DE102021108409B3 - Circuit arrangement for demodulating an AC voltage signal - Google Patents

Abstract

The invention relates to a circuit arrangement (1) for demodulating an AC voltage signal (U). The circuit arrangement comprises a first channel which comprises two track-and-hold elements each consisting of an RC element (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ). has, which the AC voltage signal (U) is supplied alternately via at least one switching element (SW ₁ ). Each of the RC elements (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ) from which the track-and-hold elements of the first channel are constructed has a time constant which is smaller by a threshold value than the period of the AC voltage signal ( U). The circuit arrangement also includes a second channel, which has two half-period integrators each consisting of at least one RC element (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ), to which the AC voltage signal (U) is fed alternately via the at least one switching element (SW ₂ ). is supplied. Each of the RC elements (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ) from which the half-period integrators of the second channel are constructed has a time constant which is greater than the period of the AC voltage signal (U) by a threshold value. The switching processes of the at least one switching element (SW ₁ , SW ₂ ) are synchronized with the period of the AC voltage signal (U) by a switching signal (I _ref ).

Description

The invention relates to synchronous demodulation of an AC voltage signal using in-phase components (hereinafter referred to as I) and quadrature components (hereinafter referred to as Q). For this purpose, a circuit arrangement is disclosed in which the demodulation takes place by means of track-and-hold elements and half-period integrators. This circuit arrangement can be used with a linear position sensor.

State of the art

$$Q=A\text{ sin }\phi$$

An I/Q method known per se can be used to demodulate an AC voltage signal. In the I/Q method, the AC voltage signal is demodulated using the mutually orthogonal in-phase components I and the quadrature components Q. The phase information of the AC voltage signal is retained. I and Q are generally defined according to formulas 1a and 1b, where A is amplitude and φ is phase. $$I=A\text{cos}\phi$$

$$Q=A\text{sin}\phi$$

Conventionally, a circuit arrangement is used in which I and Q of a reference signal having the same frequency as the AC signal are respectively mixed with the AC signal. A signal resulting from the mixing of I and the AC signal is fed to a low-pass filter to obtain the in-phase components of the AC signal and a signal resulting from the mixing of Q and the AC signal is fed to another low-pass filter to obtain the quadrature to obtain components of the AC voltage signal. Typically, one component of the reference signal, for example Q, is obtained from the other component, ie for example I, by means of a 90° phase shift. A conventional circuit arrangement has a phase shifter for this purpose. Such phase shifters increase manufacturing costs and are often difficult to adjust. In addition, such circuits can leave traces in the signal.

the GB 2517152A describes a position sensor in which an excitation circuit excites a measurement circuit. A reference signal that is also excited is divided into I and Q using a digital timer. I and Q of the reference signal are then used for demodulation.

From the U.S. 2004/0082304 A1 and the US 2020/0103473 A1 shows in each case to generate I as a reference signal and then to generate Q from I by 90° phase shift using a phase shifter. I and Q are then each mixed with the input signal by means of a mixer and then fed together to a processing unit.

From the EP 2 031 417 A1 is also known to shift the phase of an AC voltage signal by 90° by means of a phase shifter. A reference signal is also generated. The original AC voltage signal and the phase-shifted AC voltage signal by 90° are then demodulated using the reference signal.

the DE 10 2004 041 558 A1 relates to a synchronous detection method in which an input signal is averaged over a positive swing phase range and a negative swing phase range of a desired carrier wave. The in-phase component and the quadrature component can be calculated from these averagings.

In the DE 25 34 509 A1 a signal processing method is described. A control or reference signal should be in phase with an evaluation signal. Two capacitors average the positive and negative half-periods of the evaluation signal applied, specifically with a time constant RC, ie the resistance value of a resistor and the common capacitance value of the capacitors. However, the output signals are not associated with the in-phase components and quadrature components.

It is the object of the invention to provide a simple and inexpensive circuit arrangement for demodulating an AC voltage signal.

Disclosure of Invention

The object is achieved by the circuit arrangement according to the invention for demodulating an AC voltage signal in relation to a reference signal. The alternating voltage signal is continuous and harmonic and is induced in a measuring coil, for example by means of an excitation coil.

The circuit arrangement has a first channel and a second channel. The first channel has two track and hold circuits - one track and hold circuit for each half period of the reference signal. Each track-and-hold element is made up of at least one RC element, ie at least one resistor and one capacitor. For this purpose, each of the RC elements from which the track-and-hold elements of the first channel are constructed has a time constant which is smaller by a threshold value than the period of the AC voltage signal. The time constant of an RC element is defined as the product of the electrical resistance and the capacitance. A switching element alternately feeds the AC voltage signal to the two track-and-hold elements. The switching operations of the switching element are synchronized by a switching signal with the period of the reference signal. Since the RC elements each have a relatively small time constant, the AC voltage signal is sampled alternately by each RC element with half the period duration (sampling). Preferably, the AC signal is provided by an amplifier with a low output impedance. As long as the switching element establishes the connection between the signal source of the AC voltage signal via the resistor and the capacitor (closed circuit element), the capacitor absorbs the voltage from the signal source more or less simultaneously ("follow-up" function). After switching the switching element, the signal source is disconnected from the capacitor (open switching element). Since both the already open circuit element and a subsequent component such. B. an analog-to-digital converter or an amplifier stage, have a high input impedance, the capacitor is not discharged ("hold" function). Leakage currents are always possible, but the voltage of the capacitor is not significantly influenced by these during the evaluation period of the subsequent component (e.g. during digitization by the analog-to-digital converter).

The second channel has two half-period integrators - one half-period integrator for each half-period of the reference signal. Each half-period integrator is made up of at least one RC element, that is to say of at least one resistor and one capacitor. For this purpose, each of the RC elements from which the half-period integrators of the second channel are constructed has a time constant which is greater by a threshold value than the period of the AC voltage signal. A switching element alternately feeds the AC voltage signal to the two half-period integrators. The switching element can correspond to the above-mentioned switching element and in this case only one switching element can be present or preferably a further switching element is provided. The switching processes of the switching element(s) are synchronized with the period of the AC voltage signal by the switching signal mentioned above. Since the RC elements each have a relatively large time constant, the AC voltage signal is alternately integrated by each RC element with half the period. Charging and/or discharging the capacitors is of secondary relevance for the second channel. Each capacitor of the second channel has a voltage that is substantially equal to the average voltage of the incoming AC voltage over the corresponding half cycle of the switching signal.

Looking at the steady and harmonic AC voltage signal, its integral is proportional to the harmonic conjugate. Therefore, sampling the AC voltage signal with half the period (of the switching signal) and integrating the AC voltage signal with half the period (of the switching signal) results in orthogonal components of the AC voltage signal.

wobei U₀ die Amplitude ist, ω die Kreisfrequenz ist mit $\omega =\frac{2\pi }{T}$

und der Periodendauer T, φ₀ eine Phasendifferenz und V ein Versatz sind.The AC voltage signal can be written in the form of formula 2: $$u\left(t\right)=u_0\text{cos}\left(\omega t+{\phi }_0\right)+V$$

where U ₀ is the amplitude, ω is the angular frequency with $\omega =\frac{2\pi }{T}$

and the period T, φ ₀ is a phase difference and V is an offset.

$$U_2=\frac{1}{T}\left({\displaystyle \underset{0}{\overset{\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}U\left(\tau \right)d\tau }-{\displaystyle \underset{\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\overset{T}{\int }}U\left(\tau \right)d\tau }\right)$$

The quantities U ₁ and U ₂ can now be determined according to formulas 3 and 4: $${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DE102021108409B3\_0029.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\frac{1}{2}\left(u\left(0\right)-u\left(\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=\frac{1}{T}\left({\displaystyle \underset{0}{\overset{\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}u\left(\tau \right)\mathrm{i.e}\tau }-{\displaystyle \underset{\raisebox{1ex}{$\mathrm{<figure-callout\; id="2T"\; label="T"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">T</figure-callout>}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\overset{T}{\int }}u\left(\tau \right)\mathrm{i.e}\tau }\right)$$

When calculating the above differences, the offset V that can occur for U(t) (see formula 2) is omitted. The offset V therefore only affects the gain and the dynamic range of the signal and is therefore not discussed further below.

U ₁ corresponds to the deviation of the AC voltage signal from its midpoint at the beginning of the complete period of an in-phase signal. U ₂ corresponds to the mean deviation of the AC voltage signal from its midpoint over half a period (upper half of the period H) of an in-phase signal.

From formula 3 follows formula 5: $${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DE102021108409B3\_0029.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\frac{1}{2}{u}_0\left(\text{cos}\left({\phi }_0\right)-\text{cos}\left(\pi +{\phi }_0\right)\right)={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{cos}\left({\phi }_0\right)$$

And from formula 4 follows formula 6: $$\begin{array}{l}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=\frac{1}{T}2{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}u\left(\tau \right)\mathrm{i.e}\tau }=\frac{2}{T}{u}_0{\left[\text{sin}\left(\omega t+{\phi }_0\right)\cdot \frac{1}{\omega }\right]}_0^{\raisebox{1ex}{$\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">T</figure-callout>}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ ={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\frac{2}{\mathrm{<figure-callout\; id="2"\; label="T\; T"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">T</figure-callout>}}\frac{T}{}\frac{}{2\pi }\left(\text{sin}\left(\pi +{\phi }_0\right)-\text{sin}\left({\phi }_0\right)\right)=-\frac{2}{\mathrm{<figure-callout\; id="0"\; label="\pi \; u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{u}_{}{}_0\text{sin}\left({\phi }_0\right)\end{array}$$

On the other hand, the AC voltage signal in Equation 2 can also be transformed to Equation 7 by the addition theorem (the offset V is neglected as described above): $$u\left(t\right)=u_0\left(\text{cos}\left(\omega t\right)\text{cos}\left({\phi }_0\right)-\text{sin}\left(\omega t\right)\text{sin}\left({\phi }_0\right)\right)$$

$$U_Q=U_0\text{ sin}\left({\phi }_0\right)$$

If I and Q from formulas 1a and 1b are applied to the AC voltage signal according to formula 7, the in-phase components U _I according to formula 8a and the quadrature components U _Q according to formula 8b are obtained: $$u_I={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{cos}\left({\phi }_0\right)$$

$$u_Q={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{sin}\left({\phi }_0\right)$$

From formula 7 follows: $$u\left(t\right)=u_I\text{cos}\left(\omega t\right)-u_Q\text{sin}\left(\omega t\right)$$

According to the definition, U ₁ is the in-phase component of the AC voltage signal and U _Q is the quadrature component of the AC voltage signal.

$$U_Q=\frac{\pi }{2}{U}_2$$

Comparing formulas 5 and 6 with formulas 8a and 8b gives the following: $$u_I={\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DE102021108409B3\_0029.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_1$$

$$u_Q=\frac{\pi }{2}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$$

U ₁ corresponds to the in-phase component U _I of the AC voltage signal and U ₂ is proportional to the quadrature component U _Q of the AC voltage signal.

In the circuit arrangement according to the invention, in which the above-mentioned in-phase signal is the switching signal of the switching element(s), U ₁ is obtained directly from the first channel with the two track-and-hold elements: $${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="DE102021108409B3\_0029.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\frac{1}{2}\left({{\mathrm{<figure-callout\; id="1p"\; label="u"\; filenames="DE102021108409B3\_0028.png,DE102021108409B3\_0031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1p}|}_{S=H}-{u_{1n}|}_{S=L}\right)$$

Here, U _1p is the measured voltage in the first channel when the switching signal runs through the upper half of the period H of the reference signal and the switching element is switched accordingly. U _1p is measured as soon as the switching signal changes to the upper half of the H period. U _1n is the measured voltage in the first channel when the switching signal runs through the lower half of the period L of the reference signal and the switching element is switched accordingly. U _1n is measured as soon as the switching signal S changes to the lower half of the L period.

Correspondingly, in the circuit arrangement according to the invention U ₂ is obtained directly from the second channel with the half-period integrators: $${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DE102021108409B3\_0026.png,DE102021108409B3\_0030.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=u_{2p}-u_{2n}$$

Here U _2p is the measured voltage in the second channel when the switching signal runs through the lower half of the period L and the switching element is switched accordingly. U _2p is measured over the lower half of the period L or alternatively continuously. U _2n is the measured voltage in the second channel when the switching signal runs through the upper half of the period H and the switching element is switched accordingly. U _2n is measured over the upper half of the period H or alternatively continuously.

As a result, the circuit arrangement according to the invention functions as a demodulator. Only RC elements and switching elements are used to construct the circuit arrangement according to the invention. This offers the advantages that an adjustment can be carried out in a simple manner since the components leave no traces in the signal and the costs for the circuit arrangement are generally very low due to the simple components. In addition, the signal is kept constant between the switching processes, which simplifies the evaluation.

In order to achieve the most accurate possible sampling by the track-and-hold elements, the time constants of the RC elements of the first channel are chosen to be as small as possible. The time constant of each of the two RC elements from which the track-and-hold elements of the first channel are constructed is preferably smaller by a factor of at least five than the period duration of the AC voltage signal.

The time constants of the RC elements of the second channel are chosen to be as large as possible in order to cover the entire half-period during the integration and thus to achieve the most precise possible integration by the half-period integrators. The time constant of each of the two RC elements from which the half-period integrators of the second channel are formed is preferably greater by at least a factor of ten than the period of the AC voltage signal.

A switching element can be provided for both channels, with which the AC voltage signal is fed alternately to the respective RC elements. However, this can lead to an equalization between the capacitors of the different channels during the hold function. Demodulation is nevertheless possible if precise time sampling takes place at predeterminable, desired sampling points. Those skilled in the art can then use mathematical correlation to determine the in-phase I and quadrature Q components.

A separate switching element is preferably provided for each channel. A first switching element is therefore provided for the first channel, which alternately feeds the AC voltage signal first to a track-and-hold element and then to the other track-and-hold element. Likewise, a second switching element is provided for the second channel, which alternately feeds the AC voltage signal first to a half-period integrator and then to the other half-period integrator. Both switching elements are synchronized via the same switching signal. This enables a simple evaluation, since the channels can be completely separated from one another.

A reference signal is preferably provided which is synchronous with the AC voltage signal. How such a reference signal can be obtained is described further below. According to one aspect the reference signal serves directly as a switching signal for the at least one switching element. The at least one switching element can thus be synchronized with the period duration of the AC voltage signal in a simple manner without additional components.

For sampling in the first channel, when only the reference signal is used, as described above, typically only a little time remains during the hold state between two switching operations, namely essentially half a period of the reference signal. As a result, very high demands are placed on an evaluation unit, in particular on its analog/digital converter and on an interruption system of a microcontroller, or the operating frequency of the circuit arrangement is limited. Advantageously, a recursive converter is provided, which provides an output signal from a binary input signal and a reference signal, which serves as a switching signal for the first switching element. The period of the binary input signal is significantly longer than the period of the reference signal, preferably by a factor of between 10 and 100, particularly preferably between 20 and 100. An extension of the hold time by a factor of 20 already allows the use of simple microcontrollers with built-in analog digital converter. If the hold time is extended by a factor of more than 100, the data acquisition can no longer be time-critical. The factor can be selected depending on the vibration frequency and can also assume higher or lower values. If, after a status change of the binary input signal, the reference signal has the same status as the binary input signal, the output signal also changes its status. Due to the recursive converter, the output signal remains in the same state over several periods of the reference signal before it changes its state at the same time as the reference signal and the switching element is thus switched accordingly. Consequently, the hold state for each RC element of the first channel is significantly lengthened, so that the evaluation of the sample is simplified and the above limitations are overcome. The reference signal is still used directly for the second switching element, but the timing is not critical in the evaluation for the second channel.

There are several ways of providing a reference signal, which depend in particular on the origin of the AC voltage signal and on the operating conditions of the circuit arrangement. According to one aspect, the reference signal is already provided in advance and used to generate a periodic excitation in an excitation coil. The excitation coil then induces the AC voltage signal in a measuring coil that is to be demodulated. The AC voltage signal and the reference signal are supplied to the circuit arrangement according to the invention.

According to a further aspect, an oscillator generates a periodic excitation of an excitation coil. The periodic excitation is converted into a binary reference signal. The excitation coil then induces the AC voltage signal in a measuring coil that is to be demodulated.

Here, too, the AC voltage signal and the reference signal are supplied to the circuit arrangement according to the invention.

Analog-to-digital converters (A/D converters) are preferably provided for the evaluation. A first analog/digital converter is arranged in the first channel and converts the analog voltage signals from the two RC elements in the first channel into digital signals. A second analog-to-digital converter is also arranged in the second channel and converts the analog voltage signals from the two RC elements in the second channel into digital signals.

The object is also achieved by the linear position sensor according to the invention. The linear position sensor is used to measure the position of an object (also known as a target). For this purpose, the linear position sensor has an exciter coil, a measuring coil, an oscillator and the circuit arrangement according to the invention described above. The oscillator is connected to the excitation coil, preferably as a member of a parallel LC circuit, and excites it with a periodic excitation so that it generates a magnetic field. The magnetic field induces an AC voltage signal in the measuring coil. The magnetic field is disturbed by the object depending on its position, so that the AC voltage signal in the measuring coil also changes. The circuit arrangement is connected to the measuring coil and the AC voltage signal is fed to the circuit arrangement. As described above, the circuit arrangement demodulates the AC voltage signal.

For the advantages and preferred further developments of the linear position sensor, reference is made to the above description of the circuit arrangement according to the invention.

character list

• 1 zeigt eine schematische Darstellung einer Ausführungsform des erfindungsgemäßen linearen Positionssensors.
• 2 zeigt eine schematische Darstellung einer ersten Ausführungsform der erfindungsgemäßen Schaltungsanordnung.
• 3 zeigt eine schematische Darstellung einer zweiten Ausführungsform der erfindungsgemäßen Schaltungsanordnung.
• 4 zeigt ein Diagramm eines zu demodulierenden Wechselspannungssignals und eines Referenzsignals.
• 5 zeigt eine schematische Darstellung einer dritten Ausführungsform der erfindungsgemäßen Schaltungsanordnung.
• 6a zeigt ein Diagramm von Eingangssignalen und Ausgangssignalen eines rekursiven Konverters.
• 6b zeigt ein Diagramm der Ausgangssignale der Schaltungsanordnung aus 5.
• 7 zeigt ein Diagramm, bei dem der Zusammenhang zwischen den In-Phase-Anteilen und den Quadratur-Anteilen des Wechselspannungssignals für mehrere Materialien dargestellt ist.

Embodiments of the invention are shown in the drawings and explained in more detail in the following description.

• 1 shows a schematic representation of an embodiment of the linear position sensor according to the invention.
• 2 shows a schematic representation of a first embodiment of the circuit arrangement according to the invention.
• 3 shows a schematic representation of a second embodiment of the circuit arrangement according to the invention.
• 4 shows a diagram of an AC voltage signal to be demodulated and a reference signal.
• 5 shows a schematic representation of a third embodiment of the circuit arrangement according to the invention.
• 6a shows a diagram of input signals and output signals of a recursive converter.
• 6b shows a diagram of the output signals of the circuit arrangement 5 .
• 7 FIG. 12 shows a diagram showing the relationship between the in-phase components and the quadrature components of the AC voltage signal for a number of materials.

Embodiments of the invention

wobei U_e0 die Amplitude des Signals und ω die Kreisfrequenz des Signals sind. Es gilt $\omega =\frac{2\pi }{T},$

mit der Periodendauer T. In einer Ausführungsform wird das Signal, mit dem die periodische Anregung erzeugt wird, als Referenzsignal verwendet. In einer anderen Ausführungsform wird ein binäres Referenzsignal aus der periodischen Anregung erzeugt. Der In-Phase-Anteil I_ref des Referenzsignals (im Folgenden als I-Referenzsignal bezeichnet) wird an die Schaltungsanordnung 1 übertragen. 1 shows a schematic representation of an embodiment of the linear inductive position sensor according to the invention. The linear position sensor has a circuit arrangement 1 according to the invention for demodulating an AC voltage signal U. In addition, the linear position sensor has an oscillator 2 , an excitation coil 3 and a measuring coil 4 as well as an evaluation unit 5 . The oscillator 2 is connected to the excitation coil 3 and generates in the excitation coil 3 a periodic excitation in the form of $$u_e\left(t\right)={\mathrm{<figure-callout\; id="0"\; label="u\; e"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_e\text{cos}\left(\omega t\right)$$

where U _e0 is the amplitude of the signal and ω is the angular frequency of the signal. It applies $\omega =\frac{2\pi }{T},$

with the period duration T. In one embodiment, the signal with which the periodic excitation is generated is used as a reference signal. In another embodiment, a binary reference signal is generated from the periodic excitation. The in-phase component I _ref of the reference signal (referred to below as the I reference signal) is transmitted to the circuit arrangement 1 .

A magnetic field is generated in the excitation coil 3 due to the periodic excitation. The magnetic field induces a voltage U in the measuring coil 4. In this exemplary embodiment, the measuring coil 4 is a measuring coil, as is described in the patent application, which is not a prior publication DE 10 2020 134 217.9 by the applicant, to which reference is made herein. An object (target) not shown here influences the magnetic field, so that there is a phase difference φ ₀ between the periodic excitation U _e and the measured signal U. The phase difference φ ₀ is characteristic of the material of the object. The measured signal U is described with the formula 2* (as described above, the offset is not taken into account): $$u\left(t\right)={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{cos}\left(\omega t+{\phi }_0\right)$$

Using the addition theorem, formula 2* can be converted into formula 9: $$u\left(t\right)=u_I\text{cos}\left(\omega t\right)-u_Q\text{sin}\left(\omega t\right)$$

$$U_Q=U_0\text{ sin}\left({\phi }_0\right)$$

Here, U ₁ is the in-phase component of the measured signal U according to formula 8a and U _Q is the quadrature component of the measured signal U according to formula 8b: $$u_I={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{cos}\left({\phi }_0\right)$$

$$u_Q={\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="DE102021108409B3\_0029.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\text{sin}\left({\phi }_0\right)$$

The measured signal U is demodulated by the circuit arrangement according to the invention, which is described below. After the demodulation, U _I and U _Q are fed to the evaluation unit 5 .

In addition, a position-dependent distance signal S _{d is} measured and fed to the evaluation unit 5 .

The evaluation unit 5 now calculates the distance d to the object and the position P of the object. In addition, the evaluation unit 5 uses the following formula 15 to calculate the phase difference φ ₀ from U _I and U _Q . $${\phi }_0=\text{atan}\left(u_Q,u_I\right)$$

Various information regarding the material can be obtained from the phase difference. For this, refer to the description 6 referred.

In 2 a first embodiment of the circuit arrangement 1 according to the invention for demodulating an AC voltage signal is shown. The signal U recorded by the measuring coil 4 is provided here as the alternating voltage signal. In addition, the I reference signal I _ref , which is synchronous with the AC voltage signal, is provided by the oscillator 2 . The circuit arrangement 1 has two channels, which are shown here separately from one another, as described below, and to which the AC voltage signal U is supplied. Before that, the AC voltage signal U runs through an analog buffer B or, alternatively, a buffer amplifier. Additionally or alternatively, the AC voltage signal U can be supplied to an amplifier.

The first channel has a first resistor R ₁ , a first switch SW ₁ , a first capacitor C ₁₁ and a second capacitor C ₁₂ . Each of these capacitors C ₁₁ , C ₂₁ forms an RC element connected as a voltage divider with the first resistor R ₁ . For each of these two RC elements, a time constant - i.e. the product of the electrical resistance of the first resistor R ₁ and the capacitance of the first capacitor C ₁₁ or the second capacitor C ₁₂ - is significantly smaller than the period T of the AC voltage signal U (R _{1C11 <<} T; _{R1C12 <<} T). In this embodiment, the time constant is smaller than the period T by a factor of 5.

The I reference signal I _ref is fed to the first switch SW ₁ and is used as a switching signal with which the first switch SW ₁ is switched over between two switching states. If the I reference signal I _ref runs through its upper half of the period H (see 4 ), the first switch SW ₁ assumes a first switching state (in 2 denoted by “H” in switch SW ₁ ). On the other hand, if the I reference signal I _ref runs through its lower half of the period L (see 4 ), the first switch SW ₁ assumes a second switching state (in 2 denoted by “L” in switch SW ₁ ). The first switch SW ₁ is thus switched between the two switching states with the period duration of the I reference signal I _ref , which corresponds to the period duration T of the AC voltage signal U.

In the first switching state (corresponds to H), the first switch SW ₁ connects the AC voltage signal U to the first capacitor C ₁₁ via the first resistor R ₁ , while the connection to the second capacitor C ₁₂ is disconnected. The signal U _1p is measured. In the second switching state (corresponds to L), the first switch SW ₁ connects the AC voltage signal U via the first resistor R ₁ to the second capacitor C ₁₂ ; thereby the connection to the first capacitor C ₁₁ is separated. The signal U _1n is measured. The two RC elements of the first channel therefore act with the help of the _first switch SW1 as track-and-hold elements which sample the AC voltage signal U (see also 4 ).

The signals U _1p and Um of the first channel are fed to a differentiator (not shown here), which combines the signals U _1p , U _1n according to formula 12* to form the in-phase signal U _I : $$u_I=\frac{1}{2}\left({{\mathrm{<figure-callout\; id="1p"\; label="u"\; filenames="DE102021108409B3\_0028.png,DE102021108409B3\_0031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1p}|}_{S=H}-{u_{1n}|}_{S=L}\right)$$

The in-phase signal U _I is fed to an analog/digital converter, also not shown, which converts the analog signal into a digital signal. Finally, the digital in-phase signal U _I of the evaluation unit 5 is supplied.

The second channel has a second resistor R ₂ , a second switch SW ₂ , a third capacitor C ₂₁ and a fourth capacitor C ₂₂ . Each of these capacitors C ₂₁ , C ₂₂ forms an RC element connected as a voltage divider with the second resistor R ₂ . For each of these two RC elements, a time constant - i.e. the product of the electrical resistance of the second resistor R ₂ and the capacitance of the third capacitor C ₂₁ or the fourth capacitor C ₂₂ - is significantly greater than the period T of the AC voltage signal U (R _{2C21 >>} T; _R2C22 >> _T ). In this exemplary embodiment, the time constant is greater by a factor of 10 than the period duration T.

The same I reference signal I _ref is also supplied to the second switch SW ₂ and is used as a switching signal with which the second switch SW ₂ is switched between two switching states. If the I reference signal lref runs through its upper half of the period H (see 4 ), the second switch SW ₂ assumes a first switching state (in 2 denoted by “H” in switch SW ₂ ). On the other hand, if the I reference signal I _ref runs through its lower half of the period L (see 4 ), the second switch SW ₂ assumes a second switching state (in 2 denoted by “L” in switch SW ₂ ). The second switch SW ₂ is thus also switched between the two switching states with the period duration of the I reference signal I _ref , which corresponds to the period duration T of the AC voltage signal U. Accordingly, the first switch SW ₁ and the second switch SW ₂ are switched simultaneously with the aid of the I reference signal I _ref and are consequently synchronized.

In the first switching state (corresponds to H), the second switch SW ₂ connects the AC voltage signal U to the third capacitor C ₂₁ via the second resistor R ₂ , while the connection to the fourth capacitor C ₂₂ is disconnected. The signal U _2n is measured. In the second switching state (corresponds to L), the second switch SW ₂ connects the AC voltage signal U to the fourth capacitor C ₂₂ via the second resistor R ₂ ; thereby the connection to the third capacitor C ₂₁ is separated. The signal U _2p is measured. The two RC elements of the second channel therefore each act as half-period integrators with the help of the _second switch SW2, which integrate the AC voltage signal U over the corresponding half-period (see also 4 ).

The signals U _2n and U _2p of the second channel are fed to another differentiator, not shown here, which combines the signals U _2n , U _2p to form the quadrature signal U _Q according to formula 14: $$u_Q=-\frac{\pi }{2}\left({u_{2p}|}_{S=L}-{u_{2n}|}_{S=H}\right)$$

The quadrature signal U _Q is fed to an analog/digital converter, also not shown, which converts the analog signal into a digital signal. Finally, the digital quadrature signal U _Q of the evaluation unit 5 is supplied.

In 3 a second embodiment of the circuit arrangement 1 according to the invention for demodulating an AC voltage signal is shown. The second embodiment differs from the first embodiment in that instead of the two switches _SW1 and SW2 in the _two channels, a single switch SW is provided, which is arranged in a common channel from which the two channels then branch off. In addition, instead of one resistor R ₁ , R ₂ each, two resistors R ₁₁ , R ₁₂ and R ₁₂ , R ₂₂ are provided, each of which is directly connected to one of the two capacitors C ₁₁ and C ₁₂ or C ₂₁ and C ₂₂ . In 3 the first channel has the first capacitor C ₁₁ and the first resistor R ₁₁ and the second capacitor C ₁₂ and the second resistor R ₁₂ . The second channel has the third capacitor C ₂₁ and the third resistor R ₂₁ and the fourth capacitor C ₂₂ and the fourth resistor R ₂₂ .

In the first switching state (corresponds to H), the switch SW connects the AC voltage signal U to the first capacitor C ₁₁ via the first resistor R ₁₁ and to the third capacitor C _{21 via the third resistor R 21 .} The connections to the second capacitor C ₁₂ and the fourth capacitor C ₂₂ are disconnected. The signals U _1p and U _2n are measured. In the second switching state (corresponds to L), the switch SW connects the AC voltage signal U to the second capacitor C ₁₂ via the second resistor R ₁₂ and to the fourth capacitor C _{22 via the fourth resistor R 22 .} The connection Gen to the first capacitor C ₁₁ and the third capacitor C ₂₁ are separated. The signals U _1n and U _2p are measured.

If the switch SW, as in 3 shown, in the first switching state, the second capacitor C ₁₂ and the fourth capacitor C ₂₂ are decoupled from the AC voltage signal, but still connected to each other. Therefore, the voltages of capacitors C ₁₂ and C ₂₂ begin to equalize. Consequently, the measured signals U _1p and U _2n have a time dependency.

The same applies to the capacitors C ₁₁ and C ₂₁ and to the signals U _1n and U _2p in the second switching state. It is also possible to perform demodulation. For this purpose, the voltage signals U _1n , U _1p , U _2n , U _2p are sampled at predeterminable, desired sampling points by means of sampling that is precise in terms of time. The in-phase components I and the quadrature components Q can be determined via a corresponding mathematical correlation.

In 4 the I reference signal I _ref and the AC voltage signal U are shown in a common diagram over time t. The I reference signal I _ref is a square-wave signal that alternates between an upper half H period and a lower half L period. The I reference signal I _ref has the same period T as the AC voltage signal U, but it is offset in time compared to this. As described above, the I reference signal I _{ref sets} the clock for the switching processes of the switches SW ₁ and SW ₂ or the switch SW. The switches SW ₁ and SW ₂ or the switch SW switch precisely when the I reference signal changes from the upper half of the period H to the lower half of the period L or vice versa, ie after half a period duration ^T / ₂ . In the diagram in figure these points in time are marked for two periods with ^T / ₂ , T, ^3T / ₂ , 2T. The track-and-hold elements of the first channel sample the AC voltage signal U at these points in time. Between the points in time, the AC voltage signal U is integrated by the half-period integrators of the second channel. As soon as the I reference signal I _ref transitions from the lower half of the period L to the upper half of the period H, i.e. immediately after 0 (at the beginning), T and 2T, the quantity U _1p for sampling the AC voltage signal is measured in the first channel. In addition, the variable U _2n is measured in the second channel by integrating the AC voltage signal during the lower half period. As soon as the I reference signal I _ref transitions from the upper half of the period H to the lower half of the period L, ie immediately after ^T / ₂ and ^3T / ₂ , the variable U _1n for sampling the AC voltage signal is measured in the first channel. In addition, the variable U _2p is measured in the second channel by integrating the AC voltage signal during the upper half period.

In 5 a third embodiment of the circuit arrangement 10 according to the invention for demodulating an AC voltage signal is shown. Identical components are marked with the same reference symbols. The third embodiment differs from the first only in that the first switch SW ₁ is not supplied with the reference signal I _ref , but with an output signal THEN generated by a recursive converter K, which controls the switching processes of the first switch SW ₁ . The second switch SW ₂ is still controlled via the I reference signal I _ref since the processing of the signals U _2p and U _2n obtained from the integration is not time-critical. The rest of the structure and the functions correspond to the first exemplary embodiment, so that reference is made to its description.

A binary input signal THSEL and the I reference signal I _ref are fed to the recursive converter K. The binary input signal THSEL has two states and a period that is significantly longer than the period T of the AC voltage signal and the I reference signal I _ref . The recursive converter K produces the output signal THEN, which is also binary and has two states. In analogy to the I reference signal I _ref , the states of the signals THSEL and THEN are labeled “H” for the upper state and “L” for the lower state (cf 5a ). The output signal THEN changes state when the I reference signal I _ref has the same state as the binary input signal THSEL after a state change of the binary input signal THSEL. The first switch SW ₁ is then controlled via the output signal THEN (see 5b ).

6a shows a diagram of the binary input signal THSEL, the I reference signal lref and the binary output signal THEN over time t. In this example, with an oscillation frequency of the reference signal of 2.13 MHz, a period is approximately 470 ns. The period of the binary input signal THSEL is greater by a factor of approximately 17 than the period of the I reference signal I _ref . After the input signal THSEL transitions from its low state to its high state, as soon as the I reference signal I _ref also transitions from its low state to its high state, the output signal THEN transitions from its low state to its high state upper state H. Similarly, after the input signal THSEL transitions from its high state to its low state, as soon as the I reference signal lref also transitions from its high state to its low state, the output signal THEN transitions from its high state to its low state its lower state L. For the first transition at the beginning, the output signal THEN directly follows the transition of the I reference signal I _ref . The first switch _SW1 is switched only at the transitions of the output signal THEN. As a result, the first capacitor C ₁₁ and the second capacitor C ₁₂ each remain separated from the AC voltage signal U for a longer period of time, leaving more time for an evaluation.

In 6 b are the voltage signals U _2p , U _2n , U _1n and U _1p in a diagram over time t, with the same time scale as in 6a applied. The signals U _1n and U _1P , which are obtained in the first channel through the track-and-hold elements, are modulated with the output signal THEN. If, for example, the output signal THEN is in the upper state H, the second capacitor C ₁₂ is decoupled and the signal U _1p is held over several periods of the AC voltage signal U and can therefore be measured easily. In this interval, U _1n follows the period of the AC voltage signal U. If the output signal THEN changes to the lower state L, the first capacitor C ₁₁ is decoupled and the signal U _1n is held over several periods and can be measured. The signals U _2p and U _2n are not affected by this due to the significantly higher time constant of the associated RC elements.

7 shows in a diagram the correlation of the in-phase component U ₁ and the quadrature component U _Q of the AC voltage signal U for several different materials of the object. EC80 denotes structural steel, V2A denotes stainless steel and Al stands for aluminium. For fixed coil arrangements, the correlation can be clearly assigned to the material. The angle that the correlation curve assumes in the diagram is particularly important here. The curves can be recorded for different materials and then compared to the measured values to determine the material of the object.

Claims (10)

Circuit arrangement (1) for demodulating an AC voltage signal (U), having: a first channel, which consists of two RC elements each (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ; R ₁₁ , C ₁₁ ; R ₁₂ , C ₁₂ ) constructed track-and-hold elements to which the AC voltage signal (U) is supplied alternately via at least one switching element (SW ₁ ), each of the RC elements (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ; R ₁₁ , C ₁₁ ; R ₁₂ , C ₁₂ ), from which the track-and-hold elements of the first channel are constructed, has a time constant which is smaller by a threshold value than the period duration (T) of the AC voltage signal (U), and a second channel which has two half-period integrators each consisting of at least one RC element (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ; R ₂₁ , C ₂₁ ; R ₂₂ , C ₂₂ ), to which the AC voltage signal (U) is fed alternately via the at least one switching element ( SW ₂ ) is supplied, each of the RC elements (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ; R ₂₁ , C ₂₁ ; R ₂₂ , C ₂₂ ) from which the half period enintegrators of the second channel are constructed, has a time constant which is greater by a threshold value than the period (T) of the AC voltage signal (U), the switching processes of the at least one switching element (SW ₁ , SW ₂ ) being triggered by a switching signal with the period ( T) of the AC voltage signal (U) are synchronized. Circuit arrangement according to claim 1 , characterized in that the time constant of each of the two RC elements (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ; R ₁₁ , C ₁₁ ; R ₁₂ , C ₁₂ ) from which the track-and-hold elements of the first channel are constructed, is smaller by at least a factor of five than the period duration (T) of the AC voltage signal (U). Circuit arrangement according to claim 1 or 2 , characterized in that the time constant of each of the two RC elements (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ; R ₂₁ , C ₂₁ ; R ₂₂ , C ₂₂ ) from which the half-period integrators of the second channel are formed, to is at least a factor of ten greater than the period (T) of the AC voltage signal (U). Circuit arrangement according to one of Claims 1 until 3 , characterized in that a separate switching element (SW ₁ , SW ₂ ) is provided for each channel, which are synchronized via the switching signal. Circuit arrangement according to one of Claims 1 until 4 , characterized in that a reference signal (I _ref ) which is synchronous with the AC voltage signal (U) serves as a switching signal for the at least one switching element (SW ₁ , SW ₂ ). Circuit arrangement according to claim 4 , characterized in that a recursive converter (K) is provided, which provides an output signal (THEN) from a binary input signal (THSEL) and a reference signal (I _ref ) synchronous with the AC voltage signal (U), which is used as a switching signal for the first switching element (SW ₁ ), the output signal (THEN) changing its state (H, L) when the reference signal (I _ref ) has the same state (H, L) as the binary input signal (THSEL ) having. Circuit arrangement according to one of Claims 5 or 6 , characterized in that the reference signal (I _ref ) generates a periodic excitation in an excitation coil (3) and the excitation coil (3) in a measuring coil (4) induces the AC voltage signal (U). Circuit arrangement according to one of Claims 5 or 6 , characterized in that an oscillator (2) generates a periodic excitation of an excitation coil (3), the periodic excitation is converted into a binary reference signal (I _ref ) and the excitation coil (3) in a measuring coil (4) the AC voltage signal (U) induced. Circuit arrangement according to one of the preceding claims, characterized in that a first analog/digital converter is provided, the voltage signals (U _1n , U _1p ) of the two RC elements (R ₁ , C ₁₁ ; R ₁ , C ₁₂ ; R ₁₁ , C ₁₁ ; R ₁₂ , C ₁₂ ) of the first channel and a second analog-to-digital converter is provided to convert the voltage signals (U _2n , U _2p ) of the two RC elements (R ₂ , C ₂₁ ; R ₂ , C ₂₂ ; R ₂₁ , C ₂₁ ; R ₂₂ , C ₂₂ ) of the second channel. Linear position sensor comprising: - an exciter coil (3), - a measuring coil (4), - an oscillator (2), which is connected to the exciter coil (3), - and a circuit arrangement (1) according to one of Claims 1 until 9 , which is connected to the measuring coil (4), the oscillator (2) being set up to periodically excite the excitation coil (3) so that it generates a magnetic field, and the circuit arrangement (1) generating an AC voltage signal (U) which is in the Measuring coil (4) was induced by the magnetic field, demodulated.

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