Ultrasonic flow meter with subsampling of ultrasonic transducer signals

Abstract

An ultrasonic flow meter is disclosed, including a switching unit for switching electrical transmission signals between a signal generator and at least two ultrasonic transducers and for switching electrical reception signal between the transducers and a receiver circuit, wherein the switching unit is coupled to an output terminal of an operational amplifier of the signal generator and to an inverting input terminal of an operational amplifier of the receiver circuit. Furthermore, a method for characterizing an ultrasonic transducer is disclosed, including the step of determining directly from one or more supply current signals for an active component of a signal generator one or more quantities useful for characterizing the transducer. Furthermore, a method for determining the time delay of an ultrasonic signal in a flow path of an ultrasonic flow meter is disclosed, including the step of comparing physically transmitted, delayed and received signals with simulated non-delayed signals.

Claims

1. An ultrasonic flow meter comprising: a flow path for fluid flow; at least two ultrasonic transducers acoustically coupled to the flow path, a first transducer of the at least two ultrasonic transducers being arranged upstream of a second transducer of the at least two ultrasonic transducers along the flow path; a signal generator for generating electrical transmission signals to the at least two ultrasonic transducers, the signal generator comprising a first negative feedback coupled operational amplifier; a receiver circuit for receiving electrical reception signals from the at least two ultrasonic transducers, the receiver circuit comprising a second negative feedback coupled operational amplifier; a switching unit for switching the electrical transmission signals between the signal generator and the at least two ultrasonic transducers and for switching the electrical reception signal between the at least two ultrasonic transducers and the receiver circuit; and a signal processing unit for providing an output indicative of a flow rate of the fluid flow in the flow path based on the electrical reception signals; wherein the switching unit is coupled to an output terminal of the first negative feedback coupled operational amplifier of the signal generator and the switching unit is coupled to an inverting input terminal of the second negative feedback coupled operational amplifier of the receiver circuit, and wherein an output impedance of the signal generator and an input impedance of the receiver circuit are negligible, at less than 1%, compared to the impedance of the at least two ultrasonic transducers.

2. The flow meter of claim 1, wherein the signal generator and the receiver circuit share at least one active component.

3. The flow meter of claim 1, wherein all active components of the signal generator are completely separate from all active components of the receiver circuit.

4. The flow meter of claim 1, wherein one or more of the first negative feedback coupled operational amplifier and the second negative feedback coupled operational amplifier are current feedback operational amplifiers.

5. The flow meter of claim 1, wherein one or more of the first negative feedback coupled operational amplifier and the second negative feedback coupled operational amplifier are operated at an input common mode voltage, an AC component of which is substantially zero.

6. The flow meter of claim 1, wherein the at least two ultrasonic transducers are arranged to be able to transmit an ultrasound signal simultaneously.

7. The flow meter of claim 1, wherein the at least two ultrasonic transducers are two ultrasonic transducers.

8. The flow meter of claim 1, wherein the output impedance of the signal generator and the input impedance of the receiver circuit are less than 10 Ohms.

9. The flow meter of claim 1, wherein the output impedance of the signal generator and the input impedance of the receiver circuit are less than 1 Ohm.

10. The flow meter of claim 1, wherein the output impedance of the signal generator and the input impedance of the receiver circuit are less than 0.1 Ohm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the following, a few exemplary embodiments of the invention are described and explained in more detail with reference to the drawings, where

(2) FIG. 1 illustrates schematically the overall structure of an ultrasonic flow meter for transit time flow metering as known in the art,

(3) FIG. 2a illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter known in the art,

(4) FIG. 2b illustrates schematically a coupling of ultrasonic transducers in another ultrasonic flow mater known in the art,

(5) FIG. 3 illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter according to an embodiment of the invention,

(6) FIG. 4 illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter according to another embodiment of the invention,

(7) FIG. 5 illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter according to yet another embodiment of the invention,

(8) FIG. 6 shows a diagram of most of the essential electronic components in an ultrasonic flow meter according to an embodiment of the invention,

(9) FIG. 7a illustrates schematically a set-up for performing a first step in obtaining a supply current signal of an active component driving an ultrasonic transducer,

(10) FIG. 7b illustrates schematically a set-up for performing a second step in obtaining a supply current signal of an active component driving an ultrasonic transducer,

(11) FIG. 7c illustrates an advantageous way of connecting a signal generator and a receiver circuit for obtaining such supply current signals.

(12) FIG. 8a illustrates schematically a first step in obtaining characteristics of an ultrasonic transducer from supply current signals of an active component driving the transducer,

(13) FIG. 8b illustrates schematically a second step in obtaining characteristics of an ultrasonic transducer from supply current signals of an active component driving the transducer,

(14) FIG. 9 illustrates well-known equivalence diagram of an ultrasonic transducer,

(15) FIG. 10 illustrates some of the steps in the derivation of a simple equivalence diagram of an ultrasound flow meter according to the invention,

(16) FIG. 11 illustrates the differences and similarities between a physical and a simulated signal chain through a flow meter according to the invention,

(17) FIG. 12 illustrates schematically a method according to the invention for determining very precisely the time delay of the ultrasonic signal in the flow path,

(18) FIG. 13 illustrates schematically in more detail a method for calculation of the absolute transit time from response signals obtained by a method as the one illustrated in FIG. 12,

(19) FIG. 14 illustrates an equivalence diagram of a signal generator and an ultrasonic transducer connected thereto according to the invention,

(20) FIG. 15a illustrates a single pulse signal,

(21) FIG. 15b illustrates a supply current signal for a first ultrasound transducer obtained in response to the single pulse in FIG. 15a,

(22) FIG. 15c illustrates a supply current signal for a second ultrasound transducer obtained in response to the single pulse in FIG. 15a,

(23) FIG. 15d illustrates a supply current signal obtained without any ultrasound transducers in response to the single pulse in FIG. 15a,

(24) FIG. 16a illustrates a calculated single pulse response of a first ultrasound transducers,

(25) FIG. 16b illustrates a calculated single pulse response of a second ultrasound transducers,

(26) FIG. 16c illustrates a calculated single pulse response of a complete ultrasound transducer system according to the invention,

(27) FIG. 17a illustrates an emulated flow meter response,

(28) FIG. 17b illustrates a measured flow meter response,

(29) FIG. 18a illustrates the theoretical relation between the magnitudes of the real and the emulated flow meter responses in the frequency domain,

(30) FIG. 18b illustrates the theoretical phase angles between the real and the emulated flow meter responses in the frequency domain,

(31) FIG. 19 illustrates an example of corresponding emulated and measured flow meter responses,

(32) FIG. 20a illustrates the magnitude in the frequency domain of the emulated flow meter response shown in FIG. 19,

(33) FIG. 20b illustrates the magnitude in the frequency domain of the measured flow meter response shown in FIG. 19,

(34) FIG. 21a illustrates the actual phase angles between the flow meter responses shown in FIG. 19,

(35) FIG. 21b illustrates a segment of the graph shown in FIG. 21a,

(36) FIG. 22 illustrates the slopes of the segment shown in FIG. 21b,

(37) FIG. 23a illustrates an example of the frequency spectrum of a continuous signal,

(38) FIG. 23b illustrates schematically the spectral consequences of undersampling the continuous signal, whose frequency spectrum is illustrated in FIG. 23a,

(39) FIG. 23c illustrates schematically how the undersampled signal can be reconstructed by changing the sampling frequency and filtering the signal,

(40) FIG. 24a illustrates an example of a continuous signal,

(41) FIG. 24b illustrates the digital samples obtained by sampling the signal of FIG. 24a at a sampling frequency of ⅚ of the signal frequency,

(42) FIG. 25a illustrates the reconstruction of the signal of FIG. 24a using a wide band FIR reconstruction filter,

(43) FIG. 25b illustrates the reconstruction of the same signal using a narrow band FIR reconstruction filter,

(44) FIG. 26 illustrates schematically a method for finding the amplitude and phase of an undersampled continuous signal,

(45) FIG. 27 illustrates schematically a method for reconstructing an undersampled continuous signal without distortion, and

(46) FIG. 28 illustrates schematically an extended method according to the invention for determining very precisely the time delay of the ultrasonic signal in the flow path.

DETAILED DESCRIPTION OF THE INVENTION

(47) FIG. 1 shows the overall structure of an ultrasonic flow meter for transit time flow metering as known in the art. A controller unit CU controls the operation of a signal generator SG, a switching unit SU and a receiver circuit RC, where the switching unit SU sets up different electrical connections between the signal generator SG and the receiver circuit RC on one side and two ultrasonic transducers TR1, TR2 on the other side. The two transducers TR1, TR2 are arranged in a flow path FP, in which a fluid flow is to be metered, one transducer TR1 upstream of the other transducer TR2 along the flow path FP.

(48) In principle, the flow metering is performed in three steps: 1. The switching unit SU is set up to connect the signal generator SG to the first transducer TR1 and to connect the second transducer TR2 to the receiver circuit RC. An electrical transmission signal, typically a pulsating signal of a frequency of a few megahertz and duration of a few microseconds, is sent from the signal generator SG through the switching unit SU to the first transducer TR1, from which the signal is transmitted as an ultrasonic signal through the fluid to the second transducer TR2. From TR2, the signal continues as an electrical current reception signal through the switching unit SU to the receiver circuit RC, in which the reception signal is converted to a voltage signal A signal processing unit (pad of the controller unit CU in the configuration shown in FIG. 1), analyses the voltage signal, calculates the transit time of the ultrasound signal through the fluid from transducer TR1 to transducer TR2 from the delay of the electrical reception signal as compared to the electrical transmission signal, and records this transit time (t.sub.1). 2. The configuration of the switching unit SU is changed to connect the signal generator SG to the second transducer TR2 and to connect the first transducer TR1 to the receiver circuit RC. An electrical transmission signal is sent from the signal generator SG and an electrical reception signal is received by the receiver circuit RC as in step 1, only this time the ultrasonic signal is transmitted through the fluid in the opposite direction, i.e. from the second transducer TR2 to the first transducer TR1. Again, the signal processing unit calculates and records the transit time (t.sub.2) 3. The signal processing unit calculates an indication of the flow in the flow path FP from a formula of the form:

(49) $\begin{array}{cc}\mathrm{\Phi \infty K}\left(t_1-t_2,t_1-t_2\right).Math.\frac{t_1-t_2}{{\left(t_1+t_2\right)}^2}& \left(\mathrm{Equation}1\right)\end{array}$  where Φ is the flow indication, which is proportional to the fraction shown in Equation 1 multiplied by a correction factor K found in a table of correction factors, which is determined once and for all for a given type of flow meter for a given fluid. This table of correction factors takes into account a number of physical quantities, such as, for instance, the dimensions and physical configuration of the flow path FP in the flow meter and the viscosity of the fluid.

(50) As can be seen from Equation 1, once the table of correction factors has been established, the flow indication can be calculated from the two quantities (t.sub.1−t.sub.2) and (t.sub.1+t.sub.2).

(51) The first of these quantities, (t.sub.1−t.sub.2), which is the difference between the two transit times, is typically in the order of a few nanoseconds, but can easily be determined by finding the phase difference between the two reception signals. This can be done very precisely (with an accuracy of down to between 10 and 100 picoseconds) by several analogue and digital methods well-known through many years, due to the fact that the two reception signals are identical except for a phase difference due to the different transit times (t.sub.1 and t.sub.2), given that the reciprocity theorem for linear passive circuits applies. Generally, this is the case if it is assured that the impedance, as seen from the transducers TR1, TR2 is the same, regardless of whether the transducers TR1, TR2 are acting as transmitters or receivers of ultrasound.

(52) On the other hand, it is very difficult to calculate accurately the other quantity, (t.sub.1+t.sub.2), which is the sum of the two transit times, typically in the order of a few microseconds, because it involves a calculation of the exact transit times (t.sub.1 and t.sub.2), which again requires a very precise determination of the front edge of each of the reception signals, which is by no means a simple task due to the shape of the reception signals.

(53) Therefore, in many known flow meters, this quantity is, in fact, not calculated. Instead, it is estimated using the following equation:

(54) $\begin{array}{cc}\frac{d}{c}-t\approx t_1\approx t_2& \left(\mathrm{Equation}2\right)\end{array}$

(55) In this equation, d is the distance between the two transducers TR1, TR2 and c is the velocity of ultrasound in the actual fluid, the flow of which is being metered. For a given flow meter, d is known from the physical positions of the transducers TR1, TR2 in the flow path FP, and, for a given temperature, the velocity of ultrasound in a given fluid can be found in a table. Thus, by measuring the temperature of the fluid, an estimate of t.sub.1 and t.sub.2 can be found, which can then be used for estimating the quantity (t.sub.1+t.sub.2) to be used in Equation 1.

(56) FIGS. 2a and 2b illustrate schematically examples of couplings of ultrasonic transducers in ultrasonic flow meters according to the inventions of Tonnes (EP 0 846 936) and Jespersen (EP 1 438 551), respectively.

(57) Implemented correctly, both couplings assure that the reciprocity theorem for linear passive circuits applies.

(58) In the coupling shown in FIG. 2a, the electrical transmission signal is transmitted from the signal generator SG to transducer TR1 through the signal impedance Zsig. In the coupling shown in FIG. 2b, on the other hand, the signal generator SG comprises a negative feedback coupled amplifier circuit, wherein a digital pulsating signal is connected to the non-inverting input terminal of an operational amplifier OPsg and the signal impedance Zsig forms a feedback between the output terminal and the inverting input of the operational amplifier OPsg. Transducer TR1 is connected to the inverting input terminal of the operational amplifier OPsg through an adaptation impedance Zad, which is much smaller than the signal impedance Zsig and therefore, in practice, negligible.

(59) In both of the shown couplings, the switching unit SU comprises two switches SW1, SW2 arranged to be able to connect the two transducers TR1, TR2, respectively to a common conductor CC, which connects the signal generator SG to the receiver circuit. RC. In both cases, the position of each of the switches SW1, SW2 has to be changed during the flow metering in order to assure that, at the time of transmission of the electrical transmission signal from the signal generator SG, one of the transducers TR1, TR2 is connected to the common conductor CC, whereas, at the time of reception of the electrical reception signal by the receiver circuit RC, the other transducer TR2, TR1 is connected to the common conductor CC. This change of switch positions must take place after the ultrasonic signal has left the transmitting transducer TR1, TR2, but before it reaches the receiving transducer TR2, TR1. Thus, the timing is very crucial.

(60) The signal impedance Zsig through which the signal current will run in both of the couplings shown in FIGS. 2a and 2b has the function of converting the current signals received from the transducers TR2, TR1 to measurable voltage signals.

(61) The size of the voltage signals is found by multiplying the received currents by the signal impedance Zsig, a large signal impedance Zsig resulting in a large received voltage signal.

(62) Unfortunately, due to practical limitations on the supply voltage to the signal generator SG, the signal impedance Zsig also limits the electrical signal that can be supplied to the transducers TR1, TR2, because the signal impedance Zsig is also present during the transmission of a signal to the transducers TR1, TR2. Thus, the output voltage from the signal generator SG has to be larger than the signal requested on the transducers TR1, TR2. The compromise resulting in the largest received voltage signal is a value of the signal impedance Zsig in the range between 0.5 and 2 times the impedance of the ultrasonic transducers TR1, TR2 at the frequency of interest.

(63) The present invention, on the other hand, provides a stable, producible flow meter, which is capable of transmitting a high acoustical signal, at the same time amplifying the received current signal by a high signal impedance and having a low impedance at sensitive nodes in the circuitry.

(64) The basic idea in the present invention is to connect the transducers TR1, TR2 to different nodes in the transmit and receive situation making sure that the reciprocity theorem for linear passive circuits still applies, i.e. without sacrificing the characteristic that the impedance as seen from the transducer TR1, TR2 is the same regardless of whether the transducer TR1, TR2 is operated as a transmitter or as a receiver.

(65) This is achieved by coupling the switches SW1, SW2 of the switching unit SU to the output terminal of an operational amplifier OPsg of the signal generator SG and to the inverting input terminal of the operational amplifier OPrc of the receiver circuit RC as illustrated schematically in FIG. 3, which shows an embodiment of the present invention.

(66) By using an operational amplifier OPsg with a very low output impedance in the signal generator SG and by choosing feedback components resulting in appropriate feedback impedances Zfb,sg, Zfb,rc for constructing negative feedback circuits for the two operational amplifiers OPsg, OPrc, respectively, it is possible to obtain a signal generator SG with a very low output impedance and a receiver circuit RC with a very low input impedance, at the same time accounting for the parasitic components of the operational amplifiers OPsg. OPrc. The very low impedances are obtained by coupling operational amplifiers with a very high gain at the frequency of interest with a negative feedback

(67) Choosing a very low output impedance of the signal generator SG and a very low input resistance of the receiver circuit RC is advantageous for at least four reasons:

(68) First of all, if these impedances are both sufficiently low as compared to the impedances of the transducers TR1. TR2, and the parasitic components are accounted for, then, even though there may actually be a minimal difference between the output impedance of the signal generator SG and the input impedance of the receiver circuit RC, the transducers TR1, TR2 will, experience the two impedances as being sufficiently close to each other. This means that, substantially, the reciprocity theorem for linear passive circuits applies, and the flow meter is stable and producible.

(69) For a proper implementation, the output impedance of the signal generator SG and the input impedance of the receiver circuit RC should both be negligible compared to these transducer impedances, i.e. less than 1%, preferably less than 0.1%, of the transducer impedances. Depending on the transducer size and material and on the frequency of the transmitted signal, the transducer impedances at the frequencies of interest normally fall within the range from 100 Ohms to 1000 Ohms.

(70) Secondly, the choice of small output and input impedances assures that the attenuation of the electrical transmission and reception signals is minimized, maximizing the output signal received by the receiver circuit RC.

(71) Thirdly, very low impedances are chosen because mid-range values can be hard to match within negligible tolerances in different parts of the circuits, especially as it is the complex impedance and not just the absolute resistance value that has to be taken into account.

(72) Fourthly, a low circuit impedance is less susceptible to interference from external noise sources.

(73) An obvious advantage of the coupling shown in FIG. 3 is that by using two different operational amplifiers OPsg, OPrc in the signal generator SG and in the receiver circuit RC, respectively, no switching is necessary between the transmission and the reception of the ultrasonic signal between the two transducers TR1, TR2. When the switches SW1, SW2 are in the positions as shown in FIG. 3, the electrical transmission signal will pass from the signal generator SG through the second switch SW2 to the second transducer TR2, from which the ultrasonic signal will be transmitted to the first transducer TR1 through the flow path (FP), whereupon the electrical reception signal will reach the receiver circuit RC from the first transducer TR1 through the first switch SW1. In order to transmit the ultrasonic signal in the opposite direction, the positions of both switches SW1, SW2 must be inverted, and again the signal can be transmitted all the way from the signal generator SG to the receiver circuit RC without any switching taking place during the transmission. In this way, switching noise is avoided and a more accurate metering may be performed.

(74) It is known from the art that separate circuits have been used for constructing the signal generator and the receiver circuit. In these cases, however, either the transducers experience different impedances in transmit and receive situations, the amplification factors are different for the two transducers, the invention is not sufficiently disclosed to be more than theoretical, or a high impedance has been chosen.

(75) The latter has the disadvantage that designing a signal generator having an output impedance very much (100 to 1000 times) larger than the transducer impedances at the frequencies of interest (100 kHz to 10 MHz) is very challenging. It also has the disadvantage that the optimization of the output signal amplitude has to take into account the transducer impedances for obtaining optimal signal levels. This is not trivial as the impedances of ultrasonic transducers most often dependent on the temperature and differ among samples. Last but not least, such an approach is more sensitive to electrical noise.

(76) In recent years, new types of operational amplifiers have been designed that make the very low impedances feasible, even in battery operated flow meters. Especially, the so-called current feedback operational amplifiers, which have a lower input impedance on the inverting input terminal but also have a higher bandwidth and a lower power consumption and a higher gain at high frequencies than other types of operational amplifiers, are beneficial for use in the present invention.

(77) FIG. 4 illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter according to another embodiment of the invention, in which the same circuit is used as signal generator SG and as receiver circuit RC. The obvious advantage of this embodiment is that only one common operational amplifier OP and, consequently, also only one set of feedback components for providing the desired resulting feedback impedance Zfb are needed.

(78) The price to be paid for this cost saving is that a switching of the signal way is needed during the transmission of the signal. As can be seen from FIG. 4, the two switches SW1, SW2, which connect the two transducers TR1, TR2, respectively, to the combined signal generator and receiver circuit SG/RC, each have three possible positions.

(79) This means that each of the two transducers TR1, TR2 can be: 1. set up to be the transducer to transmit the ultrasonic signal by being coupled to the output terminal of the operational amplifier OP, from which it is to receive the electrical transmission signal, the common circuit SG/RC being operated as a signal generator, 2. set up to be the transducer to receive the ultrasonic signal by being coupled to the inverting input terminal of the operational amplifier OP, to which it is to transmit the electrical reception signal, the common circuit SG/RC being operated as a receiver circuit, or 3. disconnected from the common circuit SG/RC whenever the other transducer is connected to the common circuit.

(80) Thus, by setting and changing the positions of the switches SW1, SW2 appropriately at the right times, the desired signal paths of the electrical transmission signal, the ultrasonic signal and the electrical reception signal can be obtained. For transmitting an ultrasonic signal from the first transducer TR1 to the second transducer TR2, the first transducer TR1 is first set up to transmit the ultrasonic signal by connecting it to the common circuit SG/RC being operated as a signal generator while the second transducer TR2 is disconnected from the common circuit SG/RC. Subsequently, when the ultrasonic signal has been transmitted by the first transducer TR1 but before it reaches the second transducer TR2, the first transducer TR1 is disconnected from the common circuit SG/RC and the second transducer TR2 is set up to receive the ultrasonic signal by connecting it to the common circuit SG/RC being operated as a receiver circuit. For transmitting the ultrasonic signal in the opposite direction, the connections of the two transducers TR1, TR2 is simply swapped as compared to the above description.

(81) FIG. 5 illustrates schematically a coupling of ultrasonic transducers in an ultrasonic flow meter according to yet another embodiment of the invention. In this case, there are two receiver circuits RC1, RC2, each comprising an operational amplifier OPrc1, OPrc2 and a negative feedback circuit with impedances Zfb,rc1 and Ffb,rc2, respectively. This allows the two transducers TR1, TR2 to transmit an ultrasound signal simultaneously.

(82) In order to do this, both of the transducers TR1, TR2 are first connected to the signal generator SG by setting the switches SW1, SW2 in the appropriate positions. An electrical transmission signal is transmitted simultaneously to the two transducers TR1, TR2, from which it is transmitted into the flow path (FP) as an ultrasonic signal from each of the transducers TR1, TR2. Before the ultrasonic signal from the first transducer TR1 reaches the second transducer TR2 and vice versa, the positions of the switches SW1, SW2 are changed so that each of the transducers TR1, TR2 is connected to one of the receiver circuits RC1, RC2.

(83) In this way, the ultrasonic signal can be sent both upstream and downstream along the flow path FP in a single operation. However, in order to level out any possible minor metering errors due to the fact that the two receiver circuits RC1, RC2 cannot be constructed to be completely identical, it should be assured that for every transmission of the ultrasonic signals, the connections between the transducers TR1, TR2 and the receiver circuits RC1, RC2 are interchanged, so that a given transducer TR1, TR2 is only connected to the same receiver circuit RC1, RC2 every second time.

(84) Another difference in the coupling shown in FIG. 5 as compared to the couplings shown in the previous figures is that the digital pulsating signal is connected to the inverting input terminal of the operational amplifier OPsg of the signal generator SG through a filter impedance Zfilt, which is of influence on the amplification and the filtration of the electrical transmission signal, while the non-inverting input terminal of the operational amplifier OPsg is grounded.

(85) Compared to the configuration of the signal generators SG shown in the previous figures, in which the input common mode voltage of the operational amplifier will exhibit some variation as the digital pulsating signal varies, this configuration has the advantage that the input common mode voltage is kept at a constant DC level. This is of importance for some types of operational amplifiers, especially the fastest ones with the highest bandwidth,

(86) FIG. 6 shows a diagram of most of the essential electronic components in an ultrasonic flow meter according to an embodiment of the invention.

(87) In this diagram, the two inputs marked IN1 and IN2 indicate the input of two digital pulsating signals, the two resistors R4 and R7 are there for generating a symmetric transmission signal to the signal generator SC from the two digital signals, and the capacitor C7 forms an AC coupling between the incoming transmission signal and the signal generator SG.

(88) The two resistors R3 and R9 and the two capacitors C1 and C9 form a low-pass filter for the incoming transmission signal (corresponding to Zfilt in FIG. 5).

(89) OPsg is the operational amplifier of the signal generator SG, which not only amplifies the incoming transmission signal, but also is important for adjusting the output impedance of the signal generator SG to be very low, i.e. substantially zero.

(90) The three resistors R1, R2 and R40 and the two capacitors C29 and C30 together constitute the negative feedback impedance of the operational amplifier OPsg (corresponding to Zfb,sg in FIGS. 3 and 5).

(91) The three resistors R11, R41 and R45 together form a voltage divider defining the reference voltages on the non-inverting inputs of OPsg and OPrc. Because OPsg and OPrc are both configured as inverting amplifiers, the reference voltages are the same as the input common mode voltages on the two operational amplifiers OPsg and OPrc, respectively. The reference voltages to the two operational amplifiers OPsg and OPrc are decoupled by the two capacitors C2 and C25.

(92) V3 (corresponding to VCC in FIGS. 7a and 7b) is the positive supply voltage for the circuit. In low-power consumption flow meters, such as battery operated flow meters, V3 can advantageously be cut off with a switch (not shown) most of the time, so that the circuit is operated at a very low duty cycle.

(93) In the embodiment shown in FIG. 6, the switching unit SU comprises four switches implemented on a single CMOS die in an integrated circuit for coupling of the transducers TR1, TR2 to the signal generator SG and the receiver circuit RC. The pins IN1-IN4 of the switching unit SU each controls one of the four switches connected between the lines D1-S1, D2-S2, D3-S3 and D4-S4, respectively, by asserting a high voltage. In the diagram shown in FIG. 6, the switches are configured to transmit a signal from transducer TR1 to transducer TR2. For a signal to be transmitted from transducer TR2 to transducer TR1, opposite voltages must be applied to IN1-IN4 Preferable, IN1-IN4 are controlled by a microcontroller.

(94) The two resistors R10 and R36 are small current limiting resistors. The stability of the operational amplifiers OPsg and OPrc is increased by limiting the capacitive load on the amplifiers OPsg, OPrc.

(95) The two capacitors C8 and C15 provide an AC coupling of the signals to and from the transducers TR1, TR2. This allows the use of single supply voltage operational amplifiers OPsg, OPrc as the ones shown in FIG. 6 without any DC voltage on the transducers TR1, TR2.

(96) The two resistors R13 and R14 are bleeders for discharge of the transducers TR1, TR2 in case a charge is produced thereon due to pyroelectric effects or due to other circumstances.

(97) The two ultrasonic transducers TR1 and TR2 are preferably constituted by piezoelectric transducers.

(98) OPrc is the operational amplifier of the receiver signal RC, which produces an amplified output signal OUT from the electrical reception signal from the transducers TR1. TR2, but also is important for adjusting the input impedance of the receiver circuit RC to be very low, i.e. substantially zero.

(99) The resistor R44 and the capacitor C5 constitute a filtering of the supply voltage for the operational amplifier OPrc of the receiver circuit RC.

(100) The two resistors R5 and R6 and the capacitor C4 together constitute the negative feedback impedance of the operational amplifier OPrc (corresponding to Zfb,rc in FIG. 3).

(101) The two resistors R8 (corresponding to RCC in FIGS. 7a and 7b) and R43 are used for current sensing of the power supply currents to the operational amplifier OPsg. In some embodiments of the invention, R43 may be omitted for increased stability. If OPsg is chosen to be an operational amplifier with low supply voltage rejection ratio, switches (not shown) are needed to short-circuit R8 and R43 during transit time measurements.

(102) The two capacitors C6 and C33 have the purpose of decoupling the supply voltages to OPsg. If the values of these two capacitors are too high, the voltages across R8 and R43 do not properly reflect the power supply currents to the operational amplifier OPsg. If, on the other hand, the values of C6 and C33 are too low, the operational amplifier OPsg is potentially unstable.

(103) The two capacitors C13 and C14 and the two resistors R12 and R15 are components needed to combine the two supply current signals SCSa, SCSb into a single signal supply current signal SCS. R12 and R15 also define the DC voltage level for following circuits of the flow meter, such as an Analogue-Digital converter.

(104) V1 is a supply voltage needed to generate the DC voltage level for the combining circuitry C13, C14, R12, R15. By careful selection of components, V3 may be reused in place of the separate supply voltage V1.

(105) FIGS. 7a and 7b illustrate schematically the set-up for performing a first and a second step, respectively, in obtaining supply current signal SCS−, SCS+ of an active component driving an ultrasonic transducer.

(106) In the first step, which is illustrated in FIG. 7a, a first, short digital pulsating input signal DPSa is used as an input for a signal generator SG driving an ultrasonic transducer TR1, TR2 to which it may be connected through a switching unit SU. The signal generator SG may comprise a negative feedback coupled operational amplifier (OP; OPsg), as shown in the previous figure, or it may comprise another active component, which is able to amplify the input signal DPSa and provide an output impedance of the signal generator SG, which is very low, i.e. substantially zero. This active component might, for instance, be constituted by a digital circuit driving the transducer.

(107) A current sensing resistor RCC (corresponding to R8 in FIG. 6) is arranged in series between the active component of the signal generator SG and the positive voltage supply VCC (corresponding to V3 in FIG. 6) for this active component. Now, by monitoring the voltage across this current sensing resistor RCC, a first supply current signal SCSa representative of the current supplied to the active component from the positive voltage supply can be obtained as illustrated on the right side of FIG. 7a.

(108) It should be noted that when the input signal DPSa stops oscillating, the transducer will continue to be oscillating for some time, still dragging some current from the positive voltage supply through the active component. This is reflected in the first supply current signal SCSa, which comprises a higher number of oscillations than the first input signal DPSa, as is indicated in FIG. 7a, the latest part of the signal DPSa showing that the self-oscillating transducer TR1, TR2 performs a dampened oscillation.

(109) As can also be seen from the first supply current signal SCSa illustrated in FIG. 7a, this signal is truncated in the sense that only one half part of each oscillation is comprised in the signal, the signal value being zero in the other half part of each oscillation. This is due to the fact that, if the active component of the signal generator is coupled to be a non-inverting amplifier, the positive voltage supply VCC only delivers the current to the active component when the voltage of the input signal DPSa is higher than the input common mode voltage of the active component, and if the active component is coupled to be an inverting amplifier, the positive voltage supply VCC only delivers the current to the active component when the voltage of the input signal DPSa is lower than the input common mode voltage of the active component.

(110) Therefore, in order to obtain a second supply current signal SCSb comprising the other half part of each oscillation, the measurement is repeated with another digital pulsating input signal DPSb, which is identical to the first input signal DPSa with the one exception that the polarity of the signal has been inversed.

(111) It should be noted that the two supply current signals SCSa, SCSb can be obtained simultaneously from the positive and the negative voltage supplies of the active component of the signal generator SG, respectively, if a similar current sensing resistor (not shown in FIGS. 7a and 7b but corresponding to R43 in FIG. 6) is arranged in series between the active component and the negative voltage supply (not shown) for the active component.

(112) FIG. 7c illustrates an advantageous way of connecting a signal generator SG and a receiver circuit RC for obtaining such supply current signals SCSa, SCSb.

(113) In this case, the active component OPrc of the receiver circuit RC is used for amplifying the supply current signals SCSa, SCSb. The connection between the signal generator SG and the receiver circuit RC consists of a switch SWconn in series with at high pass filter consisting of a capacitor Cconn and a resistor Rconn.

(114) As the connection SWconn, Cconn, Rconn is attached to a summation point at the inverse input terminal of the active component OPrc of the receiver circuit RC, the supply current signals SCSa, SCSb do not affect the function of the ultrasonic transducers TR1, TR2 in any way.

(115) Furthermore, due to the transit time of the ultrasonic signal between the two transducers TR1, TR2 in the flow path FP, the supply current signals SCSa, SCSb and the signal transmitted between the transducers TR1, TR2 will reach the receiver circuit RC at different times.

(116) At high frequencies, non-idealities of the components potentially influence the signals, and the supply current signals SCSa, SCSb may influence the signal received through the flow path FP and vice versa. A remedy for minimizing this effect is to measure the supply current signals SCSa, SCSb and the ultrasonic signal at different times and disconnect unused circuit parts from the input terminal of the active component OPrc of the receiving circuit RC by switches SW2, SWconn.

(117) If the signal generator SG is configured as a Class A amplifier, the current drawn into the positive voltage supply pin is substantially constant, and a current sensing resistor (R43) has to be arranged in series with the negative voltage supply for a useful signal to be obtained.

(118) By subtracting the two supply current signals SCSa, SCSb from each other as illustrated in FIG. 8a, a subtraction supply current signal SCS− is obtained, from which the oscillation period Tscs of the dampened oscillation of the transducer TR1, TR2 can easily be determined by measuring the time difference between two appropriately chosen zero crossings of the signal SCS− as is also indicated in FIG. 8a.

(119) The relation between the oscillation period Tscs and the frequency f.sub.D and the angular frequency ω.sub.D of the dampened transducer oscillation is well-known:

(120) $\begin{array}{cc}\mathrm{Tscs}=\frac{1}{f_D}-\frac{1}{2\pi {\omega }_D}& \left(\mathrm{Equation}3\right)\end{array}$

(121) Furthermore, by adding the two supply current signals SCSa, SCSb to each other as illustrated in FIG. 8b, an addition supply current signal SCS+ is obtained, the envelope Escs of the decreasing part of which can be determined. This envelope Escs has the shape of an exponential curve with respect to the time t, the mathematical formula describing the envelope being
Escs=−ke.sup.α1  (Equation 4)
where k is a constant and α is the damping coefficient of the dampened oscillation of the transducer TR1, TR2.

(122) In principle, both ω.sub.D and α could be found from each of the measured supply current signals SCSa, SCSb alone. However, the two quantities can be determined with much higher accuracy using the subtraction supply current signal SCS− and the addition supply current signal SCS+ as illustrated in FIGS. 8a and 8b.

(123) The two quantities ω.sub.D and α are very useful for characterizing the transducer, being indicative of the condition of the transducer, such as, for instance, whether it might be broken or whether there might be some air around a transducer, which is supposed to be surrounded by water, etc.

(124) FIG. 9 illustrates a well-known equivalence diagram of an ultrasonic transducer TR, comprising a parallel capacitor Cpar coupled in parallel with a series connection of a series inductor Lser, a series capacitor Cser and a series resistor Rser.

(125) FIG. 10 illustrates some of the steps in the derivation of a simple equivalence diagram of an ultrasound flow meter, which can be used for simulating the signal chain through a flow meter according to the invention.

(126) The equivalence diagram in the first part of FIG. 10 illustrates how the flow meter can be equated by a system comprising two ultrasonic transducers TR1, TR2, wherein the first transducer TR1, upon which a transmission signal in the form of a voltage signal Vtr1 is impressed, transmits an ultrasound signal to the second transducer TR2, which in turn produces a reception signal in the form of a current signal Itr2.

(127) For a given input signal to the signal generator of the flow meter, the voltage signal Vtr1 impressed on the first transducer TR1 can be taken to be the same for each transit time measurement due to the fact that all components of the signal generator are the same for each measurement. This also means that the impressed signal Vtr1 can be calculated from the input signal using a filter model of the signal generator, once the filter model has been determined once and for all, or it can be recorded by an analogue-digital converter before the simulation procedure, which is described below.

(128) Introducing the equivalence diagram from FIG. 9 for each of the two transducers TR1, TR2 in the equivalence diagram of the flow meter shown in the first part of FIG. 10 results in the diagram shown in the second part of FIG. 10. Here, it is noted that, due to the fact the ultrasound signal transmitted by the first transducer TR1 is proportional to the current signal Itr1 passing through the transducer TR1, the ultrasound signal reaching the second transducer TR2 can be equated by a voltage signal Vtr2 being impressed on the transducer TR2, said voltage signal Vtr2 being proportional to the current signal Itr1 as indicated in FIG. 10 by the proportionality factor K1.

(129) The parallel capacitors Cpar1, Cpar2 have no influence on the impressed voltages Vtr1, Vtr2 across the series connections Lser1, Cser1, Rser1 and Lser2, Cser2, Rser2, respectively, in the equivalence diagram in the second part of FIG. 10 and can, thus, be ignored. Therefore, the resulting equivalence diagram of the flow meter to be used for simulating the signal chain through the flow meter is the one shown in the third and final part of FIG. 10.

(130) The relations between the impressed voltage signals Vtr1, Vtr2 and the resulting current signals Itr1, Itr2 can be found by well-known differential equations:

(131) $\begin{array}{cc}\begin{array}{c}\mathrm{ltr}1=\frac{\mathrm{Vtr}1}{s\mathrm{Lser}1+\frac{1}{\mathrm{sCser}1}+\mathrm{Rser}1}\\ =\frac{1}{\mathrm{Lser}1}\frac{s}{s^2+s\frac{\mathrm{Rser}1}{\mathrm{Lser}1}+\frac{1}{\mathrm{Lser}1\mathrm{Cser}1}}\mathrm{Vtr}1\end{array}\begin{array}{c}\mathrm{ltr}2=\frac{\mathrm{Vtr}2}{s\mathrm{Lser}2+\frac{1}{\mathrm{sCser}2}+\mathrm{Rser}2}\\ =\frac{K1\mathrm{ltr}1}{s\mathrm{Lser}2+\frac{1}{\mathrm{sCser}2}+\mathrm{Rser}2}\\ =\frac{K1}{\mathrm{Lser}1\mathrm{Lser}2}\frac{s}{s^2+s\frac{\mathrm{Rser}1}{\mathrm{Lser}1}+\frac{1}{\mathrm{Lser}1\mathrm{Cser}1}}\\ \frac{s}{s^2+s\frac{\mathrm{Rser}2}{\mathrm{Lser}2}+\frac{1}{\mathrm{Lser}2\mathrm{Cser}2}}\mathrm{Vtr}1\end{array}& \left(\mathrm{Equation}5\right)\\ =K2\frac{s}{s^2+2{\alpha }_{1}s+{\omega }_1^2}\frac{s}{s^2+2{\alpha }_{2}s+{\omega }_2^2}\mathrm{Vtr}1& \left(\mathrm{Equation}6\right)\end{array}$
α.sub.1 and α.sub.2 are the damping coefficients relating to the first ultrasonic transducer TR1 and the second ultrasonic transducer TR2, respectively, corresponding to the damping coefficients that can be found from the envelope of the addition supply current signals SCS+, as described above.

(132) ω.sub.1 and ω.sub.2 are the undampened angular oscillation frequencies of the first ultrasonic transducer TR1 and the second TR2 ultrasonic transducer, respectively. The relation between these undampened angular oscillation frequencies ω.sub.1, ω.sub.2 used in the simulation equations and the corresponding dampened angular oscillation frequencies ω.sub.D1 and ω.sub.D2 found by measuring the time difference between two appropriately chosen zero crossings of the dampened oscillation in the subtraction supply current signals SCS−, as described above, is as follows:
ω.sub.1−√{square root over (ω.sub.D1.sup.2+α.sub.1.sup.2)}∧ω2−√{square root over (ω.sub.D2.sup.2+α.sub.2.sup.2)}  (Equation 7)

(133) K2 is a proportionality factor, which can be calculated However, like the specific component values of Cser1, Lser1, Rser1, Cser2, Lser2, Rser2 of the equivalence diagram in the last part of FIG. 10, the value of K2 is not needed for using Equation 6 for simulating the signal chain through the flow meter.

(134) The last expression of Equation 6, which is a differential equation for a circuit comprising two second order oscillating circuits, can be simulated by means of well-known mathematical tools, such as for instance the Runge-Kutta method.

(135) FIG. 11 illustrates some of the differences and similarities between a physical and a simulated signal chain through a flow meter according to the invention.

(136) In the simulated signal chain, the physical transducers TR1, TR2 and the loads related to them are modelled, for instance as already described above.

(137) In the fully simulated signal chain in FIG. 11, the output from the physical signal generator, which filters a digital input signal from a signal controller and works as a driver for the first transducer TR1 by amplifying the filtered input signal, is simulated by a signal function being filtered using a filter model of the signal generator before being used as input function for the simulated transducer model. In another embodiment of the simulated signal chain, the input function for the simulated transducer model may be produced by recording the actual output from the a physical signal generator by an analogue-digital converter, thus obtaining a signal chain that is partly physical, partly a simulated model.

(138) The reception of the electrical reception signal by the receiver circuit and the subsequent signal processing in the physical signal chain is replaced by signal processing alone in the simulated signal chain, this signal processing optionally including a model (not shown) of the receiver circuit.

(139) Thus, if the signal function in the simulated signal chain does, in fact, correspond to the input signal from the signal controller in the physical signal chain, and if the filter models of the signal generator and (optionally) the receiver circuit and the transducer models are adequate, the only difference between the output of the final signal processing of the simulated signal chain and the output of the final signal processing of the physical signal chain will be the time delay t.sub.d of the ultrasonic signal in the flow path FP, which is not a part of the simulated signal chain.

(140) The simulated model response being substantially identical to the physical flow meter response except for the time delay t.sub.d of the ultrasonic signal in the flow path FP and a possible amplification factor makes it possible to determine this time delay t.sub.d very precisely by following a method like the one illustrated schematically in FIG. 12.

(141) The first step in this method is to characterize the two transducers TR1, TR2 by determining characteristic quantities, such as the angular frequency ω.sub.D and the damping coefficient α of dampened oscillations of the transducers TR1, TR2 as described above.

(142) Secondly, by using the known angular oscillation frequency of the transmission signal used in the flow meter, an equivalence model of the transducers TR1, TR2 can be found using Equations 5-7, and a numerical simulation model of the transducers TR1, TR2 and the electronic circuits of the signal generator SG and the receiver circuit RC can be established.

(143) Thirdly, the system can be simulated by entering the input signal function (or alternatively a sampled version of the physical transmission signal reaching the first transducer) into the numerical simulation model, whereby the simulation model response, i.e. the output signal from the receiver circuit RC as it would be according to the model, if there was no time delay in the transmission of the ultrasonic signal between the two transducers TR1, TR2, can be found.

(144) In the fourth step of the method, the physical flow meter response, i.e. the physical reception signal actually received by the receiver circuit RC, is recorded.

(145) Finally, the absolute transit time can be calculated by determining the time delay of the physical flow meter response as compared to the simulation model response.

(146) FIG. 13 illustrates one example of how such a calculation of the absolute transit time may be performed according to the invention.

(147) Following the above-described method, an input signal entered to the system results in a measured physical flow meter response with a certain delay and in a simulation model response with substantially no delay. As mentioned above, if the equivalence model of the transducers TR1, TR2 is adequate, the two response signals will be substantially identical except for the time delay, which is illustrated in FIG. 13.

(148) Now, the absolute transit time, i.e. the time delay between the two signals, can be determined very precisely, for instance by finding a filtered envelope of each of the two signals and determining the time difference between the two points, in which the filtered envelopes have reached 50% of their maximum value, respectively. This approach for finding the absolute transit time is illustrated schematically in FIG. 13

(149) FIG. 14 illustrates an equivalence diagram of a signal generator SG and an ultrasonic transducer TR connected thereto. Basically, the signal generator SG in FIG. 14 is of the type shown in FIG. 5 with a feedback resistance Rfb,sg and a filter resistance Rfilt, and the ultrasonic transducer TR is represented by the equivalence diagram illustrated in FIG. 9.

(150) The active component OPsg of the signal generator SG is equipped with a current sensing resistor RCC arranged in series with the positive voltage supply VCC as described above. The ultrasound transducer TR is connected to the signal generator SG through a switch SW and bypassed by a bleeder resistor Rbleed corresponding to R13 and R14 in FIG. 6.

(151) With the diagram in FIG. 14 as the point of departure, another method for determining the absolute transit time can be described, which is as precise as the method described above but even more efficient in the terms of calculations needed, and which characterizes the impulse response of the transducer system rather than characterizing the transducers TR1, TR2 themselves as described above.

(152) In this alternative method, a single pulse supply current signal SPSCS1, SPSCS2 is recorded for each of the ultrasonic transducers TR1. TR2 by connecting the respective transducer TR1, TR2 to the output of the signal generator SG and obtaining a signal corresponding to the subtraction supply current signal SCS− as described above for the other method.

(153) The difference from the previous method is that in this case, the digital pulsating input signals DPSa, DPSb have been replaced by a single pulse like the one illustrated in FIG. 15a, which result in single pulse supply current signals SPSCS1, SPSCS2 for the two transducers TR1, TR2, respectively, like illustrated in FIGS. 15b and 15c.

(154) It is obvious that the first oscillation of each of the two single pulse supply current signals SPSCS1, SPSCS2 are somewhat distorted. This is due to the fact that not all of the current supplied by the active component OPsg of the signal generator SG passes through the oscillation circuits Lser, Cser, Rser of the equivalent of the ultrasonic transducers TR1, TR2, respectively. In order to find the single pulse responses SPRTR1, SPRTR2 of these oscillating circuits, the currents through the two resistances Rfb,sg and Rfilt and the capacitance Cpar must be removed from the single pulse supply current signals SPSCS1, SPSCS2.

(155) The current through Rfb,sg, which is connected to virtual ground, can easily be found by opening the switch SW shown in FIG. 14 and repeating the measurements without any ultrasound transducers TR1, TR2 connected to the signal generator. This results in a single pulse supply current signal SPSCS0 as the one illustrated in FIG. 15d, which is proportional to the single pulse SP in FIG. 15a due to the fact that Rfb,sg is an ohmic resistance.

(156) The current through Rfilt cannot be measured as easy as the current through Rfb,sg. However, since Rfilt is an ohmic resistance connected to ground in parallel to Rfb,sg, the current through Rfilt can easily be calculated from SPSCS0, when the ratio between Rfb,sg and Rfilt is known, and the two current signals can be subtracted from each of the two single pulse supply current signals SPSCS1, SPSCS2 for the two ultrasonic transducers TR1, TR2.

(157) As for the current through Cpar, it consists of a transient spike coinciding with the leading edge of the single pulse SP and another transient spike of opposite polarity coinciding with the trailing edge of the single pulse SR. These spikes are of so short duration compared to the oscillation periods of the single pulse supply current signals SPSCS1, SPSCS2 for the two ultrasound transducers TR1, TR2, that they can easily be subtracted from each of the single pulse supply current signals SPSCS1, SPSCS2 by simple interpolation.

(158) After subtracting the currents through Rfb,sg, Rfilt and Cpar from each of the two single pulse supply currents signals SPSCS1, SPSCS2 for the two ultrasound transducers TR1, TR2 as described above, the calculated single pulse responses SPRTR1, SPRTR2 of the two ultrasound transducers TR1, TR2, respectively, which may look like illustrated in FIGS. 16a and 16b, respectively, have been obtained.

(159) The calculated single pulse response SPRSYS for the complete ultrasound transducer system, which is illustrated in FIG. 16c, is found as a convolution of the single pulse responses SPRTR1, SPRTR2 of the two ultrasound transducers TR1, TR2 and may look like illustrated in FIG. 16c.

(160) By repeating the calculated single pulse response SPRSYS a number of times with a suitable delay, an emulated flow meter response corresponding to an input signal comprising a number of pulses can be calculated, which is very similar to the actually measured flow meter response except for the time delay of the latter due to the transit time between the two ultrasound transducers TR1, TR2, FIGS. 172 and 17b illustrate an emulated flow meter response RESPem and a corresponding measured flow meter response RESPms, respectively.

(161) The absolute transit times may be determined by comparing filtered envelopes of the emulated flow meter response and the measures flow meter response, respectively, as illustrated schematically in FIG. 13 and described above, or they may be determined by using Fast Fourier Transformation (FFT) as described here below.

(162) In the time domain, the estimated flow meter response f(t) can be calculated from the equation:
z′(t)=y.sub.1(t)*y.sub.2(t)*x(t)  (Equation 8)
where y.sub.1(t) and y.sub.2(t) are the calculated single pulse responses of the two ultrasonic transducers TR1, TR2, respectively, represented by the two signals SPSCS1 and SPSCS2 in FIGS. 16a and 16b, respectively, and x(t) is the input signal on the input terminal of the active component OPsg of the signal generator SG.

(163) It should be noted that in Equation 8 above, the symbol ‘*’ is used as an operator indicating a convolution of the signals surrounding it, which is not to be confused with the multiplication operation often indicated by the same symbol.

(164) In the time domain, the relation between the estimated flow meter response z′(t) and the measured flow meter response z(t) is given by
z(t)≈z′(t−t.sub.d)  (Equation 9)
where t.sub.d is the time delay of the ultrasonic signal in the flow path FP.

(165) This reflects that the measured flow meter response and the estimated flow meter response are close to being identical with exception of the time delay t.sub.d of the former.

(166) If the estimated response had been perfect this would mean that, in the frequency domain, the magnitudes of the measured flow meter response Z(s) and of the estimated flow meter response Z′(s) would be the same for all frequencies as shown in FIG. 18a.

(167) Furthermore, the phase angle between Z(s) and Z′(s) would change linearly with the frequency as indicated in FIG. 18b, the slope of the line in FIG. 18b being the group time delay, corresponding to the time delay t.sub.d of the ultrasonic signal in the flow path FP.

(168) FIG. 19 shows an actual flow meter response RESPem estimated as described above and the corresponding actually measured flow meter response RESPms depicted in the same graph for displaying the similarity of the two signals and the time delay there between.

(169) The magnitudes |Z′(s)| and |Z(s)| of the two flow meter responses in the frequency domain, corresponding to RESPem and RESPms, respectively, are shown in FIGS. 20a and 20b, respectively. Although similar, it is clear that the two graphs are not completely identical, indicating that the estimated flow meter response RESPem deviates slightly from the measured flow meter response RESPms even if the time delay is ignored.

(170) The phase angles between Z(s) and Z′(s) for different frequencies are shown in the graph in FIG. 21a. In theory, this graph should correspond to the one shown in FIG. 18b, but it is obvious that this is not the case.

(171) Looking closer at FIG. 21a, however, it emerges that the two graphs are not as different as it seems at the first glance. Whereas the graph in FIG. 18b is linear, the graph in FIG. 21a is characterised by a generally saw-toothed pattern due to the fact that the phase angles in this graph have been ‘wrapped’ to fall within the range from −π rad to +π rad.

(172) It is obvious that the saw-toothed pattern of the graph in FIG. 21a is overlaid by a certain amount of noise, which is mainly due to small magnitudes of Z(s) and/or Z′(s) affecting the calculations at some frequencies. However, the segment of the graph between the two dotted lines, corresponding to a frequency range with large magnitudes of Z(s) and Z′(s) as can be seen from FIGS. 20a and 20b, is very close to being linear. FIG. 21b shows an enlargement of this segment of the graph in FIG. 21a. It should be noted that the slope of the linear segment can be calculated by finding the phase angle between Z(s) and Z′(s) for only two different frequencies.

(173) The slope at different frequencies of the graph segment in FIG. 21b, corresponding to the time delay t.sub.d of the ultrasonic signal in the flow path FP as described above, are shown in FIG. 22. The time unit on the vertical axis of this graph corresponds to the oscillation period of the transmission signal RESPms. Thus, according to FIG. 22, the measured flow meter response RESPms is delayed by 2.3 oscillation periods as compared to the emulated flow meter response RESPem, which is in perfect agreement with the two signal curves shown in FIG. 19.

(174) It should be noted that the variation of the calculated time delay t.sub.d, i.e. of the slope of the graph segment in FIG. 22 is only a few percent of the oscillation period, which means that the time delay t.sub.d calculated by this method is very precise as compared to other methods known in the art.

(175) In practice, the actual flow meter response RESPms is best measured using a transmission signal comprising a number of pulses, whereas the emulated flow meter response RESPem is easiest calculated through appropriate digital filtering of the single pulse response SPRSYS calculated as described above. This has no influence on the results obtained by the method.

(176) Using methods like the ones described above, the absolute transit times, corresponding to t.sub.1 and t.sub.2 in Equation 1, can be determined independently of the transducer parameters with very high absolute accuracy (down to about 100 nanoseconds for 1 MHz transducers, which is significantly more precise than what is possible in all previously known systems).

(177) Normally, flow meters according to the invention will perform flow metering at regular time intervals, typically in the range between 0.1 second and 5 seconds. However, it should be noted that, for instance in order to extend the life time of a battery supplying the electricity for a flow meter, the characterization of the transducers or the transmitted signal and the simulation of the flow meter system do not need to be repeated for every flow metering performed by the flow meter.

(178) The transducer characteristics change slowly over time due to aging of the transducers TR1, TR2 and more spontaneously due to changes in the temperature of the fluid in the flow path FP in which they are arranged.

(179) Thus, new transducer characterizations or signal characterizations and determination of an updated simulation model of the flow meter system for use in the calculation of absolute transit times may advantageously by performed at regular predetermined time intervals and/or when a change of temperature above a certain predetermine limit is detected, the temperature change being indicated by a change in the calculated transit time due to the dependency of ultrasound speed on the temperature of the medium in which the ultrasound propagates.

(180) Due to the high costs (and the high power consumption) of very fast analogue-digital converters, slower converters may advantageously be used in flow meters according to the invention. However, as is well-known from the Nyquist theorem, if a signal is sampled at a frequency lower than twice the maximum frequency occurring in the signal, the analogue signal cannot be reconstructed without a certain distortion.

(181) Thus, if a low sampling frequency is used for recording the electrical reception signal received by the receiver circuit of a flow meter according to the invention, the physical flow meter response signal will be distorted. If, however, the simulation model response is subjected to the same undersampling, a similar distortion of this signal will take place, and the two response signals can still be compared for finding a very precise measure of the absolute transit time as described above.

(182) The well-known spectral consequences of undersampling a continuous signal are illustrated schematically in FIGS. 23a-c.

(183) FIG. 23a illustrates an example of the frequency spectrum of a continuous signal, while FIG. 23b illustrates how undersampling (in this case with a sampling frequency fs of ⅚ of the signal frequency) results in the creation of an infinite number of aliases of the original spectrum.

(184) FIG. 23c illustrates schematically how the undersampled signal can be reconstructed by changing the sampling frequency to the Nyquist sampling frequency fs.sub.2 and filtering the signal with an FIR reconstruction filter, the frequency band of which is indicated in the figure.

(185) The distortion of the reconstructions of undersampled continuous signals is illustrated schematically in FIGS. 24a-b and 25a-b.

(186) FIG. 24a illustrates an example of a continuous signal, while FIG. 24b illustrates the digital samples obtained by sampling the continuous signal of FIG. 24a at a sampling frequency of ⅚ of the signal frequency.

(187) FIG. 25a illustrates the reconstruction of the signal of FIG. 24a using a wide band FIR reconstruction filter, whereas FIG. 25b illustrates the reconstruction of the same signal using a narrow band FIR reconstruction filter.

(188) From comparing the reconstructed signals shown in FIGS. 25a and 25b to the original signal shown in FIG. 24a, it is clear that the use of a narrow band FIR reconstruction filter results in a more severe distortion of the signal than does the use of a wide band FIR reconstruction filter. The optimum band width of the FIR reconstruction fitter to be used depends partly on the width of the individual aliases in the undersampled spectrum, partly on the amount of noise in the signal.

(189) FIG. 26 illustrates schematically a method for finding the amplitude and phase of an undersampled continuous signal without using any FIR reconstruction filter.

(190) The upper half of FIG. 26 comprises two frames illustrating a continuous signal and the digital samples obtained by sampling this continuous signal at a sampling frequency of ⅚ of the signal frequency, respectively.

(191) The relation between the signal frequency and the sampling frequency means that for each sixth oscillations of the continuous signal, five samples will be collected. If the continuous signal is stationary, the five samples from a period of six oscillations will correspond exactly to the five samples from the previous six oscillations and to the five samples from the following six oscillations.

(192) It a relatively long input signal is used, the midmost part of the signal can be considered to be substantially stationary as indicated in the upper half of FIG. 26, and the samples obtained from this part of the signal can be sorted out and summed up in five groups, each containing a number of “similar” samples from different periods of six oscillations of the continuous signal as illustrated in the lower half of FIG. 26.

(193) If this sorting and summing up of samples is done in an appropriate way, these five groups of samples together form an “average sampling” of a single oscillation, which corresponds to a single oscillation of the substantially stationary part of the continuous signal and from which the amplitude and phase of the continuous signal can be determined by means of Digital Fourier Transformation DFT.

(194) As mentioned above, the difference between the transit times of two different ultrasonic signals, corresponding to the quantity (t.sub.1−t.sub.2) in Equation 1, can easily be found by comparing the phases of the corresponding two electrical reception signals received by the receiver circuit RC of the flow meter. Thus, in order to find this difference in a system using undersampling, the transmission signals should advantageously be relatively long, assuring that there is enough information in the samples from the substantially stationary part of the signal to determine the phase of the signal with a sufficient accuracy.

(195) FIG. 27 illustrates schematically a method for reconstructing an undersampled continuous signal without distortion.

(196) Again, the continuous signal, which is shown in the top of FIG. 27, is sampled with an analogue-digital converter working at a sampling frequency of ⅚ of the signal frequency. However, in this method, the signal is transmitted and sampled six times, the timing of the sampling being displaced corresponding to ⅕ of the oscillation period of the continuous signal, the resulting six sets of interleaved samples from which samplings are illustrated schematically in the central part of FIG. 27.

(197) By combining the interleaved samples appropriately, samples corresponding to a sampling frequency of 5 times the signal frequency are obtained. Only two times the signal frequency needed (according to the Nyquist theorem), this is more than sufficient to reconstruct the signal without any distortion.

(198) In order to determine precise values of the absolute transit times t.sub.1 and t.sub.2 to be added together to find the quantity (t.sub.1+t.sub.2) in Equation 1, the transmission signals should advantageously be relatively sharp, short and well-defined.

(199) Taking the above consideration into account, the digital signal processing on the physical and simulated model responses of a flow meter according to the invention in order to obtain a very precise value of the absolute transit time may be performed as illustrated schematically in FIG. 28.

(200) First, if the signal is undersampled, upsampling and anti-alias filtering is performed in order to reconstruct the signal.

(201) After that, an optional filtering including bandwidth limitation may be performed in order to improve the signal-noise ratio of the signal.

(202) The relatively sharp, short and well-defined transmission signal, which is advantageous for obtaining a very precise absolute transit time determination, cf, the above, is emulated from the actual received and filtered signal in two steps:

(203) The first emulation step consists in obtaining an emulated substantially stationary signal by adding to the received signal delayed versions of the signal itself. If, for instance, the transmitted signal contains five oscillations, versions of the received and filtered signal, which are delayed by five, ten, fifteen, etc. periods of the signal are added to the actually received and filtered signal. Due to the complete linearity of the system, the principle of superposition assures that the resulting signal is exactly similar to the filtered version of the signal that would have been received if the transmission signal had contained ten, fifteen, twenty, etc. oscillation periods.

(204) The second emulation step consists in subtracting a delayed version of the emulated substantially stationary signal from the emulated substantially stationary signal itself. If, for instance, the subtracted signal is delayed by two periods of the signal, the principle of superposition assures that the resulting signal is exactly similar to the filtered version of the signal that would have been received if the transmission signal had contained two oscillation periods. If this subtraction had been done with two versions of the original received and filtered signal corresponding to a transmission signal containing only five oscillation periods, the resulting signal would be a signal corresponding to a transmitted signal having two pulses followed by a pause of three oscillation periods and then by another two pulses opposite in phase from the first two pulses. Obviously, such an odd signal would not be very suitable for the purpose.

(205) Now, the envelope of the emulated short signal is calculated and the point of time, on which 50% of the maximum value of the envelope has been reached, is found as illustrated in FIG. 13.

(206) Finally, the absolute transit time is determined by subtracting the corresponding point of time relating to the envelope of the simulation model response signal calculated from the transducer characteristics as described above.

(207) It should be noted that the scope of the invention is in no way to be understood as being limited to the above-described embodiments of the invention, which are only to be seen as examples of a multitude of embodiments falling within the scope of the invention as defined by the below patent claims.

LIST OF REFERENCE SYMBOLS

(208) CC Common conductor for signal generator and receiver circuit Cconn Capacitor in connection between signal generator power supply and receiver circuit Cpar. Parallel capacitor in equivalence diagram for ultrasonic transducer Cpar1 Parallel capacitor in equivalence diagram for first ultrasonic transducer Cpar2 Parallel capacitor in equivalence diagram for second ultrasonic transducer Cser. Series capacitor in equivalence diagram for ultrasonic transducer Cser1.Series capacitor in equivalence diagram for first ultrasonic transducer Cser2.Series capacitor in equivalence diagram for second ultrasonic transducer DFT. Digital Fourier Transformation DPSa. First digital pulsating input signal DPSb. Second digital pulsating input signal Escs. Envelope of supply current signal FP. Flow path for fluid flow fs. Undersampling frequency fs.sub.2. Nyquist sampling frequency Itr1. Current through first transducer in equivalence diagram Itr2. Current through second transducer in equivalence diagram Lser. Series inductor in equivalence diagram for ultrasonic transducer Lser1. Series inductor in equivalence diagram for first ultrasonic transducer Lser2. Series inductor in equivalence diagram for second ultrasonic transducer OP Operational amplifier common for signal generator and receiver circuit OPrc. Operational amplifier in receiver circuit OPrc1. Operational amplifier in first receiver circuit OPrc2. Operational amplifier in second receiver circuit OPsg. Operational amplifier in signal generator Rbleed. Bleeder resistor for ultrasound transducer RC. Receiver circuit RCC. Current sensing resistor for power supply current Rconn. Resistor in connection between signal generator power supply and receiver circuit RESPem. Emulated flow meter response RESPms. Measured flow meter response Rfb,sg. Feedback resistance in signal generator Rfilt. Filter resistance Rser. Series resistor in equivalence diagram for ultrasonic transducer Rser1.Series resistor in equivalence diagram for first ultrasonic transducer Rser2.Series resistor in equivalence diagram for second ultrasonic transducer SCSa. First half of supply current signal SCSb. Second half of supply current signal SCS−. Subtraction supply current signal SCS+. Addition supply current signal SG. Signal generator SP. Single pulse SPRSYS. Single pulse response of the system SPRTR1. Single pulse response of first ultrasonic transducer SPRTR2. Single pulse response of second ultrasonic transducer SPSCS0. Single pulse supply current signal without any ultrasonic transducers SPSCS1. Single pulse supply current signal for first ultrasonic transducer SPSCS2. Single pulse supply current signal for second ultrasonic transducer SPU. Signal processing unit SU. Switching unit SW. Switch SW1. First switch SW2. Second switch SWconn. Switch in connection between signal generator power supply and receiver circuit t.sub.d. Time delay of ultrasonic signal in flow path Tscs. Oscillation period of supply current signal TR1. First ultrasonic transducer TR2. Second ultrasonic transducer TR. Ultrasonic transducer VCC. Positive power supply voltage Vtr1. Voltage impressed on first transducer in equivalence diagram Vtr2. Voltage impressed on second transducer in equivalence diagram Zad. Adaptation impedance Zfb. Feedback impedance in combined signal generator and receiver circuit Zfb,rc. Feedback impedance in receiver circuit Zfb,rc1 Feedback impedance in first receiver circuit Zfb,rc2. Feedback impedance in second receiver circuit Zfb,sg. Feedback impedance in signal generator Zfilt. Filter impedance Zsig. Signal impedance α.sub.1. Damping coefficient relating to first ultrasonic transducer α.sub.2. Damping coefficient relating to second ultrasonic transducer ω.sub.1. Undampened angular oscillation frequency of first ultrasonic transducer ω.sub.2. Undampened angular oscillation frequency of second ultrasonic transducer ω.sub.D1. Dampened angular oscillation frequency of first ultrasonic transducer ω.sub.D2. Dampened angular oscillation frequency of second ultrasonic transducer