Research on the Optimization of Synchronous Switch Energy Harvesting Circuit Based on Capacitor

Abstract

As advanced systems continue to advance and fuse functions expand, the demand for higher power supply requirements for fuses has increased. Consequently, researchers have turned their attention to the recovery of energy from the environment. Piezoelectric energy harvesting has gained significant popularity due to its advantageous characteristics, such as high energy density, ease of implementation, and compact size. However, the presence of various component types within the energy harvesting circuit inevitably results in the generation of reactive power, leading to a reduction in the circuit’s power factor. To address this issue, this paper introduces the adoption of the third-order valley-fill circuit as the power factor correction circuit. The implementation process involves the utilization of Multisim software to simulate the double-limit zero-crossing detection circuit, pulse signal generation circuit, and power factor correction circuit. Furthermore, the aforementioned circuits were subjected to plate-level welding, followed by individual tests to evaluate the effectiveness of the double-limit zero-crossing detection, pulse signal test, and load voltage measurement. These findings unequivocally exemplify the successful accomplishment of the intended objective of augmenting the output power by the third-order valley-fill circuit.

1. Introduction

The advancement of Microelectromechanical Systems (MEMS) technology has led to the increased utilization of low–power devices in ammunition, including MEMS accelerometers [1], MEMS gyroscopes [2], and MEMS actuators [3]. This proliferation of devices has expanded the capabilities of ammunition systems but has also necessitated higher power supply requirements. Achieving a balance between large capacity and small size in the power supply is challenging, particularly for small caliber ammunition and submunitions. Consequently, the demand for power supply in these specific types of ammunition is becoming increasingly stringent. How to save energy and produce electricity efficiently has become a concern of many researchers.

The process of recovering energy from natural environmental systems and converting it into usable energy is called energy harvesting. It is a very practical and meaningful technology to collect energy from the surrounding environment and convert it into energy that can be used by the device.

Ammunition systems involve set–back force (refers to the recoil when the bullets and shells are ejected) and centrifugal force (refers to the outward force generated because the projectile maintains a certain speed on the trajectory) during launch, and wind resistance, centrifugal force, and other environmental forces during flight. Piezoelectric generators can effectively convert external forces in the gun and during flight into electric energy for the use of the system, such as igniting the detonator. As a component connecting the piezoelectric structure and the power supply load, the energy harvesting circuit can convert a certain frequency of alternating current into direct current. Its functions include AC–DC conversion, power conditioning, voltage stabilization, and load matching.

In recent years, the structure and parameters of the recovery circuit have been studied by domestic and foreign scholars. On the one hand, the piezoelectric energy harvesting system is becoming smaller and easier to implement and operate. On the other hand, optimizing the circuit makes the loss of the system smaller and improves the output efficiency. In 2002, Ottmans et al. first applied the standard energy harvesting circuit (SEH) [4] and carried out modeling and theoretical analysis. In 2005, Guyomar et al. developed a parallel synchronous switching circuit (P–SSHI) [5], which used an inductor–capacitor resonant circuit to achieve a voltage flip when the equivalent current of the piezoelectric sensor changed direction at the peak value. This not only increased the voltage at both ends of the piezoelectric sensor but also accelerated the voltage flip direction, resulting in reduced loss. In 2006, Lefeuvre et al. put forward a series of synchronous switch–inductor recovery circuits (S–SSHI) [6], which served switches and inductors between the piezoelectric element and the rectifier bridge. The voltage of the piezoelectric element was nonlinearly synchronized by controlling the on–off of the switch, which improved the open–circuit output voltage and reduced the charge consumption of the equivalent capacitance inside the piezoelectric element, but controlling the on–off time and sequence of the switch was difficult. They also provided a synchronous charge extraction circuit (SECE) [7], which is used to disconnect the piezoelectric element from the rear load circuit for most of the time; this made the SECE have a decoupling effect, and the output power independent of the load. In 2010, Ramadass et al. designed and implemented a high–efficiency piezoelectric vibration energy harvesting chip based on P–SSHI technology [8]. Compared with the standard energy harvesting circuit, the output power increased by about four times. In 2011, Krihely et al. advanced an improved P–SSHI circuit [9]. Under constant harmonic excitation, compared to the standard energy harvesting circuit, the output power was enhanced by 2.3 times. In 2012, Junrui Liang et al. presented an enhanced self–powered SSHI (SP–SSHI) circuit [10]. The experimental results showed that the output power raised two times compared with the full–bridge rectifier circuit. In 2014, Dongyu Shi proposed a new energy recovery interface circuit (SCEI) [11], which combines the SECE circuit and the P–SSHII circuit, and its maximum recovered power is 1.5 times that of the SECE circuit as verified by the theoretical formula derivation and experimental circuit. In 2015, Lu et al. offered a simple and efficient P–SSHI circuit [12], in which two comparators were used to monitor the change of voltage at both ends of the piezoelectric energy harvesting device, and the MOSFET was used to control the on–off of the switch. In contrast to the traditional full–bridge rectifier circuit, the energy harvesting of the self–powered P–SSHI rectifier circuit was improved by 5.8 times. In 2017, Si jun Du et al. presented a synchronous switch harvesting on a capacitor circuit (SSHC) [13]. When the current of the piezoelectric element crossed zero, the SSHC circuit realized the voltage flip of the piezoelectric element through the multi–stage charge transfer between the external capacitance and the internal capacitance of the piezoelectric element. The circuit could improve the piezoelectric flip efficiency, and the output power has heightened by 9.7 times that of the standard piezoelectric energy harvesting circuit. In 2017, Zhiyuan Chen et al. came up with an inductorless capacitor–flipping rectifier for piezoelectric energy harvesting [14]. This new development realized the multi–stage bias flipping of the voltage at both ends of the piezoelectric element and achieved accurate zero–crossing detection. In 2018, Liang Junrui et al. proposed a synchronous three–bias voltage reversal power conditioning circuit [15]. The experimental results showed that the collection power of the circuit was 24.5% higher than that of the P–SSHI circuit. In 2019, based on the traditional SSHC circuit, Mickael Lallart et al. proposed a Synchronized Switch Harvesting on Oscillator (SSHO) circuit [16]. The experimental results showed that the output power of the circuit was increased by 30%. In 2019, Sundeep Javvaji et al. put forward a multi–stage bias flip circuit [17]. The experimental results showed that the voltage flip efficiency of this circuit was as high as 89.5%. In 2020, Xiaoliang Ding et al. designed an enhanced dual–intermediate capacitor energy recovery circuit (E–DICH) [18,19]. The results showed that the recovered power of the E–DICH is load–independent, and its maximum recovered power was improved by 440% and 90% when compared to the SEH circuit and SECE circuit, respectively.

Throughout the trajectory of the projectile, the piezoelectric structure effectively harnesses and transforms the vibration energy present within the airflow resonant cavity of the fuse head into electrical energy. This phenomenon is particularly pronounced due to the projectile’s considerable velocity, resulting in the generation of vibration energy at a significantly elevated frequency, consequently yielding an electric energy output of equally heightened frequency from the piezoelectric structure. The energy harvesting circuit within the ammunition system necessitates the retrieval of electrical energy at a heightened frequency, while simultaneously minimizing energy loss and enhancing the power output of the load. The circuit presented in this paper primarily serves the purpose of rectifying and optimizing the converted electric energy. The precise control of the synchronous switch in the SSHC circuit is achieved through the implementation of a zero–crossing detection circuit and pulse signal generation circuit, enabled by synchronous switch energy harvesting technology. Additionally, a third–order valley–filling circuit is added between the rectifier bridge and the load in order to improve the circuit power factor and achieve the purpose of increasing the output power.

2. Theoretical Model

As shown in Figure 1, during the flight of a projectile, the incoming air flows through a circular nozzle placed at the head of the projectile or the fuse. Initially, the airflow undergoes a transition from laminar to turbulent flow, generating stable pulsating turbulence. Subsequently, the vortex shedding phenomenon occurs (the vortex gradually loses stability in the fluid and breaks away from the fluid) in the airflow from the nozzle outlet, which causes the static airflow in the cavity outside the resonant cavity to form a vortex ring (rotating structure formed in the fluid also known as Carmen Vortex Street). At the sharp edge of the resonant cavity in the front end of the sound pipe, the vortex ring produces an edge tone, which induces the generation of a fluid–dynamic acoustic source [20,21].

The majority of this sound wave propagates through the holes inside the resonant cavity and reaches the bottom of the cavity. After reflection at the bottom of the resonant cavity, it encounters the vortex ring again at the nozzle exit. Due to the “fluid–solid–sound” coupling effect, the sound intensity is amplified, and the enhanced sound wave is propagated back through the holes inside the resonant cavity to its bottom. It is then reflected to the sharp edge, and this process repeats. The superposition of incident and reflected waves inside the resonant cavity eventually forms a standing wave state, resulting in a stable fluid–dynamic acoustic source (the source is sinusoidal). The standing wave as the vibration source directly acts on the transducer to output electrical energy, and the electrical energy processing circuit provides stable electrical energy to the load.

The piezoelectric model of energy harvesting structure is a three–layer cantilever beam structure. The upper and lower ends are connected to two electrodes, respectively, and the piezoelectric material is in the middle, as shown in Figure 2a [22]. When the projectile is flying in the trajectory, the airflow causes the free end of the cantilever beam to deform, and the piezoelectric material attached to the surface of the cantilever beam also deforms with the bending of the cantilever beam. Due to the piezoelectric effect of the piezoelectric material, the electrical energy is output from the upper electrode and the lower electrode of the piezoelectric material, which completes the conversion from mechanical energy to electric energy.

In order to simplify the electromechanical coupling model of the piezoelectric energy harvester, the equivalent circuit method is used to simplify the piezoelectric cantilever model for theoretical calculation and model simulation. The electromechanical coupling of the piezoelectric cantilever beam can be equivalent to a single degree of freedom system of spring–mass–damping, as shown in Figure 2b [23,24]. Since the acoustic source acting on the piezoelectric element is a stable fluid–dynamic acoustic source, which will be assumed to be sinusoidal in the article, the acoustic source acts on the piezoelectric element to cause vibration of the piezoelectric element, and therefore the motion displacement of the piezoelectric element is sinusoidal. Ignoring the loss of resistance of the piezoelectric element, the piezoelectric element can be equivalent to a circuit model with a current source and a capacitor in parallel, as shown in Figure 2c [25].

According to the kinetic law of energy conservation, the electromechanical equation and motion equation of the piezoelectric cantilever beam are

$$F+F_p=M\ddot{u}+C\dot{u}+\left(K_{PE}+K_S\right)u+\alpha V$$

(1)

$$I=\alpha \dot{u}-C_P\dot{V}$$

(2)

where F denotes the external excitation force applied to the piezoelectric energy harvester; $F_p$ indicates the reaction force generated by the inverse piezoelectric effect on the piezoelectric cantilever beam; $u$ specifies the equivalent mass displacement; $C$ refers to the equivalent damping of the piezoelectric energy harvester; $K_S$ dictates the equivalent stiffness coefficient; $M$ is the equivalent mass, at the same time; $V$ and $I$ designate the output voltage and output current of the piezoelectric element, respectively; $\alpha$ stands for the stress intensity factor of the piezoelectric element; $C_P$ denotes the equivalent capacitance of the piezoelectric element; and $K_{PE}$ dictates the short–circuit equivalent stiffness coefficient of the piezoelectric element.

The individual parameters in Equations (1) and (2) are calculated as follows:

$$C_P=\frac{{\epsilon }_{33}^S{A}_{xy}}{d_0}$$

(3)

$$\alpha =\frac{e_{31}{A}_{yz}}{l}$$

(4)

where ${\epsilon }_{33}^S$ refers to the dielectric constant when S is zero or constant; $e_{31}$ stands for the piezoelectric stress factor; $d_0$ and $l$ denote the thickness and length of the piezoelectric element respectively; $A_{xy}$ and $A_{yz}$ designate the area of the upper and lower surfaces of the piezoelectric element and the lateral area respectively.

Suppose $u=-U_M\cos \left(\omega t\right)$, Equation (2) becomes

$$I=\omega \alpha U_M\sin \left(\omega t\right)-C_P\dot{V}$$

(5)

Since $I_P=\omega \alpha U_M$, Equation (5) becomes

$$I=I_M\sin \left(\omega t\right)-C_P\dot{V}$$

(6)

The RMS value of the open circuit voltage at both ends of the piezoelectric element is

$$V_P=\frac{I_M}{\sqrt{2}\omega C_P}=\frac{\alpha U_M}{\sqrt{2}{C}_P}$$

(7)

3. SSHC Circuit of Single Capacitor

In Figure 3a,b, a single capacitor SSHC circuit diagram [26] and a timing diagram of the SSHC circuit [27] are shown. The circuit uses capacitance instead of inductance to realize the charge transfer of capacitance $C_P$. The charge transfer between capacitance $C_P$ and $C_1$ is controlled by opening and closing the switch, which accelerates the flip of the voltage at both ends of the piezoelectric element and improves the energy harvesting efficiency. Figure 3 shows the process of $V_{PT}$ flipping from positive to negative in the SSHC circuit of a single capacitor.

The working principle is as follows: in the whole working process, all switches are in the off state most of the time. Figure 3a shows the operation of the circuit before the voltage $V_{PT}$ flips from positive to negative, and the output of the piezoelectric element powers the load through the rectifier bridge. When the vibration displacement of the piezoelectric element reaches the maximum value, as shown in Figure 3c, the current $I_P$ is about to pass zero–point from the positive to negative, and the switch S₂ is closed so that the capacitor $C_P$ charges $C_1$. Charging is completed until the voltages of the two capacitors are equal. At this time, the first phase of the voltage flip is completed, and the switch S₂ is disconnected. Therefore, the voltage across $C_P$ and $C_1$ is

$$V_1=V_{PT}=\frac{C_P}{C_P+C_1}\left(V_R+2V_D\right)$$

(8)

where $V_1$, $V_{PT}$, $V_R$, and $V_D$ are the voltages across the $C_1$, piezoelectric element, $R_L$, and diode conduction voltage, respectively.

As shown in Figure 3d, in the second stage, switch S₁ is closed, which leads to the capacitor $C_P$ being short–circuited, and its voltage drops rapidly to zero, so that switch S₁ is disconnected. Hence, the voltage across $C_P$ and $C_1$ at the end of the second phase is

$$V_1=\frac{C_P}{C_P+C_1}\left(V_R+2V_D\right)$$

(9)

$$V_{PT}=0$$

(10)

As shown in Figure 3e, in the third stage, switch S₃ is closed, capacitors $C_P$ and $C_1$ are connected in reverse parallel, and capacitor $C_1$ reverses the charging of $C_P$ until the voltages of the two capacitors are equal. The third stage of voltage flip–flop is completed, and switch S₃ is disconnected. At this time, the voltages $V_{PT}$ and $V_1$ at the end of the third phase are

$$V_1=V_{PT}=-\frac{C_P{C}_1}{{(C_P+C_1)}^2}\left(V_R+2V_D\right)$$

(11)

From Equation (11), it follows that $V_{PT}$ after flip–flop can take its maximum value when $C_P$ and $C_1$ take equal values. The voltage flip efficiency is defined as the absolute value of the voltage ratio before and after the reversal; the efficiency of this voltage flip is 25%.

Since the $V_{PT}$ does not reach the threshold of diode conduction, the current source will charge the internal capacitor $C_P$. After reaching the threshold, the diode is turned on and supplies power to the load. When the $I_P$ passes the zero–point from the negative to positive, the second voltage flip begins.

After the second voltage flip, the voltage at both ends of $C_P$ and $C_1$ is

$$V_1=V_{PT}=\frac{5}{16}\left(V_R+2V_D\right)$$

(12)

The result $\left|V_{PT}\right|$ at the end of the nth voltage flipping stage is

$$\left|V_{PT}\right|=\frac{1}{3}\left(V_R+2V_D\right)\left(\mathrm{n}\to \infty \right)$$

(13)

From Equation (11), the voltage flip efficiency of the single–capacitor SSHC circuit is 33%.

The output voltage $V_S$ and power $P_S$ at the two ends of the load are, respectively,

$$V_S=\frac{2\alpha U_M{R}_L}{\pi +(1-\lambda )\omega R_L{C}_P}$$

(14)

$$P_S=\frac{V_S^2}{R_L}=\frac{4{\alpha }^2{U}_M^2{\omega }^2{R}_L}{{[\pi +(1-\lambda )\omega R_L{C}_P]}^2}$$

(15)

The relationship between the output voltage ripple ∆V and the input capacitance C_r of the valley–fill circuit is

$$△V=\frac{△I}{2f{C}_r}=\frac{\pi △I}{\omega C_r}$$

(16)

where ∆I is the ripple amplitude of load current and f denotes the frequency of the circuit.

4. Materials and Methods

4.1. Circuit Design Scheme

In the proposed energy harvesting circuit, the traditional zero–crossing detection is generally realized by a hardware zero–crossing comparator. However, in practical applications, the comparator is easily affected by offset voltage, noise, and harmonics. There is a large error between the zero point of the actual voltage and the extracted zero point, resulting in the output delay of the zero point signal, leading to a decrease in the output power of the circuit. In the traditional SSHC circuit, the discharge time of the capacitor is generally adjusted by manually controlling the value of the capacitor, and then the pulse width of the synchronous control signal is changed. On the one hand, this method is not accurate enough. On the other hand, it cannot adjust the pulse width adaptively, resulting in reduced output power.

Based on the above shortcomings, it can be seen from Scheme 1 that, based on the SSHC circuit of a single capacitor, this paper introduces a sampling resistor R₁, and the zero–crossing signals PN and NP are output. After receiving two zero–crossing signals, the pulse generation circuit generates switch control signals K₁, K₂, and K₃ to accelerate the voltage flip. In addition, a passive power factor correction circuit is added between the rectifier circuit and the load, which quickly stores power by series connection of capacitors during charging and releases more power by parallel connection of capacitors during discharging to increase the active power of the circuit.

4.2. Operational Principle

4.2.1. Double–Limit Zero–Crossing Detection Circuit

The double–limit zero–crossing detection circuit is to collect the zero–crossing signal of the current source. By extracting the voltage waveform, the two zero–crossing signals of the current source are obtained, namely from positive to negative and from negative to positive. As shown in Figure 4, this circuit is a double–limit zero–crossing detection circuit. The characteristic of the circuit is that the pulse width of the zero–crossing signal can be controlled by adjusting V₂ and V₃, and then the accuracy of the circuit control can be adjusted.

The circuit’s working principle is as follows: in a cycle, when the input signal V_in > V₂, the 1–pin and 2–pin of the comparator output high level and low level, respectively, and through the AND gate output low level. When V₃ < V_in < V₂, the comparator’s 1–pin output remains unchanged, the 2–pin becomes high, and the high level is output through the AND gate. When V_in < V₃, the comparator 1–pin output low level, 2–pin output unchanged, and through the AND gate output low level. When V₃ < V_in < V₂ occurs again, the comparator’s 1–pin output high level, the 2–pin output unchanged, and through the AND gate output high level. The above output signal through the AND gate is a zero–crossing signal V₀, which is not distinguished. Input the V₀ signal into the JK flip–flop whose J and K terminals are both high, pass the signal at the output of the JK flip–flop through the NOT gate, and then pass the output signal of the NOT gate and the V₀ signal through the AND gate to obtain the PN signal. The signal at the output of the JK flip–flop and the V₀ are passed through the AND gate to obtain the NP signal. The PN signal and the NP signal in the above represent the zero crossing signals of voltage from positive to negative and from negative to positive at the ends of the piezoelectric element, respectively. The double–limit zero–crossing detection circuit can adjust the reference voltage according to the required accuracy in order to meet the design requirements.

4.2.2. Pulse Signal Generation Circuit

As shown in Figure 5, the pulse signal generation circuit is driven by the zero–crossing signal in order to control the switches accurately in the SSHC circuit.

When V_PT first flips from positive to negative, the working principle of the pulse signal generation circuit is as follows:

In the first stage, P₁ is low level initially, then P₁ and zero–crossing signal PN pass through the AND gate to make K₁ high level, resulting in the switch S₂ becoming closed, and C_p begins to charge C₁. In the process of charging, the current flows through R₁, and the voltage difference between the two ends of R₁ is generated. The output signal amplified by the amplifier is reversed to obtain the A₁ signal. The A₁ signal is connected to the pulse extraction module, and the P₁ signal will copy the rising edge signal of A₁ and keep the high level to the PN signal clearing. At this time, the reverse P₁ and PN pass through the AND gate, which leads to the K₁ signal becoming low level, and the control switch S₂ is disconnected. At the same time, since P₂ is low level and K₂ becomes high level, therefore, the switch S₁ is closed.

In the second stage, after the A₁ signal and the P₁ signal after delay pass through the AND gate, the pulse of A₁ in the first stage is filtered out. Then the rising edge of the A₁ signal is extracted, and the P₂ becomes and remains at a high level until the zero–crossing signal is cleared. At this time, P₂ becomes low level and the switch S₁ is disconnected. At the same time, since P₃ is low level and K₃ becomes high level, the switch S₃ is closed.

In the third stage, the A₁ signal and P₂ after delay pass through the AND gate, filter out the pulses in the first two stages of A₁, and then extract the rising edge, and P₃ becomes and remains high level until the zero–crossing signal is cleared. At this time, K₃ becomes low level, and the switch S₃ is disconnected.

The above three stages are the description of the positive to negative flip process of voltage V_PT, and the process of negative to positive flip is similar and no longer described.

4.2.3. Passive Power Factor Correction Circuit

The entire piezoelectric energy harvesting system uses a large number of nonlinear components, increasing the reactive power of the system, and, at the same time, leading to a lower power factor and a lower active power provided to the load. By correcting the power factor, the power factor angle of the entire system is increased, thereby improving the recovery efficiency.

As shown in Figure 6, the third–order Valley–fill circuit is charged and discharged by a capacitor paralleled behind the rectifier diode, so that the current flowing through the load R_L is no longer a pulsating peak pulse. The working principle is as follows: when the voltage at both ends of the load R_L begins to rise, the diodes D₅ and D₆ are turned on, and the diodes D₇, D₈, D₉, and D₁₀ are cut off. The steady–state sinusoidal excitation begins to charge the capacitors C₂, C₃, and C₄ in the valley–fill circuit. At this time, C₂, C₃, and C₄ are in series. According to the capacitance series formula, the total capacitance after the series is reduced, the capacitance will be filled quickly, and the capacitance filling time is reduced. When the voltage at both ends of the load R_L begins to decrease after the peak, the diodes D₇, D₈, D₉, and D₁₀ are turned on, and the diodes D₅ and D₆ are cut off. The voltage generated by the steady–state sinusoidal excitation is smaller than the voltage across the capacitors C₂, C₃, and C₄. The rectifier diode is turned off, and the capacitors C₂, C₃, and C₄ are connected in parallel to supply power to the load R_L until the next rectifier voltage peak arrives.

Compared to the second–order valley–fill circuit, the third–order valley–fill circuit has a faster capacitor charging and discharging speed, so that in a cycle of the piezoelectric vibrator displacement, the rectifier diode has more conduction time, and the harmonic content of the current waveform is less, thereby increasing more power factor angles and higher energy harvesting efficiency.

5. Results

5.1. Simulation Results

The circuit designed in this paper is simulated and analyzed by Multisim software. Due to the similar working process of voltage flipping from positive to negative and from negative to positive, this paper just simulates and analyzes the voltage flipping process from positive to negative. Because the ammunition system is small in size and thick in the wall, its natural frequency is high (generally kHz level). In this paper, 1 kHz is selected as the frequency of the current source.

In this paper, the piezoelectric ceramic is selected as the piezoelectric sheet, the diameter of the piezoelectric sheet is 30 mm, the thickness is 0.2 mm, at the same time, ${\epsilon }_{33}^S=2.08\times {10}^{-8} \mathrm{F}/\mathrm{m}$, $e_{31}=1.48 \mathrm{N}/\mathrm{V}\mathrm{m}$, and then the piezoelectric element is equivalent to the parallel connection of the current source and capacitance. After calculating and analyzing, the parameters of the main components are shown in

Table 1. Parameters of the main components.

Parameters	Notation	Value
Current source	IP	5 mA,1 kHz
equivalent capacitance of the piezoelectric element	CP	147 nF
stress intensity factor	α	0.93 mN/V
Flip–flop capacitor	C1	147 nF
Capacitance in valley–filling circuits	C2= C3= C4= Cr	1 μF

.

From Figure 7a, the voltage V₁ at both ends of the capacitor C₁ always flips at the time of zero crossing, which is in line with expectations. From Figure 7b,c, it can be seen that NP and PN act as zero–crossing signals from positive to negative and from negative to positive in the zero–crossing waveform, respectively, realizing the distinction between the two zero–crossing signals. From Figure 7b,c, it can be seen that V₂ and V₃ are ±0.05 V and ±0.5 V respectively, and the width of the zero–crossing signal varies greatly, which also verifies the effectiveness of the double–limit zero–crossing.

Figure 7d,e shows the whole process of signal P₁ generation. From the diagram, it can be seen that when the zero–crossing signal PN is high level, the A₁ signal becomes the signal A₂ after delay. When signal A₂ is the rising edge, the signal P₁ is triggered from low level to high level and maintained until the zero–crossing signal PN becomes low level. It can be seen that the signal P₁ remains high level throughout the zero–crossing period after being triggered, which provides the condition for the subsequent AND operation to filter the signal.

Through the above description, it can be inferred that the generation process of signals P₁, P₂, and P₃ is similar, and the difference is that the time and order are different. As shown in Figure 7f, all three signals are triggered after the delay of the signal A₁ and remain until the zero–crossing signal PN becomes low level.

Figure 7g–i shows the generation process of switching signals K₁, K₂, and K₃ in the main circuit, that is, when V_PT flips from positive to negative or from negative to positive, the closing sequence of switching signals is different. From the diagram, when V_PT flips from positive to negative, the closing sequence is K₁–K₂–K₃. When V_PT flips from negative to positive, the closing sequence is K₃–K₂–K₁. The closing time of the three switching signals is also different, the reason is that the voltage at both ends of the flip capacitor and the time of charge transfer are different in the three stages of voltage flip.

The observation depicted in Figure 8a reveals a positive correlation between the load and the output voltage, with the rate of increase gradually diminishing. Additionally, Figure 8b demonstrates that higher C_r values enhance the stability of the output voltage, albeit at the cost of increased response time. Stability is mainly characterized by the fluctuation of the voltage value within a certain range, the smaller the range the better the stability. Response time is mainly the time it takes for the voltage value to reach a stabilized value. Due to the circuit’s application in a fuse, it becomes imperative to ascertain the value of Cr. In this study, a value of 1 μF has been chosen. As depicted in Figure 8c, it is evident that the load’s output voltage and output power exhibit an inverse relationship as the load intensifies, eventually reaching a state of gradual stabilization. Based on the data presented in Figure 8d, when the current source is 5 mA and the load is 10 kΩ, the voltage at both ends of the load remains constant at 3.75 V in the absence of the power factor correction circuit. Furthermore, the output power is measured to be 1.41 mW. Conversely, when the power factor correction circuit is employed, the voltage across the load stabilizes at 4 V, resulting in an output power of 1.6 mW. Consequently, it can be deduced that the implementation of the power factor correction circuit leads to a relative increase in output power of 13.5%.

5.2. Experimental Tests

In order to test the actual effect of the designed circuit, the proposed circuit is tested at the board level. Due to the limited laboratory conditions, the AC current source cannot be provided, so the piezoelectric element part is replaced by the output voltage source of the signal generator. The power supply of the active device is provided by the regulated power supply. The circuit part is welded as a PCB board. According to the data, the open circuit voltage of the piezoelectric element is 5~8 V. It is known through simulation that the voltage at the two ends of the equivalent circuit of the piezoelectric element is a sinusoidal waveform with a peak value of 5 V. Therefore, in this paper, a voltage source with a peak value of 5 V is used to replace the piezoelectric element. Figure 9 is the experimental picture, including the regulated power supply, signal generator, oscilloscope, and circuit board. The model of the regulated power supply is MT–152D, three–digit display, and display accuracy is plus or minus 0.5%. The display range of voltage is 0.00–9.99–16.0 V, and the display range of current is 000.–999. mA–2.1 A and the rated power is 30 W. The model of the signal generator is AFG–2225, which has a dual–channel output; the frequency range of its sine wave is 1 μHz~25 MHz, and the resolution is 1 μHz. The model of oscilloscope Tektronix DPO 4102B has a resolution of 8 bit, and the minimum measurement accuracy is 1 mV/div.

Figure 10 is the experimental waveform of the double–limit zero–crossing detection circuit. Figure 10a,d are PN, indicating that I_P is zero–crossing from positive to negative, and Figure 10b,d are NP, indicating that I_P is zero–crossing from negative to positive. By adjusting the size of the two reference voltages, the width of the zero–crossing signal can be changed to achieve a double–limit function.

Figure 11a shows the on–off of switches K₁, K₂, and K₃ when the voltage V_PT flips from positive to negative. Since the oscilloscope used in the experiment shows at most two channel waveforms at the same time, the following figures compare the waveforms of PN and K₁, K₁, and K₂, and K₂ and K₃, respectively. It can be seen that the timing of the switch closure is K₁–K₂–K₃, which is consistent with the simulation data. Figure 11b is the on–off condition of the switch K₁, K₂, and K₃ when the voltage V_PT flips from negative to positive. It can be inferred that the pulse generation circuit accelerates the voltage flip by controlling the on–off of the switch.

Figure 12 provides the curve of the theoretical prediction, simulation results, and experimental results of the output voltage variation with the load R_L, which shows that although there is a certain gap between the simulation results and the experimental results compared to the theoretical prediction, the variation trend is the same and in line with the expectation.

When the generator outputs a sinusoidal voltage with a peak value of 5 V, the voltage at both ends of the uncorrected load is 3.7 V, and the load power is 1.369 mW, with a power factor of 0.75. The voltage at the piezoelectric element and the capacitor in the third–order valley–fill circuit is 4.3 V and 1.2 V, respectively. The voltage at both ends of the load with the power correction circuit is 3.9 V, and the output power is 1.52 mW, and the power factor of 0.93. The voltage at the piezoelectric element is 4.7 V, and the voltage of three capacitors in the third–order valley–fill circuit are all 1.3 V, The output power has increased by 11.1%, and the power factor has increased by 24%.

Table 2. Performance comparison of synchronous switch harvesting on capacitor circuit.

Reference	[13]	[15]	[17]	[18,19]	[27]	This Work
Rectifier type	SSHC	P–S3BF	SSHI	E–DICH	SSHC	SSHC
CP	45 nF	28.42 nF	14 nF	51 nF	33 nF	147 nF
Open–circuit voltage	2.5 V	15 V	2 V	10 V	6.5 V	5 V
Frequency	92 Hz	2π × 24.9 Hz	441 Hz	23.2 Hz	140 Hz	1 kHz
Output voltage	5 V	3 V	1.8 V	5.9 V	4.24 V	3.9 V
Output power	0.45 mW	24 μW	24 μW	348.1 μW	1.80 mW	1.52 mW
$\frac{P_S}{P_{FBR}}$	9.7	2.876	4.48	5.4	4	4.2

demonstrates the performance comparison of synchronous switch harvesting on a capacitor circuit, and it can be seen that the circuit proposed in this paper can not only operate at high frequencies for fusing environments but also that the output voltage and output power are improved with the addition of the power factor correction circuit. According to the information obtained, the minimum ignition voltage for a detonator is 2.7 V, indicating that the voltage generated by the energy harvesting circuit designed in this article is sufficient to reliably ignite the detonator.

6. Conclusions

The primary purpose of the circuit described in this paper is to convert the mechanical energy produced during the flight of the projectile into detonation electric energy through the utilization of a piezoelectric element. The circuit possesses the capability to not only regulate the pulse width of the zero–crossing signal, but also effectively govern the synchronous switch, and incorporate a power factor correction circuit to fulfill the voltage and power requirements during detonator detonation. Through the implementation of simulation analysis, it was observed that when the current source is 5 mA and the connected load is 10 kΩ, the voltage at both ends of the load in the absence of a power factor correction circuit measures 3.75 V, resulting in an output power of 1.41 mW. The voltage at both ends of the load with the power factor correction circuit is 4 V, and the output power is 1.6 mW, which relatively increases by 13.5%. The experimental results show that when the open circuit voltage of the piezoelectric element is 5 V, the frequency is 1 kHz, the load resistance is 10 kΩ, the voltage across the load without power factor correction is 3.7 V, and the power is 1.369 mW, with a power factor of 0.75. The voltage across the load with the power correction circuit is 3.9 V, and the calculated output power is 1.52 mW, and the power factor of 0.93. The output power is promoted by 11.1%, and the power factor has increased by 24%. Based on the current results, the future research direction of this project is the miniaturization and high efficiency of circuits.