# US 11,307,230 B2 · System and method for providing the amplitude and phase delay of a sinusoidal signal

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 11,307,230 B2
- Document ID: US11307230B2
- Status: Granted
- Kind: B2
- Application number: 16/308,659
- Filed: 2017-06-09
- Published: 2019-10-10
- Granted: 2022-04-19
- Earliest claimed: 2016-06-10
- Assignees: Office National d'Etudes et de Recherches Aerospatiales
- Applicants: Office National D'Etudes Et De Recherches AéRospatiales
- Inventors: Jean Guerard; Béatrice Verlhac; Pierre Lavenus; Raphaël Levy
- Web page: https://patentgrep.com/patent/US11307230B2

## CPC

- G01R 25/00: Arrangements for measuring phase angle between a voltage and a current or between voltages or currents
- G01C 19/5776: Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
- G01P 15/097: by vibratory elements
- G01R 19/04: Measuring peak values {or amplitude or envelope} of AC or of pulses
- G01R 19/175: Indicating the instants of passage of current or voltage through a given value, e.g. passage through zero
- G06F 17/12: Simultaneous equations {, e.g. systems of linear equations}
- G01P 15/18: in two or more dimensions
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)
- G01P: MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT (measuring or recording blood flow A61B5/02, A61B8/06; monitoring speed or deceleration of electrically-propelled vehicles B60L3/00; vehicle lighting systems adapted to indicate speed B60Q1/54; determining position or course in navigation, measuring ground distance in geodesy or surveying G01C; combined measuring devices for measuring two or more variables of movement G01C23/00; measuring velocity of sound G01H; measuring velocity of light G01J7/00; measuring direction or velocity of solid objects by reception or emission of radiowaves or other waves and based on propagation effects, e.g. Doppler effect, propagation time, direction of propagation, G01S; measuring speed of nuclear radiation G01T; measuring acceleration of gravity G01V; {measuring or recording the speed of trains B61L23/00; speed indicators incorporated in motor vehicles B60K35/00; measuring frequency or phase G01R; traffic control G08G})
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Disclosed is a system and method that provide an amplitude value and a phase delay value which relate to a sinusoidal signal to be measured. For this purpose, phase values of a reference signal, at which the signal to be measured exceeds or falls below the reference signal, are collected and transmitted to a computation unit. The computation unit determines the amplitude and delay values from the collected phase values. The system can be implemented in a cost-effective manner, in particular using an ASIC circuit or an FPGA circuit.

## Claims

### Claim 1

A system for providing an amplitude value (A) and a phase delay value (Φ) which relate to a signal to be measured (s(t)) having sinusoidal variations over time (t) with a frequency F, said system comprising:
a synthesis unit (1), adapted to generate a reference signal (r(t)) having a sinusoidal form of time-variations, in continual phase coherence with the signal to be measured (s(t)), said reference signal having an amplitude (Aref) larger than the amplitude (A) of the signal to be measured (s(t)) and having a frequency equal to Fref=F×P/Q, where P and Q are two fixed, non-zero positive integers, P being greater than Q;
a comparator (130) connected to receive the signal to be measured (s(t)) and the reference signal (r(t)) on two inputs of said comparator, and adapted to output a signal transition each time the signal to be measured becomes less than the reference signal, or each time the signal to be measured becomes greater than the reference signal;
a latch register (140) connected to receive instantaneous values on a data input of said register, and to receive a signal that is outputted by the comparator (130) on an enabling input of said register, and adapted to select those of the instantaneous values (ψk) that are received by said register at the same time as a transition of the signal produced by the comparator, the comparator and the register thus forming an acquisition channel (2) for the signal to be measured (s(t)); and
a computation unit (3) connected to receive the selected values, and adapted to calculate values of the amplitude (A) and phase delay (Φ) of the signal to be measured (s(t)) from said selected values,
wherein the latch register (140) is connected for receiving instantaneous values of a phase (ψ(t)) of the reference signal (r(t)) on the data input of said register,
wherein the computation unit (3) is connected for receiving the selected values (ψk) of the phase (ψ(t)) of the reference signal (r(t)), and is adapted for calculating the values of the amplitude (A) and phase delay (Φ) of the signal to be measured (s(t)) from said values selected for the phase of the reference signal, and
wherein the computation unit (3) is adapted to calculate
an in-phase amplitude value (X) of the signal to be measured (s(t)), equal to a·cosΦ where Φ is the value of the phase delay of the signal to be measured and a is a quotient of the amplitude (A) of the signal to be measured (s(t)) divided by the amplitude (Aref) of the reference signal (r(t)), and
a quadrature amplitude value (Y) of the signal to be measured, equal to a·sinΦ, from a system of affine equations having coefficients, for the in-phase amplitude (X) and the quadrature amplitude (Y) of the signal to be measured (s(t)), which depend on the selected values (ψk) for the phase of the reference signal (r(t)).

### Claim 2 (depends on 1)

The system according to claim 1, wherein the integer P is equal to the integer Q plus one.

### Claim 3 (depends on 2)

The system according to claim 2, wherein at least one among the synthesis unit (1), the latch register (140), and the computation unit (3) is formed by a programmable logic circuit (FPGA) or a dedicated circuit (ASIC).

### Claim 4 (depends on 2)

The system according to claim 2, wherein the computation unit (3) is adapted to calculate the coefficients of the system of affine equations from the selected values (ψk) for the phase of the reference signal (r(t)), and to calculate the values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)) by applying an algorithm for solving said system of affine equations, for example an affine equation inversion algorithm or a least-square resolution algorithm.

### Claim 5 (depends on 2)

The system according to claim 2, wherein the computation unit (3) is adapted to determine approximate values for the coefficients of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured s(t) in the system of affine equations, said approximate values of the coefficients being independent of the selected values (ψk) for the phase of the reference signal (r(t)), and said selected values for the phase of the reference signal constituting affine terms of said system of affine equations, and the computation unit is further adapted to calculate approximate values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), as linear combinations of the selected values for the phase of the reference signal.

### Claim 6 (depends on 2)

The system according to claim 2, wherein the computation unit (3) is adapted to calculate amplitudes of fundamental in-phase (H1p) and quadrature components (H1q) and of harmonic components (H2p, H2q, . . . ) for the selected values (ψk) for the phase of the reference signal (r(t)), and the computation unit is further adapted to calculate approximate values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), from linear combinations of said amplitudes of the fundamental in-phase and quadrature components and the harmonic components of the selected values for the phase of the reference signal.

### Claim 7 (depends on 1)

The system according to claim 1, wherein at least one among the synthesis unit (1), the latch register (140), and the computation unit (3) is formed by a programmable logic circuit (FPGA) or a dedicated circuit (ASIC).

### Claim 8 (depends on 7)

The system according to claim 7, wherein the computation unit (3) is adapted to calculate the coefficients of the system of affine equations from the selected values (ψk) for the phase of the reference signal (r(t)), and to calculate the values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)) by applying an algorithm for solving said system of affine equations, for example an affine equation inversion algorithm or a least-square resolution algorithm.

### Claim 9 (depends on 7)

The system according to claim 7, wherein the computation unit (3) is adapted to determine approximate values for the coefficients of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured s(t) in the system of affine equations, said approximate values of the coefficients being independent of the selected values (ψk) for the phase of the reference signal (r(t)), and said selected values for the phase of the reference signal constituting affine terms of said system of affine equations, and the computation unit is further adapted to calculate approximate values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), as linear combinations of the selected values for the phase of the reference signal.

### Claim 10 (depends on 1)

The system according to claim 1, wherein the computation unit (3) is adapted to calculate the coefficients of the system of affine equations from the selected values (ψk) for the phase of the reference signal (r(t)), and to calculate the values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)) by applying an algorithm for solving said system of affine equations, for example an affine equation inversion algorithm or a least-square resolution algorithm.

### Claim 11 (depends on 1)

The system Systcm according to claim 1, wherein the computation unit (3) is adapted to determine approximate values for the coefficients of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured s(t) in the system of affine equations, said approximate values of the coefficients being independent of the selected values (ψk) for the phase of the reference signal (r(t)), and said selected values for the phase of the reference signal constituting affine terms of said system of affine equations, and the computation unit is further adapted to calculate approximate values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), as linear combinations of the selected values for the phase of the reference signal.

### Claim 12 (depends on 1)

The system according to claim 1, wherein the computation unit (3) is adapted to calculate amplitudes of fundamental in-phase (H1p) and quadrature components (H1q) and of harmonic components (H2p, H2q, . . . ) for the selected values (ψk) for the phase of the reference signal (r(t)), and the computation unit is further adapted to calculate approximate values of the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), from linear combinations of said amplitudes of the fundamental in-phase and quadrature components and the harmonic components of the selected values for the phase of the reference signal.

### Claim 13 (depends on 12)

The system according to claim 12, wherein the computation unit (3) is adapted to calculate approximate values for the amplitudes of the fundamental in-phase (H1p) and quadrature (H1q) components and the harmonic components (H2p, H2q, . . . ) of the selected values (ψk) for the phase of the reference signal (r(t)), as combinations of additions and subtractions of said selected values for the phase of the reference signal, and the computation unit is further adapted to calculate approximate the values for the in-phase amplitude (X) and quadrature amplitude (Y) of the signal to be measured (s(t)), from linear combinations of the approximate values for the amplitudes of the fundamental in-phase and quadrature components and the harmonic components of the selected values for the phase of the reference signal.

### Claim 14 (depends on 13)

The system according to claim 13, wherein P is a multiple of 60.

### Claim 15 (depends on 1)

The system according to claim 1, adapted to provide amplitude values (A) and phase delay values (Φ) relating to a plurality of signals to be measured (s0(t), s1(t), . . . ) each having sinusoidal variations over time (t), said signals to be measured all having the frequency F,
said system comprising respective acquisition channels (20, 21, . . . ) individually dedicated to the signals to be measured (s0(t), s1(t), . . . ), each acquisition channel comprising a comparator (130, 131, . . . ) and a latch register (140, 141, . . . ) adapted and connected in accordance with claim 1, separately from the other acquisition channels,
the synthesis unit (1) being common to all the acquisition channels (20, 21, . . . ), for transmitting the reference signal (r(t)) simultaneously to all the comparators (130, 131, . . . ) and for transmitting the instantaneous values of the phase (ψ(t)) of said reference signal simultaneously to all the latch registers (140, 141, . . . ).

### Claim 16 (depends on 11)

The system Systcm according to claim 11, wherein the synthesis unit (1) comprises
an input for receiving a clock signal;
a first cyclic accumulator (102) adapted to generate a phase of an excitation signal (E(t)) from the clock signal in accordance with a first accumulation increment (W1);
a second cyclic accumulator (103) adapted to generate a phase (ψ(t)) of the reference signal (r(t)) from the clock signal in accordance with a second accumulation increment (W2);
a first signal-shaping unit (110) for producing the excitation signal (E(t)) with a sinusoidal form of time-variations, from the phase generated by the first cyclic accumulator (102); and
a second signal-shaping unit (111) for producing the reference signal (r(t)) from the phase (ψ(t)) generated by the second cyclic accumulator (103);
the system being adapted to provide the excitation signal (E(t)) to an external device (200), and to collect the signal to be measured (s(t)) as a response of said external device to the excitation signal,
and wherein the first (W1) and second (W2) accumulation increments are positive integers, such that a quotient of the first accumulation increment (W1) divided by Q is equal to a quotient of the second accumulation increment (W2) divided by P, and is also equal to a positive integer (W0) called cycle increment,
such that the frequency F is equal to a first product of a frequency (FCLK) of the clock signal multiplied by the integer Q and by the cycle increment (W0), divided by 2NA where NA is the number of bits used in each cyclic accumulator (102, 103),
and the reference frequency FREF is equal to a second product of the frequency (FCLK) of the clock signal multiplied by the integer P and by the cycle increment (W0), divided by 2NA.

### Claim 17 (depends on 1)

A method for providing an amplitude value (A) and a phase delay value (Φ) which relate to a signal to be measured (s(t)) having sinusoidal variations over time (t) with a frequency F, said method comprising the following steps:
generating a reference signal (r(t)) having a sinusoidal form of time-variations, in continual phase coherence with the signal to be measured (s(t)), said reference signal having an amplitude (Aref) larger than the amplitude (A) of the signal to be measured, and having a frequency equal to Fref =F×P/Q, where P and Q are two fixed, non-zero positive integers, P being greater than Q;
selecting instantaneous values for which the signal to be measured (s(t)) becomes smaller than the reference signal, or for which the signal to be measured becomes larger than the reference signal; and
calculating the values of the amplitude (A) and the phase delay (Φ) of the signal to be measured (s(t)) from the selected values,
wherein the instantaneous values which are selected are instantaneous values (ψk) of a phase (ψ(t)) of the reference signal (r(t)),
wherein the values of the amplitude (A) and phase delay (Φ) of the signal to be measured (s(t)) are calculated from the values selected (ψk) for the phase of the reference signal (r(t)), and
wherein a computation unit (3) calculates an in-phase amplitude value (X) of the signal to be measured (s(t)), equal to a·cosΦ where Φ is the value of the phase delay of the signal to be measured and a is a quotient of the amplitude (A) of the signal to be measured (s(t)) divided by the amplitude (Aref) of the reference signal (r(t)), and a quadrature amplitude value (Y) of the signal to be measured, equal to a·sinΦ, from a system of affine equations having coefficients, for the in-phase amplitude (X) and the quadrature amplitude (Y) of the signal to be measured (s(t)), which depend on the selected values (ψk) for the phase of the reference signal (r(t)), wherein the method is carried out using a system according to claim 1.

### Claim 18

A method for providing an amplitude value (A) and a phase delay value (Φ) which relate to a signal to be measured (s(t)) having sinusoidal variations over time (t) with a frequency F, said method comprising the following steps:
generating a reference signal (r(t)) having a sinusoidal form of time-variations, in continual phase coherence with the signal to be measured (s(t)), said reference signal having an amplitude (Aref) larger than the amplitude (A) of the signal to be measured, and having a frequency equal to Fref =F×P/Q, where P and Q are two fixed, non-zero positive integers, P being greater than Q;
selecting instantaneous values for which the signal to be measured (s(t)) becomes smaller than the reference signal, or for which the signal to be measured becomes larger than the reference signal; and
calculating the values of the amplitude (A) and the phase delay (0) of the signal to be measured (s(t)) from the selected values,
wherein the instantaneous values which are selected are instantaneous values (ψk) of a phase (ψ(t)) of the reference signal (r(t)),
wherein the values of the amplitude (A) and phase delay (Φ) of the signal to be measured (s(t)) are calculated from the values selected (ψk) for the phase of the reference signal (r(t)), and
wherein a computation unit (3) calculates an in-phase amplitude value (X) of the signal to be measured (s(t)), equal to a·cosΦ where Φ is the value of the phase delay of the signal to be measured and a is a quotient of the amplitude (A) of the signal to be measured (s(t)) divided by the amplitude (Aref) of the reference signal (r(t)), and a quadrature amplitude value (Y) of the signal to be measured, equal to a·sinΦ, from a system of affine equations having coefficients, for the in-phase amplitude (X) and the quadrature amplitude (Y) of the signal to be measured (s(t)), which depend on the selected values (ψk) for the phase of the reference signal (r(t)).

### Claim 19 (depends on 18)

The method according to claim 18, used for characterizing a response of a resonator vibrated by an excitation signal (E(t)) having a sinusoidal form of time-variations with frequency F, the signal to be measured (s(t)) being the response of said resonator to the excitation signal.

### Claim 20 (depends on 19)

The method according to claim 19, wherein the resonator is part of a vibrating accelerometer or a vibrating gyroscope, and the values of the amplitude (A) and phase delay (Φ) relating to the signal to be measured (s(t)) are then used to calculate acceleration or rotational speed values of a device or a vehicle carrying the accelerometer or gyroscope.