High Precision Measurement For Ultrasonic Wave Transmission Time Based On FFT

Ultrasonic technology has been widely used in the measurement of velocity in solid,liquid and gas. In fact, the measurement of speeds of waves is composed of the measurementof acoustic transmission time (time of waves) and acoustic transmission distance (distance ofwaves), usually, the distance of waves is a known quantity, so the measurement of the speedsof waves is just the measurement of time of the waves. When the distance is unknown, thevelocity is known, and the measurement of the distance is actually the measurement oftransmission time of waves. So the study on the transmission time has important significanceto improve the precision of the measurement of ultrasonic velocity, ultrasonic ranging, gasconcentration detection and other applications.Counting is usually used in the traditional measurement of time, but the method ofcounting has the problem that the starting of waveform can not be determined leading toinaccurate result, and1count quantization error is existed. When the frequency ofmeasured signal is higher, the requirements of the circuit are also higher, and general chip forcounting is hard to work normally, thereby the cost of hardware is great increasing. Themethod for high precision measuring transmission time based on phase difference has lowhardware cost and high precision, without counting. Usually there is Gauss noise in thetransmission of waves. To estimate the ultrasonic transmission time accurately under thebackground of white Gaussian noise, the influence of A/D quantizing error was consideredbased on that traditional phase difference measurement only considered the error in the resultof Gaussian noise. Using error theory, the sine signal A/D quantizing error was deduced, andthe final root mean square (RMS) formula of total error of the phase difference was presented,The error of transmission time under specific distance was obtained by using the relationshipof time and phase difference. For the two cases that the ultrasonic frequency was known andknown, the method of phase difference based on fast Fourier transform (FFT) and the methodof phase difference based on all phase FFT (apFFT) were analyzed and compared with. Toavoid the interference of circuit and sensors, the double homologous sine sending signals withdifferent transmission distance was used.Theoretical analysis and simulation results showed that, when signal frequency wasknown, the phase difference based on FFT had a good result. When signal frequency was40kHz, Signal Noise Ratio (SNR) was25dB, sampling points was2048,A/D bits were11bitsand the sampling rate was200kHz, the error of the measurement of transmission time wasless than10ns. When signal frequency was unknown, the phase difference based on apFFThad a good result. On the platform of FPGA hardware, program with Quartus II to realize the measurementof transmission time of real-time ultrasonic waves. Compared with the simulation results, thereal-time results showed that phase difference method based on FFT and phase differencemethod based on all phase FFT could reach very high precision. When signal frequency wasknown, the phase difference based on FFT had a good result. When signal frequency wasunknown, the phase difference based on apFFT had a good result.