dB) (GHz) (µW) (pJ) (pJ)	(mm 2 )	(nm)
	[2]	0.61 0.9	2.0	0.5GHz 2.9-3.8 184	65	1.60 2 0.60 (die)	90
	[5]	0.65 1.0	3.0	0.5GHz 3.5-4.5 96	47	3.17 1 0.08 (core) 90
	[6]	0.45 1.0	3.0	1.0GHz 3.5-4.5 5	30	0.54 2 0.42 (core) 90
	[7]	1.42 1.2	0.5	6.8GHz 7.3	3200	6.4	0.64 2 0.54 (die)	130
	[9]	0.16 1.5	3.5	0.5GHz 3.8	3900	17	0.11 2 0.66 (die)	180
	[16]	0.60 1.0	2.5	0.5GHz 2.1-5.7 124	17	1.75 2 0.07 (core) 90
	[17]	0.09 0.9	3.5	0.5GHz 3.5-4.5 170	12	0.03 2 0.03 (core) 65
	[18]	0.45 0.9	2.4	0.5GHz 3.5-4.5 2.8	29	1.20 1 1.30 (die)	90
	This work 2.00 1.2	0.6	5.2GHz 6.3	3.91	68	2.37 2 0.56 (die)	130

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Computed with (6)

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Computed with

[START_REF] Bourdel | A 9-pJ/Pulse 1.42-Vpp OOK CMOS UWB Pulse Generator for the 3.1-10.6GHz FCC Band[END_REF]