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Electronic circuit design for reciprocal operation of transit-time ultrasonic flow meters
Flow Measurement and Instrumentation 32 (2013) 5–13
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Electronic circuit design for reciprocal operation of transit-time ultrasonic flow meters Yang Bo n, Cao Li Department of Automation Tsinghua University Beijing, 100084, PR China
a r t i c l e i n f o
abstract
Article history: Received 19 May 2012 Received in revised form 4 February 2013 Accepted 19 February 2013 Available online 27 February 2013
The reciprocal operation theory has been used in the circuit design of transit-time ultrasonic flow meters (USMs) to promote their zero flow performances. In this paper, the authors analyzed the transfer functions of the inter-conversion between acoustic and electric signals on each transducer, indicated that the equivalent load consistency for each transducer between the transmitting and the receiving phases would guarantee the transmitting and the receiving transfer functions equal, and thus guarantee the reciprocal operation of the USM system. In order to achieve the ‘‘load consistency’’ condition in practical systems with non-ideal parameters, a method of applying short pulse excitation and fixing the equivalent load in the ‘‘free oscillation period’’ of the transmitting transducer is proposed. Based on this method, several circuit designs are shown in the paper, the impedance preferences are also analyzed. Practical experiments done with these circuits show clear improvement in both promoting the accordance of the signals received in both directions and reducing the zero flow error in the measurement. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Ultrasonic flow metering Electroacoustic reciprocity Reciprocal operation Zero flow error
1. Introduction The basic principle of ultrasonic flow meters is to obtain the velocity of fluid through the transit-times or transit-time difference (TTD) of upstream and downstream traveling ultrasound signals. A general model of ultrasonic flow meter is shown in Fig. 1, in which the piezoelectric transducers are placed face-toface at both ends of the pipe. Assuming v is the flow velocity in the pipe, the upstream and downstream transit times of ultrasound signals tu and td would be tu ¼
l , cv
td ¼
l cþv
ð1Þ
in which l is the length of the metering section and c is the sound speed in the still fluid. Since in liquids ccv, the flow velocity v can be calculated as v
lDt 2t 20
ð2Þ
in which the TTD Dt ¼tu td, and t0 represents the mean transit time in both directions. Since t0 remains almost unchanged when v is low, v can be considered as proportional to Dt. Several algorithms can be used to detect the Dt from the signals received in both directions, of which the zero-crossing n
Corresponding author. E-mail addresses: [email protected] (Y. Bo), [email protected] (C. Li).
0955-5986/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2013.02.003
method and the correlation methods are most commonly used. However, for both methods, the accordance of received signal waveforms in both upstream and downstream directions is crucial for the TTD measurement [1]. If these signal waveforms are different, a non-zero TTD would be obtained when the fluid is still, which is called the zero error. In practice, the dry calibration method is usually used to cancel the zero error, but the calibration in one situation may fail when measurement environment, such as temperature, changes [2,3]. Since low zero error is important for achieving accurate flow metering, it is necessary to promote the accordance of the signal received in both directions, or to say, to improve the reciprocal operation of the measurement system. The ‘‘reciprocal operation’’ is quite different from the concept of ‘‘electroacoustic reciprocity’’. The well-known electroacoustic reciprocity theory states that, for most two-port passive linear electroacoustic networks, the transfer impedances from either port to another are equal. This theory can be applied on transducers and also on the USM system containing both transducers and the fluid in-between [4]. However, unless special design is made, a reciprocal USM system may not be reciprocally operated, in which the zero error may still exist. In the past decades, the theory of reciprocal operation has been addressed by many researchers. One way to achieve reciprocal operation in the metering system is to implement identical transducers. In 2002, Deventer and Delsing [5] simulated the received waveforms in both directions in an USM system by the equivalent circuit model
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introduced by Leach [6]. The researchers compared the zero errors caused by varieties of non-symmetric factors in the metering system, and indicated that the reciprocal operation holds when the transducers implemented in the USM are identical. Since manufacturing identical transducers is not practical, many researchers focused on achieving the reciprocal operation through the design of the electronic interfaces employed in the USMs. Early in 1980s, Hemp discussed the problem of reciprocal operation in ultrasonic, electromagnetic and coriolis flow meters, indicated that in USMs the problem can be solved by using highimpedance source excitation and open-circuit reception [7,8]. Based on this idea, Borg et al. [9] designed an ingenious ‘‘pulse current source’’ to achieve similar high impedance load for both transmitting and receiving circuits, and obtained good performance in reducing the zero error in the practical tests. In 2005, Lunde et al. [10,11] analyzed the reciprocal operation of the USM
system by considering the acoustic part, including the transducers and the still fluid, as a two-port reciprocal circuit. In the research he took into account the effects of finite impedances of the circuits and transducers, and derived the design criteria for achieving ‘‘sufficient reciprocal operation’’, which greatly extended the previous research. In the present research, through the analysis of the transfer functions of signal inter-conversions between acoustic and electric signals by Mason’s equivalent circuits, the authors indicated that for each transducer, keeping the load impedances consistent in both transmitting and receiving periods would guarantee identical transfer functions of the inter-conversion between acoustic and electric signals, and thus to guarantee the reciprocal operation of the USM. In order to achieve this ‘‘load consistency condition’’ practically in the flow meters, a ‘‘pulse and fix’’ method is proposed in the paper. If the method is implemented in the transmitting circuit, even when the internal impedance of the electric source is unknown or inconstant, the ‘‘load consistency’’ condition can still be approached, and so is the reciprocal operation of the whole USM system. After the theoretical analyses, several practical circuit designs are proposed in the paper, and the preference of the impedance applied is also discussed. Comparing with the ‘‘current source’’ method in Ref. [9], the authors attempt to achieve the reciprocal operation of the USM by using low-impedance load in both transmitting and receiving circuits, which can be adjusted flexibly to meet different requirements. Several TTD measurement experiments on actual metering pipe for liquid are taken to verify the method and the circuit designs, the results of which show that with the ‘‘pulse and fix’’ method, the proposed circuit designs can greatly reduce the zero error of the metering system; the preference of the impedance choice is also discussed and tested.
2. Theory 2.1. Reciprocal operation
Fig. 1. A typical structure of ultrasonic flow meters.
According to Deventer and Delsing [12], if the acoustic signal traveling through fluids can be considered as a plane wave, the fluid through which the signal travels can be simulated by a section of transmission line. This simulation method represents a significant simplification with respect to description of sound propagation from a transducer, which does not cover several
Fig. 2. Equivalent circuit model for signal transmission in both directions. (a) Upstream signal transmission and (b) Downstream signal transmission.
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
important acoustic effects including nearfield, farfield, geometrical spreading, beam pattern, attenuation, etc. However, the line model can be used in the discussion of reciprocal operation of the USMs, to represent a symmetric transmission path. Thus, the signal transmission and receiving in both directions in a USM system can be analyzed by the circuit model shown in Fig. 2. In Fig. 2, VEIN represents the excitation voltage signal applied on the transmitting transducer which is generated by an ideal voltage source, the ZAS, ZBS, ZAL and ZBL are the load impedances for transducers A and B respectively. The denoted V and I are the voltage over and the current through the transducers, and the denoted f and u are the acoustic force and particle velocity on the surfaces at which the transducers attached to the fluid. The subscript A and B are used for transducers A and B, and the subscript 1 and 2 are used for upstream and downstream propagation respectively. The fluid is simulated by a section of transmission line with the characteristic impedance ZaW, which equals to f(A1)/u(A1), or f(B2)/u(B2). In Fig. 2(a), the transfer function of the total transmitting part (including the voltage source, the impedance ZAS and the transducer A), describing the signal conversion from exciting voltage to output particle velocity, can be written as TAT(s)¼u(A1)/VEIN. In the same way, the receiving transfer function of the receiving part, including the transducer B and the load ZBL, describing the signal conversion from acoustic force to output current can be written as TBR(s)¼I(B1)/f(B1). In this model, the process of signal traveling through the fluid can be simply considered as a pure time delay. Thus, the received current signal in the upstream process can be written as IðB1Þ ¼ V EIN T AT ðsÞestu Z aW T BR ðsÞ
ð3Þ
in which the characteristic impedance of the transmission line ZaW, converts the u signal to the f signal; and the estu term describes the time delay during the upstream transmission in the fluid. Correspondingly, the received current signal in the downstream process can be written as IðA2Þ ¼ V EIN T BT ðsÞestd ZaW T AR ðsÞ
7
Fig. 3 shows the Mason equivalent circuits [13] for the transmitting and receiving process on transducer A, assuming that the transducers work in the thickness extensional(TE) mode which is commonly used in USMs. Fig. 3(a) and (b) shows the model of signal conversion in the transmitting phase (during the upstream transmission) and in the receiving phase (during the downstream transmission) on transducer A respectively. The part between the two vertical dashed lines is the Mason model of a piezoelectric transducer, in which the C0 is the static capacitance, ZB is the equivalent impedance representing the backing of the transducer. The transmission line inside the transducer model is presented in the lumped form, in which the Z0, b, d are respectively the characteristic impedance, the wavenumber and the length of the transmission line. These parameters can be calculated according to the physical parameters of the transducer. The transformer in the model is used to achieve the inter-conversion between electric and acoustic signals, the h in the transformerratio hC0 is the piezoelectric stress constant of the material. Since the reflected signal in the fluid is not considered in this model, the transmission line representing the fluid can be considered as infinitely long, and simulated as the terminal impedance ZaW. Same consideration is applied in Fig. 3(b), in which the incoming sound force excitation is modeled as an ideal ‘‘force’’ source fAIN with the impedance ZaW. The impedances ZAS, ZAL and the denoted V, I, f, u in Fig. 3 are the same as those in Fig. 2. A significant application of the Mason’s model is to calculate and simulate the mechanic signals through electric methods by using the analogs of mechanic and electric signals. In the mechanical stage of the Mason’s model, 1 A is analogous to 1 m/s and 1 V is analogous to 1 N. Applying these analogs, the circuits in Fig. 3 can be considered as electrical circuits, in which the variables I(uA1), I(uA2), V(fA1), V(fAIN), ZW noted in gray is analogs to u(A1), u(A2), f(A1), fAIN, ZaW respectively. In these analogs, the values of the variables remain unchanged. Applying Tellegen’s law on the two-port network inside the dashed box in Fig. 3, we have ½V ðA1Þ IðA2Þ V ðA2Þ IðA1Þ þ ½V ðf AINÞ IðuA1Þ ¼ 0
ð5Þ
ð4Þ In the figure there are also
The definition of TBT, TAR, td are similar as TAT, TBR, tu in (3), but in the opposite direction. Despite the time of arrival tu and td, the difference on the ‘‘shapes’’ of I(B1) and I(A2) is decided by the transfer functions TAT, TBR and TBT, TAR in (3) and (4) respectively. These transfer functions can be analyzed by the equivalent circuit model of piezoelectric transducers as shown in the Fig. 3.
V ðA1Þ ¼ V EIN IðA1Þ Z AS ,
V ðA2Þ ¼ IðA2Þ Z AL ,
IðA1Þ ¼
V EIN Z AS þZ EA
in which ZEA is the equivalent electric impedance of the transducer A, which is noted in the figure. With these equations, applying the analogs between the mechanical and electrical signals again,
Fig. 3. Mason equivalent model for transmitting and receiving processes on transducer A.
8
(5) can be rewritten as Z AL Z AS T AT ¼ T AR 1 þ Z AS þ Z EA
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
ð6Þ
In the same way, the relation between transmitting and receiving transfer functions on transducer B can also be written as Z BL Z BS T BT ¼ T BR 1þ ð7Þ Z BS þ Z EB in which ZEB is the equivalent electric impedance of the transducer B. From (6) and (7), it can be seen that if ZAS ¼ ZAL, ZBS ¼ZBL, the transmitting and receiving transfer functions for each transducer would be equal, namely TAT ¼TAR, TBT ¼TBR, and then the transfer functions TATTBR and TBTTAR in (3) and (4) would be equal. That is to say, the reciprocal operation of the metering system can be achieved by keeping the load impedance of each transducer consistent, whether it is used for transmitting or receiving. In many circuit designs in which the transmitting and receiving circuits are shared by both transducers in which ZAS ¼ZBS, ZAL ¼ZBL, the ‘‘load consistency’’ means the load of the transmitting circuit ZS equals to the load of the receiving circuit ZL, which is called ‘‘perfect circuit symmetry’’ in previous literatures. Without loss of generality, following discussions are based on the ZS ¼ZL condition. 2.2. Implementation However, fixing the load of a transducer at a specified value during both transmitting and receiving phase is not easy in practical circuits. When the transducer is used for receiving, the load ZL is constant anytime; yet in the transmitting phase, when being driven, the transducer would generally be connected to a signal source of which the output impedance is usually unknown or inconstant; after the excitation, the transducer would be disconnected from the signal source, and continue a period of ‘‘free oscillation’’ which gradually decays to zero. In other words, unless special source with fixed output impedance is used, the load of the transducer ZS when it is being driven and the ZS during the free oscillation period cannot be literally ‘‘consistent’’, which makes the matching of the ZS and the consistent ZL difficult. However, if E(s) is an ideal impulse excitation d(t), the response of the transmitting transducers would simply be the ‘‘impulse response’’, which can be calculated by the inverse Laplace transformation of the corresponding transfer function TAT or TBT. The core idea of the impulse excitation is to shorten the time of the ‘‘forced excitation’’ period to zero, and to leave the major part of transmitted signal generated by the ‘‘free oscillation’’ of the transducer. In that case, the ZS during the ‘‘free oscillation’’ period decides the output acoustic signal, leaving the ZS in the ‘‘forced excitation’’ period unimportant. Considering both the output amplitude and the need of shortening the ‘‘forced excitation’’ period, a half-period width pulse can be used to imitate the impulse excitation d(t). Fig. 4 illustrates such a method. Applying ‘‘short pulse excitation’’ and fixing the load of the transducer ZS equal to ZL immediately afterwards, this ‘‘pulse and fix’’ method can promote the ‘‘load consistency’’ and thus to improve the reciprocal operation of the USM system without considering the output impedance of the actual excitation source, and can be easily implemented in varieties of simple electric circuits.
3. Methods: circuit designs 3.1. Transmitting circuit design A nature thought to fix the output impedance after the excitation at a certain value is to apply a ‘‘source follower’’ circuit,
Fig. 4. Acoustic response of a short-pulse excitation.
or just connect the transducer and a load resistor to an ideal voltage source. Fig. 5 shows a typical bipolar source follower circuit, which is commonly seen in USM applications. In Fig. 5, þVEX and VEX are positive and negative voltage sources, Q1 and Q2 are a pair of MOSFETs(Metal-Oxide-Semiconductor Field Effect Transistors), the gate, source and drain electrodes of each MOSFET are denoted as ‘‘G’’, ‘‘S’’ and ‘‘D’’ in the figure respectively. VCON is the control signal applied on the gate electrodes of both Q1 and Q2, which conducts Q1 and Q2 alternatively to apply bipolar voltage excitation to the transducer. The RS is an implemented resistor, and the ZS shows the load impedance of the transducer. These denotations are also of the same meaning in the following Figs. 6 and 7. However, due to the non-ideal internal impedance of the voltage source and the switching characteristics of the MOSFETs, the circuit shown in Fig. 5 cannot ideally fix the load impedance of the transducer immediately after the driving pulse. In order to achieve the ‘‘pulse and fix’’ condition, several modifications have to be made. 3.1.1. Circuit TrA: unipolar excitation The simplest way to transmit an impulse excitation is to apply a unipolar excitation circuit, as shown in Fig. 6. The control signal VCON conducts Q1 for a short time and then turns negative to conduct Q2, which would send a pulse excitation to the transducer. The VCON signal keeps Q2 conducting afterwards, until the ‘‘free oscillation’’ of the transducer decays to zero. If the drain to source on-state resistance RDS(on) of Q2 (smaller than 0.5 O typically) can be neglected, the electric potential at node 1 would be a constant zero after Q2 is on(meaning the S and D electrodes are connected), the transmitting transducer would oscillate with a fixed load ZS ¼RS. 3.1.2. Circuit TrB: a forced grounded design For most practical USMs, bipolar pulse is used to achieve higher power transmission and thus to achieve better receiving SNR(Signal-Noise Ratio), like the circuit in Fig. 5. In that case, a possible way fixing the electric load for the transmitting transducer is to ground the far side of RS, as denoted node 10 in Fig. 7. In the design shown in the figure, the MOSFET Q3 keeps shut when Q1 and Q2 conduct alternatively to make the bipolar excitation, and conducts afterwards immediately by the controlling signal F_GND, forcing node 10 at a constant zero level during the free oscillation period of the transmitting transducer. After the free oscillation of the transducer decays to zero, Q3 shuts again to
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
9
Fig. 7. TrB: forced grounding circuit.
Fig. 5. A traditional type of excitation circuit.
Fig. 6. TrA: unipolar excitation circuit.
prepare for the next transmitting phase. The capacitor CISO is used to avoid short between –VEX and ground through Q2 and Q3, and because of this capacitor, the actual excitation signal at node 10 would be a 0–2VEX (providing VCON 4VEX) unipolar pulse. In this design, the electric impedance ZS of the transmitting transducer would also be equal to RS during the free oscillation period of the transducer.
3.2. Receiving circuit design Comparing with the transmitting circuit, since it is not necessary to ‘‘switch’’ in the receiving process, the equivalent input impedance of the receiving circuit can be set and fixed. In our designs, an operational amplifier (Op. Amp) is used to control the load of the transducer ZL during the receiving phase. Both the ‘‘Current amplifier’’ and the ‘‘Voltage amplifier’’ designs are proposed and tested in our experiments.
3.2.1. Circuit RvA: the current amplifier The charge amplifier, as shown in Fig. 8(a), is a kind of current amplifier which is commonly used for the signal pre-process for capacitive sensors including piezoelectric transducers. In Fig. 8(a), ZL shows the equivalent load of the transducer; Cint and Rfb are the integrating capacitor and the feedback resistor of the charge amplifier. When the open-loop gain of the Op. Amp is sufficiently large, the equivalent load of the transducer ZL is very small and can be neglected. Thus, a matching resistor RL can be inserted between the transducer and the Op. Amp, as shown in Fig. 8(b), to make the equivalent load of the receiving transducer ZL ERL. It is worth mentioning that the RL inserted would make the ‘‘cable effect’’ no longer negligible, which violates the greatest advantage of the charge amplifier. However, as the cables connecting the circuits and the transducers can be considered inside the two-port network in the dashed box in Fig. 3, the effects brought by them would not violate the reciprocal operation of the system. 3.2.2. Circuit RvB: voltage amplifier Although voltage mode amplification is seldom used for piezoelectric sensors because of the cable effect, it is still a simple and effective method to specify the input impedance of the receiving circuit. A typical approach to fix the load of the receiving transducer is to apply a voltage follower, as shown in Fig. 9. In Fig. 9, the RL is an implemented resistor to set the load of the receiving transducer. As the input impedance of the non-inverting input pin of the Op. Amp can be considered infinite, the ZL can be considered equal to RL. 3.3. Impedance choice According to the theory described in Section 2, achieving ZS ¼ZL, namely RS ¼RL if the circuit designs shown in Figs. 6–9 are implemented, would approach the reciprocal operation of the measurement system. Since for both transmitting and receiving circuits, the equivalent loads for the transducer, namely ZS and ZL, can be fixed at any given value using circuit designs proposed above, it is necessary to discuss the resistance choice for RS(or RL). 3.3.1. For circuit RvA For both transmitting circuits TrA and TrB, a smaller RS leads to higher power transmission efficiency. For the circuit RvA, as it can
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Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
Fig. 8. (a) Charge amplifier (b) RvA: using charge amplifier to set ZL.
0.034 O, are the resistors representing the air backings of the transducers. The excitation signal is a 500 V voltage pulse which lasts 250 ns. The output voltage signals are obtained from the node noted ‘‘OUT’’, the load Rload is 1 MO. In Fig. 10(b), the ratio of the peak–peak amplitude Vp–p of each received signal and the pulse voltage Vpul when applying different RS( ¼RL) were plotted. As can be seen in the figure, the profile of the received amplitude versus RS( ¼RL) decreases slowly after the peak, which means the range of RS( ¼RL) that achieves ‘‘good sensitivity’’ is quite large. Comparing with the current-based amplification in circuit RvA, RvB would achieve better reciprocal operation when RS(or RL) is small, since the effect of non-ideal Op. Amp causes less impedance imbalance.
4. Practical experiments Fig. 9. RvB: using voltage follower to set ZL.
4.1. Experiment setup be seen as an inverting integrator, better sensitivity would also be achieved by a smaller RL. Choosing a small RS(or RL) would achieve better receiving amplitude. However, there would be also problems if RS and RL employed are too small. In practical circuit, such as those shown in Figs. 6–9, it should be actually considered that ZS0 ¼ RS þ eZS and ZL0 ¼RL þ eZL, in which eZS and eZL are the small impedance terms brought by some uncontrolled non-ideal components such as MOSFET and Op. Amps. If it is the non-ideal ZS0 and ZL0 considered instead of ZAS and ZAL in (6) or instead of ZBS and ZBL in (7), it would be concluded that higher RS(or RL) would bring TAT and TAR, or TBT and TBR closer, which would make signals received in both directions in (3) and (4) more identical. Therefore, when circuit RvA is used for receiving, the choice of the RS(or RL) is a trade-off between the receiving amplitude and the reciprocal operation of the system.
3.3.2. For circuit RvB In the voltage follower circuit RvB, larger RL would obviously achieve better receiving amplitude. As larger RS decreases the transmitting efficiency and the reciprocal operation of the system requires equal RS and RL, there would be an optimum choice for RS( ¼RL) to achieve the best receiving amplitude. Fig. 10 shows a SPICE(Simulation Program with Integrated Circuit Emphasis) simulation for the variation on received amplitude versus RS( ¼RL), in which an equivalent circuit model for ultrasonic system [12], as shown in Fig. 10(a), is used. In the simulation, both transducers are set as ideal 2 MHz PZT-5 thickness extensional circular disks without any coupling layer. The diameter of the transducers is 10 mm. The fluid in the simulation is set as pure water, of which the density and the sound speed are set as 1000 kg/m3 and 1470 m/s. The small RAirT and RAirR, set as
In order to verify the ‘‘pulse and fix’’ method, the circuit designs and the effects of the impedance choices, a number of experiments were taken under practical environment. The measurement pipeline used in the experiments was a PFA(Perfluoroalkoxy) pipe UCUF-4P [14] from TokyoKeiso, of which the length is 94 mm and the inner diameter is 4 mm. The transducers were attached face to face on the 3 mm PFA layers at both ends of the pipe. The total structure is the same as the pipe shown in Fig. 1. Three different types of transducers are used in the experiments. Type A is the PZT-5 piezoelectric ceramic disks with matching layers and heavy backing layers, which is originally used in the metering pipe products, Type B is the PZT-5 piezoelectric ceramic disks without any backing or matching layer, and Type C is the composite piezoelectric disk with 1 mm matching layer. All three types of transducers are circular disks working in the thickness extensional mode, the diameters of the disks are about 10 mm and the thickness was around 1 mm for Type A and B, 0.6 mm for Type C. The serial resonance frequencies of them are about 2 MHz for Type A and B, 2.5 MHz for Type C. For each type there are a pair of transducers with similar parameters, while between different types, the characteristics of the transducers are quite different. The transmitting and receiving circuit designs are tested with varieties of circuit combinations and RS(RL) choices. For each circuit setup, the signal waveforms received in both directions are sampled by a 40 Msps ADC(Analog-Digit Converter) and transferred to PC. The whole test system was made by the authors, in which the timing of signal transmission, receiving and sampling are controlled by an FPGA(Field programmable gate array) chip. The structure of the test system is shown in Fig. 11. The zero errors(ZE) of the transit-time difference, and the correlation coefficients(CC) calculated from waveforms acquired
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
11
Fig. 10. Simulation investigating received amplitude vs. RS(or RL) choice for circuit RvB (a) Simulation model and (b) Simulation results.
in both directions are calculated in the PC. The zero errors were calculated from the first 80 points of the received waveforms in both directions by the cross-correlation method; the parabolic interpolation method was used to enhance the precision. Smaller zero error indicates better reciprocal operation. The correlation coefficients Corr(U,D) were calculated by PN CorrðU,DÞ ¼ PN
i¼1
U i Di PN
i¼1
UiUi
i¼1
Di Di
1=2
ð8Þ
in which U and D are the sampling sequence of the total upstream and downstream waveforms. The coefficient is a number located between 1 and 1. The closer the CC is to 1, of better reciprocal operation is the system. All tests below were done when the fluid was still.
4.2. Experiment result 4.2.1. Verification of the circuit designs The proposed transmitting and receiving circuits TrA, TrB, RvA and RvB are combined to form measurement systems and tested on the measurement pipe with a pair of Type B transducers. The signal waveforms received in both directions were acquired to calculate both the zero error and the correlation coefficient. In the circuits designed for reciprocal operation, namely TrA, TrB, RvA and RvB, the RS and the RL are both set at 100 O. The VEX is set to 15 V in TrA and 12 V in TrB. The Rfb and Cint in the RvA circuit are around 4 kO and 20pf in the experiment. A reference circuit set disregarding the condition for reciprocal operation was also included in the experiment, in which the circuit in Fig. 5 with RS ¼18 O, VEX ¼15 V, was used as the transmitting circuit, and the circuit RvA with RL ¼100 O was used as the receiving circuit. In all experiments on these circuit sets, the controlling signal VCON is a single 15 V þ15 V pulse of 250 ns width; after the pulse, VCON fells back to and stays at 15 V. The received waveforms in both directions obtained from different circuit combinations are shown in Fig. 12, on which the upstream and downstream waveforms are respectively shown by the solid and dashed lines. The subplot denoted ‘‘Ref’’ shows the waveforms obtained from the reference circuit described above. The mean ZE and CC calculated from 100 waveform pairs are noted in the figure. The decrease of the zero flow error and the promotion on the accordance of the received waveforms brought by circuit designs can be seen comparing to the results and the waveforms obtained from the reference circuit set.
4.2.2. Reciprocal operation and pairing situation Both good and bad transducer pairing situations were tested using the reference circuit described above and the circuits proposed for reciprocal operation. The ‘‘good pairing’’ situation means using a pair of transducers of the same type and the ‘‘bad pairing’’ situation means using two transducers of different types to perform the measurement. The circuits used for reciprocal operation in the experiments were TrA and RvA with RS ¼RL ¼ 500 O. The excitation signal is a þ15 V single pulse with 250 ns width. For each combination of the pairing and the circuit, 100 upstream and downstream received signal pairs were acquired and calculated. The averaged ZE and CC of them are shown in Table 1. The correlation coefficients presented here are calculated by the averaged waveforms in each case, in order to prevent the influence caused by random noise. It can be seen from Table 1, the results of the zero flow error from the circuit combination of TrA and RvA are much smaller than the results from the reference circuit systems. The zero flow error in the ‘‘good pairing’’ situations are smaller than those in the ‘‘bad pairing’’ situations. The promotion on correlation coefficient is also obvious. The zero error of the TTD obtained when the same type of transducers are applied in Table 1 is no larger than 50 ps, for the metering pipe on which the experiment was taken, this would cause a flow velocity error less than 0.6 mm/s or a flow rate error less than 0.45 ml/min, which is much smaller than the nominated 8 ml/min of the product.
4.2.3. Impedance choice The effect of impedance choice in the circuit design was also tested on actual metering pipe by practical circuits. In these experiments, the transmitting circuit was circuit TrA, and the excitation signal was a single þ15 V pulse with 250 ns width. Both receiving circuits RvA and RvB were tested respectively with the transmitting circuit when different RS(or RL) were implemented. A pair of Type B transducers was used in the experiment. The actual measurement results of the receiving peak amplitude, the CC and the ZE calculated from the data acquired from circuit RvA and RvB are listed in Tables 2 and 3 respectively. Each data listed is the average of 40 measurement results, the ‘‘LSB’’ in the tables means ‘‘Least Significant Bit’’ of the sampling ADC used. It can be seen in Table 2, as the RS(or RL) increases, better zero error and correlation coefficient would be achieved, which means of better reciprocal operation the system is. However, at the mean time the amplitude of the received signal decreases significantly. When RS ¼RL ¼100 O, the received signal is merely 1/3 strong
12
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Fig. 11. Structure of the test system.
Fig. 12. Waveforms and ZE, CC results from different circuit combinations.
Table 1 Mean ZE and CC of averaged waveforms in different transducer pairing situations. Transducers pairing Reference circuits
TrA/RvA
Zero error (ps) Corr. Coeff. Zero error (ps) Corr. Coeff. Type Type Type Type Type Type
A/A B/B C/C A/B A/C B/C
1804.6 208.72 5779.0 2189.7 2405.1 2437.7
0.9447 0.9992 0.9738 0.9807 0.9332 0.9838
49.66 22.31 20.82 196.07 233.43 298.91
0.9999 1.0000 0.9999 0.9999 0.9998 0.9999
Table 2 Measurement data from TrA/RvA. RS(¼RL) (Ohm)
Peak amplitude (LSB)
Zero error (ps)
Corr. Coeff.
0 10 25 50 75 100
255(saturated) 238 181.25 126.13 93 74.2
139.92 135.741 109.31 1.88 46.88 23.88
0.9877 0.9921 0.9954 0.9977 0.9983 0.9982
Table 3 Measurement data from TrA/RvB. RS(¼RL) (Ohm)
Peak amplitude (LSB)
Zero error (ps)
Corr. Coeff.
25 50 75 100 125 150 200 300 500 800 1000
132.24 190.20 205.98 210.86 206.88 198.08 180.44 151.56 109.60 76.12 65.76
15.22 48.86 83.51 61.01 89.54 90.92 51.06 64.98 42.16 34.44 53.60
0.99928 0.99964 0.99971 0.99974 0.99975 0.99974 0.99967 0.99959 0.99866 0.99787 0.99675
comparing with the situation when RS ¼RL ¼10 O, and the CC starts to fall due to the influence of the noise. The impedance choice when circuit RvA is implemented is a trade-off between reciprocal operation and the receiving SNR, and should be selected differently from case to case. As can be inferred from Table 3, the receiving circuit RvB can achieve low zero error and good correlation coefficient even the RS and RL are chosen very low. No obvious trend was found in the zero error as the RS(or RL) increases. The variation of the CC was small, and
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
was mainly due to the variation of the SNR. As can be seen in the table, there was an optimum RS(RL) choice for the receiving amplitude, which is around 100 O in the experiments. The trend of received amplitude fits completely with the analysis and the simulation.
5. Conclusion In ultrasonic flow meters using piezoelectric transducers as both the transmitter and receiver of the ultrasound signal, keeping the equivalent load of each transducer consistent between the transmitting and the receiving phase is a valid way to achieve reciprocal operation of the system and thus to suppress the zero error. By applying a short pulse excitation and fixing the transducer’s transmitting load ZS equal to its receiving load ZL during the ‘‘free oscillation’’ period, the ‘‘load consistency’’ condition can be approached in practical measurement circuit, regardless of the output impedance of the signal source. Circuit designs proposed in the paper can be used to achieve such condition, in which the equivalent load impedance of the transducers can be set flexibly to meet varieties of requirements. If the current amplifier as RvA proposed is implemented for receiving, the impedance choice is a trade-off between the signal amplitude and the reciprocal operation of the system, while if the voltage amplifier as RvB is implemented, the reciprocal operation would not be sensitive to the impedance choice, and there would be an optimum impedance choice to achieve the best receiving amplitude. Further works will be done mainly on the research of implementing variable or/and complex impedances in the measurement circuits, and developing the USM system in which the reciprocal operation can be self-adjusted.
Acknowledgment The authors are truly grateful to TokyoKeiso Co. Ltd. for their support.
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References [1] Takamoto M, Ishikawa H, Shimizu K, Monji H, Matsui G. New measurement method for very low liquid flow rates using ultrasound. Flow Measurement and Instrumentation 2001;12(4):267–273. [2] Bo Y, Li C, Yupin L. Forced oscillation to reduce zero flow error and thermal drift for non-reciprocal operating liquid ultrasonic flow meters. Flow Measurement and Instrumentation 2011;22(4):257–264. [3] Lunde P, Froysa K, Vestrheim M. Challenges for improved accuracy and traceablilty in ultrasonic fiscal flow metering. In: Proceedings of the 18th Internernational North Sea Flow Measurement Workshop. Gleneagles, Scotland; 24–27 October 2000. [4] Foldy LL, Primakoff H. A general theory of passive linear electroacoustic transducers and the electroacoustic reciprocity theorem. I. Journal of the Acoustical Society of America 1945;17(2):109–120. [5] van Deventer J, Delsing J. Apparent transducer non-reciprocity in an ultrasonic flow meter. Ultrasonics 2002;40(1–8):403–405. [6] Jr Leach WM. Controlled-source analogous circuits and SPICE models for piezoelectric transducers. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 1994;41(1):60–66. [7] Hemp J. Theory of transit time ultrasonic flowmeters. J Sound Vib 1982;84(1):133–147. [8] Hemp J. Flowmeters and reciprocity. Q J Mech Appl Math 1988;41:503–520. [9] Borg J, Johansson J, van Deventer J, Delsing J. Reciprocal operation of ultrasonic transducers: experimental results. 2006 IEEE Ultrasonics Symposium. Vancouver, Canada; 3–6 October 2006. p. 1013–6. [10] Lunde P, Vestrheim M, Bø R, Smørgrav S, Abrahamsen AK. Reciprocity and its utilization in ultrasonic flow meters. In: Proceedings of the 23rd International North Sea Flow Measurement Workshop. Tønsberg, Norway; 18–21 October 2005. [11] Lunde P, Vestrheim M, Reidar B, Smorgrav S, Abrahamsen AK. Reciprocal operation of ultrasonic flow meters: criteria and applications. 2007 IEEE Ultrasonics Symposium. New York, USA, 28–31 October 2007. p. 381–6. [12] van Deventer J, Lofqvist T, Delsing J. PSpice simulation of ultrasonic systems. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 2000;47(4):1014–1024. [13] Steven, MA. Equivalent circuit modeling for thin disk and bar type piezoelectric transducers. Master’s thesis. University of Tulsa; 2006. [14] Tokyo Keiso co. ltd.. Ultra-clean ultrasonic flowmeter UCUF-P Series Technical guidance. /http://www.tokyokeiso.co.jp/english/products/download/tg/ UCUF-P_TG-F994E.pdfS; 2004.
Contents lists available at SciVerse ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Electronic circuit design for reciprocal operation of transit-time ultrasonic flow meters Yang Bo n, Cao Li Department of Automation Tsinghua University Beijing, 100084, PR China
a r t i c l e i n f o
abstract
Article history: Received 19 May 2012 Received in revised form 4 February 2013 Accepted 19 February 2013 Available online 27 February 2013
The reciprocal operation theory has been used in the circuit design of transit-time ultrasonic flow meters (USMs) to promote their zero flow performances. In this paper, the authors analyzed the transfer functions of the inter-conversion between acoustic and electric signals on each transducer, indicated that the equivalent load consistency for each transducer between the transmitting and the receiving phases would guarantee the transmitting and the receiving transfer functions equal, and thus guarantee the reciprocal operation of the USM system. In order to achieve the ‘‘load consistency’’ condition in practical systems with non-ideal parameters, a method of applying short pulse excitation and fixing the equivalent load in the ‘‘free oscillation period’’ of the transmitting transducer is proposed. Based on this method, several circuit designs are shown in the paper, the impedance preferences are also analyzed. Practical experiments done with these circuits show clear improvement in both promoting the accordance of the signals received in both directions and reducing the zero flow error in the measurement. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Ultrasonic flow metering Electroacoustic reciprocity Reciprocal operation Zero flow error
1. Introduction The basic principle of ultrasonic flow meters is to obtain the velocity of fluid through the transit-times or transit-time difference (TTD) of upstream and downstream traveling ultrasound signals. A general model of ultrasonic flow meter is shown in Fig. 1, in which the piezoelectric transducers are placed face-toface at both ends of the pipe. Assuming v is the flow velocity in the pipe, the upstream and downstream transit times of ultrasound signals tu and td would be tu ¼
l , cv
td ¼
l cþv
ð1Þ
in which l is the length of the metering section and c is the sound speed in the still fluid. Since in liquids ccv, the flow velocity v can be calculated as v
lDt 2t 20
ð2Þ
in which the TTD Dt ¼tu td, and t0 represents the mean transit time in both directions. Since t0 remains almost unchanged when v is low, v can be considered as proportional to Dt. Several algorithms can be used to detect the Dt from the signals received in both directions, of which the zero-crossing n
Corresponding author. E-mail addresses: [email protected] (Y. Bo), [email protected] (C. Li).
0955-5986/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2013.02.003
method and the correlation methods are most commonly used. However, for both methods, the accordance of received signal waveforms in both upstream and downstream directions is crucial for the TTD measurement [1]. If these signal waveforms are different, a non-zero TTD would be obtained when the fluid is still, which is called the zero error. In practice, the dry calibration method is usually used to cancel the zero error, but the calibration in one situation may fail when measurement environment, such as temperature, changes [2,3]. Since low zero error is important for achieving accurate flow metering, it is necessary to promote the accordance of the signal received in both directions, or to say, to improve the reciprocal operation of the measurement system. The ‘‘reciprocal operation’’ is quite different from the concept of ‘‘electroacoustic reciprocity’’. The well-known electroacoustic reciprocity theory states that, for most two-port passive linear electroacoustic networks, the transfer impedances from either port to another are equal. This theory can be applied on transducers and also on the USM system containing both transducers and the fluid in-between [4]. However, unless special design is made, a reciprocal USM system may not be reciprocally operated, in which the zero error may still exist. In the past decades, the theory of reciprocal operation has been addressed by many researchers. One way to achieve reciprocal operation in the metering system is to implement identical transducers. In 2002, Deventer and Delsing [5] simulated the received waveforms in both directions in an USM system by the equivalent circuit model
6
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
introduced by Leach [6]. The researchers compared the zero errors caused by varieties of non-symmetric factors in the metering system, and indicated that the reciprocal operation holds when the transducers implemented in the USM are identical. Since manufacturing identical transducers is not practical, many researchers focused on achieving the reciprocal operation through the design of the electronic interfaces employed in the USMs. Early in 1980s, Hemp discussed the problem of reciprocal operation in ultrasonic, electromagnetic and coriolis flow meters, indicated that in USMs the problem can be solved by using highimpedance source excitation and open-circuit reception [7,8]. Based on this idea, Borg et al. [9] designed an ingenious ‘‘pulse current source’’ to achieve similar high impedance load for both transmitting and receiving circuits, and obtained good performance in reducing the zero error in the practical tests. In 2005, Lunde et al. [10,11] analyzed the reciprocal operation of the USM
system by considering the acoustic part, including the transducers and the still fluid, as a two-port reciprocal circuit. In the research he took into account the effects of finite impedances of the circuits and transducers, and derived the design criteria for achieving ‘‘sufficient reciprocal operation’’, which greatly extended the previous research. In the present research, through the analysis of the transfer functions of signal inter-conversions between acoustic and electric signals by Mason’s equivalent circuits, the authors indicated that for each transducer, keeping the load impedances consistent in both transmitting and receiving periods would guarantee identical transfer functions of the inter-conversion between acoustic and electric signals, and thus to guarantee the reciprocal operation of the USM. In order to achieve this ‘‘load consistency condition’’ practically in the flow meters, a ‘‘pulse and fix’’ method is proposed in the paper. If the method is implemented in the transmitting circuit, even when the internal impedance of the electric source is unknown or inconstant, the ‘‘load consistency’’ condition can still be approached, and so is the reciprocal operation of the whole USM system. After the theoretical analyses, several practical circuit designs are proposed in the paper, and the preference of the impedance applied is also discussed. Comparing with the ‘‘current source’’ method in Ref. [9], the authors attempt to achieve the reciprocal operation of the USM by using low-impedance load in both transmitting and receiving circuits, which can be adjusted flexibly to meet different requirements. Several TTD measurement experiments on actual metering pipe for liquid are taken to verify the method and the circuit designs, the results of which show that with the ‘‘pulse and fix’’ method, the proposed circuit designs can greatly reduce the zero error of the metering system; the preference of the impedance choice is also discussed and tested.
2. Theory 2.1. Reciprocal operation
Fig. 1. A typical structure of ultrasonic flow meters.
According to Deventer and Delsing [12], if the acoustic signal traveling through fluids can be considered as a plane wave, the fluid through which the signal travels can be simulated by a section of transmission line. This simulation method represents a significant simplification with respect to description of sound propagation from a transducer, which does not cover several
Fig. 2. Equivalent circuit model for signal transmission in both directions. (a) Upstream signal transmission and (b) Downstream signal transmission.
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
important acoustic effects including nearfield, farfield, geometrical spreading, beam pattern, attenuation, etc. However, the line model can be used in the discussion of reciprocal operation of the USMs, to represent a symmetric transmission path. Thus, the signal transmission and receiving in both directions in a USM system can be analyzed by the circuit model shown in Fig. 2. In Fig. 2, VEIN represents the excitation voltage signal applied on the transmitting transducer which is generated by an ideal voltage source, the ZAS, ZBS, ZAL and ZBL are the load impedances for transducers A and B respectively. The denoted V and I are the voltage over and the current through the transducers, and the denoted f and u are the acoustic force and particle velocity on the surfaces at which the transducers attached to the fluid. The subscript A and B are used for transducers A and B, and the subscript 1 and 2 are used for upstream and downstream propagation respectively. The fluid is simulated by a section of transmission line with the characteristic impedance ZaW, which equals to f(A1)/u(A1), or f(B2)/u(B2). In Fig. 2(a), the transfer function of the total transmitting part (including the voltage source, the impedance ZAS and the transducer A), describing the signal conversion from exciting voltage to output particle velocity, can be written as TAT(s)¼u(A1)/VEIN. In the same way, the receiving transfer function of the receiving part, including the transducer B and the load ZBL, describing the signal conversion from acoustic force to output current can be written as TBR(s)¼I(B1)/f(B1). In this model, the process of signal traveling through the fluid can be simply considered as a pure time delay. Thus, the received current signal in the upstream process can be written as IðB1Þ ¼ V EIN T AT ðsÞestu Z aW T BR ðsÞ
ð3Þ
in which the characteristic impedance of the transmission line ZaW, converts the u signal to the f signal; and the estu term describes the time delay during the upstream transmission in the fluid. Correspondingly, the received current signal in the downstream process can be written as IðA2Þ ¼ V EIN T BT ðsÞestd ZaW T AR ðsÞ
7
Fig. 3 shows the Mason equivalent circuits [13] for the transmitting and receiving process on transducer A, assuming that the transducers work in the thickness extensional(TE) mode which is commonly used in USMs. Fig. 3(a) and (b) shows the model of signal conversion in the transmitting phase (during the upstream transmission) and in the receiving phase (during the downstream transmission) on transducer A respectively. The part between the two vertical dashed lines is the Mason model of a piezoelectric transducer, in which the C0 is the static capacitance, ZB is the equivalent impedance representing the backing of the transducer. The transmission line inside the transducer model is presented in the lumped form, in which the Z0, b, d are respectively the characteristic impedance, the wavenumber and the length of the transmission line. These parameters can be calculated according to the physical parameters of the transducer. The transformer in the model is used to achieve the inter-conversion between electric and acoustic signals, the h in the transformerratio hC0 is the piezoelectric stress constant of the material. Since the reflected signal in the fluid is not considered in this model, the transmission line representing the fluid can be considered as infinitely long, and simulated as the terminal impedance ZaW. Same consideration is applied in Fig. 3(b), in which the incoming sound force excitation is modeled as an ideal ‘‘force’’ source fAIN with the impedance ZaW. The impedances ZAS, ZAL and the denoted V, I, f, u in Fig. 3 are the same as those in Fig. 2. A significant application of the Mason’s model is to calculate and simulate the mechanic signals through electric methods by using the analogs of mechanic and electric signals. In the mechanical stage of the Mason’s model, 1 A is analogous to 1 m/s and 1 V is analogous to 1 N. Applying these analogs, the circuits in Fig. 3 can be considered as electrical circuits, in which the variables I(uA1), I(uA2), V(fA1), V(fAIN), ZW noted in gray is analogs to u(A1), u(A2), f(A1), fAIN, ZaW respectively. In these analogs, the values of the variables remain unchanged. Applying Tellegen’s law on the two-port network inside the dashed box in Fig. 3, we have ½V ðA1Þ IðA2Þ V ðA2Þ IðA1Þ þ ½V ðf AINÞ IðuA1Þ ¼ 0
ð5Þ
ð4Þ In the figure there are also
The definition of TBT, TAR, td are similar as TAT, TBR, tu in (3), but in the opposite direction. Despite the time of arrival tu and td, the difference on the ‘‘shapes’’ of I(B1) and I(A2) is decided by the transfer functions TAT, TBR and TBT, TAR in (3) and (4) respectively. These transfer functions can be analyzed by the equivalent circuit model of piezoelectric transducers as shown in the Fig. 3.
V ðA1Þ ¼ V EIN IðA1Þ Z AS ,
V ðA2Þ ¼ IðA2Þ Z AL ,
IðA1Þ ¼
V EIN Z AS þZ EA
in which ZEA is the equivalent electric impedance of the transducer A, which is noted in the figure. With these equations, applying the analogs between the mechanical and electrical signals again,
Fig. 3. Mason equivalent model for transmitting and receiving processes on transducer A.
8
(5) can be rewritten as Z AL Z AS T AT ¼ T AR 1 þ Z AS þ Z EA
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
ð6Þ
In the same way, the relation between transmitting and receiving transfer functions on transducer B can also be written as Z BL Z BS T BT ¼ T BR 1þ ð7Þ Z BS þ Z EB in which ZEB is the equivalent electric impedance of the transducer B. From (6) and (7), it can be seen that if ZAS ¼ ZAL, ZBS ¼ZBL, the transmitting and receiving transfer functions for each transducer would be equal, namely TAT ¼TAR, TBT ¼TBR, and then the transfer functions TATTBR and TBTTAR in (3) and (4) would be equal. That is to say, the reciprocal operation of the metering system can be achieved by keeping the load impedance of each transducer consistent, whether it is used for transmitting or receiving. In many circuit designs in which the transmitting and receiving circuits are shared by both transducers in which ZAS ¼ZBS, ZAL ¼ZBL, the ‘‘load consistency’’ means the load of the transmitting circuit ZS equals to the load of the receiving circuit ZL, which is called ‘‘perfect circuit symmetry’’ in previous literatures. Without loss of generality, following discussions are based on the ZS ¼ZL condition. 2.2. Implementation However, fixing the load of a transducer at a specified value during both transmitting and receiving phase is not easy in practical circuits. When the transducer is used for receiving, the load ZL is constant anytime; yet in the transmitting phase, when being driven, the transducer would generally be connected to a signal source of which the output impedance is usually unknown or inconstant; after the excitation, the transducer would be disconnected from the signal source, and continue a period of ‘‘free oscillation’’ which gradually decays to zero. In other words, unless special source with fixed output impedance is used, the load of the transducer ZS when it is being driven and the ZS during the free oscillation period cannot be literally ‘‘consistent’’, which makes the matching of the ZS and the consistent ZL difficult. However, if E(s) is an ideal impulse excitation d(t), the response of the transmitting transducers would simply be the ‘‘impulse response’’, which can be calculated by the inverse Laplace transformation of the corresponding transfer function TAT or TBT. The core idea of the impulse excitation is to shorten the time of the ‘‘forced excitation’’ period to zero, and to leave the major part of transmitted signal generated by the ‘‘free oscillation’’ of the transducer. In that case, the ZS during the ‘‘free oscillation’’ period decides the output acoustic signal, leaving the ZS in the ‘‘forced excitation’’ period unimportant. Considering both the output amplitude and the need of shortening the ‘‘forced excitation’’ period, a half-period width pulse can be used to imitate the impulse excitation d(t). Fig. 4 illustrates such a method. Applying ‘‘short pulse excitation’’ and fixing the load of the transducer ZS equal to ZL immediately afterwards, this ‘‘pulse and fix’’ method can promote the ‘‘load consistency’’ and thus to improve the reciprocal operation of the USM system without considering the output impedance of the actual excitation source, and can be easily implemented in varieties of simple electric circuits.
3. Methods: circuit designs 3.1. Transmitting circuit design A nature thought to fix the output impedance after the excitation at a certain value is to apply a ‘‘source follower’’ circuit,
Fig. 4. Acoustic response of a short-pulse excitation.
or just connect the transducer and a load resistor to an ideal voltage source. Fig. 5 shows a typical bipolar source follower circuit, which is commonly seen in USM applications. In Fig. 5, þVEX and VEX are positive and negative voltage sources, Q1 and Q2 are a pair of MOSFETs(Metal-Oxide-Semiconductor Field Effect Transistors), the gate, source and drain electrodes of each MOSFET are denoted as ‘‘G’’, ‘‘S’’ and ‘‘D’’ in the figure respectively. VCON is the control signal applied on the gate electrodes of both Q1 and Q2, which conducts Q1 and Q2 alternatively to apply bipolar voltage excitation to the transducer. The RS is an implemented resistor, and the ZS shows the load impedance of the transducer. These denotations are also of the same meaning in the following Figs. 6 and 7. However, due to the non-ideal internal impedance of the voltage source and the switching characteristics of the MOSFETs, the circuit shown in Fig. 5 cannot ideally fix the load impedance of the transducer immediately after the driving pulse. In order to achieve the ‘‘pulse and fix’’ condition, several modifications have to be made. 3.1.1. Circuit TrA: unipolar excitation The simplest way to transmit an impulse excitation is to apply a unipolar excitation circuit, as shown in Fig. 6. The control signal VCON conducts Q1 for a short time and then turns negative to conduct Q2, which would send a pulse excitation to the transducer. The VCON signal keeps Q2 conducting afterwards, until the ‘‘free oscillation’’ of the transducer decays to zero. If the drain to source on-state resistance RDS(on) of Q2 (smaller than 0.5 O typically) can be neglected, the electric potential at node 1 would be a constant zero after Q2 is on(meaning the S and D electrodes are connected), the transmitting transducer would oscillate with a fixed load ZS ¼RS. 3.1.2. Circuit TrB: a forced grounded design For most practical USMs, bipolar pulse is used to achieve higher power transmission and thus to achieve better receiving SNR(Signal-Noise Ratio), like the circuit in Fig. 5. In that case, a possible way fixing the electric load for the transmitting transducer is to ground the far side of RS, as denoted node 10 in Fig. 7. In the design shown in the figure, the MOSFET Q3 keeps shut when Q1 and Q2 conduct alternatively to make the bipolar excitation, and conducts afterwards immediately by the controlling signal F_GND, forcing node 10 at a constant zero level during the free oscillation period of the transmitting transducer. After the free oscillation of the transducer decays to zero, Q3 shuts again to
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
9
Fig. 7. TrB: forced grounding circuit.
Fig. 5. A traditional type of excitation circuit.
Fig. 6. TrA: unipolar excitation circuit.
prepare for the next transmitting phase. The capacitor CISO is used to avoid short between –VEX and ground through Q2 and Q3, and because of this capacitor, the actual excitation signal at node 10 would be a 0–2VEX (providing VCON 4VEX) unipolar pulse. In this design, the electric impedance ZS of the transmitting transducer would also be equal to RS during the free oscillation period of the transducer.
3.2. Receiving circuit design Comparing with the transmitting circuit, since it is not necessary to ‘‘switch’’ in the receiving process, the equivalent input impedance of the receiving circuit can be set and fixed. In our designs, an operational amplifier (Op. Amp) is used to control the load of the transducer ZL during the receiving phase. Both the ‘‘Current amplifier’’ and the ‘‘Voltage amplifier’’ designs are proposed and tested in our experiments.
3.2.1. Circuit RvA: the current amplifier The charge amplifier, as shown in Fig. 8(a), is a kind of current amplifier which is commonly used for the signal pre-process for capacitive sensors including piezoelectric transducers. In Fig. 8(a), ZL shows the equivalent load of the transducer; Cint and Rfb are the integrating capacitor and the feedback resistor of the charge amplifier. When the open-loop gain of the Op. Amp is sufficiently large, the equivalent load of the transducer ZL is very small and can be neglected. Thus, a matching resistor RL can be inserted between the transducer and the Op. Amp, as shown in Fig. 8(b), to make the equivalent load of the receiving transducer ZL ERL. It is worth mentioning that the RL inserted would make the ‘‘cable effect’’ no longer negligible, which violates the greatest advantage of the charge amplifier. However, as the cables connecting the circuits and the transducers can be considered inside the two-port network in the dashed box in Fig. 3, the effects brought by them would not violate the reciprocal operation of the system. 3.2.2. Circuit RvB: voltage amplifier Although voltage mode amplification is seldom used for piezoelectric sensors because of the cable effect, it is still a simple and effective method to specify the input impedance of the receiving circuit. A typical approach to fix the load of the receiving transducer is to apply a voltage follower, as shown in Fig. 9. In Fig. 9, the RL is an implemented resistor to set the load of the receiving transducer. As the input impedance of the non-inverting input pin of the Op. Amp can be considered infinite, the ZL can be considered equal to RL. 3.3. Impedance choice According to the theory described in Section 2, achieving ZS ¼ZL, namely RS ¼RL if the circuit designs shown in Figs. 6–9 are implemented, would approach the reciprocal operation of the measurement system. Since for both transmitting and receiving circuits, the equivalent loads for the transducer, namely ZS and ZL, can be fixed at any given value using circuit designs proposed above, it is necessary to discuss the resistance choice for RS(or RL). 3.3.1. For circuit RvA For both transmitting circuits TrA and TrB, a smaller RS leads to higher power transmission efficiency. For the circuit RvA, as it can
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Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
Fig. 8. (a) Charge amplifier (b) RvA: using charge amplifier to set ZL.
0.034 O, are the resistors representing the air backings of the transducers. The excitation signal is a 500 V voltage pulse which lasts 250 ns. The output voltage signals are obtained from the node noted ‘‘OUT’’, the load Rload is 1 MO. In Fig. 10(b), the ratio of the peak–peak amplitude Vp–p of each received signal and the pulse voltage Vpul when applying different RS( ¼RL) were plotted. As can be seen in the figure, the profile of the received amplitude versus RS( ¼RL) decreases slowly after the peak, which means the range of RS( ¼RL) that achieves ‘‘good sensitivity’’ is quite large. Comparing with the current-based amplification in circuit RvA, RvB would achieve better reciprocal operation when RS(or RL) is small, since the effect of non-ideal Op. Amp causes less impedance imbalance.
4. Practical experiments Fig. 9. RvB: using voltage follower to set ZL.
4.1. Experiment setup be seen as an inverting integrator, better sensitivity would also be achieved by a smaller RL. Choosing a small RS(or RL) would achieve better receiving amplitude. However, there would be also problems if RS and RL employed are too small. In practical circuit, such as those shown in Figs. 6–9, it should be actually considered that ZS0 ¼ RS þ eZS and ZL0 ¼RL þ eZL, in which eZS and eZL are the small impedance terms brought by some uncontrolled non-ideal components such as MOSFET and Op. Amps. If it is the non-ideal ZS0 and ZL0 considered instead of ZAS and ZAL in (6) or instead of ZBS and ZBL in (7), it would be concluded that higher RS(or RL) would bring TAT and TAR, or TBT and TBR closer, which would make signals received in both directions in (3) and (4) more identical. Therefore, when circuit RvA is used for receiving, the choice of the RS(or RL) is a trade-off between the receiving amplitude and the reciprocal operation of the system.
3.3.2. For circuit RvB In the voltage follower circuit RvB, larger RL would obviously achieve better receiving amplitude. As larger RS decreases the transmitting efficiency and the reciprocal operation of the system requires equal RS and RL, there would be an optimum choice for RS( ¼RL) to achieve the best receiving amplitude. Fig. 10 shows a SPICE(Simulation Program with Integrated Circuit Emphasis) simulation for the variation on received amplitude versus RS( ¼RL), in which an equivalent circuit model for ultrasonic system [12], as shown in Fig. 10(a), is used. In the simulation, both transducers are set as ideal 2 MHz PZT-5 thickness extensional circular disks without any coupling layer. The diameter of the transducers is 10 mm. The fluid in the simulation is set as pure water, of which the density and the sound speed are set as 1000 kg/m3 and 1470 m/s. The small RAirT and RAirR, set as
In order to verify the ‘‘pulse and fix’’ method, the circuit designs and the effects of the impedance choices, a number of experiments were taken under practical environment. The measurement pipeline used in the experiments was a PFA(Perfluoroalkoxy) pipe UCUF-4P [14] from TokyoKeiso, of which the length is 94 mm and the inner diameter is 4 mm. The transducers were attached face to face on the 3 mm PFA layers at both ends of the pipe. The total structure is the same as the pipe shown in Fig. 1. Three different types of transducers are used in the experiments. Type A is the PZT-5 piezoelectric ceramic disks with matching layers and heavy backing layers, which is originally used in the metering pipe products, Type B is the PZT-5 piezoelectric ceramic disks without any backing or matching layer, and Type C is the composite piezoelectric disk with 1 mm matching layer. All three types of transducers are circular disks working in the thickness extensional mode, the diameters of the disks are about 10 mm and the thickness was around 1 mm for Type A and B, 0.6 mm for Type C. The serial resonance frequencies of them are about 2 MHz for Type A and B, 2.5 MHz for Type C. For each type there are a pair of transducers with similar parameters, while between different types, the characteristics of the transducers are quite different. The transmitting and receiving circuit designs are tested with varieties of circuit combinations and RS(RL) choices. For each circuit setup, the signal waveforms received in both directions are sampled by a 40 Msps ADC(Analog-Digit Converter) and transferred to PC. The whole test system was made by the authors, in which the timing of signal transmission, receiving and sampling are controlled by an FPGA(Field programmable gate array) chip. The structure of the test system is shown in Fig. 11. The zero errors(ZE) of the transit-time difference, and the correlation coefficients(CC) calculated from waveforms acquired
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
11
Fig. 10. Simulation investigating received amplitude vs. RS(or RL) choice for circuit RvB (a) Simulation model and (b) Simulation results.
in both directions are calculated in the PC. The zero errors were calculated from the first 80 points of the received waveforms in both directions by the cross-correlation method; the parabolic interpolation method was used to enhance the precision. Smaller zero error indicates better reciprocal operation. The correlation coefficients Corr(U,D) were calculated by PN CorrðU,DÞ ¼ PN
i¼1
U i Di PN
i¼1
UiUi
i¼1
Di Di
1=2
ð8Þ
in which U and D are the sampling sequence of the total upstream and downstream waveforms. The coefficient is a number located between 1 and 1. The closer the CC is to 1, of better reciprocal operation is the system. All tests below were done when the fluid was still.
4.2. Experiment result 4.2.1. Verification of the circuit designs The proposed transmitting and receiving circuits TrA, TrB, RvA and RvB are combined to form measurement systems and tested on the measurement pipe with a pair of Type B transducers. The signal waveforms received in both directions were acquired to calculate both the zero error and the correlation coefficient. In the circuits designed for reciprocal operation, namely TrA, TrB, RvA and RvB, the RS and the RL are both set at 100 O. The VEX is set to 15 V in TrA and 12 V in TrB. The Rfb and Cint in the RvA circuit are around 4 kO and 20pf in the experiment. A reference circuit set disregarding the condition for reciprocal operation was also included in the experiment, in which the circuit in Fig. 5 with RS ¼18 O, VEX ¼15 V, was used as the transmitting circuit, and the circuit RvA with RL ¼100 O was used as the receiving circuit. In all experiments on these circuit sets, the controlling signal VCON is a single 15 V þ15 V pulse of 250 ns width; after the pulse, VCON fells back to and stays at 15 V. The received waveforms in both directions obtained from different circuit combinations are shown in Fig. 12, on which the upstream and downstream waveforms are respectively shown by the solid and dashed lines. The subplot denoted ‘‘Ref’’ shows the waveforms obtained from the reference circuit described above. The mean ZE and CC calculated from 100 waveform pairs are noted in the figure. The decrease of the zero flow error and the promotion on the accordance of the received waveforms brought by circuit designs can be seen comparing to the results and the waveforms obtained from the reference circuit set.
4.2.2. Reciprocal operation and pairing situation Both good and bad transducer pairing situations were tested using the reference circuit described above and the circuits proposed for reciprocal operation. The ‘‘good pairing’’ situation means using a pair of transducers of the same type and the ‘‘bad pairing’’ situation means using two transducers of different types to perform the measurement. The circuits used for reciprocal operation in the experiments were TrA and RvA with RS ¼RL ¼ 500 O. The excitation signal is a þ15 V single pulse with 250 ns width. For each combination of the pairing and the circuit, 100 upstream and downstream received signal pairs were acquired and calculated. The averaged ZE and CC of them are shown in Table 1. The correlation coefficients presented here are calculated by the averaged waveforms in each case, in order to prevent the influence caused by random noise. It can be seen from Table 1, the results of the zero flow error from the circuit combination of TrA and RvA are much smaller than the results from the reference circuit systems. The zero flow error in the ‘‘good pairing’’ situations are smaller than those in the ‘‘bad pairing’’ situations. The promotion on correlation coefficient is also obvious. The zero error of the TTD obtained when the same type of transducers are applied in Table 1 is no larger than 50 ps, for the metering pipe on which the experiment was taken, this would cause a flow velocity error less than 0.6 mm/s or a flow rate error less than 0.45 ml/min, which is much smaller than the nominated 8 ml/min of the product.
4.2.3. Impedance choice The effect of impedance choice in the circuit design was also tested on actual metering pipe by practical circuits. In these experiments, the transmitting circuit was circuit TrA, and the excitation signal was a single þ15 V pulse with 250 ns width. Both receiving circuits RvA and RvB were tested respectively with the transmitting circuit when different RS(or RL) were implemented. A pair of Type B transducers was used in the experiment. The actual measurement results of the receiving peak amplitude, the CC and the ZE calculated from the data acquired from circuit RvA and RvB are listed in Tables 2 and 3 respectively. Each data listed is the average of 40 measurement results, the ‘‘LSB’’ in the tables means ‘‘Least Significant Bit’’ of the sampling ADC used. It can be seen in Table 2, as the RS(or RL) increases, better zero error and correlation coefficient would be achieved, which means of better reciprocal operation the system is. However, at the mean time the amplitude of the received signal decreases significantly. When RS ¼RL ¼100 O, the received signal is merely 1/3 strong
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Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
Fig. 11. Structure of the test system.
Fig. 12. Waveforms and ZE, CC results from different circuit combinations.
Table 1 Mean ZE and CC of averaged waveforms in different transducer pairing situations. Transducers pairing Reference circuits
TrA/RvA
Zero error (ps) Corr. Coeff. Zero error (ps) Corr. Coeff. Type Type Type Type Type Type
A/A B/B C/C A/B A/C B/C
1804.6 208.72 5779.0 2189.7 2405.1 2437.7
0.9447 0.9992 0.9738 0.9807 0.9332 0.9838
49.66 22.31 20.82 196.07 233.43 298.91
0.9999 1.0000 0.9999 0.9999 0.9998 0.9999
Table 2 Measurement data from TrA/RvA. RS(¼RL) (Ohm)
Peak amplitude (LSB)
Zero error (ps)
Corr. Coeff.
0 10 25 50 75 100
255(saturated) 238 181.25 126.13 93 74.2
139.92 135.741 109.31 1.88 46.88 23.88
0.9877 0.9921 0.9954 0.9977 0.9983 0.9982
Table 3 Measurement data from TrA/RvB. RS(¼RL) (Ohm)
Peak amplitude (LSB)
Zero error (ps)
Corr. Coeff.
25 50 75 100 125 150 200 300 500 800 1000
132.24 190.20 205.98 210.86 206.88 198.08 180.44 151.56 109.60 76.12 65.76
15.22 48.86 83.51 61.01 89.54 90.92 51.06 64.98 42.16 34.44 53.60
0.99928 0.99964 0.99971 0.99974 0.99975 0.99974 0.99967 0.99959 0.99866 0.99787 0.99675
comparing with the situation when RS ¼RL ¼10 O, and the CC starts to fall due to the influence of the noise. The impedance choice when circuit RvA is implemented is a trade-off between reciprocal operation and the receiving SNR, and should be selected differently from case to case. As can be inferred from Table 3, the receiving circuit RvB can achieve low zero error and good correlation coefficient even the RS and RL are chosen very low. No obvious trend was found in the zero error as the RS(or RL) increases. The variation of the CC was small, and
Y. Bo, C. Li / Flow Measurement and Instrumentation 32 (2013) 5–13
was mainly due to the variation of the SNR. As can be seen in the table, there was an optimum RS(RL) choice for the receiving amplitude, which is around 100 O in the experiments. The trend of received amplitude fits completely with the analysis and the simulation.
5. Conclusion In ultrasonic flow meters using piezoelectric transducers as both the transmitter and receiver of the ultrasound signal, keeping the equivalent load of each transducer consistent between the transmitting and the receiving phase is a valid way to achieve reciprocal operation of the system and thus to suppress the zero error. By applying a short pulse excitation and fixing the transducer’s transmitting load ZS equal to its receiving load ZL during the ‘‘free oscillation’’ period, the ‘‘load consistency’’ condition can be approached in practical measurement circuit, regardless of the output impedance of the signal source. Circuit designs proposed in the paper can be used to achieve such condition, in which the equivalent load impedance of the transducers can be set flexibly to meet varieties of requirements. If the current amplifier as RvA proposed is implemented for receiving, the impedance choice is a trade-off between the signal amplitude and the reciprocal operation of the system, while if the voltage amplifier as RvB is implemented, the reciprocal operation would not be sensitive to the impedance choice, and there would be an optimum impedance choice to achieve the best receiving amplitude. Further works will be done mainly on the research of implementing variable or/and complex impedances in the measurement circuits, and developing the USM system in which the reciprocal operation can be self-adjusted.
Acknowledgment The authors are truly grateful to TokyoKeiso Co. Ltd. for their support.
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