TDC7200_15 Datasheet, PDF (37/50 Pages) Texas Instruments – TDC7200 Time-to-Digital Converter for Time-of-Flight Applications in LIDAR,Magnetostrictive and Flow Meters

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TDC7200
SNAS647C – FEBRUARY 2015 – REVISED AUGUST 2015
9.2.2.2 Transmit Time in Ultrasonic Flow Meters
Transit-time ultrasonic flow meters works based on the principle that sound waves in a moving fluid travel faster
in the direction of flow (downstream), and slower in the opposite direction of flow (upstream).
The system requires at least two transducers. The first transducer operates as a transmitter during the upstream
cycle and as a receiver during the downstream cycle, and the second transducer operates as a receiver during
the upstream cycle and as a transmitter during the downstream cycle. An ultrasonic flow meter operates by
alternating transmit and receive cycles between the pair of transducers and accurately measuring the time-of-
flight both directions.
In this example, the upstream TOF is defined as:
H
P_$# = _{:? . R;}
where
• l is the path length between the two transducers in meters (m)
• c is the speed of sound in water in meters per second (m/s)
• v is the velocity of the water in the pipe in meters per second (m/s)
(4)
In this example, the downstream TOF is defined as:
where
• l is the path length between the two transducers in meters (m)
• c is the speed of sound in water in meters per second (m/s)
• v is the velocity of the water in the pipe in meters per second (m/s)
(5)
The difference of TOF is defined as:
¿$ = 2_ . 2_
where
• t_BA is the upstream TOF from transducer B to transducer A in seconds (s)
• t_AB is the downstream TOF from transducer A to transducer B in seconds (s)
(6)
After the difference in time-of-flight (ΔTOF) is calculated, the water velocity inside the pipe can be related to the
ΔTOF using the following equation:
¿61( × ?²
R=
2×H
where
• c is the speed of sound in water in meters per second (m/s)
• l is the path length between the two transducers in meters (m)
(7)
Finally, the mass flow rate can be calculated as follows:
! = /×4×
where
• k is the flow-meter constant
• v is the velocity of the water in the pipe in meters per second (m/s)
• A is the cross-section area of the pipe in meters-squared (m²)
(8)
9.2.2.3 ΔTOF Accuracy Requirement Calculation
Based on the minimum mass flow requirement and accuracy requirements in Table 25, the ΔTOF accuracy
needed can be calculated as follows:
1. Convert the mass flow rate to m³/s:
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