Cavitation Detection in a Tonpilz-Type Transducer for Active SONAR Transmission System

Abstract

The active sound navigation and ranging (SONAR) transmission system emits acoustic pulses underwater using a wave generator, a SONAR power amplifier (SPA), and a projector. The acoustic pulse travel in the direction of the target and return as an echo to a hydrophone to learn the range or speed of the object. Often the same device is used as a hydrophone and a projector; in this context, it is known as a transducer. In order to obtain a maximum range of detection in the SONAR, it is desirable to generate the maximum amount of acoustic power until the point in which the echo can be detectable in an atmosphere with non-wished noise. Therefore, a high value of source level (SL) is required that depends largely on the value of electrical power applied to the transducer ($P_e$). However, when trying to obtain the maximum range of detection in the SONAR system there are the following three peculiar limitations that affect performance: The cavitation, the reverberation, and the effect of interaction in the near field. In this paper, an experimental measurement methodology is presented to detect the cavitation effects in a tonpilz-type transducer for an active SONAR transmission system using a transducer as a projector and a calibrated hydrophone in a hydroacoustic tank by measuring the parameters of total harmonic distortion of the fundamental waveform (THD-F) of the generated acoustic pulse, transmitting voltage response (TVR) to characterize the system and sound pressure level (SPL) that indicates the intensity of sound at a given distance. Whereas the reverberation and the interaction effect in the near field are objects of other study cases. A 570.21 W and THD-F < $5\%$ switched-mode power amplifier (SMPA) prototype was developed to excite the electroacoustic transducer employing a full-bridge inverter (FBI) topology and a digital controller using a field-programmable gate array (FPGA) for unipolar sine pulse width modulation (SPWM) to generate a continuous wave (CW) acoustic pulse at a frequency 11.6 kHz. The results obtained show that from the level of $P_e=196.05$ W with the transducer at 1 $\mathrm{m}$ of depth, the value of THD-F increases significantly while the behavior of the TVR and SPL parameters is affected since it is not as expected and is attributed when cavitation occurs.

1. Introduction

Today, the sound navigation and ranging (SONAR) systems are widely used in military applications such as the classification and detection of submarines, mines, or surface ships, as well as for subaqueous communications and identification of obstacles. In commercial applications, the SONAR is used to look for fossil deposits, banks of fish, seismic exploration, characterization, and measurement of the depth of the seabed. The word SONAR was coined after the war as the counterpart of radio detection and ranging (RADAR), as it is mentioned in [1]. Figure 1 shows the general architecture of a SONAR system.

The SONAR operates in passive and active modes. Passive SONAR only listens to underwater acoustic sound radiated by various noise sources using a hydrophone and employs signal processing to analyze the nature of the signal in the frequency spectrum. The active SONAR emits acoustic pulses underwater using a wave generator, a SONAR power amplifier (SPA), and a projector. The acoustic pulse travel in the direction of the target and return as an echo to a hydrophone to learn the range or speed of the object. Often the same device is used as a hydrophone and a projector; in this context, it is known as a transducer [2]. In order to obtain a maximum range of detection in the SONAR, it is desirable to generate the maximum amount of acoustic power until the point in which the echo can be detectable in an atmosphere with non-wished noise. Therefore, a high value of source level (SL) is required and is defined by Equation (1) at a radial distance in far-field (r) of 1 $\mathrm{m}$. SL depends largely on the value of electrical power applied to the transducer ($P_e$) and of directivity index (DI), which generally takes a value between 10 and 30 $\mathrm{d}\mathrm{B}$ for a flat wave as it is mentioned [3].

$$\mathrm{S}\mathrm{L}=170.8+10\log Pe+\mathrm{D}\mathrm{I}$$

(1)

In general, the main topic of the articles found in the literature regarding passive SONAR is focused on signal processing with the development of object detection and classification algorithms. While the main topic of active SONAR focuses on the topology of the SPA to excite the transducer, increase the energy efficiency with the selection of power transistors and reduce the amount of total harmonic distortion of the fundamental waveform (THD-F) using different modulation techniques. Therefore, the experimentation literature on the operation of the active SONAR transmission system is limited, specifically when trying to obtain the maximum range of detection in the SONAR system there are the following three peculiar limitations that affect performance [1]: The cavitation generates bubbles on the surface of the transducer face and causes beam pattern degradation and acoustic power losses, the reverberation generates multiple echoes of the transmitted acoustic pulse from targets that are not of interest to the same source in the area from which the transmission is made and which becomes unwanted acoustic noise and the effect of interaction in the near field that is part of the SONAR design and occurs in large arrays of closely spaced projector elements. In this paper, an experimental measurement methodology is presented to detect the cavitation effects in a tonpilz-type transducer for an active SONAR transmission system using a transducer as a projector and a calibrated hydrophone in a hydroacoustic tank by measuring the parameters of THD of the generated acoustic pulse, transmitting voltage response (TVR) to characterize the system and sound pressure level (SPL) that indicates the intensity of sound at a given distance. Whereas the reverberation and the interaction effect in near-field are objects of other study cases.

2. Proposed Methodology

The measurement of electroacoustic parameters is essential to detect the effects of cavitation in the tonpilz transducer since cavitation is one of the main limiting factors in the performance of the active SONAR transmission system. Before the description of the experimental measurement methodology proposed to detect cavitation, the topics described below are addressed.

2.1. Cavitation

It is a phenomenon that takes place in the transducer when a negative pressure is generated, this happens when the signal emitted in the average hearing aid surpasses the environmental noise. Therefore, with little depth or in shallow water, more cavitation occurs, leading to bubbles forming on the surface of the transducer face. This, as a result, gives a degradation in the pattern of the beam, and there are losses of acoustic power radiated by the projector ($P_a$) due to the absorption and dispersion of the underwater waves by the bubbles, the transferred efficiency of the transmission system to the transducer is reduced. Therefore, with the increase in $P_e$ in some point, cavitation will take place. The cavitation is based on the depth and the intensity of the radiated acoustic power of the projector ($I_{pa}$) that can be minimized to avoid exceeding the threshold that is shown in Figure 2.

Because cavitation takes a finite amount of time to build up, the threshold changes based on the pulse length and the transmission frequency, as mentioned in [1,2,4]; this is shown in Figure 3. It is observed that for pulse length ($T_p$), the threshold is increased by about 3 for pulses up to 0.5 $\mathrm{m}\mathrm{s}$, but between 10 and 100 $\mathrm{m}\mathrm{s}$, it changes little, and for the frequency ($f$), the threshold changes little up to 10 $\mathrm{k}\mathrm{H}\mathrm{z}$, but between 10 and 300 $\mathrm{k}\mathrm{H}\mathrm{z}$ it increases linearly with the frequency.

The value of the maximum electrical power applied to the projector ($P_{em}$) to avoid cavitation in the transducer is defined by Equation (2). It is observed that the limiting factor to diminish cavitation is the capacity to control the value of $I_{pa}$ through $P_e$.

$$P_{em}=A_r·U_c·k_L·k_f$$

(2)

where:

• $A_r$ = Radiated surface area, ${\mathrm{m}}^2$;
• $U_c$ = Value of the cavitation threshold, $\mathrm{k}\mathrm{W}$;
• $k_L$ = Factor of pulse length;
• $k_f$ = Transmission frequency factor, $\mathrm{k}\mathrm{H}\mathrm{z}$.

When cavitation bubbles occur on the face of the transducer, the sound pressure waveform can be affected in three different ways, as mentioned in [5] these are shown in Figure 4. In (a), the cavitation does not occur, while in (b), the negative peak touches the zero pressure line as the signal increases, which represents the threshold of cavitation, in (c), the excitation level of the transducer increases, and mild cavitation occurs that distorts the waveform, and in (d) violent cavitation occurs that causes a total rupture of the pressure wave and greatly distorts the waveform.

2.2. Transducer

Diverse types of transducers, such as projectors and hydrophones, exist that are used in passive or active SONAR. Figure 5 shows the tonpilz-type transducer that was used as the projector for this paper, such as the designs and models that appear in [6,7,8,9,10], which are found in active SONAR systems since they generally work in a frequency range below 20 $\mathrm{k}\mathrm{H}\mathrm{z}$.

The transducer uses piezoelectric material as a sensible element based on Lead Zirconate Titanate (PZT) - $Pb\left[{Zr}_{\left(x\right)}{Ti}_{(1-x)}\right]O_3$ by its chemical nomenclature. In general, a transducer is a process or device that turns energy from one form to another one. Therefore, the acoustic transducer has the property to turn the electrical energy into acoustic energy or vice versa, as it is shown in Figure 6.

The frequency behavior of the transducer is shown in Figure 7a, where a low impedance in the resonance frequency appears ($f_r$), whereas in the antiresonance frequency ($f_a$), a high impedance is obtained. These frequencies are determined by the characteristics of the piezoelectric ceramics of the transducer due to the composition of material, thickness, volume, and form of the element as described in [11] with the equivalent electrical circuit of the transducer Butterworth-Van Dyke as shown in Figure 7b.

The equivalent circuit considers the capacitance of the mechanical circuit (${\mathrm{C}}_{\mathrm{m}})$, Inductance of the mechanical circuit (${\mathrm{L}}_{\mathrm{m}}$), resistance caused by mechanical losses (${\mathrm{R}}_{\mathrm{m}}$) and ${\mathrm{C}}_0$ which is (capacitance of ceramic at $f_r$) − (${\mathrm{C}}_{\mathrm{m}}$).

The value of the impedance of the transducer ($Z_t$) in air and water is different. When $Z_t$ is measured in the water changes $f_r$ and $f_a$, because the impedance of radiation in the water is much greater than in the air since the radiation load is added to the mass of radiation ($M_r$) and the radiation resistance ($R_r$). The air density is small, and the load of mass of radiation is $M_r\ll M$ for typical underwater-sound transducers, where $M$ is the dynamic mass of the transducer and the mechanical resonance occurs at the frequency at which the mass reactance (${\omega M}_e$) cancels the compliance reactance ($1/\omega C_{\mathrm{m}}^E$), where $C_{\mathrm{m}}^E=1/K_{\mathrm{m}}^E$ is the electrical/mechanical deformation and $K_{\mathrm{m}}^E=M{{\omega }_r}^2$ is the electrical/mechanical stiffness that occurs in resonance. When the transducer is submerged, add the mass of water to the mass $M_r$ as shown in Figure 8, and it produces that $f_r$ will be reduced in a value between 10 and 20% for piston-type transducers, as mentioned in [6].

The electrical circuit can represent a mechanical vibrating system by replacing the voltage $\mathrm{V}$ with a force $F$, the current $\mathrm{I}$ with a velocity $\mathrm{u}$, $N$ is the turns ratio of the ideal transformer with the transduction coefficient, the inductor $M_{Tail}$ is the tail mass between AB, $G_O=\mathrm{I}/\mathrm{V}$ is electrical loss conductance and $F_b$ is the acoustic radiation source such as a projector.

On the other hand, because of the equivalent electrical circuit of the transducer, it has the parallel capacitor ${\mathrm{C}}_0$, which affects the transferred efficiency of the SPA to the transducer, as mentioned in [11]. Normally a parallel inductor ($L_p$) or a series inductor ($L_s$) is usually placed to the transducer as shown in the electric circuit in Figure 9 and that are defined by Equations (3) and (4), respectively. With the inductor, the impedance phase of the transducer (${\theta }_{zt}$) is tuned, ideally near zero degrees in $f_r$ to cancel the effect of $C_0$ to increase the efficiency. From the point of view of the total impedance ($Z_T$) of the Equation (5), the aim is to cancel the capacitive reactance ($X_C$) by means of the inductive reactance ($X_L$) where resonance occurs and obtain a resistive load so that the electrical power is consumed with greater efficiency.

$$L_p=\left(\frac{1}{{\left(2\pi ·f_a\right)}^2{C}_0}\right)$$

(3)

$$L_s=\left(\frac{1}{{\left(2\pi ·f_r\right)}^2{C}_0}\right)$$

(4)

$$Z_T=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$$

(5)

Usually, $P_e>P_a$ due to the electrical-acoustics conversion. The relation of these two powers defines the electro-acoustic efficiency (${\mathrm{ɲ}}_p$) of the transducer-like projector through Equation (6), and its value generally varies between 20 and 70% depending on the construction of the transducer and its bandwidth, as mentioned in [1,2,6]. Generally, the transducer that operates as a projector has a narrow band and thus is consequently activated near $f_r$ where a greater amount of $P_e$ is obtained.

$${\mathrm{ɲ}}_p=\frac{P_a}{P_e}$$

(6)

The measurement of $Z_t$ was carried out with the Analog Discovery 2 impedance analysis equipment with the WaveForms software from the manufacturer Digilent, as shown in Figure 10. Whereas Figure 11 shows a frequency sweep of 5 $\mathrm{k}\mathrm{H}\mathrm{z}$ to 20 $\mathrm{k}\mathrm{H}\mathrm{z}$ applied to the transducer tonpilz, where the value is shown $Z_t$ and ${\theta }_{zt}$ in air and water, where is observed that a balance must be chosen between efficiency and electrical power. The values measurements of the $f_r$, $f_a$, $Z_t$ and ${\theta }_{zt}$ referred in the air will be $f_{ra}$, $f_{aa}$, $Z_{ta}$ and ${\theta }_{zta}$, and the measurements when the transducer is submerged in the water will be $f_{rw}$, $f_{aw}$, $Z_{tw}$ and ${\theta }_{ztw}$ respectively.

Table 1. Transducer measurements values.

Medium	$\mathit{f}\mathit{r}$ ($\mathbf{k}\mathbf{H}\mathbf{z}$)	$\mathit{f}\mathit{a}$ ($\mathbf{k}\mathbf{H}\mathbf{z}$)	$\mathit{Z}\mathit{t}$ ($\mathsf{\Omega }$)	$\mathit{\theta }\mathit{z}\mathit{t}$ (°)
Air	12.8	14.3	816.8	−47.25
Water	11.6	14.3	1427	−67.90

shows a summary of the values obtained from the measurements and shows that the value of $f_{rw}$ is 9.3% less to $f_{ra}$ and $Z_{tw}$ is 74.7% greater than $Z_{ta}$.

2.3. SONAR Power Amplifier

The SONAR power amplifier (SPA), in general terms, is an electronic power system that increases the voltage magnitude of an electrical input signal that is typically in the range of 1–3 V RMS to apply it to the transducer and generate acoustic energy as shown in Figure 12. Generally, the output voltage of the SPA is greater than 1 $\mathrm{k}\mathrm{V}$ due to the high impedance of the transducer.

The SPA topologies are characterized by their mode of operation and can be linear or switched. The linear power amplifier (LPA) activates BJT transistors in the active region, so the electrical efficiency is around 60% and employs topologies such as those shown in

Table 2. Conduction characteristics of LPA.

Class	Conduction Angle
A	Complete cycle $\theta =2\pi$
B	Half cycle $\theta =\pi$
AB	More that $\pi <\theta <2\pi$
C	Less that de $\theta <\pi$

and mentioned in [12,13]. Active SONAR transmission systems generally handle powers from 1 to 40 kilowatts ($\mathrm{k}\mathrm{W}$), as mentioned in [2], which are installed to operate on submarines or surface units such as ships that require minimizing as much as possible the space and weight of installed equipment. This makes the LPA impractical for these applications because it presents a low energy efficiency since obtaining a high power implies having a large, expensive, and inefficient system.

On the other side, the block diagram of the switch-mode power amplifier (SMPA) is shown in Figure 13, which employs topologies such as class B (push-pull), D, S, etc. The efficiency of the SMPA is between 85 and 95%, as mentioned in [14,15], and it has low electrical losses because the MOSFET transistors are not activated all time since a bipolar or unipolar pulse-width modulation (PWM) is often used; therefore, its efficiency is greater than that of LPA. In order to control the SPA gain and decrease the total harmonic distortion (THD), sinusoidal pulse-width modulation (SPWM) is usually used, as shown in [16], by comparing a triangular carrier signal ($C_s$) and a sine modulator signal ($M_s$) as shown in Figure 14. The ratio of peak voltage amplitudes of the modulating signal ($V_m$) and carrier signal ($V_p$) is the amplitude modulation index ($M_a$), which can vary between 0 and 1 and which is defined in Equation (7). Furthermore, $M_s$ should be considered to be 10 times less than the value of $C_s$ to obtain an acceptable waveform quality.

$$M_a=\left(\frac{V_m}{V_p}\right)$$

(7)

In order to raise the voltage and obtain a greater amount of $P_e$, a transformer is used to provide galvanic isolation and impedance coupling between the energy source and the connected load. The voltage level is controlled by the transformation relation ($a$), which is defined by Equation (8) and indicates that if $a<1$ raises the voltage or if $a>1$ reduces the voltage. The output power ($P_o$) and the apparent impedance of the primary winding (${Z_L}^{\prime }$) of the transformer are defined by Equations (9) and (10), respectively. Figure 15 shows an ideal transformer in which the losses it presents are not considered, as mentioned in [17].

$$\frac{I_s}{I_p}=\frac{V_p}{V_s}=\frac{N_p}{N_s}=a$$

(8)

$${Z_L}^{\prime }=a^2{Z}_L$$

(9)

$$P_o=V_s{I}_s\cos \theta$$

(10)

where:

• $I_{p,s}$ = Current of the primary or secondary winding;
• $V_{p,s}$ = Voltage of the primary or secondary winding;
• $N_{p,s}$ = Number of turns of the primary or secondary winding;
• $\theta$ = Phase angle of voltage concerning current.

In the SPA, there are three types of second-order Butterworth low-pass LC filters used, which can be of bridge-tied load (BTL) configuration or its equivalent in single-ended (SE), as shown in Figure 16 and mainly depend on whether the modulation is bipolar or unipolar. The selection of inductor (L) or capacitor (C) values is a critical parameter to attenuate the high frequency of $C_s$ and obtain an output voltage at the fundamental frequency of $M_s$, as mentioned in [18]. The ratio of impedance LC filter ($Z_f$) and $Z_t$ determine the damping factor (DF) that is defined by Equation (11), where it is observed that the higher its value, the better the vibration of the transducer will be controlled by the SPA.

$$\mathrm{D}\mathrm{F}=\frac{Z_t}{Z_f}$$

(11)

The cut-off frequency ($f_c$), the quality factor ($Q$) should ideally be $0.707=1/\sqrt{2}$, the inductor and capacitor are defined by Equations (12), (13), (14) and (15) respectively, where $\omega =2\pi f_c$ and $R_L$ is the load resistance.

$$f_c=\frac{1}{2\pi \sqrt{LC}}$$

(12)

$$Q=Z_t\sqrt{C/L}$$

(13)

$$L=\frac{Z_t\sqrt{2}}{\omega }$$

(14)

$$C=\frac{1}{\omega Z_t\sqrt{2}}$$

(15)

In the literature, there are several topologies of SMPA to excite the transducer, which mainly focus on increasing energy efficiency with the selection of power transistors and reducing the content of THD using different modulation techniques.

Table 3. Characteristics of SPA topologies.

Topology	Class B	Class D	Full-Bridge	Multilevel	T-Type
m	2	2	3	$2\mathrm{\ast }{S}_{DC}+1$	3
Vout	$Vin·\frac{Ns}{Np}$	$\frac{Vin}{2}$	$Vin$	$V_{a1}\dots +V_{a\left[\right(m-1)/2]}$	$\frac{Vin}{2}$
Transistors	2	2	4	($2$ ($m-1$))	6
THD	High	High	Low	Low	Low
PWM	Bipolar	Bipolar	Unipolar	Unipolar	Unipolar
Power	<1 kW	<1 kW	<100 kW	<100 kW	<1 kW

m: voltage levels, $N$: winding turns, $S_{DC}:$ DC voltage sources, $V_a:$ phase voltage.

shows a summary of the most important characteristics of commonly used SPA technologies such as class B [19,20,21], class D [22,23,24], full-bridge inverter (FBI) [25,26,27,28], multilevel inverter (MLI) [29,30] and T-type inverter [31,32].

The SPA topology selected for the active SONAR transmission system is a full-bridge inverter with an SPWM controller, as shown in Figure 17. This topology offers good performance, such as low THD, uses four transistors, so the control is simple, has high power capacity, and the implementation is practical since the size is moderate compared to the power capacity handled by the system. The transistors are activated with a unipolar SPWM modulation technique to have a modulated output voltage $V_{o}1$ of three levels ($+\mathrm{V}\mathrm{C}\mathrm{D},0$ and $-\mathrm{V}\mathrm{C}\mathrm{D}$), which is incremented by means of a transformer and passes through an LC filter of BTL Type-2 configuration in common mode to obtain a voltage $V_{o}2$ that is applied to the transducer connected with $L_p$.

2.4. Pulse Types

The underwater acoustic pulses transmitted by the active SONAR transmission system are generated by an oscillator and waveform controller and returned as echoes to the transducer or hydrophone. The most commonly used pulses in active SONAR are continuous wave (CW) and frequency modulation (FM) as mentioned in [2,4,33,34].

The CW pulse is a transmission pulse of constant frequency and duration of pulse length ($T_p$) in seconds. It is narrowband with a bandwidth pulse $B_p=1/T_p$ Hz, has low range resolution, high Doppler effect, and can be a shapeless pulse where the amplitude is constant for $T_p$ or shaped pulse where the amplitude changes during $T_p$, as shown in Figure 18.

The FM pulse, also known as the CHIRP pulse, is a transmission pulse where the frequency changes the ascending or descending order during $T_p$ in seconds, while in the SONAR, the pulse is not frequency modulated at all. It is broadband where the value of $B_p$ is not the inverse of $T_p$, has a high definition in range, a low Doppler effect, and which is classified as linear frequency modulation (LFM), nonlinear frequency modulation (NLFM), and hyperbolic frequency modulation (HFM) as shown in Figure 19.

2.5. Measurement Methodology

The measurement parameters to detect the cavitation effects in a tonpilz-type transducer for an active SONAR transmission system are through the THD-F of the generated acoustic pulse to know the quality of the waveform, TVR to characterize the SONAR system and the SPL that indicates the intensity of the sound at a specified distance. Once the behavior of the system with the TVR is known, the aim is to measure how the cavitation bubbles affect the SPL.

The TVR is measured in decibels ($\mathrm{d}\mathrm{B}$) and provides the pressure in a medium of transmission per unit electrical excitation related to the transmission frequency, which is measured in the direction of the maximum response axis (MRA), as shown in Figure 20. The TVR is the most used electroacoustic parameter to estimate the performance of transducers, underwater electroacoustic systems, or some part of the SONAR system. To obtain the TVR there are various calibration methods for projectors, as mentioned in [35], which can be made by measurements of voltage, current, phase, sound pressure, speed of the particle, or its proportions. The measurement method proposed in this paper is the comparison calibration method, due to one of the fastest and simplest methods. This method uses a calibrated hydrophone at a radial separation distance in a far field ($r$) of 1 $\mathrm{m}$ from the projector with an acoustic reference pressure in the water ($p_r$) of 1 $\mathsf{\mu }\mathrm{P}\mathrm{a}$. The proposed TVR measurement system using the comparison method is shown in Figure 21, where voltage measurements are made to obtain the TVR value using Equation (16), as mentioned in [5].

$$20\log \mathrm{T}\mathrm{V}\mathrm{R}=\left(P_1\right)-20\log M_h+20\log r-\left(P_2\right)$$

(16)

where:

• $P_1=$ $\left(20\mathit{log}{V}_{hc}-G_{pr}+A_h\right)$;
• $P_2=$ $\left(20\mathit{log}{V}_{ap}-R_{vp}-G_{am}\right)$;
• $V_{hc}$ = Hydrophone open-circuit voltage;
• $G_{pr}$ = Preamplifier gain;
• $A_h$ = Hydrophone voltage coupling loss;
• $M_h$ = Hydrophone sensitivity;
• $V_{ap}$ = Voltage applied to the projector;
• $R_{vp}$ = Amplifier voltage ratio;
• $G_{am}$ = Amplifier gain.

On the other hand, SPL is a widely used parameter for sound pressure measurements in acoustic systems. In practical measurement terms, it is defined by Equation (17), where the characteristics of the emission source do not intervene. The objective of measuring the SPL is that with the increase in the electrical power $P_e$, the acoustic power $P_a$ will increase, and at some point, cavitation will occur due to the characteristics of the projector that limit the amount of $P_e$. Cavitation causes bubbles to form on the surface of the projector face, and that causes a decrease $P_a$.

$$20\mathit{log}\mathrm{S}\mathrm{P}\mathrm{L}=\left(P_1\right)-20\mathit{log}{M}_h+20\mathit{log}r$$

(17)

For the square-face tonpilz-type transducer, the minimum separation criterion between the projector and the hydrophone ($r_m$) should be considered with Equation (18), where $L_t$ is the length of one side of the face of the square-face transducer and λ is the wavelength. It is recommended that the measurement is in the far field and not in the near field, as mentioned in [1,2]. Near-field measurement causes large variations with undesired behavior, so far-field measurement is preferable.

$$r_m\ge \frac{{\left(L_t\right)}^2}{\lambda }$$

(18)

2.6. Calibrate Hydrophone

The calibrated hydrophone is essential for underwater measurements due to its frequency response at the reception; it has low variation and high sensitivity within a bandwidth. The calibrated hydrophone used is the model 8103 from the manufacturer Brüel & Kjær, as shown in Figure 22, and its characteristics are presented as follows: Frequency range: 4 $\mathrm{k}\mathrm{H}\mathrm{z}$ a 200 $\mathrm{k}\mathrm{H}\mathrm{z}$ ± 1 $\mathrm{d}\mathrm{B}$, $M_h$: −211.5 $\mathrm{d}\mathrm{B}$ $re$ $1 \mathrm{V}/\mathsf{\mu }\mathrm{P}\mathrm{a}$ = 26.6 $\mathsf{\mu }\mathrm{V}/\mathrm{P}\mathrm{a}$. The values obtained from the hydrophone calibration are provided by the manufacturer and are shown in Figure 23 [36].

3. Implementation and Results

Figure 24 shows the implementation of the SPA with the tonpilz transducer, which has an isolated FBI with a transformer, a type-2 LC filter, and a Cmod-A7 controller that incorporates a 12 $\mathrm{M}\mathrm{H}\mathrm{z}$ clock and a field-programmable gate array (FPGA) Artix-7 for unipolar SPWM modulation. The design of the magnetic components was carried out with the geometry of the core ($K_g$), as mentioned in [37]. For the transformer, the $K_g$ value was obtained by Equation (19), and the nickel/zinc (Ni/Zn) ferrite core of the manufacturer TDK model PQ 40/40 was used. While for the inductors $\mathrm{L}\mathrm{B}1=\mathrm{L}\mathrm{B}2$ and $L_p$, the value of $K_g$ was obtained by Equation (20), and an iron powder toroid core from manufacturer Micrometals model T131-26 was used.

$$K_g=\frac{P_T}{2K_e\alpha }$$

(19)

$$K_g=\frac{{E_h}^2}{K_e\alpha }$$

(20)

where:

• $P_T=$ Total apparent power;
• $\alpha =$ Voltage regulation that has a value $\alpha \le$ 5%;
• $K_e=$ Electrical conditions coefficient;
• $E_h=$ Energy-handling capability.

Figure 25 shows the waveform of the full-bridge inverter output voltage with a value of $M_a=0.9$ with unipolar SPWM modulation and an effective input voltage of 150 $\mathrm{V}\mathrm{C}\mathrm{D}$ with frequencies of $M_s=11.6 \mathrm{k}\mathrm{H}\mathrm{z}$ and $C_s=187.5 \mathrm{k}\mathrm{H}\mathrm{z}$ while Figure 26 shows the value of $P_e=1100 \mathrm{V}·565 \mathrm{m}\mathrm{A}·\mathrm{c}\mathrm{o}\mathrm{s}\left(23.44°\right)=570.21 \mathrm{W}$ by Equation (10) with a value of $M_a=0.9$. On the other hand, the amount of total harmonic distortion of the fundamental waveform (THD-F) of the output voltage of the SPA or voltage applied to the projector ($V_{ap}$) depends on several considerations in the parameters such as the values of $M_s$, $C_s$, $Z_t$ and $P_e$ that is controlled by means of $M_a$. Therefore, when changing any value of these parameters, the value of THD-F will change. Figure 27 shows a value of THD-F $=4.52\%$ with a CW transmission pulse with values of $M_s=11.6 \mathrm{k}\mathrm{H}\mathrm{z}$, $C_s=187.5 \mathrm{k}\mathrm{H}\mathrm{z}$ and $M_a=0.9$.

Table 4. Electrical power and THD-F of $V_{ap}$ vs. M_a.

$${\mathit{M}}_{\mathit{a}}$$	$${\mathit{V}}_{\mathit{r}\mathit{m}\mathit{s}}\mathbf{\left(}\mathbf{V}\mathbf{\right)}$$	$${\mathit{I}}_{\mathit{r}\mathit{m}\mathit{s}}\mathbf{\left(}\mathbf{m}\mathbf{A}\mathbf{\right)}$$	Lag (°)	$${\mathit{P}}_{\mathit{e}}\mathbf{\left(}\mathbf{W}\mathbf{\right)}$$	$$\mathbf{THD}-\mathbf{F}\mathbf{(}\mathbf{\%}\mathbf{)}$$
0.1	12.1	20.9	66.98	0.098	3.18
0.2	83.1	62.6	53.58	3.08	4.15
0.3	181	106	35.16	15.68	3.27
0.4	266	142	31.32	32.26	3.04
0.5	381	195	28.12	65.52	2.65
0.6	511	248	25.74	114.15	2.84
0.7	677	318	24.40	196.05	2.93
0.8	858	405	23.83	317.86	3.24
0.9	1100	565	23.44	570.21	4.52

M_s = 11.6 kHz.

shows a summary of $P_e$ and THD-F of $V_{ap}$ with different values of $M_a$.

A way to detect cavitation is visual. Therefore, as an observation method, the transducer was placed in the infrastructure of a hydroacoustic tank that is covered with sound-absorbing wedges and has dimensions of 9 $\mathrm{m}$ long, 4.5 $\mathrm{m}$ wide, and 4.5 $\mathrm{m}$ depth, as shown in Figure 28. The projector was mounted on a structural aluminum profile with a longitudinal and transverse middle location of the hydroacoustic, where only for this observation test a waterproof camera was placed inside the tank as shown in Figure 29. The value of $P_{em}$ was obtained with Equation (2) and was the following values: $A_r=0.036{\mathrm{m}}^2$, $U_c=0.4kW$ for a depth = 1 $\mathrm{m}$, $k_L=1$ for $T_p\le 0.5\mathrm{m}\mathrm{s}$ and $k_L=3$ for $T_p>0.5\mathrm{m}\mathrm{s}$, $k_f=1.16$ for $M_s=11.6\mathrm{k}\mathrm{H}\mathrm{z}$. When P_e > P_m the cavitation occurs, forming bubbles in the face of the transducer, as shown in Figure 30, and

Table 5. Observation of transducer cavitation.

${\mathit{M}}_{\mathit{a}}$	${\mathit{T}}_{\mathit{p}}=0.5\mathbf{m}\mathbf{s}$	${\mathit{T}}_{\mathit{p}}=5\mathbf{m}\mathbf{s}$
	${\mathit{P}}_{\mathit{e}\mathit{m}}=50\mathbf{W}$	${\mathit{P}}_{\mathit{e}\mathit{m}}=16\mathbf{W}$
	Cavitation	Cavitation
0.1	×	×
0.2	×	×
0.3	×	×
0.4	×	×
0.5	×	×
0.6	×	✓
0.7	×	✓
0.8	✓	✓
0.9	✓	✓

$M_s=11.6$ kHz, depth = 1 $\mathrm{m}$.

shows a summary of transducer cavitation observation, which for this observation experiment was presented from a value of $M_a=0.8$ with power value $\left(4{·P}_e\right)>P_{em}$ with respect to the results of Table 4, where × indicates no cavitation and ✓ presence of cavitation.

In order to detect cavitation with a measurement parameter, the projector, and the hydrophone were mounted in the hydroacoustic tank, as shown in Figure 31, while Figure 32 shows the instruments and measurement equipment that were used, and their characteristics are briefly described below:

• Oscilloscope MDO3024, Bandwidth $200\mathrm{M}\mathrm{H}\mathrm{z}$, Sampling Rate $2.5\mathrm{G}\mathrm{S}/\mathrm{s}$;
• Function generator AFG3022C, Bandwidth $25\mathrm{M}\mathrm{H}\mathrm{z}$, Sampling Rate $250\mathrm{M}\mathrm{S}/\mathrm{s}$;
• Low-Noise Preamplifier SR560, Bandwidth $1\mathrm{M}\mathrm{H}\mathrm{z}$, 4 nV/√Hz input noise.

Table 6. THD-F of $V_{hc}$ vs. M_a.

${\mathit{M}}_{\mathit{a}}$	${\mathit{V}}_{\mathit{r}\mathit{m}\mathit{s}}$ ($\mathbf{V}$)	$\mathbf{THD}-\mathbf{F}$ (%)
0.1	0.019	2.33
0.2	0.134	2.93
0.3	0.269	3.12
0.4	0.395	3.20
0.5	0.561	3.85
0.6	0.754	4.05
0.7	0.870	6.17
0.8	0.999	10.2
0.9	1.07	18.5

M_s = 11.6 kHz, preamplifier gain (G_pr = 20 dB).

shows a summary of the results obtained in the measurement of THD-F of the generated acoustic pulse, which is the open circuit voltage of the calibrated hydrophone ($V_{hc}$) with different values of $M_a$. The results show that the cavitation bubbles affect the $V_{hc}$ waveform; the amount of THD-F begins to increase significantly from a value of $M_a=0.7$ and slightly changes its amplitude, as shown in Figure 33.

The TVR and SPL measurement parameters that generally measure the performance of the active SONAR transmission system were obtained with the measurements of the voltages $V_{ap}$ and $V_{hc}$ are placed in a program with MATLAB^® software where a local area network (LAN) of Ethernet communication is available, assigning internet protocol (IP) addresses to the computer equipment, the oscilloscope, and the function generator. The program sends and receives commands in backus-naur form (BNF) notation that uses different symbols and special characters in ASCII code, based on a standard commands for programmable instruments (SCPI) language using a programming environment defined by messages, instrument response, and data format [38,39]. For example SOURce1:FREQuency 100% Generator source signal at the frequency of 100 $\mathrm{H}\mathrm{z}$. It is important to mention that in order for the instruments to communicate the computer equipment with MATLAB^®, the NI-VISA package must be installed [40]. This package is an instrument controller that uses an application programming interface (API).

Figure 34 shows the TVR, which indicates the frequency where the active SONAR system is most efficient in transmitting the underwater acoustic pulse. It can be seen that the highest value of the TVR is in $f_{rw}=11.6$ kHz that corresponds to the measurement of $Z_{tw}$, which is shown in Figure 11. The TVR was obtained with the following characteristics:

• Initial frequency ($f_{ini}$): $5\mathrm{k}\mathrm{H}\mathrm{z}$;
• Final frequency ($f_{fin}$): $20\mathrm{k}\mathrm{H}\mathrm{z}$;
• Frequency step (${ST}_f$): $100\mathrm{H}\mathrm{z}$;
• Signal type: CW burst;
• Pulse length ($T_p$) = $0.5\mathrm{m}\mathrm{s}$;
• Pulse Repetition Interval (PRI): $5\mathrm{s}$;
• Amplifier voltage ratio ($R_{vp}$): Direct measurement;
• Electrical attenuation of the hydrophone ($A_h$): $-1.5\mathrm{d}\mathrm{B}$;
• Radial distance of hydrophone to the projector ($r$): 1 m;
• Depth: $1\mathrm{m}$;
• Amplifier gain ($G_{am}$): Direct measurement;
• Preamplifier gain ($G_{pr}$): $20\mathrm{d}\mathrm{B}$.

Figure 35 shows the TVR with different levels of $M_a$, and it can be seen that in most cases, the TVR tends to have a similar behavior because the values of $P_e$ and $P_a$ increase or decrease in the same proportion. However, the results show that from a value of $M_a=0.7$ the behavior of the TVR is not as expected, where the most significant change in the behavior of the TVR occurs at the resonance frequency where the cavitation occurs. On the other hand, Figure 36 shows the SPL with different levels of $M_a$ at a distance of 1 m from the projector with respect to the calibrated hydrophone. The results show that the SLP generated by the active SONAR transmission system gradually increases with respect to the value of $M_a$. However, for the cases where the value of $M_a=0.8$ and $0.9$ where cavitation occurs, the behavior of the SPL is not as expected. The behavior of the TVR and SPL parameters is similar for the cases where cavitation occurs, as shown in Table 5 and Table 6, where it affects the amplitude and, consequently, the performance of the system. Therefore, the previous results show the values of $M_a$ where cavitation is detected.

4. Conclusions

An experimental measurement methodology is presented to detect the cavitation effects in a tonpilz-type transducer for an active SONAR transmission system using a transducer as a projector and a calibrated hydrophone in a hydroacoustic tank. In the active SONAR transmission system, the transducer was excited using a developed prototype of SPA with an electrical output power of 570.21 W and THD-F < $5\%$. A full-bridge inverter topology with SPWM modulation was used to generate a CW acoustic pulse, and the efficiency of the system was increased with the connection of the parallel inductor to the transducer, obtaining a lag of 23.44° of the current with respect to the voltage.

The results show that the cavitation in the transducer was detected with a visual observation method with a waterproof camera where the cavitation occurred at the levels of $M_a=0.8$ and $0.9$ with the transducer at 1 $\mathrm{m}$ of depth. Cavitation was also detected by measuring the amount of THD-F of $V_{hc}$ from the value of $M_a=0.7$, which corresponds to a value of $P_e=196.05$ W, and it is suggested to measure this parameter with an oscilloscope. On the other hand, the results of the measurements of the behavior of the TVR and SPL parameters show that cavitation is detected from the value of $M_a=0.8$, because the behavior of these parameters is not as expected, and it is suggested that they be measured to know in more detail the performance of the active SONAR transmission system.

With the results obtained, it can be deduced that a practical application to detect cavitation in an active SONAR transmission system that is in operation is by measuring the amount of THD-F of the echo of the acoustic pulse that returns to the same transducer or hydrophone. Therefore, the power controller of the SONAR system must regulate the level of $P_e$ based on the experimentation of the value of THD-F of the echo of the acoustic pulse.

As future work for the developed active SONAR transmission system, the implementation of a closed-loop controller to regulate the $P_e$ level and prevent cavitation in the transducer by measuring the amount of THD-F of the echo of the acoustic pulse. Moreover, add in the SPA a closed loop circuit to control the SPL level for CW and FM acoustic transmission pulses at different frequencies.