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Microsystem Technologies

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Open Access 08-02-2018 | Technical Paper

Investigation and analysis of the influence of excitation signal on radiation characteristics of capacitive micromachined ultrasonic transducer

Authors: Hongliang Wang, Xiangjun Wang, Changde He, Chenyang Xue

Published in: Microsystem Technologies | Issue 7/2018

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Abstract

CMUT based on micro-electro-mechanical systems technology has a significant advantage that traditional piezoelectric ultrasonic transducers do not have, and has become the mainstream transducer for the new generation of ultrasound imaging systems. In this paper, the state equation is deduced and the analysis model is established in SIMULINK environment based on the lumped parameter system model of the CMUT micro-unit. Through the state equation-SIMULINK model, the influence of the parameters such as the DC bias voltage, the amplitude, frequency and period number of the AC excitation signal on the radiation characteristics is analyzed comprehensively. These results provide the important theoretical basis and reference for further optimization of structural design and application testing in the future.

1 Introduction

Compared with traditional piezoelectric ultrasonic transducers, The CMUT has significant advantages in improving bandwidth, improving imaging resolution, reducing size, reducing costs, achieving mass production and so on (Oralkan et al. 2002; Fouan and Bouakaz 2016; Sautto et al. 2017; Greenlay and Zemp 2017; Wang et al. 2014). And it has a broad application prospects in 3D medical ultrasound imaging (Bhuyan et al. 2013), intracardiac ultrasound detection (ICUS) (Nikoozadeh et al. 2009), intravascular ultrasound detection (IVUS) (Levent Degertekin et al. 2006), tissue harmonic imaging (THI) (Legros et al. 2011), high intensity focused ultrasound (HIFU) treatment (Wong et al. 2007). More and more research institutions and companies in the world are carrying out the relevant research work.

As one of the key components of the ultrasound imaging system, the performance of the CMUT directly affects the quality of ultrasound imaging. And the performance of the internal CMUT micro-unit has a direct impact on the performance of the CMUT. In order to develop a CMUT that has good performance, the analysis of the CMUT characteristics is a very necessary part before processing, which can provide a basis for further optimization of design parameters. In the analysis of the characteristics, it is necessary to analyze the characteristics of the CMUT micro-unit from electrics, mechanics, acoustics and so on, and to consider various factors to obtain relatively optimized design parameters. There are many ways to analyze the characteristics of the CMUT micro-unit. At present, the common analysis models includes the equivalent circuit model (Lohfink and Eccardt 2005), the finite element analysis model (Yaralioglu et al. 2005), the finite difference model (Certon et al. 2005) and so on. These models make various analyses of the CMUT micro-unit with different analytic methods, which are with their own characteristics.

The initial equivalent circuit model was the small signal equivalent circuit model. It was the model that based on Mason’s Equivalent Circuit Theory, which was the linearization of the plate capacitance model through the equivalent parameters of the lumped parameter system (Ladabaum et al. 1998). Then many scholars improved it, and the nonlinear equivalent circuit model and the large signal equivalent circuit model appeared (Koymen et al. 2012). The finite element analysis model can create 2D or 3D finite element models for vibrating films of any complex shape to obtain optimized design parameters by analysis and calculation, which is usually through ANSYS, COMSOL and other professional finite element analysis software. When the CMUT that contains many micro-units takes the finite element analysis model, the calculation process will be very time-consuming, which makes the simulation analysis and optimization design cycle longer (Satir et al. 2013). The finite difference model reduces the analysis time through thin plate theory and boundary element method. However, the current finite difference model cannot analyze the nonlinearity of CMUT micro-units, and not for large signals as well. Only the small signal linear model can be accurately analyzed (Satir et al. 2013).

In order to quickly and effectively analyze the characteristics of CMUT micro-units, The state equation of the system and its analysis model in the SIMULINK environment, which is called the state equation-SIMULINK model, are established in this paper by using the equivalent parameters of the lumped parameter system, which is based on the CMUT lumped parameter system model. The model can be analyzed for small signal models and can be analyzed for large signal models. The model can analyze both the small signal model and the large signal model. Then, a full range of the radiation characteristic analysis of CMUT micro-units is carried out by using the state equation-SIMULINK model established in this paper, and the influence of different input excitation signals on the radiation characteristics is studied and analyzed. These results provide an important theoretical reference for CMUT structural optimization design and application testing in the future.

2 The structure of the CMUT micro-unit and lumped parameter system model

In general, the small vibration unit (referred to as micro-unit) that makes up the CMUT is usually composed of a metal upper electrode, a diaphragm, an edge support, a cavity, an insulating layer, a lower electrode and a base. The diaphragm is usually designed in circular, square, hexagonal and other regular shapes. Figure 1 shows the structure of the micro-unit with the circular diaphragm. In the figure, r_e is the radius of the upper electrode, r_m is the radius of the vibrating film, t_e is the thickness of the upper and lower electrodes, t_m is the thickness of the vibrating film, t_g is the height of the cavity, and t_i is the thickness of the insulating layer. Table 1 shows the main structure parameters of the CMUT micro-unit designed in this paper. Simultaneously, we find it that its natural frequency in air and water were 1.642 MHz and 628 kHz, respectively, after model and analyze it through the COMSOL software.

Table 1

Main design parameters of the CMUT micro-unit

Structure unit	Design parameters
Structure unit	Radius (μm)	Thickness/height (μm)	Materials	Young modulus (GPa)	Poisson’s ratio	Density (kg/m³)
Film	90	3	Si	169	0.299	2332
Electrode	45	0.2	Al	70	0.350	2700
Insulating layer	90	0.1	SiO₂	72	0.170	2200
Cavity	85	0.7	Vacuum

For the structure of the CMUT micro-unit shown in Fig. 1, it can be described and analyzed by the lumped parameter system model consisting of a mass block, a spring and a damper as shown in Fig. 2. In the lumped parameter system model, the equivalent mass is M, the elasticity coefficient is K, the resistance coefficient is R, the displacement of the vibration film is w, and the external force acting on the CMUT micro-unit is F. The vibration equation as shown in Formula (1) is obtained based on Newton’s second law. The calculation method of the equivalent mass M, the elastic coefficient K and the resistance coefficient R is described and illustrated in detail in literature (Wygant et al. 2008), so no more details here.

$$ M\frac{{d^{2} w}}{{dt^{2} }} + R\frac{dw}{dt} + Kw = F. $$

(1)

3 The state equation-SIMULINK model of the CMUT in radiation state

In fact, the lumped parameter system shown in Fig. 2 is a nonlinear system. Due to the nonlinearity of the electrostatic force F_e, the system state equation can be deduced based on Formula (1), and the system is built in SIMULINK environment, and then the system simulation and analysis are carried out directly to obtain more accurate analysis results.

When the CMUT is in the radiation state, the force acting on the CMUT is the electrostatic force Fe. Its expression can be easily obtained based on the plate capacitance model theory. Formula (2) can be obtained by substituting it into Formula (1). In the equation, ε₀ is the vacuum dielectric constant, A is the effective area of the electrode, and g₀ is the initial distance between the upper and lower electrodes.

$$ M\frac{{d^{2} w}}{{dt^{2} }} + R\frac{dw}{dt} + Kw = \frac{{\varepsilon_{0} AV^{2} }}{{2(g_{0} - w)^{2} }}. $$

(2)

If we set w₁ = w, w₂ = dw₁/dt, the differential equation shown in Formula (2) can be transformed into the state equation as shown in Formula (3).

$$ \left\{ \begin{aligned} \dot{w}_{1} = w_{2} \hfill \\ \dot{w}_{2} = \frac{1}{M}\left[ {\frac{{\varepsilon_{0} AV^{2} }}{{2(g_{0} - w_{1} )^{2} }} - Rw_{2} - Kw_{1} } \right] \hfill \\ \end{aligned} \right.. $$

(3)

It should be noted that the zero point of the displacement is the position at which the vibrating film is stationary and the positive direction is below the vibrating film in the plate capacitance model and the lumped parameter system model. Thus, the displacement curve plotted in the Cartesian coordinates is just opposite to the direction of the displacement of the vibrating film. In order to describe the change of the displacement of the vibrating film with time more intuitively, it is usually described by − w. And the electrostatic force becomes − F_e with taking into account the directionality of the electrostatic force and set w₁ = − w, w₂ = dw₁/dt. Thereby, the Formula (3) is transformed into the state equation shown in Formula (4).

$$ \left\{ \begin{aligned} \dot{w}_{1} = w_{2} \hfill \\ \dot{w}_{2} = \frac{1}{M}\left[ { - \;\frac{{\varepsilon_{0} AV^{2} }}{{2(g_{0} + w_{1} )^{2} }} - Rw_{2} - Kw_{1} } \right] \hfill \\ \end{aligned} \right.. $$

(4)

For the state equations shown in Formulas (3) and (4), the numerical integration method can be used to solve them directly. Or the system module diagram can be constructed in SIMULINK environment, and then perform the system simulation analysis of them. In view of the nonlinearity of the electrostatic force, the system is divided into two parts: the nonlinear module (electrostatic force) and the linear module (CMUT vibration system) as the system model is being built. The electrostatic force Fe can be calculated through the nonlinear module, and the displacement and speed can be obtained based on the linear module. The CMUT transmits the acoustic signal to the external media, producing the sound pressure. The output sound pressure can be obtained by multiplying the vibration velocity of the CMUT film by its radiation resistance. Therefore the SIMULINK model of the CMUT micro-unit in the radiation state model can be established, as shown in Fig. 3. The nonlinear module (electrostatic force) is shown in Fig. 4, and linear module (CMUT vibration system) is shown in Fig. 5.

4 Radiation characteristics analysis of the CMUT under different input signals

Typically, the CMUT input voltage V contains a DC bias voltage V_DC and an AC voltage signal, and the AC voltage signal can be represented by a sinusoidal signal. Then, the input voltage V can be expressed by Formula (5), and its square V² can be expressed by Formula (6), where f_s represents the frequency of sinusoidal AC signal.

$$ V = V_{DC} + V_{AC} \sin (2\pi f_{s} t) $$

(5)

$$ \begin{aligned} V^{2} =\, & [V_{DC} + V_{AC} \sin (2\pi f_{s} t)]^{2} \\ =\, & V_{DC}^{2} + \frac{1}{2}V_{AC}^{2} + 2V_{DC} V_{AC} \sin (2\pi f_{s} t) - \frac{1}{2}V_{AC}^{2} \cos (4\pi f_{s} t). \\ \end{aligned} $$

(6)

Formula (6) indicates that V² also contains the sinusoidal signal with the frequency of 2f_s, besides the sinusoidal signal with the frequency of f_s. That is the second harmonic signal.

In this paper, the collapse phenomenon of the CMUT micro-unit under the water and the displacement and sound pressure characteristics of the CMUT micro-unit in different transmitted signals will be analyzed through the SIMULINK model for the CMUT micro-unit that was designed. In the analysis, set the effective range of displacement from − g₀ to 0. These analysis results will provide an important theoretical basis for the subsequent practical application and testing.

4.1 Analysis of the collapse phenomenon

According to the calculation formula of the collapse voltage V_PI in literature (Ladabaum et al. 1998), it can be calculated that the collapse voltage of the CMUT micro-unit designed in this paper is about 134.13 V. In order to verify its collapse phenomenon, three step functions of different amplitudes is selected as the input voltage of the CMUT micro-unit in the radiation state. Make the amplitudes of the step function jump respectively from 0 to 133.63, 134.13, 134.63 V at 1 s. And observe the changes in vibration displacement respectively, as shown in Fig. 6. It can be seen from the figure, when the input voltage is 133.63 V, the maximum vibration displacement is about 0.21 m. When the input voltage as the collapse voltage is 134.13 V, the maximum vibration displacement is about 0.23 mm, which is one-third of the cavity height of 0.7 mm. When the input voltage increases from the collapse voltage to 134.63 V, the maximum vibration displacement is about 0.7 mm, where it collapses to the bottom of the cavity. It should be noted that the impact of external pressure isn’t taken into consideration in the analysis of the collapse phenomenon. In fact, due to the external pressure, the collapse voltage is lower than the theoretical value.

4.2 Analysis of radiation characteristics with small V_AC

First, for a specific AC signal of the small amplitude, as V_AC ≪ V_DC, the influence of the DC bias voltage on the radiation characteristics of the CMUT micro-unit is analyzed by selecting the different amplitude of the DC bias voltage. The sinusoidal signal is selected as the AC input signal, and the amplitude is 2 V, the frequency is 600 kHz, the duration is 5 periods. And the time domain waveform and the normalized power spectrum of it are shown in Fig. 7a, b, respectively.

Respectively, select 0.1V_PI, 0.4V_PI, 0.7V_PI, 0.9V_PI as the DC bias voltage. The vibration displacement of the CMUT micro-unit is shown in Fig. 8a. The output sound pressure is shown in Fig. 8b, and the normalized power spectrum of the output sound pressure is shown in Fig. 9.

It can be seen from Fig. 8a, b that as V_AC ≪ V_DC, the vibration displacement of the CMUT micro-unit and the amplitude of the output sound pressure are related to the DC bias voltage. They increase as the DC bias voltage increases. Also, it can be seen obviously from Fig. 8a that the vibration range of the film expands as the DC bias voltage increases.

Figure 9a, b indicate that the DC bias voltage affects the center frequency of the output sound pressure. When the DC bias voltage is 0.1V_PI, the center frequency is about 654 kHz. When the DC bias voltage is 0.4V_PI, the center frequency is about 644 kHz. When the DC bias voltage is 0.7V_PI, the center frequency is about 600 kHz. When the DC bias voltage is 0.9V_PI, the center frequency is about 494 kHz. As the DC bias voltage increases, the center frequency will decrease. This is mainly due to the fact that the equivalent spring of the CMUT micro-unit has softened, causing the reduction in its equivalent elasticity coefficient.

Then, for a particular DC bias voltage, the influence of the amplitude of the AC signal on the radiation characteristics of the CMUT micro-unit is analyzed as V_AC ≪ V_DC, by selecting the AC signals of different amplitudes. With 0.7V_PI as the DC bias voltage, select the sinusoidal signal of which the frequency is 600 kHz and the duration is 5 periods as the AC input signal, and 0.01, 0.04, 0.07, 0.10V_PI as its amplitude, respectively. The waveform is similar to Fig. 7, but its amplitude is a little different from that.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 10a, and the output sound pressure is shown in Fig. 10b, and the normalized power spectrum of the output sound pressure is shown in Fig. 11. It can be seen from Fig. 10a, b that, as V_AC ≪ V_DC, the vibration displacement of the CMUT micro-unit and the output sound pressure are related to the voltage amplitude of the AC signal at a specific DC bias voltage, and they increase with the increasing amplitude of the AC signal voltage. It can be seen from Fig. 11a, c that the change in the amplitude of the AC signal voltage has little effect on the center frequency of the output sound pressure at a specific DC bias voltage as V_AC ≪ V_DC. However, Fig. 11b shows that, with the increase of the amplitude of the AC signal voltage, the center frequency of the output sound pressure has a slight decreasing tendency. But, for the AC signals of different amplitudes, the center frequency of the output sound pressure is not much different from the center frequency (600 kHz) generated by the specific DC bias voltage 0.7V_PI as a whole. In addition, it can be seen from Fig. 11c that the second harmonic signal (1.2 MHz) appearing in the output sound pressure is enhanced with the increase of the amplitude of the AC signal voltage, but it is very weak and can be neglected.

Finally, for a particular DC bias voltage, the influence of the frequency of the AC signal on the radiation characteristics of the CMUT micro-unit is analyzed as V_AC ≪ V_DC, by selecting the AC signals of different frequencies. With 0.7V_PI as the DC bias voltage, select the sinusoidal signal of which the amplitude is 2 V and the duration is 5 periods as the AC input signal, and 100 kHz, 300 kHz, 600 kHz, 1 MHz as its frequency, respectively. The waveform is similar to Fig. 7, but its frequency is a little different from that. The normalized power spectrum of the AC input signals of the four different frequencies is shown in Fig. 12.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 13a, the output sound pressure is shown in Fig. 13b, and the normalized power spectrum of the output sound pressure is shown in Fig. 14.

It can be seen from Fig. 13a, b that the frequency change of the AC signal will affect the vibration displacement and output sound pressure of the CMUT micro-unit at a specific DC bias voltage as V_AC ≪ V_DC. For the above four AC signals of different frequencies, the AC signal of 600 kHz frequency generates the maximum vibration displacement and output sound pressure, and the other three AC signals are equivalent. It is shown that only when the frequency of the AC signal is close to the center frequency generated by the specific DC bias voltage, a larger vibration displacement and output sound pressure can be obtained. It can be seen from Fig. 14a, b, the change in the frequency of the AC signal affects the frequency characteristic of the output sound pressure at a specific DC bias voltage as V_AC ≪ V_DC. When the frequency of the AC signal is lower than the effective frequency range corresponding to the specific DC bias voltage, such as 100 and 300 kHz, the signal with the frequency similar to that of the AC signal will appear in the output sound pressure. When the frequency of the AC signal is higher than its effective frequency range, such as 1 MHz, its influence on the output sound pressure frequency will be very small. In addition, for the AC signal of different frequencies, there will be the frequency component similar to the center frequency (600 kHz) corresponding to the specific DC bias voltage 0.7V_PI in the power spectrum of the output sound pressure.

4.3 Analysis of radiation characteristics with large V_AC

First, for a specific AC signal of the large amplitude, as V_AC is large, the influence of the DC bias voltage on the radiation characteristics of the CMUT micro-unit is analyzed by selecting the different amplitude of the DC bias voltage. The sinusoidal signal is selected as the AC input signal, and the amplitude is 0.2V_PI, the frequency is 600 kHz, the duration is 5 periods. The waveform is similar to Fig. 7, but its amplitude is a little different from that. Respectively, select 0.2, 0.4, 0.7, 0.9V_PI as the DC bias voltage.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 15a, and the output sound pressure is shown in Fig. 15b, and the normalized power spectrum of the output sound pressure is shown in Fig. 16. It can be seen from Fig. 15a, b that when V_AC is large, the vibration displacement and output sound pressure of CMUT micro-unit increase with the increase of the DC bias voltage, and the vibration range of the film constantly expands. Figure 16a, b indicate that the frequency of the output sound pressure generated by the different DC bias voltage is also different. When V_AC is close to the DC bias voltage, there will be some lower frequency signals in the output sound pressure. But when V_AC is more different from the DC bias voltage, the frequency components of output sound pressure are relatively single. The reason is mainly due to the nonlinearity of the CMUT micro-unit.

Then, for a specific DC bias voltage, as V_AC is large, the influence of the amplitude of the AC signal on the radiation characteristics of the CMUT micro-unit is analyzed by selecting the AC signals of different amplitudes. With 0.6V_PI as the DC bias voltage, select the sinusoidal signal of which the frequency is 600 kHz and the duration is 5 periods as the AC input signal, and 0.15, 0.20, 0.25, 0.30V_PI as its amplitude, respectively. The waveform is similar to Fig. 7, but its amplitude is a little different from that.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 17a, and the output sound pressure is shown in Fig. 17b, and the normalized power spectrum of the output sound pressure is shown in Fig. 18.

It can be seen from Fig. 17a, b that as V_AC is large, the vibration displacement of the CMUT micro-unit and the output sound pressure are related to the voltage amplitude of the AC signal at a specific DC bias voltage, and they increase with the increasing amplitude of the AC signal voltage.

It can be seen from Fig. 18a–c that the change in the amplitude of the AC signal voltage will affect the center frequency of the output sound pressure at a specific DC bias voltage as V_AC is large. And Fig. 18b shows that, with the increase of the amplitude of the AC signal voltage, the center frequency of the output sound pressure has a decreasing tendency. The reason is also due to the nonlinearity of the CMUT micro-unit.

Finally, the influence of the frequency of the AC signal on the radiation characteristics of the CMUT micro-unit is analyzed as V_AC is large, by selecting the AC signals of different frequencies. With V_DC = 0.6V_PI, V_AC = 0.2 V_PI, select the sinusoidal signal of which the amplitude is 2V and the duration is 5 periods as the AC input signal, and 100 kHz, 300 kHz, 600 kHz, 1 MHz as its frequency, respectively. The waveform is similar to Fig. 7, but its amplitude and frequency are a little different from that. The normalized power spectrum is similar to Fig. 12.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 19a, the output sound pressure is shown in Fig. 19b, and the normalized power spectrum of the output sound pressure is shown in Fig. 20.

It can be seen from Fig. 19a, b that the change in the frequency of the AC signal will affect the vibration displacement and output sound pressure of the CMUT micro-unit as V_AC is large. For the above four AC signals of different frequencies, the AC signal of 600 kHz frequency generates the maximum vibration displacement and output sound pressure, the second is the AC signal of 300 kHz frequency, the third is the AC signal of 1 MHz frequency and the final is the AC signal of 100 kHz frequency. This is mainly due to the fact that the frequency 600 kHz is close to the center frequency corresponding to the DC bias voltage V_DC = 0.6V_PI, which make it generate the maximum vibration displacement and output sound pressure. For the AC signal with a frequency of 300 kHz, the second harmonic signal (600 kHz) in V² is evident clearly because of the large V_AC, and the frequency of the second harmonic is also close to the center frequency corresponding to the DC bias voltage V_DC = 0.6V_PI. Therefore, the vibration signal and the output sound pressure generated by the AC signal with the frequency of 300 kHz are larger than that of the AC signal at 100 kHz and 1 MHz.

It can be seen from Fig. 20a, b, as V_AC is large, the frequency change of the AC signal has a effect on the output sound pressure which is similar to that as V_AC ≪ V_DC. When the frequency of the AC signal is lower than the effective frequency range corresponding to the specific DC bias voltage, such as 100, 300 kHz, the signal with the frequency similar to that of the AC signal will appear in the output sound pressure. When the frequency of the AC signal is higher than its effective frequency range, such as 1 MHz, its influence on the output sound pressure frequency will be very small. In addition, for the AC signal of different frequencies, there will be the frequency component similar to the center frequency corresponding to the specific DC bias voltage in the power spectrum of the output sound pressure.

4.4 Analysis of radiation characteristics as V_DC = 0

When V_DC = 0, Formula (7) can be obtained based on Formula (6). Formula (7) shows that as V_DC = 0, if the AC signal with the frequency of f_s/2 is directly selected as the input voltage, then that can make the input voltage of the square V² only contains the signal with the frequency of f_s. Thus, it is assumed that the desired output voltage with the frequency of f_s can be obtained.

$$ V^{2} = \frac{1}{2}V_{AC}^{2} - \frac{1}{2}V_{AC}^{2} \cos (4\pi f_{s} t) = \frac{1}{2}V_{AC}^{2} - \frac{1}{2}V_{AC}^{2} \cos (2\pi f^{\prime}_{s} t). $$

(7)

In order to obtain the output sound pressure with the frequency of 600 kHz, select the sinusoidal signal of which the frequency is 300 kHz and the duration is 5 periods as the AC input signal, and 0.2, 0.4, 0.6, 0.8V_PI as its amplitude, respectively. The waveform is similar to Fig. 7, but its amplitude and frequency is a little different from that.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 21a, and the output sound pressure is shown in Fig. 21b, and the normalized power spectrum of the output sound pressure is shown in Fig. 22.

It can be seen from Fig. 21a, b that as V_DC = 0, the vibration displacement and the output sound pressure of the CMUT micro-unit are related to the voltage amplitude of the AC signal at a specific DC bias voltage, and they increase with the increasing amplitude of the AC signal voltage.

Figure 22a, b show that, as V_DC = 0, the AC signal with frequency f_s/2 is directly used as the input voltage, and the generated output sound pressure contains the signal with frequency f_s. Also, it contains the harmonic signals of other different orders of the AC signal. The reason for this is that the nonlinearity of the CMUT is more strongly affected by the dynamic space g than V². Therefore, it is actually invalid to eliminate the harmonic effect by using the Formula (7) simply. To reduce the influence of the nonlinear harmonic in the output sound pressure of the CMUT on the image quality, the filtering, signal compensation and other methods can be used to achieve it (Novell et al. 2009).

4.5 Analysis of the influence of the period number of AC signal on radiation characteristics

It is in the above analyses that the AC input signal with the duration of 5 periods are used. And there will be a analysis of the influence of the period number of the AC input signal on the radiation characteristics of the CMUT for the AC input signals of different period number.

First, the influence of the period number of the AC input signal on the radiation characteristics of the CMUT is analyzed as V_AC ≪ V_DC. In addition, with 0.7V_PI as the DC bias voltage, the sinusoidal signal of which the amplitude is 2V and the frequency is 600 kHz is selected as the AC input signal, and the duration of it is 1 period, 5 periods, 10 periods and 20 periods, respectively. Its time domain waveform and normalized power spectrum are shown in Fig. 23a, b, respectively. It can be seen from the power spectrum shown in Fig. 23b that the effective bandwidth of the AC input signal becomes narrower as the period number increases.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 24a, and the output sound pressure is shown in Fig. 24b, and the normalized power spectrum of the output sound pressure is shown in Fig. 25.

It can be seen from Fig. 24a, b that as V_AC ≪ V_DC, the period number of the AC input signal mainly affects the vibration displacement and the output sound pressure of the CMUT micro-unit duration and attenuation rate. With the increase of the period number, the duration of the vibration displacement and the output sound pressure becomes longer and the attenuation becomes slower. In addition, the longer the duration of the AC input signal is, the larger the amplitude of the output sound pressure and the vibration displacement of the CMUT micro-unit will become.

It can be seen from Fig. 25a, b that as V_AC ≪ V_DC, the period number of the AC input signal mainly affects the effective bandwidth of the output sound pressure, and the effective bandwidth of the output sound pressure gradually becomes narrower as the period number increases.

Then, the influence of the period number of the AC input signal on the radiation characteristics of the CMUT is analyzed as V_AC is large. In addition, with 0.6V_PI as the DC bias voltage, the sinusoidal signal of which the amplitude is 2 V and the frequency is 600 kHz is selected as the AC input signal, and the duration of it is 1 period, 5 periods, 10 periods and 20 periods, respectively. The waveform is similar to Fig. 23, but its amplitude is a little different from that.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 26a, and the output sound pressure is shown in Fig. 26b, and the normalized power spectrum of the output sound pressure is shown in Fig. 27.

It can be seen from Fig. 26a, b that as V_AC is large, the influence of the period number of the AC input signal is similar to that when V_AC ≪ V_DC. With the increase of the period number, the duration of the vibration displacement and the output sound pressure becomes longer and the attenuation becomes slower.

It can be seen from Fig. 27a, b, as V_AC is large, the center frequency of the output sound pressure tends to decrease gradually with the increase of the period number of the AC input signal, and its effective bandwidth gradually becomes narrow, but its second harmonic signal becomes more and more evident.

Finally, the influence of the period number of the AC input signal on the radiation characteristics of the CMUT is analyzed as V_DC = 0. Here, the sinusoidal signal of which the amplitude is 0.8V_PI and the frequency The frequency is 300 kHz which is half of the desired frequency, and the duration of it is 1 period, 5 periods, 10 periods, 20 periods, respectively. The waveform is similar to Fig. 23, but its amplitude and frequency are a little different from that.

At this time, the vibration displacement of the CMUT micro-unit is shown in Fig. 28a, and the output sound pressure is shown in Fig. 28b, and the normalized power spectrum of the output sound pressure is shown in Fig. 29.

It can be seen from Fig. 28a, b that as V_DC = 0, the influence of the period number of the AC input signal is similar to that when V_AC ≪ V_DC and V_AC is large. With the increase of the period number, the duration of the vibration displacement and the output sound pressure becomes longer and the attenuation becomes slower.

It can be seen from Fig. 29a, b, as V_DC = 0, with the period number of the AC input signal increases, the desired vibration frequency (600 kHz) is gradually increased and the effective bandwidth of the output sound pressure becomes narrower. However, the second and third harmonic signals of the desired frequency also become more and more evident. In addition, it can be clearly seen that for an AC input signal with the duration of one period, the bandwidth of the corresponding radiation sound pressure is very wide and the desired frequency component cannot be distinguished. This is mainly due to the fact that the duration of the output sound pressure is too short. Therefore, as V_DC = 0, it is not appropriate to select an AC input signal with a duration of one period.

5 Conclusions

Based on the lumped parameter system model of the CMUT micro-unit, the state equation in the radiation state is deduced in this paper, and there is the modeling analysis through SIMULINK. With the analysis of the influence of different input signals on its radiation characteristics, the following conclusions can be drawn:

As V_AC is small, the DC bias voltage, the amplitude and frequency of the AC signal will affect the vibration displacement and output sound pressure of the CMUT micro-unit. The frequency characteristics of the output sound pressure of the CMUT micro-unit are greatly influenced by the DC bias voltage, and less affected by the amplitude of the AC signal. But, the frequency change of the AC signal will also affect the frequency characteristics of the output sound pressure of the CMUT micro-unit. In practical applications, in order to obtain a large output sound pressure, the frequency of the AC signal should be close to the center frequency corresponding to the specific DC bias voltage and the amplitude should be increased as much as possible.

As V_AC is large, the DC bias voltage, the amplitude and frequency of the AC signal will affect the vibration displacement and output sound pressure of the CMUT micro-unit. The frequency characteristics of the output sound pressure of the CMUT micro-unit are greatly influenced by the DC bias voltage, and less affected by the amplitude of the AC signal. In this case, the influence on the radiation characteristics is similar to that when V_AC is small, and there is little difference between them.

As V_DC = 0, the AC signal with frequency f_s/2 is used as the input voltage, and the output sound pressure generated by the CMUT micro-unit contains not only the signal with frequency f_s, but also the harmonic signal of other different orders. The filtering, signal compensation and other effective measures must be taken to suppress this nonlinear phenomenon to further improve the image quality.

With the increase of the period number, the duration of the vibration displacement and the output sound pressure becomes longer and the attenuation becomes slower. Its effective bandwidth gradually becomes narrow, and its harmonic components become more and more evident.

Therefore, in practical applications, it is necessary to select reasonably the DC bias voltage, the parameters of the AC input signal such as amplitude, frequency and period number combined with specific circumstances, in order to obtain high-quality test results.

Acknowledgements

The authors wish to thank the Special Fund Support of the Shanxi Province Natural Science Foundation (201701D121066); the open project of Key Laboratory of Mcro Opto-electro Mechanical System Technology, Tianjin University, Ministry of Education; the open project of Key Laboratory of Dynamic Measurement (North University of China), Ministry of Education, North University of China; the Major State Basic Research Development Program of China (2016YFC0101900), the Fund for Shanxi ‘1331 Project’ Key Subject Construction (1331KSC).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Title: Investigation and analysis of the influence of excitation signal on radiation characteristics of capacitive micromachined ultrasonic transducer
Authors: Hongliang Wang
Xiangjun Wang
Changde He
Chenyang Xue
Publication date: 08-02-2018
Publisher: Springer Berlin Heidelberg
Published in: Microsystem Technologies / Issue 7/2018
Print ISSN: 0946-7076
Electronic ISSN: 1432-1858
DOI: https://doi.org/10.1007/s00542-018-3783-8

Springer Professional

Abstract

1 Introduction

2 The structure of the CMUT micro-unit and lumped parameter system model

3 The state equation-SIMULINK model of the CMUT in radiation state

4 Radiation characteristics analysis of the CMUT under different input signals

4.1 Analysis of the collapse phenomenon

4.2 Analysis of radiation characteristics with small VAC

4.3 Analysis of radiation characteristics with large VAC

4.4 Analysis of radiation characteristics as VDC = 0

4.5 Analysis of the influence of the period number of AC signal on radiation characteristics

5 Conclusions

Acknowledgements

Compliance with ethical standards

Conflict of interest

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4.2 Analysis of radiation characteristics with small V_AC

4.3 Analysis of radiation characteristics with large V_AC

4.4 Analysis of radiation characteristics as V_DC = 0