# EETE OCT 2014

ANALOGUE DESIGN Measuring the accuracy of an ultrasonic heat meter with the MAX35101 By Jim Mitrosky Simulation and corelation of flow-rate measurement in an ultrasonic heat-meter design is critical to the success of the heat-meter development process. Flow-rate measurement provides the designer with beneficial insight into the entitled accuracy of the heat-meter system measurement electronics, as well as a means of developing the individual product specifications. Without the knowledge of an expected level of performance for the electronic system used to measure the time-of-flight acoustic path in the meter spool body, the designer would be only guessing at the potential performance limits of the design. Once the simulations are completed, the meter’s actual flow-rate accuracy can be measured using the MAX35101 Time-to-Digital Converter with Analog Front-End (AFE) and matching piezoelectric transducers mounted in a spool body with the same dimensions as those used in the simulation model. Ultrasonic Time-of-Flight flow-measurement principle A typical ultrasonic time-of-flight heat-meter spool body is depicted in figure 1. Fig. 1: Typical ultrasonic time-of-flight heat meter spool body. The dimensions L and D are unique for every pipe size. The arrangement of the reflector surfaces within the flow spool body is also unique to every meter manufacturer. Consequently, the ultrasonic time-of-flight principle is based upon the time-offlight of an acoustic signal in the water. The upstream time-offlight is longer than the downstream time-of-flight, since the water velocity aids the acoustic signal in the downstream direction and impedes the acoustic signal in the upstream direction. This difference in time-of-flight can be exploited to determine the velocity of the flowing water. The acoustic time-of-flight of an ultrasonic signal in the downstream direction is: ����!!! =   ����/2 ����! ����/2 ����! + ���� + (����! + ����) + ����/2 ����!                            (��������. 1) ����!!! =   The acoustic time-of-flight of an ultrasonic signal in the upstream ����!!! =   ����/2 ����! + ���� ����! − ���� + ����/2 ����!                            (��������.    2) Where: C_O is the speed of sound in water ! ! ! 44 Electronic Engineering Times Europe October 2014 www.electronics-eetimes.com ���� =     (����!!! − ����!!!) ∗ ����! 2 ∗ ���� !  (��������. 3) direction is: ���� (����! + ����) + ����/2 ����!                            (��������. 1) ����!!! =   ����/2 ����! + ���� ����! − ���� + ����/2 ����!                            (��������.    2) ���� =     (����!!! − ����!!!) ∗ ����! 2 ∗ ����  (��������. 3) v is the velocity of the water Subtracting Equation 2 from Equation 1 and simplifying the results, followed then by solving for v, yields the velocity of the water: ����!!! =   ����/2 ����! + ���� (����! + ����) + ����/2 ����!                            (��������. 1) ����!!! =   ����/2 ����! + ���� ����! − ���� + ����/2 ����!                            (��������.    2) ���� =     (����!!! − ����!!!) ∗ ����! 2 ∗ ����  (��������. 3) ����! =  ���� ∗ ���� ∗ ����! 4                              (��������. 4) The volumetric flow of the water is then simply calculated with knowledge of the cross-sectional area of the flow diameter of the spool body: ����!!! =   ����/2 ����! + ���� (����! + ����) + ����/2 ����!                            (��������. 1) ����!!! =   ����/2 ����! + ���� ����! − ���� + ����/2 ����!                            (��������.    2) ���� =     (����!!! − ����!!!) ∗ ����! 2 ∗ ����  (��������. 3) ����! =  ���� ∗ ���� ∗ ����! 4                              (��������. 4) This volumetric flow-rate measurement is the basis for determining the flow rate in a heat-meter system. Flow-rate simulation of a typical ultrasonic ToF heat meter Using a spreadsheet, the time-of-flight can be calculated and then converted to a volumetric flow rate using Equations 1 through 4. By simulating the time-to-digital converter electronics error of the time-of-flight measurement of the acoustic wave, plots of the entitled accuracy of the system can be created. Note that Equation 3 shows a dependency on the speed of sound in water, where C_Ois dependent upon the temperature of the water. Accurate temperature measurement of the water flow is needed by the heat meter so it can compute the energy consumed. If we assume that the water temperature is +70°C and can be measured accurately, the plot for the simulated flow rate for the typical ultrasonic time-of-flight heat meter shown above is depicted in figure 2. Notice from the plot of figure 2 that the simulated flow-rate accuracy, using the delta-time accuracy of the MAX35101 of 20ps Jim Mitrosky is a Principal Member of Technical Staff at Maxim Integrated - www.maximintegrated.com Fig. 2: Simulated flow-rate accuracy of the typical ultrasonic time-of-flight heatmeter spool body. Fig. 3: Block diagram of the MAX35101 time-to-digital converter with analog front-end.

EETE OCT 2014