## 3 Results and Discussion
### Measurements and Discussion
The measured noise floor of the accumulated waveform is around 82 least-significant bits (LSBs). Therefore, the root-mean-square (RMS) value of noise for one ensemble is estimated to be around 5.3 LSBs. As mentioned before, the waveform of accumulated ensemble differences is fed into a BPF. The output waveform of the BPF output is illustrated in Figure 18a. As shown in Figure 18a, the DC component along with low-frequency components are sufficiently removed. By applying the BPF output into a hysteresis comparator, as shown in Figure 8, the signal _Range gate_ is generated, as shown in Figure 18b. The middle focal-depth value, which corresponds to the middle time point of high duration of the _Range gate_ signal, is utilized to sort out Doppler sample volumes. Figure 19a illustrates the measured Doppler sample volumes. This waveform was acquired by resampling ensembles at the focal-depth value, which corresponds to the middle time point of high duration of the _Range gate_ signal. A spectrum of Doppler sample is shown in Figure 19b. The spectrum has a peak power at a frequency of 82.4 Hz, and most of the signal powers are concentrated in the vicinity of 82.4 Hz. Considering relevant parameters, such as the fluid velocity of 6 cm/s, center frequency of 2 MHz, angle of 60\({}^{\circ}\), and speed of sound of 1540 m/s, the expected Doppler shift frequency is 79 Hz. Thus, the measured peak-power frequency shows a good agreement with the theoretical Doppler shift frequency. Figure 16: Flow phantom model. Figure 17: Measured digital waveforms using flow phantom model: (**a**) ensemble signal with index 0, (**b**) ensemble signal with index 1, and (**c**) accumulated ensemble differences, \(\sum|E_{\text{N}}-E_{\text{N}-1}|\). Figure 18: Measured (**a**) band-pass filter output for accumulated ensemble differences, and (**b**) _Rangegate_ signal from the flow phantom model. To evaluate the performance of the proposed circuit system, this work established an experimental environment that can arbitrarily control a fluid velocity. Figure 20a shows the measured arbitrary supply voltage waveform applied to the water pump. This signal was generated using an arbitrary waveform generator (AFG31102, Tektronix, Beaverton, OR, USA) and was supplied to the water pump through an analog buffer implemented with discrete commercial chips. The water pump regulates the fluid flow rate depending on the magnitude of the supply voltage. Figure 20b shows the Doppler data obtained with the range gate allocated by the automatic range-gate-positioning scheme. The oscillation components in the measured waveform are consistently observed, and this reflects that the position of the range gate is maintained stably. Figure 20c illustrates the recovered spectrogram. The dominant velocity profile of the spectrogram in Figure 20c shows good agreement with the profile of the supply-voltage waveform of the water pump. A comparison of automatic vessel detection methods is presented in Table 2. There are several relevant works [16; 29; 30], including single-element-based systems and array-based systems. In addition, the image-based algorithm shown in Table 2 can be applied to single-scanline data by elaborating its primary concept. The previous works of [16; 29; 30] are based on recognition of specific patterns in either A-mode or B-mode. Therefore, those works are dedicated to tracking specific target vessels. On the other hand, the proposed system has a concept of monitoring Doppler amplitude deviation. Thus, it can detect a low-resistance arbitrary vessel. In addition, since the proposed system can detect a vessel regardless of the time-domain echo aliasing, the center frequency can be lowered by considering the hardware implementation. Figure 19: Measured (**a**) Doppler sample volume and (**b**) spectrum from the flow phantom model. The utilized center frequency of 2 MHz corresponds to an almost-lowest boundary of the feasible center frequency in the Doppler mode of ultrasound devices.