Abstract:
A device for measurement of ultrasonic wave transit times of an ultrasonic flow sensor consists of: 1) a synchronization signal generator, 2) a reference pulse generator, 3) a sine wave generator, 4) an analog signal amplifier, 5) a comparator, 6) a plurality of latch circuits, 7) a digital adder, 8) an integrator, 9) an A/D converter, 10) a master counter, 11) a plurality of edge counters, and 12) an arithmetic circuit. The device measures the ultrasonic wave transit times using a method of averaging the ultrasonic wave arriving times at different measuring points (triggering point). This method has less dependency on triggering threshold level and the ultrasonic signal amplitude, and thus has less dependency on threshold drift, threshold stability, system gain fluctuation, electronic noise and signal amplitude variations. As a result, the method can greatly improve the velocity measurement accuracy and system robustness of an ultrasonic flow sensor.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Not Applicable. 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable. 
       REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISC APPENDIX 
       [0003]    Not Applicable. 
       FIELD OF THE INVENTION 
       [0004]    The present disclosure relates to a device for measuring ultrasonic wave transit times from the transmitter to the receiver of an ultrasonic flow sensor. 
       BACKGROUND OF THE INVENTION 
       [0005]    The statements in this section merely provide background information related to the present disclosure and may not constitute prior art. 
         [0006]    An ultrasonic flow sensor measures the average velocity of liquid or gaseous media by means of ultrasonic transducers based on the principle that the transit time of an ultrasonic wave from the transmitter of a transducer to the corresponding receiver is determined by the fluid velocity and the ultrasonic wave propagating direction. Normally, a pair of transducers is used, one is installed in upstream and the other is installed in downstream. Each transducer can be used as a transmitter or a receiver. One ultrasonic wave is transmitted from the upstream transducer to the downstream transducer. The second ultrasonic pulse is transmitted from the downstream transducer to the upstream transducer. The transit time in each direction is measured by an electronic device. The difference of the two transit-time data is proportional to flow velocity. It is then used to calculate the average flow velocity of the fluid. 
         [0007]    In conventional electronic devices of an ultrasonic flow sensor, the ultrasonic wave transit time is measured by a time counter to count a reference clock using the following method. 1) Sending ultrasonic pulse wave to the transmitter, starting the timer counter. 2) Monitoring the ultrasonic signal received by the receiver, when the received signal becomes higher than the predefined threshold value, immediately stopping the time counter, and recording the arriving time. This arriving time is treated as the transmit time. 
         [0008]    In the above approach, an analog integrator may be used to measure the residual time from the counter stopping moment to the rising edge of the next cycle of the reference clock. This residual time is then combined with the previous transit-time to obtain a transit-time with higher accuracy. 
         [0009]    However, this measurement method is susceptible to electronic noise and condition variation. Both the strength of the received signal and the predefined threshold value are subject to electronic noise. In addition, the strength of the received signal varies with the fluid properties such as temperature, velocity, turbulence, solids concentration, etc. As a result, the measured transit time changes not only with flow velocity, but with the fluid properties and electronic noise level. This significantly reduces the velocity measurement accuracy and stability of an ultrasonic flow sensor. 
       BRIEF SUMMARY OF THE INVENTION 
       [0010]    Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. 
         [0011]    The object of the present invention is to provide an electronic device which can accurately and reliably measure the transit times from the transmitter to the receiver and hence improving the velocity measurement accuracy of an ultrasonic flow sensor. 
         [0012]    In more detail the present invention provides an electronic device for measurement of ultrasonic wave transit times of an ultrasonic flow sensor consists of: 1) a synchronization signal generator, 2) a reference pulse generator, 3) a sine wave generator, 4) an analog signal amplifier, 5) a comparator, 6) a plurality of latch circuits, 7) a digital adder, 8) an integrator, 9) an A/D converter, 10) a master counter, 11) a plurality of edge counters, and 12) an arithmetic circuit (microprocessor). The device measures the ultrasonic wave transit times using a threshold level to trigger both the rising edge and falling edge of the received ultrasonic signal, and using a method of averaging the ultrasonic wave arriving times at different measuring points. This method has less dependency on the threshold level and the ultrasonic signal amplitude, thus, has less dependency on threshold drift, threshold stability, system gain fluctuation, electronic noise and signal amplitude variations. As a result, this method can greatly improve the velocity measurement accuracy and system robustness of an ultrasonic flow sensor. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0013]    The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way. 
           [0014]      FIG. 1  shows a block diagram of the first embodiment of a device for measurement of the ultrasonic wave transit times of the present disclosure. 
           [0015]      FIG. 2  shows the operational waveform diagram of the device shown in  FIG. 1 . 
           [0016]      FIG. 3(   a ) illustrates the transit time measurement error caused by the threshold fluctuation of prior art. 
           [0017]      FIG. 3(   b ) illustrates the transit time measurement error caused by the signal amplitude fluctuation of prior art. 
           [0018]      FIG. 4(   a ) illustrates the transit time measurement error reduction of the first embodiment of the present disclosure against threshold fluctuation interference. 
           [0019]      FIG. 4(   b ) illustrates the transit time measurement error reduction of the first embodiment of the present disclosure against signal amplitude fluctuation interference. 
           [0020]      FIG. 5  shows a block diagram of the second embodiment of a device for measurement of the ultrasonic wave transit times of the present disclosure. 
           [0021]      FIG. 6  shows the operational waveform diagram of the device shown in  FIG. 5 . 
           [0022]      FIG. 7(   a ) illustrates the transit time measurement error reduction of the second embodiment of the present disclosure against threshold level fluctuation interference. 
           [0023]      FIG. 7(   b ) illustrates the transit time measurement error reduction of the second embodiment of the present disclosure against signal amplitude fluctuation interference. 
           [0024]      FIG. 8  shows a block diagram of the third embodiment of a device for measurement of the ultrasonic wave transit times of the present disclosure. 
           [0025]      FIG. 9  shows the operational waveform diagram of the device shown in  FIG. 8 . 
           [0026]      FIG. 10  illustrates the transit time measurement error reduction of the third embodiment of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0027]    The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features. 
         [0028]      FIG. 1  illustrates the first embodiment of an electronic device for measuring the ultrasonic wave transit times of the present disclosure. In this first embodiment, the device  10  consists of a synchronization signal generator  20 , a reference pulse generator  30 , a sine wave generator  40 , an analog signal amplifier  60 , a comparator  70 , two latch circuits  80  and  81 , a digital adder  90 , an integrator  100 , an A/D converter  110 , a master pulse counter  120 , an edge counter  121 , and an arithmetic circuit  130 . 
         [0029]    Referring to  FIGS. 1 and 2 , the synchronization signal generator  20  outputs a pulse shown in  FIG. 2   a . This pulse is used to perform the following functions: 1) initiating the measurement cycle, 2) triggering the sine wave generator  40  to start sending sine wave signal to the transmitter of the ultrasonic flow sensor  50 , 3) triggering the reference pulse generator  30  to start generating high frequency clock signal, and 4) commanding the master counter  120  to start counting the reference pulses. 
         [0030]    Referring to  FIGS. 1 and 2 , after receiving the synchronization pulse, the reference pulse generator  30  starts sending high frequency clock signal to: 1) the master counter  120 , 2) the edge counter  121 , and 3) the two latch circuits  80 - 81 , as shown in  FIG. 2   e.    
         [0031]    Referring to  FIGS. 1 and 2 , after receiving the synchronization pulse, the sine wave generator  40  starts sending sine wave signals ( FIG. 2   b ) to the transmitter of the ultrasonic flow sensor  50 . After certain period of time delay, the sine wave signal arrives at the receiver of the ultrasonic flow sensor  50  with modulated amplitude, as shown in  FIG. 2   c.    
         [0032]    Referring to  FIGS. 1 and 2 , the AC-coupled analog signal amplifier  60  amplifies the output signal from the receiver of the ultrasonic flow sensor  50 . 
         [0033]    Referring to  FIGS. 1 and 2 , the comparator  70  compares the signal received from the analog signal amplifier  60  with the predefined threshold value. When the received signal becomes higher than the threshold value, it outputs a positive pulse. On the other hand, when the received signal becomes lower than the threshold value, it outputs a negative pulse, as shown in  FIG. 2   d.    
         [0034]    Referring to  FIGS. 1 and 2 , after receiving the positive pulse from the comparator  70 , the master counter  120  stops counting the reference clock, as shown in  FIG. 2   e . The time interval, C0, measured by the master counter  120  can be described by the equation: 
         [0000]        C 0 =NTr.    
         [0000]    Where N is the output of the mater counter  120 , Tr is the period of the reference clock. The master counter  120  can only count complete clock cycles, its output N is a positive integer number, any time less than one clock cycle will not be counted. 
         [0035]    Referring to  FIGS. 1 and 2 , after receiving the positive pulse from the comparator  70 , the edge counter  121  starts counting the reference pulses. After receiving the negative pulse from the comparator  70 , the edge counter  121  stops counting the pulses, as shown in  FIG. 2   e . The time interval, C1, measured by the edge counter  121  can be described by the equation: 
         [0000]        C 1 =N 1 Tr.    
         [0000]    Where N1 is the output of the first counter  121 . Similar to the master counter, the edge counter  121  can only count complete clock cycles, its output N1 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0036]    Referring to  FIGS. 1 and 2 , the latch circuit  80  is used to measure the time interval t1, between the positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  121 , as shown in  FIG. 2   f.    
         [0037]    Referring to  FIGS. 1 and 2 , the latch circuit  81  is used to measure the time interval t2, between the negative pulse from the comparator  70  and the next upward edge of the reference clock after the edge counter  121  is stopped, as shown in  FIG. 2   f.    
         [0038]    Referring to  FIG. 1 , the outputs of the latch circuits  80  and  81  are fed into the adder circuit  90 . They are added together, and then output to the integrator circuit  100 . 
         [0039]    Referring to  FIGS. 1 and 2 , since the t1 and t2 time intervals from the latch circuits  80  and  81  are very short, the integrator circuit  100  is used to convert these short pulses to analog exponential waves, as shown in  FIG. 2   g.    
         [0040]    Referring to  FIG. 1 , the analog signal from the integrator  100  is then converted to a digital value by the A/D converter  110 , and fed into the arithmetic circuit  130 . 
         [0041]    Referring to  FIG. 2 , the arriving time of the ultrasonic wave, T1, measured at the first measurement point P1, can be described by the equation: 
         [0000]        T 1 =C 0 −t 1 =NTr−t 1 
         [0042]    Referring to  FIG. 2 , the arriving time of the ultrasonic wave, T2, measured at the second measurement point P2, can be described by the equation: 
         [0000]        T 2 =C 0 +C 1 −t 2=( N+N 1) Tr−t 2. 
         [0043]    Referring to  FIG. 2 , the arithmetic circuit  130  calculates the ultrasonic wave transit time based on the following formula: 
         [0000]        Tm =( T 1 +T 2)/2 =NTr+N 1 Tr/ 2−( t 1 +t 2)/2.
 
         [0044]    Referring to  FIGS. 3(   a ) and ( b ), the ultrasonic wave transit time with prior art is based on the following formula: 
         [0000]        Tm=NTr−t 1.       Obviously, the transit-time Tm obtained by prior art differs from the one obtained by the first embodiment of the present disclosure by N1Tr/2. This difference does not have any impact on the flow measurement, because the flow rate is calculated based on transit-time difference between upstream Tm and downstream Tm. In addition, the difference can be calibrated so to have accurate transit-time measurement.         
         [0046]      FIG. 3  ( a ) illustrates the transit time measurement error caused by the threshold level fluctuation of prior art. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1|.
 
         [0047]      FIG. 3  ( b ) illustrates the transit time measurement error caused by signal amplitude fluctuation of prior art. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1|.
 
         [0048]      FIG. 4(   a ) illustrates the transit time measurement error caused by threshold fluctuation of the first embodiment of the present disclosure. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1 +Δt 2|/2.
 
         [0049]      FIG. 4(   b ) illustrates the transit time measurement error caused by signal amplitude fluctuation of the first embodiment of the present disclosure. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1 +Δt 2|/2.
 
         [0000]    It is noted from the  FIGS. 4(   a ) and ( b ) that Δt1 and Δt2 change in opposite direction in similar magnitude, when Δt1 increases, Δt2 decreases, and vice versa. i.e.: 
         [0000]      Δ t 1 ≈−Δt 2
 
         [0000]    As a result, their average, ΔTm, is always smaller than |Δt1|. In effect, 
         [0000]      Δ Tm≈ 0.
 
         [0000]    This indicates that the transit-time obtained by the present invention does not change with threshold drifting or signal amplitude variation. By contract, the transit-time obtained by prior art is sensitive to threshold drifting and signal amplitude variation. As a result of this, the transit time measurement accuracy and reliability are greatly improved by using the method of the present disclosure compared to the method of prior art. 
         [0050]      FIG. 5  illustrates the second embodiment of an electronic device for measuring the ultrasonic wave transit times of the present disclosure. In this second embodiment, the device  10  consists of a synchronization signal generator  20 , a reference pulse generator  30 , a sine wave generator  40 , an analog signal amplifier  60 , a comparator  70 , four latch circuits  80 - 83 , a digital adder  90 , an integrator  100 , an A/D converter  110 , a master counter  120 , three edge counters  121 - 123 , and an arithmetic circuit  130 . 
         [0051]    Referring to  FIGS. 5 and 6 , the synchronization signal generator  20  outputs a pulse shown in  FIG. 6   a . This pulse is used to perform the following functions: 1) initiating the measurement cycle, 2) triggering the sine wave generator  40  to start sending sine wave signal to the transmitter of the ultrasonic flow sensor  50 , 3) triggering the reference pulse generator  30  to start generating high frequency clock signal, and 4) commanding the master counter  120  to start counting the reference clock cycles. 
         [0052]    Referring to  FIGS. 5 and 6 , after receiving the synchronization pulse, the reference pulse generator  30  starts sending high frequency clock signal to: 1) the master counter  120 , 2) the edge counters  121 - 123 , and 3) the latch circuits  80 - 83 , as shown in  FIG. 6   e.    
         [0053]    Referring to  FIGS. 5 and 6 , after receiving the synchronization pulse, the sine wave generator  40  starts sending sine waves ( FIG. 6   b ) to the transmitter of the ultrasonic flow sensor  50 . After certain period of time delay, the sine wave signal arrives at the receiver of the flow meter with modulated amplitude, as shown in  FIG. 6   c.    
         [0054]    Referring to  FIGS. 5 and 6 , the AC-coupled analog signal amplifier  60  amplifies the output signal from the receiver of the ultrasonic flow sensor  50 . 
         [0055]    Referring to  FIGS. 5 and 6 , the comparator  70  compares the signal received from the analog signal amplifier  60  with the predefined threshold value. When the received signal becomes higher than the threshold value, it outputs a positive pulse. On the other hand, when the received signal becomes lower than the threshold value, it outputs a negative pulse, as shown in  FIG. 6   d.    
         [0056]    Referring to  FIGS. 5 and 6 , after receiving the positive pulse from the comparator  70 , the master counter  120  stops counting the reference clock, as shown in  FIG. 6   e . The time interval, C0, measured by the master counter  120  can be described by the equation: 
         [0000]        C 0 =NTr,    
         [0000]    where N is the output of the mater counter  120 , Tr is the period of the reference clock. The master counter  120  can only count complete clock cycles, its output N is a positive integer number, any time less than one clock cycle will not be counted. 
         [0057]    Referring to  FIGS. 5 and 6 , after receiving the first positive pulse from the comparator  70 , the edge counter  121  starts counting the reference clock. After receiving the first negative pulse from the comparator  70 , the edge counter  121  stops counting the clock, as shown in  FIG. 6   e . The time interval, C1, measured by the edge counter  121  can be described by the equation: 
         [0000]        C 1 =N 1 Tr,    
         [0000]    where N1 is the output of the counter  121 . Similar to the master counter  120 , the edge counter  121  can only count complete clock cycles, its output N1 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0058]    Referring to  FIGS. 5 and 6 , after receiving the first negative pulse from the comparator  70 , the edge counter  122  starts counting the reference clock. After receiving the second positive pulse from the comparator  70 , the edge counter  122  stops counting the clock, as shown in  FIG. 6   e . The time interval, C2, measured by the edge counter  122  can be described by the equation: 
         [0000]        C 2 =N 2 Tr,    
         [0000]    where N2 is the output of the counter  122 . Similar to the master counter  120 , the edge counter  122  can only count complete clock cycles, its output N2 is a positive integer number, any time less than one cycle pulse will not be counted. 
         [0059]    Referring to  FIGS. 5 and 6 , after receiving the second positive pulse from the comparator  70 , the edge counter  123  starts counting the reference clock. After receiving the second negative pulse from the comparator  70 , the edge counter  123  stops counting the reference clock, as shown in  FIG. 6   e . The time interval, C3, measured by the edge counter  123  can be described by the equation: 
         [0000]        C 3 =N 3 Tr,    
         [0000]    where N3 is the output of the counter  123 . Similar to the master counter  120 , the edge counter  123  can only count complete clock cycles, its output N3 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0060]    Referring to  FIGS. 5 and 6 , the latch circuit  80  is used to measure the time interval t1 between the first positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  121 , as shown in  FIG. 6   f . Since time interval t1 is less than one complete reference clock, it cannot be measured by the master counter  120 . 
         [0061]    Referring to  FIGS. 5 and 6 , the latch circuit  81  is used to measure the time interval t2 between the first negative pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  122 , as shown in  FIG. 6   f . Since time interval t2 is less than one complete reference clock, it cannot be measured by the edge counter  121 . 
         [0062]    Referring to  FIGS. 5 and 6 , the latch circuit  82  is used to measure the time interval t3 between the second positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  123 , as shown in  FIG. 6   f . Since time interval t3 is less than one complete reference clock, it cannot be measured by the edge counter  122 . 
         [0063]    Referring to  FIGS. 5 and 6 , the latch circuit  83  is used to measure the time interval t4 between the second negative pulse from the comparator  70  and the next upward edge of the reference clock after the edge counter  123  is stopped, as shown in  FIG. 6   f . Since time interval t4 is less than one complete reference clock, it cannot be measured by the edge counter  123 . 
         [0064]    Referring to  FIG. 5 , the outputs of latch circuits  80 - 83  are fed into the adder circuit  90 . They are added together and then output to the integrator circuit  100 . 
         [0065]    Referring to  FIGS. 5 and 6 , since the time intervals t1-t4 from the latch circuits  80 - 83  are very short, the integrator circuit  100  is used to convert these short pulses to triangular waves, as shown in  FIG. 2   g.    
         [0066]    Referring to  FIG. 5 , the analog signal from the integrator  100  is then converted to a digital value by the A/D converter  110 , and fed into the arithmetic circuit  130 . 
         [0067]    Referring to  FIG. 6 , the arriving time of the ultrasonic wave, T1, measured at the first measurement point P1, can be described by the equation: 
         [0000]        T 1 =C 0 −t 1 =NTr−t 1. 
         [0068]    Referring to  FIG. 6 , the arriving time of the ultrasonic wave, T2, measured at the second measurement point P2, can be described by the equation: 
         [0000]        T 2 =C 0 +C 1 −t 2=( N+N 1) Tr−t 2. 
         [0069]    Referring to  FIG. 6 , the arriving time of the ultrasonic wave, T3, measured at the third measurement point P3, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     3 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       3. 
                     
                   
                 
               
             
           
         
       
     
         [0070]    Referring to  FIG. 6 , the arriving time of the ultrasonic wave, T4, measured at the fourth measurement point P4, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     4 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       4 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       4 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       T 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                       t 
                        
                       
                           
                       
                        
                       3 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       4 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       4. 
                     
                   
                 
               
             
           
         
       
     
         [0071]    Referring to  FIG. 5 , the arithmetic circuit  130  calculates the ultrasonic wave transit time based on the following formula: 
         [0000]    
       
         
           
             
               
                 
                   Tm 
                   = 
                     
                    
                   
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               
                                 T 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                               + 
                               
                                 T 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             ) 
                           
                           / 
                           2 
                         
                         + 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     T 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                   + 
                                   
                                     T 
                                      
                                     
                                         
                                     
                                      
                                     4 
                                   
                                 
                                 ) 
                               
                               / 
                               2 
                             
                             - 
                             Tx 
                           
                           ) 
                         
                       
                       ] 
                     
                     / 
                     2 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     NTr 
                     + 
                     
                       T_ 
                        
                       123 
                     
                     - 
                     
                       
                         ( 
                         
                           
                             t 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                         ) 
                       
                       / 
                       4. 
                     
                   
                 
               
             
           
         
       
       
         
           
             Here Tx is the period of the received ultrasonic signal. The center of T3 and T4 is always one period away from the center of T1 and T2. T — 123 is expressed as following, 
           
         
       
     
         [0000]        T   — 123=(3 N 1+2 N 2 +N 3) Tr/ 4 −Tx/ 2. 
         [0073]      FIG. 7  illustrates the transit time measurement error of the second embodiment of the present disclosure. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1 +Δt 2 +Δt 3 +Δt 4|/4.
 
         [0000]    Since (Δt1, Δt2) and (Δt3, Δt4) change in opposite directions, their average is always smaller than |t1|. This indicates that the ultrasonic wave transit time measurement accuracy is greatly improved using the method of the present disclosure compared to the method of prior art. 
         [0074]      FIG. 8  illustrates the third embodiment of an electronic device for measuring the ultrasonic wave transit times of the present disclosure. In this embodiment, the device  10  consists of a synchronization signal generator  20 , a reference pulse generator  30 , a sine wave generator  40 , an analog signal amplifier  60 , a comparator  70 , eight latch circuits  80 - 87 , a digital adder  90 , an integrator  100 , an A/D converter  110 , a master counter  120 , seven edge counters  121 - 127 , and an arithmetic circuit  130 . 
         [0075]    Referring to  FIGS. 8 and 9 , the synchronization signal generator  20  outputs a pulse shown in  FIG. 9   a . This pulse is used to perform the following functions: 1) initiating the measurement cycle, 2) triggering the sine wave generator  40  to start sending sine wave signal to the transmitter of the ultrasonic flow sensor  50 , 3) triggering the reference pulse generator  30  to start generating high frequency clock signal, and 4) commanding the master counter  120  to start counting the reference clock cycles. 
         [0076]    Referring to  FIGS. 8 and 9 , after receiving the synchronization pulse, the reference pulse generator  30  starts sending high frequency clock signal to: 1) the master counter  120 , 2) the edge counters  121 - 127 , and 3) the latch circuits  80 - 87 , as shown in  FIG. 9   e.    
         [0077]    Referring to  FIGS. 8 and 9 , after receiving the synchronization pulse, the sine wave generator  40  starts sending sine wave signals ( FIG. 9   b ) to the transmitter of the ultrasonic flow sensor  50 . After certain period of time delay, the sine wave signal arrives at the receiver of the ultrasonic flow sensor  50  with modulated amplitude, as shown in  FIG. 9   c.    
         [0078]    Referring to  FIGS. 8 and 9 , the AC-coupled analog signal amplifier  60  amplifies the output signal from the receiver of the ultrasonic flow sensor  50 . 
         [0079]    Referring to  FIGS. 8 and 9 , the comparator  70  compares the signal received from the analog signal amplifier  60  with the predefined threshold value. When the received signal becomes higher than the threshold value, it outputs a positive pulse. On the other hand, when the received signal becomes lower than the threshold value, it outputs a negative pulse, as shown in  FIG. 9   d.    
         [0080]    Referring to  FIGS. 8 and 9 , after receiving the positive pulse from the comparator  70 , the master counter  120  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C0, measured by the master counter  120  can be described by the equation: 
         [0000]        C 0 =NTr,    
         [0000]    where N is the output of the mater counter  120 , Tr is the period of the reference clock. The master counter  120  can only count complete clock cycles, its output N is a positive integer number, any time less than one clock cycle will not be counted. 
         [0081]    Referring to  FIGS. 8 and 9 , after receiving the first positive pulse from the comparator  70 , the edge counter  121  starts counting the reference clock. After receiving the first negative pulse from the comparator  70 , the edge counter  121  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C1, measured by the edge counter  121  can be described by the equation: 
         [0000]        C 1 =N 1 Tr,    
         [0000]    where N1 is the output of the counter  121 . Similar to the master counter  120 , the edge counter  121  can only count complete clock cycles, its output N1 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0082]    Referring to  FIGS. 8 and 9 , after receiving the first negative pulse from the comparator  70 , the edge counter  122  starts counting the reference clock. After receiving the second positive pulse from the comparator  70 , the edge counter  122  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C2, measured by the edge counter  122  can be described by the equation: 
         [0000]        C 2 =N 2 Tr,    
         [0000]    where N2 is the output of the counter  122 . Similar to the master counter  120 , the edge counter  122  can only count complete clock cycles, its output N2 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0083]    Referring to  FIGS. 8 and 9 , after receiving the second positive pulse from the comparator  70 , the edge counter  123  starts counting the reference clock. After receiving the second negative pulse from the comparator  70 , the edge counter  123  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C3, measured by the edge counter  123  can be described by the equation: 
         [0000]        C 3 =N 3 Tr,    
         [0000]    where N3 is the output of the counter  123 . Similar to the master counter  120 , the edge counter  123  can only count complete clock cycles, its output N3 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0084]    Referring to  FIGS. 8 and 9 , after receiving the second negative pulse from the comparator  70 , the edge counter  124  starts counting the reference clock. After receiving the third positive pulse from the comparator  70 , the edge counter  124  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C4, measured by the edge counter  124  can be described by the equation: 
         [0000]        C 4 =N 4 Tr,    
         [0000]    where N4 is the output of the counter  124 . Similar to the master counter  120 , the edge counter  124  can only count complete clock cycles, its output N4 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0085]    Referring to  FIGS. 8 and 9 , after receiving the third positive pulse from the comparator  70 , the edge counter  125  starts counting the reference clock. After receiving the third negative pulse from the comparator  70 , the edge counter  125  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C5, measured by the edge counter  125  can be described by the equation: 
         [0000]        C 5 =N 5 Tr,    
         [0000]    where N5 is the output of the counter  125 . Similar to the master counter  120 , the edge counter  125  can only count complete clock cycles, its output N5 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0086]    Referring to  FIGS. 8 and 9 , after receiving the third negative pulse from the comparator  70 , the edge counter  126  starts counting the reference clock. After receiving the fourth positive pulse from the comparator  70 , the edge counter  126  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C6, measured by the edge counter  126  can be described by the equation: 
         [0000]        C 6 =N 6 Tr,    
         [0000]    where N6 is the output of the counter  126 . Similar to the master counter  120 , the edge counter  126  can only count complete clock cycles, its output N6 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0087]    Referring to  FIGS. 8 and 9 , after receiving the fourth positive pulse from the comparator  70 , the edge counter  127  starts counting the reference clock. After receiving the fourth negative pulse from the comparator  70 , the edge counter  127  stops counting the reference clock, as shown in  FIG. 9   e . The time interval, C7, measured by the edge counter  127  can be described by the equation: 
         [0000]        C 7 =N 7 Tr,    
         [0000]    where N7 is the output of the counter  127 . Similar to the master counter  120 , the edge counter  127  can only count complete clock cycles, its output N7 is a positive integer number, any time less than one clock cycle will not be counted. 
         [0088]    Referring to  FIGS. 8 and 9 , the latch circuit  80  is used to measure the time interval t1 between the first positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  121 , as shown in  FIG. 9   f . Since time interval t1 is less than one complete reference clock, it cannot be measured by the master counter  120 . 
         [0089]    Referring to  FIGS. 8 and 9 , the latch circuit  81  is used to measure the time interval t2 between the first negative pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  122 , as shown in  FIG. 9   f . Since time interval t2 is less than one complete reference clock, it cannot be measured by the edge counter  121 . 
         [0090]    Referring to  FIGS. 8 and 9 , the latch circuit  82  is used to measure the time interval t3 between the second positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  123 , as shown in  FIG. 9   f . Since time interval t3 is less than one complete reference clock, it cannot be measured by the edge counter  122 . 
         [0091]    Referring to  FIGS. 8 and 9 , the latch circuit  83  is used to measure the time interval t4 between the second negative pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  124 , as shown in  FIG. 9   f . Since time interval t4 is less than one complete reference clock, it cannot be measured by the edge counter  123 . 
         [0092]    Referring to  FIGS. 8 and 9 , the latch circuit  84  is used to measure the time interval t5 between the third positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  125 , as shown in  FIG. 9   f . Since time interval t5 is less than one complete reference clock, it cannot be measured by the edge counter  124 . 
         [0093]    Referring to  FIGS. 8 and 9 , the latch circuit  85  is used to measure the time interval t6 between the third negative pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  126 , as shown in  FIG. 9   f . Since time interval t6 is less than one complete reference clock, it cannot be measured by the edge counter  125 . 
         [0094]    Referring to  FIGS. 8 and 9 , the latch circuit  86  is used to measure the time interval t7 between the fourth positive pulse from the comparator  70  and the first upward edge of the reference clock fed into the edge counter  127 , as shown in  FIG. 9   f . Since time interval t7 is less than one complete reference clock, it cannot be measured by the edge counter  126 . 
         [0095]    Referring to  FIGS. 8 and 9 , the latch circuit  87  is used to measure the time interval t8 between the fourth negative pulse from the comparator  70  and the upward edge of the next reference clock after the edge counter  127  is stopped, as shown in  FIG. 9   f . Since time interval t8 is less than one complete reference clock, it cannot be measured by the edge counter  127 . 
         [0096]    Referring to  FIG. 8 , the outputs of the latch circuits  80 - 87  are fed into the adder circuit  90 . They are added together and then output to the integrator circuit  100 . 
         [0097]    Referring to  FIGS. 8 and 9 , since the time intervals t1-t8 from the latch circuits  80 - 87  are short pulses, the integrator circuit  100  is used to convert these short pulses to triangular waves, as shown in  FIG. 9   g.    
         [0098]    Referring to  FIG. 8 , the analog signal from the integrator  100  is then converted to a digital value by the A/D converter  110 , and fed into the arithmetic circuit  130 . 
         [0099]    Referring to  FIG. 9 , the arriving time of the ultrasonic wave, T1, measured at the first measurement point P1, can be described by the equation: 
         [0000]        T 1 =C 0 −t 1 =NTr−t 1. 
         [0100]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T2, measured at the second measurement point P2, can be described by the equation: 
         [0000]        T 2 =C 0 +C 1 −t 2=( N+N 1) Tr−t 2. 
         [0101]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T3, measured at the third measurement point P3, can be described by the equation: 
         [0000]        T 3 =C 0 +C 1 +C 2 −t 3=( N+N 1 +N 2) Tr−t 3. 
         [0102]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T4, measured at the fourth measurement point P4, can be described by the equation: 
         [0000]        T 4 =C 0 +C 1 +C 2 +C 3 −t 4=( N+N 1 +N 2 +N 3) Tr−t 4. 
         [0103]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T5, measured at the fourth measurement point P5, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     5 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       4 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       5 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             4 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       5. 
                     
                   
                 
               
             
           
         
       
     
         [0104]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T6, measured at the fourth measurement point P6, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     6 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       4 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       5 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       6 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             4 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             5 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       6. 
                     
                   
                 
               
             
           
         
       
     
         [0105]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T7, measured at the fourth measurement point P7, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     7 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       4 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       5 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       6 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       7 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             4 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             5 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             6 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       7. 
                     
                   
                 
               
             
           
         
       
     
         [0106]    Referring to  FIG. 9 , The arriving time of the ultrasonic wave, T8, measured at the fourth measurement point P8, can be described by the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                         
                     
                      
                     8 
                   
                   = 
                     
                    
                   
                     
                       C 
                        
                       
                           
                       
                        
                       0 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                     + 
                     
                         
                     
                      
                     
                       C 
                        
                       
                           
                       
                        
                       3 
                     
                     + 
                     
                         
                     
                      
                     
                       C 
                        
                       
                           
                       
                        
                       4 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       5 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       6 
                     
                     + 
                     
                       C 
                        
                       
                           
                       
                        
                       7 
                     
                     - 
                     
                         
                     
                      
                     
                       t 
                        
                       
                           
                       
                        
                       8 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             4 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             5 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             6 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             7 
                           
                         
                         ) 
                       
                        
                       Tr 
                     
                     - 
                     
                       t 
                        
                       
                           
                       
                        
                       8. 
                     
                   
                 
               
             
           
         
       
     
         [0107]    Referring to  FIG. 8 , the arithmetic circuit  130  calculates the ultrasonic wave transit time based on the following formula: 
         [0000]    
       
         
           
             
               
                 
                   Tm 
                   = 
                     
                    
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                     + 
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 2 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                     + 
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 2 
                               
                               - 
                               Tx 
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                     + 
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 2 
                               
                               - 
                               
                                 2 
                                  
                                 Tx 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                     + 
                                     
                                       T 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 2 
                               
                               - 
                               
                                 3 
                                  
                                 Tx 
                               
                             
                           
                         
                       
                       ] 
                     
                     4 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           N 
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             4 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             5 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             6 
                           
                           + 
                           
                             N 
                              
                             
                                 
                             
                              
                             7 
                           
                         
                         ) 
                       
                       / 
                       8 
                     
                     - 
                     
                       1.5 
                        
                       Tx 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     NTr 
                     + 
                     
                       T_ 
                        
                       1 
                        
                       _ 
                        
                       8 
                     
                     - 
                     
                       
                         ( 
                         
                           
                             t 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             2 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             3 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             4 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             5 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             6 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             7 
                           
                           + 
                           
                             t 
                              
                             
                                 
                             
                              
                             8 
                           
                         
                         ) 
                       
                       / 
                       8. 
                     
                   
                 
               
             
           
         
       
     
         [0108]    Here Tx is the period of the received ultrasonic signal. The center of T3 and T4 is always one period away from the center of T1 and T2. Similarly, the center of T5 and T6 is always one period away from the center of T3 and T4, and etc. The term T — 1 — 8 can be expressed as follows, 
         [0000]        T   — 1 — 8=(7 N 1+6 N 2+5 N 3+4 N 4+3 N 5+2 N 6 +N 7) Tr/ 8−1.5 Tx.  
 
         [0109]      FIG. 10  illustrates the transit time measurement error of the third embodiment of the present disclosure. In this case the time measurement error is: 
         [0000]      Δ Tm=|Δt 1 +Δt 2 +Δt 3 +Δt 4 +Δt 5 +Δt 6 +Δt 7 +Δt 8|/8.
 
         [0110]    (Δt1, Δt2), (Δt3, Δt4), (Δt5, Δt6), and (Δt7, Δt8) change in opposite directions. As a result, their average is always smaller than |Δt1|. In effect, ΔTm≈0. This indicates that the ultrasonic wave transit time measurement accuracy is greatly improved using the method of the present disclosure compared to the method of prior art. 
         [0111]    Noise in the received signal could cause threshold triggering error, thus, cause transit time measurement error. However, with multiple triggering mechanisms as illustrated in  FIGS. 7 and 10 , the transit times obtained at each triggering point are averaged to provide a result with reduced error. This not only makes the whole system more robust, but also improves the transit-time measurement accuracy, thus, the flow velocity accuracy, significantly.