WO2009071782A2 - Method for modelling the sensitivity of a cell of analogue and/or radio-frequency type and software implementing this method - Google Patents

Abstract

The invention relates to a method of modelling the sensitivity to noise of a cell (5, 7) of analogue and/or radio-frequency type. In this method, after having identified the class to which the cell belongs, a selection is made of the noise injection inputs (n1 k-nN k) of the cell as well as the output impacts (i1 k-ip k) influenced by the injection of noise at the input. The sensitivity model is then calculated, ensuring the relation (fk) between the noise signals injected on the noise injection inputs (n1 k-nN k) and the impacts (i1 k-ip k) selected, and this sensitivity model is associated with the description of the cell studied. The sensitivity model can be obtained by an analytic procedure, an empirical procedure or a combination of the two.

Description

 Method for modeling the sensitivity of an analog and / or radio-frequency type cell and software implementing this method

The invention relates to a method for modeling the sensitivity of a cell of analog and / or radio-frequency (RF) type as well as the software implementing this method. The object of the invention is in particular to define and model the sensitivity of the analog and / or RF circuits to external noise injected near these circuits.

The invention finds a particularly advantageous, but not exclusive, application in the field of CAD (Computer Aided Design), for the design of mixed electronic systems comprising analog and digital components.

By way of non-restrictive example, the electronic systems include integrated circuits on a single silicon block, or on several silicon substrates in the same package, for example SoCs (System on Chips) and SiPs (System in Package or System in a Box). By extension, the invention could also be applied for the design of electronic systems comprising components (integrated or not) on a printed circuit.

The manufacture of electronic systems is a very expensive operation, particularly when the system comprises one or more components integrated on silicon. Therefore, before starting a mass production, it is essential to control all the manufacturing parameters, and to give some of the values that maximize the probability that the manufactured circuit works properly.

To this end, there is a set of software products, called "electronic design automation tools", which help to design electronic systems from the description of the system specifications to be realized until the masks are made. photolithography used in the manufacture of the system.

One of the important elements in the design of an electronic system is to quantify the noise produced by the circuits, especially in a system. mixed. For this purpose, noise generating circuits (the aggressors) and noise sensitive circuits (the victims) are identified.

More precisely, all the circuits of the system can be considered as noise generators (aggressors). However, it is preferable to choose the noise generating circuits in the group comprising: digital circuits, memory cells, analog and radio-frequency (RF) circuits, such as VCOs (Voltage Controlled Oscillator), amplifiers power, and input-output circuits.

In particular, digital circuits tend to generate noise when switching their input signals. Of course, a circuit comprising at least one noise generating circuit is itself considered as a noise generating circuit.

The noise-sensitive circuits (victims) are selected from the group consisting of: analog and RF circuits, such as amplifiers, filters, oscillators, mixers, sample-and-hold devices, memory type digital circuits, phase, input-output circuits, frequency dividers / multipliers, automatic gain controllers (AGCs), and voltage references. Of course, a circuit comprising at least one noise-sensitive circuit is itself considered to be sensitive to noise.

The noise generated by the attackers, in particular the switching noise generated by the digital cells as well as the noise injected by the analog / RF / mixed cells (VCO, PLL, etc.), spreads to the victims via the substrates on which are mounted circuits, metal interconnects and housings. This noise tends to degrade the performance of the victims. This degradation may be such that the sensitive functions no longer meet the initial specifications. In the rest of the document, noise will be understood to mean any signal generated by an aggressor block that has an unwanted influence on the victims.

There is therefore a need to define and model the sensitivity of sensitive cells (analog and / or RF cells) to minimize the risk disruption of the functionalities of these cells due to the noise injected by the aggressive cells.

In practice, on the one hand, designers develop proprietary blocks, known as IP, analog and / or RF blocks, of which only the function they perform is perfectly known, the interior architecture being carefully kept secret in order to protect the know-how. On the other hand, integrators (who are often part of a team or company other than the IP designer) combine these IP blocks together to create complete mixed systems. The integrator needs the collaboration of the IP block designer to model the sensitivity of the IP block as part of the complete system it plans to implement.

Currently, the most used sensitivity modeling method is based on real simulations (behavioral or any transistor) of the functions concerned, when these functions are integrated on the complete system or only after retroannotation noise simulated or measured on the circuit full. By retro-annotation is meant the method which consists first of all in simulating or measuring the noise reaching critical input points of an analog or RF cell on a complete system and in a second time in adding the sources of noise equivalent to the netlist of the cell to simulate its behavior in the presence of this noise.

However, this method comes up against sometimes blocking limitations. Indeed, these simulations (complete systems or even relevant functions after retro-annotation), are very expensive in computing time and in memory and are sometimes impossible to implement for very complex systems.

In addition, very often, the designer of the IP block transmits to the integrator only the minimum information necessary for the integration of the circuit that he has developed, so as we have seen to protect his know-how. However, this minimum information is generally not sufficient to simulate the behavior of the block vis-à-vis the integrity of the analog and RF signals. In other words, the integrators often do not have sufficient knowledge of the functionality of the IP blocks to be integrated for perform the necessary simulations to model the sensitivity of these blocks.

Another method is to define, for each block of analog IP and / or RF to integrate, a maximum noise mask tolerated by the considered block. For a noise having a level higher than the threshold indicated by the template of the cell, the integrator considers that the cell does not meet the initial specifications. While for a noise having a level below the threshold indicated by the template, the integrator may consider that the cell meets the initial specifications.

This method runs up against the fact that it offers the system integrator only a small margin of maneuver: the comparison of the noise level reaching a cell with a threshold mask gives only a binary response of the "pass" type. Or "do not pass".

However, in practice, the integrator of a given system has a set of specifications to be respected, these specifications generally being set by the specifications (or the standard). It therefore has the ability to distribute the noise tolerable by the circuit (noise budget) on all blocks to achieve a balance respecting the specifications, which does not allow the method implementing the templates.

The invention solves the aforementioned problems by allowing in particular the system integrator to have the exact response of a given block noise reaching after integration.

For this purpose, in the invention, each analog cell or RF is considered to be a transfer function between: an aggression (noise) injected on one or more points of entry of the cell, these entry points being able to correspond to the cell inputs, such as the inputs receiving the signals to be processed or the supply voltages or at points of injection of noise internal to the cell, and - noise-influenced output impacts and reflecting the degradation of one or more features of the circuit. These output impacts may for example be the amplitude or the frequency of an output signal of the sensitive cell, a difference between the ideal output level and the actual output level, or the figure of noise observable on a given output, or a more abstract data such as information indicating whether the cell is working or not.

More precisely, to characterize the sensitivity of the cells of a studied system, it is firstly known to which class the sensitive circuits belong. The different classes of analog and / or RF circuits used in SoCs / SiPs correspond to the different types of sensitive circuits identified above, namely: amplifiers (power or low noise), frequency mixers, dividers / multipliers Frequency Controllers, AGC (Amplifier Gain Control), Oscillators (Quartz, Voltage Controlled (VCO), Relaxed ..) and Phase Locked Loops (PLLs); filters, mixed systems aggregating many of these cells.

Then, for each identified sensitive circuit, the noise injection points on the circuit, the outputs impacted by the injected noise, and the noise coupling between the input noise forms and the impacts on the functionalities of the circuit are identified. cell.

The noise injection points in the sensitive cell can be determined manually, thanks to the expertise of the analog / RF designer, or automatically through a series of dedicated simulations. At least the supply inputs of the analog and / or RF sensitive circuit are selected as noise injection inputs.

Then, cell sensitivity modeling can be performed using an analytical model, an empirical model, or a hybrid model to establish a relationship between the identified inputs and outputs. The choice of the model depends on the level of knowledge one has of the interaction between the noise inputs and the impacts on the outputs observed.

Thus, an analytical model is chosen when the propagation phenomena of the noise in the sensitive cell can be isolated and mathematically described. For example, the noise on the lines Power supply or control signal refers mainly to the output of a VCO (Voltage Controlled Oscillator) by AM-FM conversion, governed by the amplitude and frequency modulation equations. It is then a question of identifying and calculating the different parameters governing the model chosen thanks to specific simulations.

On the other hand, an empirical model is chosen when the phenomena involved are too complex to be described analytically. It is then necessary to carry out a certain number of simulations to characterize the sensitivity of the circuit and to capture the function of transfer by techniques ad hoc.

In an example of an empirical model, neural networks are used to characterize the transfer function establishing the relationship between the noise injection inputs and the output impacts.

An application of this empirical modeling consists in characterizing the degradation of the output of a power amplifier attacked by an external noise in terms of inter-channel interference, a typical measurement of which is the Adjacent Channel Power Ratio (ACPR), by Fourier Envelope simulations using a commercial RF simulator.

In some cases, one can also choose a hybrid model that is a combination of an analytic model and an empirical model, the analytic part modeling the behaviors of the cell that can be expressed as mathematical equations, the empirical model modeling cell behaviors too complex to model as mathematical equations.

In addition, a complex system can be treated as a single cell if a methodology for simulating its noise sensitivity can be applied directly and in reasonable time. In the opposite case, the system can be broken down into functional blocks and each block is characterized individually, the noise disturbances at the output of a block being added to the inputs of the next block. In this case, the model of the system results from the composition of the models of the different blocks. In the case of looped systems, the models of the blocks constituting each loop must be applied according to an iterative process until convergence. More precisely, at a given iteration of this process, the open-loop system is considered, which makes it possible to calculate the noise disturbance at the loop output by composition. This disturbance is reported on the input of the loop at the next iteration. In the case of a stable system, a finite number of iterations makes it possible to obtain forms of noise no longer evolving significantly from one iteration to another: it is said that the process has converged.

Similarly, a system composed of a set of cells can be treated in the same way, that is to say by combining the models of the different cells that make it up.

Thanks to the invention, the designers of analog and RF IP blocks have the possibility of modeling the sensitivity of the block concerned. This modeling allows them first of all to maximize the block's immunity to external noise, and then to attach to the block, a noise impact modeling, which will be used during the physical implementation.

Indeed, the integrator will be able to directly and rapidly determine the degradation of the critical functions of this circuit within a complete system by applying the noise forms (measured or simulated by dedicated tools) to the inputs of the sensitivity models obtained. by the designer at the modeling stage.

The system integrator will thus be able to predict the degradation of the functionalities of the block, that is to say the impact of the noise after the integration, without having to carry out any complex and expensive transistor simulations, and without the need of access detailed data from the block (for example the netlist) kept secret by the IP designer, which facilitates the dialogue between the designer and the integrator of IP blocks.

In addition, the invention allows the integrator to better manage the maximum noise on the circuit, offering him a wider margin of maneuver to distribute the noise in the circuit and result in a positive balance of noise distribution. The invention therefore relates to a method for modeling the sensitivity to noise of a sensitive electronic circuit of analog and / or radio frequency type, characterized in that it comprises the following steps:

the class of the sensitive circuit is identified, the noise injection inputs of the cell on which noise signals outside the cell are likely to be injected are selected from among the terminals of the cell;

selection of output impacts, such as the amplitude or the frequency of the signal of one of the outputs of the cell or the value of a noise band in an output signal of the cell, influenced by the injection of the input noise signals, and

the sensitivity model providing the relationship between the noise signals injected on the noise injection inputs and the selected output impacts is calculated, and this sensitivity model is associated with the description of the sensitive cell, this description of the sensitive cell containing the data of the sensitive cell necessary for its integration but not all the details of its structure.

Those skilled in the art understand that the data necessary for the integration include the layout of the sensitive circuit corresponding to the description of the masks of the circuit showing the various elements making up the circuit and their interconnections with each other.

In one implementation, the class of the sensitive circuit is selected from the group consisting of: power or low noise amplifiers, frequency mixers, frequency dividers / multipliers, automatic gain controllers, oscillators and loops phase-locked filters, the systems comprising several of the aforementioned cells.

In one implementation, in order to calculate the sensitivity model, the analytical function corresponding to the group of the determined sensitive circuit is determined, this function having coefficients that depend on the model of the circuit used and simulations are performed in order to extract the values of these coefficients. In one implementation, the cell being a VCO, the noise injection points are chosen from the ground terminal, the power supply terminal and the control signal terminal, and the impacts are selected from the nearby noise band. the oscillation frequency of the output signal, the amplitude of the output signal at the oscillation frequency of the output signal, or the oscillation frequency of the output signal.

In one implementation, for a noise signal injected on the ground terminal, the amplitude value of the parasitic lines having a frequency equal to the oscillation frequency increased or decreased by a multiple of the noise frequency depends of

the amplitude of the output signal at the oscillation frequency weighted by

- the relationship between

the product of the amplitude of the injected noise signal and the sensitivity of the oscillation frequency of the VCO to the noise on the mass, and the frequency of the noise signal,

this ratio being raised to the power of the multiple of the frequency considered.

In one implementation, the amplitude of the output signal at the oscillation frequency of the VCO depends on the amplitude of the output signal at the oscillation frequency when no noise is injected multiplied by the product, for all the noise signals, of the Bessel Jo function of the first kind and of order 0 applied to the modulation index of each of these signals.

In one implementation, the sensitivity of the VCO frequency to the noise on the mass is defined by the ratio between - the variation of the frequency of the VCO, and

- the variation of the ground voltage,

- for a given VCO control frequency.

In one implementation, the actual oscillation frequency of the VCO output signal depends on the sum of - the ideal oscillation frequency of the VCO and

the sum, for all the noise inputs considered, of the products of the DC voltage component of the noise signal injected on a given input and of the sensitivity of the VCO frequency to this input. In one implementation, the sensitivity of the VCO frequency to the noise at a given input is defined by the ratio between

- the variation of the oscillation frequency, and

- the variation of the voltage applied to the input considered, - for a control voltage of the given VCO.

In one implementation, to extract the parameters of the amplitude at the oscillation frequency when no noise is injected, the oscillation frequency when no noise is injected, the sensitivity of the oscillation frequency to noise on one of the noise injection inputs, and the sensitivity of the amplitude of the VCO to the noise on one of the noise injection inputs, in a test environment,

a series of simulations is performed without the addition of an external noise source on the modeled VCO, this series of simulations making it possible to extract the amplitude and the oscillation frequency of the VCO for each of the control voltage values,

a parametric simulation is performed for each of the values of the control voltage, the noise sources then being considered as DC voltage sources whose amplitude is varied over a range of values from one micron to one millivolt, the amplitude and oscillation frequency at the output of the VCO are extracted for each amplitude of the noise sources, and

by a conventional slope calculation, the values of the sensitivity parameters of the amplitude and the oscillation frequency of the VCO are obtained for each noise input and for each control voltage value. According to one implementation, the test environment is defined in particular by the range of values of the control voltage of the VCO and its granularity.

According to one implementation, to carry out the simulations, the parameters of the RF simulations, the number of harmonics to be considered during the analysis depending on the non-linearity of the VCO, the desired accuracy, and performance options are defined.

According to one implementation, the data relating to the sensitivity model is encrypted in a binary file in a specific format, allowing its exchange between development teams. According to one implementation, to determine the sensitivity model,

a neural network is configured by defining a number of layers of neurons,

analog, RF or mixed type simulations are performed on the circuit so as to obtain a set of input / impact measurement pairs,

the neural network is trained with the data collected by simulation, and

- the training process is stopped when the model obtained reproduces the simulation experiments with the desired precision.

According to one implementation, the training method of the neural network is the Levenberg-Marquardt method.

According to one implementation, the circuit is divided into several functional blocks, each block being individually modeled, the circuit model resulting from the combination of the models of the different blocks.

According to one implementation, in a macroscopic analysis system, the use of the method according to the invention is combined with that of noise injection and propagation modeling methods in order to determine the influence of the noise on the entire electronic circuit.

The invention further relates to a software or an equivalent electronic circuit implementing the method according to the invention.

The invention will be better understood on reading the description which follows and on examining the figures which accompany it. These figures are given for illustrative but not limiting of the invention. They show :

Figure 1: a diagram of the steps of the modeling method according to the invention in the case of an analytical approach and in the case of an empirical approach;

Figure 2 is a schematic representation of a single sensitive electronic circuit modeled by the method according to the invention;

3: a schematic representation of a complex complex system decomposed into functional blocks modeled by the method according to the invention; Figures 4-5: respectively detailed and overall schematic representations of a conventional VCO (Voltage Controlled Oscillator) and different noise injection points;

FIG. 6: a graphical representation of the spectrum of a signal applied at the input of a VCO and the spectrum of an observable signal at its output highlighting the noise coupling phenomena identified for the implementation of the invention;

FIG. 7: a schematic representation of the implementation of a calculation algorithm according to the invention making it possible to obtain the amplitudes of the lines observable at the output of the VCO for an input noise signal having four lines;

FIG. 8: a table indicating in line the order and in column the index of the Bessel series term used in the sensitivity models of the VCO according to the invention;

9: a graphical representation of the spectrum of the output signal of the sensitivity model of the VCO according to the invention for different cases of noise injection (best case, worst case, typical case);

Figure 10: a schematic representation of a power amplifier whose sensitivity is modeled according to the empirical approach according to the invention;

11: a schematic representation of the spectrum of a signal observable at the ground and the spectrum of the output signal of the amplification highlighting the noise coupling phenomena identified for the implementation of the invention;

Figure 12: a schematic representation of the different frequency channels associated with the power amplifier and considered for the implementation of the invention;

Figure 13: a schematic representation of an example of integration of the sensitivity modeling tool according to the invention in a global noise modeling system of an electronic system. Identical elements retain the same reference from one figure to another.

FIG. 1 shows a diagram of the sensitivity modeling method according to the invention in the case of an analytical approach and in the case of an empirical approach.

In a first step 1.1 common to the analytical and empirical approach, the noise injection inputs of the cell as well as the output impacts reflecting the degradation of the functionality of the cell, such as the amplitude or frequency of the cell. an output signal, a gap between the ideal output level and the actual output level, or the observable noise pattern on a given output, are identified.

In a second step 1.2 of the analytical approach, analytical expressions are determined that make it possible to derive the transfer functions between a noise signal applied to the inputs and the impacts on the outputs observed.

In a third step 1.3, the parameters of the analytical equations to be determined for adapting the analytical equations to the studied cell are identified.

In a fourth step 1.4, the values of the parameters are determined by simulation from a description of the circuit, and analysis parameters.

In a fifth step, the sensitivity model is generated from the model interfaces (selected inputs / outputs), analytical equations, and extracted parameters.

In the empirical approach, after the identification of the inputs and the output impacts, a large number of simulations (nonlimiting examples: analog, RF, mixed, SPICE, VERILOG, VHDL) is performed on the circuit in a step 2.3, so as to obtain a set of input / output measurement pairs (output impacts) describing the system. For this purpose, a large number of noise signal values are applied to the input of the sensitive cell and the output impact corresponding to each of the input values is measured by simulation. In practice, the determination of the adequate number of inputs and outputs depends on the class and complexity of the cell studied and uses the expertise of the analog / RF designer who has the knowledge and simulation tools dedicated to this. type of investigation.

A neural network is configured in a step 2.2, in particular by defining the properties of the network necessary for the modeling, in particular the number of layers, the number of neurons per layer, the learning method, its parameterization, the criteria related to the convergence of the method and the desired precision of the model.

In a learning step 2.4, the neural network is driven with the data collected during the simulation step based on principles of retro-propagation. The so-called back propagation method consists in calculating the gradient of the error of each neuron of the network, from the last layer to the first one. This technique makes it possible to correct the errors (by modifying the synaptic weights of the network) according to the importance of the elements which have precisely contributed to the realization of these errors. The training process is stopped when the model obtained reproduces the experiments (the pairs of inputs / outputs obtained by simulation) with the desired precision.

FIG. 2 shows a simple system whose sensitivity has been modeled by a block 5 having N noise injection points and P output showing the degradation have been identified, N and P being equal or different. The P impacts can each take the form of a physical quantity, such as the amplitude or frequency of an output signal, or a message indicating whether the sensitive output is working properly or not. The function f modeling the sensitivity of the cell ensures the relation between the inputs ni ... n _N and the output impacts ii ... i _P.

When an electronic system with a complex function can be broken down into functional blocks with simple functions, its sensitivity model is considered to result from the composition of the sensitivity models of the single blocks. FIG. 3 thus shows a sensitivity model of a complex system 7 resulting from the composition of the models of two functional blocks k and k + 1 (7.1 and 7.2).

The noise signals are applied to the noise injection inputs n / ... n _N ^k of the sensitivity model of the cell k whose function f makes it possible to obtain the corresponding output impacts h ^k ... ip ^k at these inputs, the output impacts being values of the observable noise at the output of the cell k.

The noise disturbances h ^k ... ip ^k observable at the output of the block k are then applied as inputs to the block k + 1, the noise generated by the cell k influencing the sensitive output impacts ii ^{k + 1} ... i _L ^{k + 1} of the k + 1 cells. In fact, the noise of the cell k propagates towards the cell k + 1 via the substrate, the interconnections and the housing of the system 7.

Moreover, noise signals are injected on the M injection inputs of the cell k + 1. The function f ¹ ^ ¹ of the cell calculates the values of the sensitive output impacts of the cell k + 1 as a function of the values of the noise signals applied to the inputs.

In one example, the processing chain of a radio frequency signal after reception by the antenna of a telephone is formed of a LNA followed by a mixer, itself controlled by a VCO. As a result, the sensitivity model of this processing chain results from the combination of the sensitivity models of these three elements.

Below is an example of modeling the sensitivity of an LC-tank type VCO to external noise by an analytical approach.

FIGS. 4 and 5 respectively show a detailed and global diagram of a VCO 12 which delivers a positive output signal VOUT + or negative VOUT- having an oscillation frequency LO (Local Oscillator). This LO frequency depends on the continuous value of the VCONTROL control voltage.

In a conventional manner, this VCO 12 is formed by transistors M1-M4, diodes D1, D2 and inductors L1 and L2 connected to each other and to the supply points VDD and VSS (ground) as shown in FIG. The external noise signals B1-B3 are mainly injected by the VCONTROL control voltage terminal, the VSS ground terminal and the VDD power terminal.

Figure 6 shows the spectrum 9 of a VCO output signal obtained when an input signal having the frequency spectrum 10 is applied to one of the VCO noise inputs. This figure shows the dominant noise coupling mechanisms and performance degradation of the VCO 12 due to the impact of the B1-B3 noise signals applied to the noise injection inputs.

In particular, a noisy signal applied to the ground terminal can impact the output spectrum of the VCO in two different ways. Thus, by an AM-FM conversion phenomenon, the noise present in the baseband 11 around the DC component of the input signal injected by the ground lines is found in the RF band 13 of the output of the VCO, in the surroundings of the LO frequency, as shown by the arrow A in Figure 6.

While by a modulation phenomenon (less important than the AM-FM conversion phenomenon), the noise present in the frequency band 15 of width BW situated around the frequency LO is found in the RF band 13, as shown by FIG. arrow A 'in FIG.

The output signal of the VCO is impacted in several ways by the noise injected on the inputs: the oscillation frequency LO of the output signal being erroneous, the amplitude of the output signal at the frequency LO being erroneous, and noise occurring near the LO frequency due to noise injected into the noise injection inputs.

To obtain the sensitivity model of the VCO, the transfer functions between a noise signal injected on one of the noise injection inputs and the frequency and / or amplitude of the VCO output signal are determined analytically, and / or the amplitude of parasitic lines that appear around the LO frequency.

In the remainder of the example, the sensitivity model is based on the dominant injection mechanism (AM-FM conversion) non-ideal metals of the mass. A noise source B2 is added on the VSS port to model this non-ideality of the mass. However, most of the following observations apply with respect to other noise injection inputs.

We therefore seek the sensitivity model which establishes the relation between a noise signal injected on the VSS ground input and the frequency and / or amplitude of the VCO output signal, and / or the amplitude of the parasitic lines that appear around of the LO frequency.

For this purpose, the equations derived from the basic theory of frequency modulation discussed below are used.

Consider a voltage signal with a fixed frequency in the form: v {t) = Vsin {ω _c t + θ) (1)

where ω _c is the fixed angular frequency and θ is the phase. When the voltage signal is at a variable frequency, we have: v {t) = Vsm {φ {ή) (2)

where φ (t) is the total angular displacement at time t. The instantaneous frequency in radians / sec is:

For example, a constant frequency ω _c implies

Φ {t) = ω _c t + Θ (4)

In this case: dΦ {t) _{/ κ} . ω ' ^{= ~} dt ^{= (ϋc ()}

In this way, a frequency modulated wave with sinusoidal modulation has an instantaneous frequency: / Xt) = I ₊ AfCOSlKfJ (6)

where / _c is the average frequency of the carrier, and Af is the maximum deviation of the instantaneous frequency from the average frequency. It should be noted that Af is proportional to the amplitude peak of the modulating signal and is independent of the modulation frequency / _m . Starting from equations (3) and

(6), we see that:

- - = ω _c + 2πΔ / cosωj (7) dt φ ( _t ) = ω _t + ^ -sin ω t + θ (8)

Neglecting, we then have the frequency-modulated signal from equation (2):

(t) = Fsin ω _c t + - sinω _m t (9) ω

Equation (9) is generally written in the form:

v (t) = V sin (ω _c t + m _f sin ωj) (10) or

2W ₌ V ₍₁₁₎

The quantity m _f is the modulation index. It is proportional to the amplitude peak of the modulating signal and has an enl // _m dependency.

As can be seen in equation (6), Δ / ^" is proportional to the maximum amplitude of the modulation signal, V _1n , and Af = K _n (VCONTROL) - V _m (12)

OR

K _1n [VCONTROL] = - ^ - (13) to V _m

is the sensitivity of the VCO relative to the amplitude of the input noise signal (which depends on the VCONTROL control voltage of the VCO). Using trigonometric equality: sin (A + B) = sm AcosB + cosAsm B (14)

Equation (10) becomes v (t) = V sinωj cos (m _f sinω _m t) + V cosωj sin (m _f sinωj) (15)

Bessel expansions are used:

COs (W ₇ sin ωj) = J ₀ {m _f ) + ₂ J ₂ (m _f ) cos (2ωj) + 4J ₄ (m _f ) cos (4ω _m t) + ... (16)

And sin (m _f sin ωj) = 2J ₁ (m _f ) sin (ωj) + 2J ₃ (m _f ) sin (3ωj) + ... (17)

Equation (15) can now be expanded to Bessel functions of the first kind, order n and argument m _f :

v {t) / V = sin Gy [J _o K) + ^2J ₂ cos (2ov) + .. J r / \ / \ / \ (\ i ( ¹⁸ )

+ cosω _c t [2J _! \ m _f jsin (ω _m ?) + 2J ₃ \ m _f jsin (3ω _m ?) + ... J

Using the trigonometric identities of sum and differences of angles, one obtains: v {t) / V = J ₀ (m _f) sïnω _c t

+ J ₁ (m _/ | sin (ω _c + ω _m > -sin (ω _c -ω _m ) t]

+ J ₂ (m _f ) [sin (ω _c + 2ω _m > - sin (ω _c - 2ω _m >] (19)

+ J ₃ (m _f ) [sin (ω _c + 3ω _m > - sin (ω _c - 3ω _m ) t]

+ ...

Thus, a frequency-modulated signal consists of a carrier and a large number of side lines with amplitudes given by Bessel functions of the first kind and the modulation index argument m _f . The Bessel function of the first kind of order n is:

(20)

The dominant term in equation (20) is for / = 0, and m _f has a \ / f _m dependency. Thus, J _n {m _f ) has a dependence on l // _m ". In the same way, it has a dependence in Δ /".

Then, the amplitude of the parasitic lines is determined. From the above and neglecting the terms (l> 0) in (20), we deduce the following equations for the first three parasitic lines:

A τs-FM i

V (f + f LO ¹ ^ GND ^ nois

'out \ J LO - J noise) / | ι = e (21)

J noist

_K FM _j

¹ LO ^ GND ^ noise

'out VJ LO - ^ J noise \ (22)

J noisy

A _K FM _j

LO ^ GND ^ -noise

^ out VJ LO - ^ J noise \ (23)

48 J noise or v _out = (VOUT +) - (VOUT-) is the differential output voltage of the VCO, f _L0 is the oscillation frequency of the VCO,

/ _BOke is the frequency of the input sinusoidal noise,

At _L0 is the amplitude of the output voltage of the VCO,

A _note is the amplitude of the sinusoidal input noise

K ™ _D is the sensitivity of the VCO frequency to the noise on the mass, defined by

KZiVCONTROL) = ^ (24) dV, GND

Equation (21) has been published in academic studies of Méndez and Soens ("Phase noise degradation of LC-tank VCOs due to substrate noise and package coupling" proc., 31st ESCIR pages 105-108, September 2005; Performance degradation of an LC-tank VCO by impact of digital switching noise "presented at the conference" European Solid-State circuits "in 2004, pages 119-121;" RF performance degradation due to coupling of digital switching noise in lightly doped substrates " February 2003. These studies are all based on the "small signal" hypothesis, which considers that the amplitude of the injected noise is negligible compared to the main signals present in a given circuit.

However, this hypothesis remains insufficient to take into account precisely the non-linearities inherent to the analog / RF functions. This remark is all the more true in the context of "worst-case" simulations in which the worst noise that can be injected into the sensitive inputs is injected. In such a case, the "little signal" hypothesis is no longer verified at all.

Therefore the invention implements equations (22) and (23) to the harmonics of 2 ^nd and 3 ^rd order, and the general equation below (25) in order to understand all coupling mechanisms with sufficient precision, and this in all possible aggression scenarios. These equations were validated by comparison with simulations.

The following general equation is a good approximation of the behavior of the VCO:

A LO K GND ^ Anoise

'out \ J LO -' V noise \ (25)

2 ^k k J noist

Simulations to validate the principle of superposition of harmonics and signals have also been performed. The superposition is valid for low level noise inputs (as an order of magnitude, this assumption is valid for a level below the millivolt). When the "small signal" hypothesis is no longer valid, the use of the empirical method must be considered for optimal precision.

Considering the AM and FM theories, we then calculate the amplitude of the output signal at the oscillation frequency LO of the VCO which depends on two main mechanisms:

- The continuous noise term (DC), due to the cyclic variations of the digital activity, linearly increases the amplitude of the output signal at the oscillation frequency LO. The corresponding model is as follows:

OR

 _L0 is the amplitude of the output signal at LO oscillation frequency when no noise is injected,

KL _e ^{is a} DC voltage injected noise,

KZ is the sensitivity of the amplitude at the LO frequency to the noise at the mass, defined by

T) A KZ [VCONTROL] = ± j £ - (28) to V _GND - The harmonic content FM modulates the amplitude LO according to a quadratic law (terms I = O and I = 1 of the Bessel development). For a purely sinusoidal noise, the corresponding model is:

where A _L ^* ₀ is the amplitude of the output signal at the LO oscillation frequency when no noise is injected, f _no i ^{_is' a} frequency sinusoidal noise at the input, A _{o, ^is} the amplitude of sinusoidal noise,

K ™ _D is the sensitivity of the amplitude at the LO frequency to the ground noise defined by equation (24).

Based on the superposition hypothesis, the equation modeling the amplitude of the VCO output signal is deduced when several noise signals / harmonics are injected into the circuit. The FM theory then gives:

Ku _t (fLθ] = Aθ = 4θU ^J M) (30)

where Jo is the Bessel function of the first kind and order O, and m ^ is the modulation index of the signal ^18. For small signal noise sources, the product operator can be approximated by a sum without loss of precision. Then, the oscillation frequency LO mainly influenced by the DC terms of the noise is calculated:

Λ ₀ = /; ₀ + ΣΛ ^βc < ^M (31) n where f ^* ₀ is the oscillation frequency LO of the VCO when no noise is injected,

A ° ^c is the DC voltage of the noise injected at the input n,

Kζ ^M is the sensitivity of the LO frequency to the noise at the input n, defined by

_K ^FM {ycONTROL) = ^ - (32)

BV _n

The parameters necessary to determine equations (25), (27), (29) and (31) are:

At _L ^* ₀ : amplitude of the output signal at the oscillation frequency LO when no noise is injected, f _L0 : oscillation frequency LO when no noise is injected, K ™ _D : sensitivity of the frequency of the VCO at the noise on the mass, K _{ç D} : sensitivity of the amplitude of the VCO to the noise on the mass.

To generalize to any number of noise inputs (power supply

VDD, control voltage, ...), the parameters to be calculated are, for each input n, the sensitivity of the frequency Kζ ^M and the sensitivity of the amplitude

Kf ⁴ from VCO to noise on input n.

It should be emphasized that in the case of a VCO, its behavior is preferably characterized for a certain range of control voltage values. The different parameters of the equations must then be determined for each control voltage value.

Then, the values of the parameters of the equations of the model for the circuit studied above are extracted by means of dedicated RF simulations. These simulations are based on the harmonic balancing method which allows to determine the established regime of the autonomous circuit. For this purpose, the user provides:

a description of the VCO schematic, such as a netlist or transistor models,

- the parameters of the RF analyzes, such as the estimated LO frequency, the number of harmonics to be considered during the analysis which depends on the non-linearity of the VCO, the desired accuracy, the performance options and the accuracy of the simulations, and

the test environment defined in particular by the ideal value of the bias voltage, the range of values of the control voltage and its granularity.

A first series of simulations without addition of external noise source (ideal case) is carried out, making it possible to extract the amplitude and the oscillation frequency LO of the VCO (parameters λ _L0 and f ^* ₀ ) for each of the voltage values. applied controls.

In a second step, a parametric simulation is automatically performed for each of the values of the control voltage. The sources of noise are then considered as sources of DC voltage whose amplitude is varied over a range of values of the order of one micron to one millivolt. It is thus possible to extract the amplitude and the oscillation frequency LO at the output of the VCO for each amplitude of the noise sources.

By a conventional slope calculation, the values of the parameters Kf ¹ and Kζ ^{M are} calculated for each noise input n and for each control voltage value.

Once the step of extraction of the parameters of the analytical equations is finished, all the data necessary for the generation of the final sensitivity model are available namely:

- the model interface: the definition of noise inputs and modeled output impacts; as well as

the core of the model defined by the set of equations and the values of the parameters for each applied control voltage value.

These data are encrypted in a binary file in a specific format allowing its exchange between the different teams of development, and for example with the integrator of the system. It can then apply the noise signals (measured or simulated by dedicated tools) reaching the victim studied (in this case, a VCO) and obtain very quickly model outputs and thus determine the impact on sensitive functionality. .

Once the model is developed, it can be used to simulate the impact corresponding to noise signals injected on the model inputs.

For this purpose, the user provides a list of input parameters, namely:

- the fundamental frequency of the noise (frequency of the numerical activity if it is about switching noise in the case of a mixed system),

the number of harmonics of the noise (number of lines of interest), or a frequency band,

- the range of control voltage values and its granularity,

- the precision parameters of the simulation of the model, as well as - the noise spectra reaching the victim.

The output of the simulation of the sensitivity applied to a specific VCO block is, for each control voltage value, the frequency LO and the amplitude of the output voltage LO, and a given number K of parasitic amplitude amplitudes around of the LO frequency: \ V _out {f _LO ± kf _nose ], k = 0, 1, ..., K. In this presentation, only one control voltage is considered for simplicity. It is clear that the terms A [ _o {yCONTROL), f _LO (vCONTROL),

Kf ¹ {VCONTROL) and K ™ {VCONTROL) are calculated using interpolation, for example, 2-fold piecewise polynomial interpolation, from modeled tabulated values to simulated control voltages. For future developments, it is more interesting to formulate the Bessel coefficients in the form:

OR

N is the identifier of the noise input, p is the order of Bessel (see table figure 8), k is the harmonic index,

I is the term index in the Bessel series (see table figure 8),

AV _n k _k is the amplitude of the harmonic ^ιeme k of the noise signal n, u _n = κ _n ^FM lf _NMSE and (34) (35)

By observing the values of β _Λp for the first values of / and p, it is clear that only a small number of Bessel terms can be considered to have sufficient precision (see table in Figure 8).

Preferably, at least all the terms for / = 0 are taken into account (cells filled with dots in the table of FIG. 8). However, since the precision of the LO amplitude is crucial, it is recommended to consider the term (/, p) = (1, 0) (obliquely shaded cell in the table figure 8). An improvement can be made by calculating the terms (/, p) =

(2, 0), (/, p) = (1, 1) and (/, p) = (1, 2) (cells hatched horizontally in the table figure 10). The other terms are negligible in practice.

The number of terms p {p = 0..P) taken into account depends on the order of non-linearity of the required model p (the precision with which the model supports the deviation of the hypothesis of small-signals). P = 1 is the minimum value, it can be increased according to the degree of non-linearity of the cell.

The number of lines (in other words the number of harmonics of the noise frequency) to be considered is noted K thereafter.

From the foregoing, the amplitude of the output signal at the oscillation frequency LO can be decomposed into a contribution of the continuous noise terms and an FM contribution of the harmonic content of the noise: A ₁₀ = A ^ ₊ A ™ (36)

The first term is calculated by

not

The second term is calculated by

<= 4π n ή k = \ ^j o ⁽ ^ ⁾ (38) An alternative of lesser precision allowing nevertheless to save in computing time consists in replacing the product operator π by that of the sum Σ in the equation (38). In addition, the actual oscillation frequency is calculated according to equation (31).

Moreover, the amplitudes of the lines of the VCO output signal are calculated for k = 1..K. To explain the procedure, take for example K = 4 and P = 3 and a single noise input n.

Figure 7 illustrates the algorithm for determining the contributions of each input line to the output noise.

More precisely, the lines A _n , i; A _n , 2; A _n , 3; A _n , 4; An input noise signal is applied to Bessel operators that indicate the contributions of each of them to the output noise. For each harmonic of a given order, the contributions are added to each other by means of the adders 18.1-18.3. The resulting contributions are then multiplied by the amplitude of the observable VCO at the oscillation frequency by means of the cells 19.1-19.4, in order to obtain the amplitude of the parasitic lines of order 1 to 4 observable at the output of the VCO.

In this example, the amplitudes of the parasitic lines are deduced from the following equations:

A _0Uta = A _L0 [j ₂ (n, \) + J ₁ (^ l)] (39b)

A _outj = A _LO [j ₃ {n, \) + J ₁ [Uj)] (39c)

A _0UtA = A _w [ ^j ₂ (n, 2) + J ₁ (TiA)] (39d)

The extension of the methodology to the general case (N lines) is obvious to those skilled in the art.

Figure 9 shows an example of a graphical output of the VCO sensitivity model (VCO output signal spectrum) for several noise injection cases and for a VCONTROL control voltage of 1V.

The curve 23 represented in dashed lines shows the observable output spectrum when the lowest possible noise is applied to the inputs noise injection (best case). This curve 23 is close to the ideal output spectrum comprising a single component at the oscillation frequency LO, the parasitic lines around this frequency having a very low amplitude.

Curve 24 shown in dotted lines shows the observable output spectrum when the highest possible noise signal is applied to the noise injection inputs (worst case). The amplitude of the parasitic lines around the oscillation frequency LO is greater than in the best case, so that the peak of the curve 24 has a wider base than that of the curve 23.

The solid line curve 25 shows the spectrum of the VCO output signal when a typical (ie, medium level) noise signal is input to the model. This curve 25 is close to the curve 24 representing the worst case, which implies that the designer still has some leeway to immunize his circuit noise.

The following is an example of modeling the sensitivity of a power amplifier (PA) to external noise by an empirical approach, using a neural network.

We have the SPICE netlist of the PA amplifier. Figure 10 shows an overall diagram of the amplifier whose role is to increase the power of the input signal (Pin) by deforming it as little as possible.

In this example, the following assumptions are made:

it is considered that the ground lines constitute the main coupling path for the external noise (VSS input in FIG. 10): this hypothesis can be verified by means of RF simulations,

for simplicity, the RF signal is a pure sine wave at the fundamental frequency of 900 megahertz,

- the frequency band of interest of the RF signal is wide of 3 MegaHertz of 898.5 MegaHertz to 901.5 MegaHertz, - the clock frequency of the external noise B4 attacking the amplifier by its lines of mass is 1 MegaHertz, the amplifier PA being weakly nonlinear, only the following two noise transfer mechanisms are considered (FIG. 11): amplification (direct coupling) of the noise harmonics of the RF band, this mechanism being referenced by the arrow 2, o mixture by inter-modulation (indirect coupling) of the harmonics of the baseband with the RF signal, this mechanism being referenced by the arrow 1.

The impact of noise on the output signal is characterized in terms of Adjacent Channel Power Ratio (ACPR), which is the ratio of the power in an adjacent channel to the power in the main channel. As illustrated schematically in FIG. 12, the ACPR corresponding to the lower adjacent channel (from 895.5 megahertz to 898.5 megahertz) is measured on the LOAD output, ACPR | _0W er, and at the upper adjacent channel (from 901.5 MegaHertz to 903.5 MegaHertz), ACPR _upP er. These merit figures can be extracted by post-processing the Fourier Envelope simulation results (available in commercial RF simulators).

We can then proceed to the initialization of the data necessary for the actual modeling:

- definition of the name of the model, the netlist of the corresponding sub-circuit, the name of the inputs / outputs;

- choice of simulator and analysis: in our case, we use the Mentor Graphics © RF simulator, namely Eldo RF ™, and the Fourier Envelope method (modsst directive); development of the input file defining the simulation: analysis directive and its complete parameterization (fundamental frequency, number of harmonics, duration of simulation ...), extraction instructions of measurements characterizing the sensitivity of the cell ( calculation of

- definition of the number of experiments (simulations) to be performed to characterize the sensitivity of the amplifier with sufficient precision: in this example, a hundred simulations are launched;

- definition of the fundamental frequency of the noise, the frequency bands and the amplitude range of the external noise: in this For example, the fundamental frequency of noise is 1 MegaHertz, the frequency bands are the baseband (1.5 MegaHertz wide) and the RF band (3 MegaHertz wide); the noise arriving at the mass follows a Gaussian distribution of nominal value -50 dB (Volts) and standard deviation 0.96;

- definition of the size of the neural network according to the number of inputs (magnitude and phase of the 4 harmonics of the noise in the considered bands), outputs (the 2 ACPR measurements) and the complexity of the problem to be modeled: in in this example, the network comprises a single hidden (internal) layer whose number of neurons is twice the number of inputs, definition of the neural network learning method as well as stopping criteria: in this example, the Levenberg-Marquardt method is chosen for its rapid convergence qualities. The first step is the characterization of the sensitivity of the amplifier by simulation (thanks to the Eldo RF ™ third party simulator). Once the simulation data has been collected, then the initialization of the neural network and its training (learning phase) begins. In this example, ten iterations make it possible to obtain an accuracy of 0.1% on the response of the model to the simulation data.

The model thus obtained is scanned into a binary file which can then be reused to apply "real" noise forms (simulated or measured on the complete system) to the input of the model and quickly obtain ACPR outputs by simulating the neural network. The system integrator can thus evaluate the impact of the noise on the sensitive amplifier without knowing the detail of this block nor having the know-how necessary for the simulation of this block.

Figure 13 shows a schematic representation of the integration of the invention in a global platform for modeling the injection and sensitivity to noise. Such a platform is described in French Patent Application No. 0552363.

More specifically, a netlist 27 of an IP block to be modeled is applied to the input of the module 30, this netlist comprising information relating to the elements of this block and to the interconnections between these elements. In addition, data 28 relating to the sensitivity of the block sensitivity directives are also transmitted to the module 30.

The module 30 then defines the noise injection inputs, the identified impacts, the functions to be modeled establishing the relation between the noise injection inputs and the impacts, the simulation parameters, such as the number of input-impact couples. to simulate in an empirical mode of operation, as well as the modeling parameters.

These parameters, together with the description 33 of the assembly of the complete electronic system, are transmitted to the module 31 called "WaveModeler" which uses them to develop a model of sensitivity of the cell, a noise propagation model within the cell if applicable and, in the case of an aggressive cell, a noise injection model.

Noise injection and noise propagation models used in the invention are respectively described in French Patent Applications No. 0650438 and No. 0652642.

These models are transmitted to the module 35 called "WaveAnalyst" which simulates for example, from the description of the assembly of the complete system and the presence described by the input 34 of the sensitive cells and the noise generating cells, the impacts observed in the best case, the worst case or the typical case of noise injection.

The module 39 then represents the result of the simulations in graphical or table form which indicates the sensitive outputs (impacts) as a function of the injected noise signals. The invention may for example be implemented for the design of systems type SoC (System on Chip) and SiP (System In Package) to study their sensitivity to noise.

The invention can thus for example be implemented for: - low-cost, low-power wireless connections, - low cost "single chip" circuits, and low consumption for Bluetooth or RFID applications, - cellular telephone circuits for digital video broadcasting to DVB-H, DVB-S, T-DMB, S-DMB and for software defined radio (Software Defined Radio),

circuits intended for wireless communication between chips on a box ("On board wireless communication between chips"),

- high-definition analog / digital converters,

- circuits for high definition DVDs,

- very high speed digital circuits (PLLs, input-output blocks), or

microprocessors, for example of the parallel architecture type,

For each of these electronic systems, the invention is used:

- to understand and improve external noise immunity when designing IP blocks, and / or

- to characterize their sensitivity, for example during the validation ("sign-off") of the IP block in order to verify the proper operation of the block in a more complex system such as an IP block resulting from the assembly of sub blocks, a single-chip integrated circuit, a system incorporating several integrated circuits, a printed circuit, and the combinations of all the aforementioned systems.

The invention also relates to the software or the equivalent electronic circuit implementing the steps of the method according to the invention.

Claims

1. A method for modeling the sensitivity to noise of a sensitive electronic circuit of analog and / or radio frequency type, characterized in that it comprises the following steps:

identifying which class the sensitive circuit belongs to (5, 7),

one selects, among the terminals of the circuit, the inputs (ni ^k -nN ^k ) of noise injection of the cell on which noise signals outside the cell are likely to be injected, the injection inputs of noise including in particular the supply inputs of the sensitive circuit,

selection of output impacts (ii ^k -ip ^k ), such as the amplitude or the frequency of the signal of one of the outputs of the cell or the value of a noise band in the signal of one of the outputs of the cell, influenced by the injection of the noise signals on the noise injection inputs, and - the sensitivity model (f ¹ *) ensuring the relationship between noise signals injected on the inputs ( ^k -n _N ^k ) noise injection and the output impacts (h ^k -ip ^k ) selected, and

this sensitivity model (f) is associated with a description of the sensitive cell (5, 7), this description of the sensitive cell (5, 7) comprising the data of the sensitive cell necessary for its integration but not all the detail of its structure.

2. Method according to claim 1, characterized in that the class of the sensitive circuit (5, 7) is chosen from the group comprising: power amplifiers or low noise, frequency mixers, frequency dividers / multipliers, automatic gain controllers, oscillators and phase-locked loops, filters, systems comprising a plurality of the aforementioned cells.

3. Method according to claim 1 or 2, characterized in that for calculating the sensitivity model, the analytic function is determined

(IVout (fLo ± kfnoise) l, IV _or t (fL.o) l) corresponding to the group of the determined sensitive circuit, this function having coefficients {K ™ _D , K ^ _D ) which depend on the model of the circuit used and performs simulations to extract the values of these coefficients.

4. Device according to one of claims 1 to 3, characterized in that, the cell being a VCO, the noise injection inputs are selected from the ground terminal (VSS), power supply (VDD) and the terminal (VCONTROL) of the control signal, and the impacts are selected from the noise band near the oscillation frequency (LO) of the output signal, the amplitude (A _L o) of the output signal at the frequency oscillation (LO) of the output signal, or the oscillation frequency (LO) of the output signal.

5. Method according to claim 4, characterized in that for a noise signal injected on the ground terminal (VSS), the amplitude value of the parasitic lines having a frequency equal to the oscillation frequency (LO) increased or decreased by a multiple (k) of the noise frequency (f _n0 ise) depends on - the amplitude (A _L o) of the output signal at the oscillation frequency (LO) weighted by

- the relationship between

the product of the amplitude of the injected noise signal and the sensitivity (K ™ _D ) of the oscillation frequency of the VCO to the noise on the mass, and

- the frequency (f _n0 ise) of the noise signal,

this ratio being raised to the power of the multiple (k) of the frequency considered.

Method according to claim 4 or 5, characterized in that the amplitude (A _LO ) of the output signal at the oscillation frequency of the VCO is dependent on

the amplitude of the output signal at the oscillation frequency when no noise is injected multiplied by the product, for all the noise signals, of the Bessel Jo function of the first kind and of the applied order O to the modulation index (m _f ^ι ) of each of these signals.

7. Method according to claim 5 or 6, characterized in that the sensitivity of the frequency of the VCO to the noise on the mass (VSS) is defined by the ratio between - the variation of the frequency of the VCO (dfι_o), and

the variation of the ground voltage (dV _G ND),

- for a given VCO control frequency.

8. Method according to one of claims 4 to 7, characterized in that the actual oscillation frequency (fι_o) of the VCO output signal depends on the sum between

- the ideal oscillation frequency (f \ o) of the VCO and

the sum, for all the noise inputs considered, of the products of the DC voltage component of the noise signal injected on a given input (n) and of the sensitivity of the frequency (K ™ _D ) of the VCO at this input.

9. Method according to claim 5 or 6, characterized in that the sensitivity of the frequency of the VCO to noise at a given input is defined by the ratio between

the variation of the oscillation frequency (dfι_o), and

the variation of the voltage (dV _n ) applied to the input considered,

- for a control voltage (VCONTROL) of the given VCO.

10. Method according to one of claims 4 to 9, characterized in that, to extract the parameters of the amplitude at the oscillation frequency when no noise is injected (A ^* _L0 ), the oscillation frequency (f ^* _L0 ) when no noise is injected, the sensitivity (Kζ ^M ) of the oscillation frequency to the noise on one of the noise injection inputs, and the sensitivity {K ^ ^M ) of the amplitude of the VCO to noise on one of the noise injection inputs, in a test environment,

a series of simulations is performed without the addition of an external noise source on the modeled VCO, this series of simulations making it possible to extract the amplitude A _L ^* ₀ and the frequency f _L ^* ₀ LO of the VCO for each of the voltage values control,

a parametric simulation is carried out for each of the values of the control voltage (VCONTROL), the noise sources then being considered as sources of DC voltage whose amplitude is varied over a range of values of the order of one micron at millivolt, the amplitude and oscillation frequency at the output of the VCO are extracted for each amplitude of the noise sources, and

by a conventional slope calculation, the values of the parameters Kf ¹ and K ™ are obtained for each noise input (n) and for each control voltage value.

11. The method of claim 10, characterized in that the test environment is defined in particular by the range of values of the control voltage (VCONTROL) of the VCO and its granularity.

Method according to claim 10 or 11, characterized in that for carrying out the simulations:

the parameters of the RF simulations, the number of harmonics to be considered during the analysis depending on the non-linearity of the VCO, the desired accuracy, and performance options are defined.

13. Method according to one of claims 1 to 12, characterized in that the data relating to the sensitivity model are encrypted in a binary file in a specific format, allowing its exchange between development teams.

14. Method according to one of claims 1 to 13, characterized in that to determine the sensitivity model,

configuring (2.2) a network of neurons by defining a number of layers of neurons,

analog simulations, RF or mixed simulations are performed on the circuit so as to obtain a set of input / impact measurement pairs,

- driving (2.4) the neural network with the data collected by simulation, and

- the training process is stopped when the model obtained reproduces the simulation experiments with the desired precision.

15. The method of claim 14, characterized in that the training method of the neural network is the Levenberg-Marquardt method.

16. Method according to one of claims 1 to 15, characterized in that the circuit is cut into several functional blocks, each block being modeled individually, the circuit model resulting from the combination of the models of the different blocks.

17. Method according to one of claims 1 to 16, characterized in that, in a macroscopic analysis system, its implementation is combined with that of noise injection and propagation modeling methods to determine the influence of noise on the entire electronic circuit.