A Dual-Mode Hybrid Step-Up Converter with Stable Output for Vibration Energy Harvesting

Abstract

A dual-mode hybrid step-up circuit for electromagnetic energy harvesting (EVEH) is proposed in this paper, with the merits of continuous output power delivery with and without external vibrations, simple architecture, and no need for extra circuits to start up. The proposed hybrid converter combines a multi-stage voltage multiplier (VM) with a boost regulator, which utilizes the winding inductance of the electromagnetic energy harvester as a boost inductor. With external vibration, the proposed circuit powers the load and stores energy in the super-capacitor through VM mode. When external vibration disappears, it automatically switches to boost mode and powers the load using the energy stored in the supercapacitor. For hybrid mode operation, the number of VM stages is optimized considering the following three aspects: sufficient voltage gains when vibration is on, time durations to provide constant power when vibration is off for as long as possible, and low losses at VM stage. A GaN-based dual-mode hybrid converter is built to verify the output regulation capability with an in-house-designed electromagnetic energy harvester. The outputs of the hybrid circuit achieve 4.05 V and 1.64 mW at a 100-Hz external vibration frequency and an acceleration of 0.7 g. The peak efficiency of the proposed hybrid converter reaches 60.7%. When external vibration disappears, the circuit is able to maintain a stable output for 13 s with a super-capacitor of 0.1 F.

1. Introduction

With the development of the Internet of Things (IOT), the demand for wireless sensors is increasing. Traditional battery-powered sensors can hardly ensure continuous operation and a long lifetime in remote areas and harsh environments [1]. Energy harvesting is a technology which harvests and converts the energy from the environment to electricity in order to power low-voltage electronic devices [2,3,4,5]. With the power requirement of sensors being reduced to sub-milli- to micro-watts, EH has become a promising technology to replace batteries, with the advantages of a long lifetime, being free of maintenance, and environmental friendliness.

Vibration, one of the most widely distributed energies in the environment, has become a premium energy source for EH [6]. With the merits of high output power and low cost, electromagnetic vibration energy harvesting (EVEH) has been widely adopted. According to the Faraday law of electromagnetic induction, the magnetic flux in the coil of EVEH changes and results in induced electromotive force. Figure 1 depicts the basic architecture of EVEH, which is composed of an energy harvester, an energy converter and an energy storage module. The energy harvester can be modeled as a voltage source v_i(t) in series with equivalent resistance R_EH and inductance L_EH. An energy converter is required to regulate the low-voltage AC to DC level.

Vibration energy in the environment has a wide dynamic range of frequencies and amplitudes. For example, the vibration of the bridge is related to its traffic flow [7], with an average vibration frequency of around 40 Hz and a peak frequency of up to 500 Hz when two vehicles meet oppositely side-by-side [8]. A conventional energy harvester is usually narrow banded, with one resonant frequency for maximum power harvesting [9]. When the vibration frequency deviates from the resonant frequency of EVEH, the ability to harvest energy will decrease significantly, which lead to no or very little output power. Therefore, energy storage is necessary to provide energy to the output when the vibration fluctuates or disappears.

However, some existing works did not include a storage element [10,11,12]. Existing converters with energy storages were relatively complex in circuit topology and control strategy while ensuring stable output. Although an energy storage component was included in [13,14], it was directly applied to power the load when vibration disappears. Such a configuration failed to maintain a stable voltage for the sensors, which leads to increased power consumptions or the degradation of the sensors’ performances [15]. In order to maintain a stable output voltage level when vibration disappears, the voltage level of energy storage component needs to be regulated before sending it to the load. As shown in Figure 2, the energy storage module acted as an intermediate DC bus, and an additional DC-DC converter was employed to power the load [16,17,18]. Another typical approach is the three-port converter, as depicted in Figure 3 [19,20]. Both the energy storage component and load are charged by the vibration source once it exists. When the vibration disappears, the energy storage component will become the power source for the load through the AC-DC converter. Such architectures and their control strategies are complex and high cost.

In our previous work [21], a new dual-mode hybrid step-up converter was proposed with dual-mode operation to realize the resistance of the input vibration disturbance in a simple architecture. However, a converter based on a double-voltage circuit cannot achieve satisfactory output when the input voltage is low. In order to expand the range of input voltage, a converter based on a multiple-voltage circuit is proposed on the basis of [21], as shown in Figure 4. The converter merges the voltage multiplier (VM) and boost regulator, and utilizes the super-capacitor as the energy storage module. When vibration exists, the hybrid converter works in VM mode to power the load and store energy in the supercapacitor. When vibration disappears, the output is powered through the energy stored in the supercapacitor, and the hybrid converter is switched to boost mode. Furthermore, the proposed converter will start working once the output of the EVEH is higher than the forward voltage drop of the diodes and no extra start-up circuits are required [12,19].

The organization of the rest of the paper is as follows: Section 2 discusses the structure and working process of the proposed converter. Section 3 analyzes the output characteristics. Control strategies are provided briefly in Section 4. Section 5 explores the design principles of the proposed circuit, including the selection of the number of stages and the super-capacitor, loss analysis, targeting at sufficient voltage amplification at VM mode, and long operation duration in boost mode. The measurement results are further given in Section 6. Finally, conclusions are drawn in Section 7.

2. System Architecture and Mode Control

Figure 5 shows the full schematic of the proposed dual-mode hybrid VM-boost converter, which consists of the main power stage, the mode switching circuit and the PWM regulation module. A low-dropout regulator (LDO) is used to further stabilize the output level. The main power stage is a n-stages VM with boost mode merged with the first stage of VM, where the winding inductance from the electromagnetic energy harvester is adopted as the boost inductor. C₁ is a large super-capacitor for energy storage and serves as an energy source when vibration disappears. The mode switching circuit determines the VM and boost operation modes for the proposed converter.

The reference voltages used in the circuit follow the relationship V_{O_VM} > V_hys+ > V_com > V_{O_boost} = V_ref > V_hys−. V_{O_VM} and V_{O_boost} represent the output for VM mode and boost mode, respectively. Under VM mode, U₁ is shut down by setting the sd terminal at a low level. When the output falls below V_com because of the disappearance of vibration, the converter will switch to boost mode with the sd terminal enabled. The output voltage is controlled by the PWM regulation module with V_ref in boost mode. V_hys+ is used to ensure that C₁ is pre-charged first by VM mode. Otherwise, boost mode will be enabled at the system’s start-up transient. As soon as the voltage level in C₁ is dropped below V_hys−, the converter will stop boost mode operation, and the system is shut down where there is insufficient energy in C₁ to meet the load requirement. The mode control strategies and key operation waveforms of the proposed converter are summarized in Figure 6.

t₀–t₁: At t₀, the vibration appears and the converter starts to work in VM mode. v_O will gradually rise to the stabilized value of V_{O_VM}.

t₁–t₂: The vibration disappears at t₁. VM mode stops and v_O begins to drop according to the load requirement.

t₂–t₃: v_O drops to V_com at t₂ and the hybrid converter will switch to boost mode. The load will be powered by C₁. The output is regulated to V_{O_boost} and the voltage of the C₁ drops gradually.

t₃–t₄: Vibration resumes at t₃, and v_O begins to rise above V_{O_boost}. However, v_O is still lower than V_com in this period, such that the boost mode is not disabled. The hybrid converter operates with the coexistence of VM mode and boost mode.

t₄–t₅:v_O rises above V_com at t₄ and the converter starts to work in VM mode. v_O will be maintained at V_{O_VM}.

t₅–t₆: Vibration disappears at t₅. This interval is the same as [t₁–t₂].

t₆–t₇: v_O drops to V_com at t₆ and the hybrid converter will switch to boost mode. This interval is the same as [t₂–t₃]. The time duration for which the converter is able to provide a stable output is defined as t_boost.

t₇–t₈: At t₇, the energy stored in C₁ is not enough to maintain the output at V_{O_boost}. Although the converter is still in boost mode, v_O will decrease from V_{O_boost}.

t₈–: When v_O drops to V_hys− at t₈, the system is shut down. The output voltage and the voltage across C₁ will gradually drop to zero. If the vibration resumes, the process starting from t₀ is repeated.

3. Output Characteristics

As shown in Figure 5, the converter works in the VM mode and the main power transistor M is off when vibration exists. When v_i(t) is negative, v_i(t) and C_{2i(i = 1,2…n−1)} charge the capacitor C_{2i+1(i = 1,2…n−1)} through D_{2i+1(i = 1,2…n−1)}. According to Kirchhoff’s voltage law (KVL) and the law of the conservation of electric charge (CEC), the capacitors’ voltage in this interval can be expressed as

$$\begin{array}{l}{V}_{C1}^{-}=V_p-V_D-I_{\mathrm{VM}\_avg}{R}_{\mathrm{EH}}\\ V_{C2i-1(i=2,3\dots n)}^{-}=V_{C2i-2(i=2,3\dots n)}^{-}+V_p-V_D-I_{\mathrm{VM}\_avg}{R}_{\mathrm{EH}}\\ V_{C2i(i=1,2\dots n)}^{-}=V_{C2i(i=1,2\dots n)}^{+}-\frac{\Delta Q_{\mathrm{VM}}}{C_{2i(i=1,2\dots n)}}\end{array}$$

(1)

where R_O is the load of the converter, and f_vib is the frequency of vibration. V_p is the peak amplitude of v_i(t), and V_D is the forward voltage drop of the diodes. ΔQ_VM is the transferred charge in one vibration period, and satisfies ΔQ_VM = V_{O_VM}/(R_O f_vib). I_{VM_avg} is the average current of v_i(t).

When v_i(t) is positive, v_i(t) and the capacitor C_{2i−1(i = 1,2…n)} provide energy to C_{2i(i = 1,2…n)} through D_{2i(i = 1,2…n)}. According to KVL and CEC, the capacitors’ voltage in this interval can be expressed as

$$\begin{array}{l}{V}_{C2i(i=1,2\dots n)}^{+}=V_{C2i-1(i=1,2\dots n)}^{+}+V_p-V_D-I_{\mathrm{VM}\_avg}{R}_{\mathrm{EH}}\\ V_{C2i-1(i=1,2\dots n)}^{+}=V_{C2i-1(i=1,2\dots n)}^{-}-\frac{\Delta Q_{\mathrm{VM}}}{C_{2i-1(i=1,2\dots n)}}\end{array}$$

(2)

By combining (1) and (2), the output of VM mode can be derived by charge conservation as

$$V_{\mathrm{O}\_\mathrm{VM}}=V_{C2n}=\frac{V_{C2n}^{-}+V_{C2n}^{+}}{2}=\frac{2n(V_p-V_D)}{1+\frac{4n^2{R}_{\mathrm{EH}}}{R_{\mathrm{O}}}+\frac{X_{C\_\mathrm{vib}}}{R_{\mathrm{O}}}}$$

(3)

where $X_{C\_\mathrm{vib}}=\frac{1}{f_{\mathrm{vib}}}({\displaystyle \sum _{i=1}^{2n-1}\frac{1}{C_i}}+\frac{1}{2C_{2n}})$. According to CEC, I_{VM_avg} = 2nI_O = 2nV_{O_VM}/R_L. According to (1), the voltage over super-capacitor C₁ is charged to:

$$V_{C1}=\frac{(V_p-V_D)(X_{C\_\mathrm{vib}}+R_{\mathrm{O}})}{4n^2{R}_{\mathrm{EH}}+X_{C\_\mathrm{vib}}+R_{\mathrm{O}}}$$

(4)

When vibration disappears, the converter will switch to boost mode and the energy stored in C₁ starts to discharge in order to provide power to the output. Figure 7 shows the equivalent circuits and charge flow paths when M is off and on in one switching cycle. A constant current source (I_O) is used as the load. ΔQ_Boost represents the transferred charge in one switching period, and satisfies ΔQ_Boost = I_O/f_s, where f_s is the switching frequency in boost mode.

When M turns off in the (1 − D) T_s interval, as shown in Figure 7a, C₁ and L_EH charge C₂ through D₂ with ΔQ_Boost transferred, where D is the duty ratio of boost mode. Simultaneously, C₃ and L_EH charge C₄ through D₄ with ΔQ_Boost transferred, as do C_{2i−1(i = 1,2…n)} and L_EH. Therefore, the total charge dissipated from L_EH becomes nΔQ_Boost. Assuming that the inductor current is continuous, the average inductor current can be expressed as: I_{L_avg} = nΔQ_Boostf_s/(1 − D). As such, the voltage drop across R_EH is V_REH = I_{L_avg} × R_EH = nI_OR_EH/(1 − D). Furthermore, the voltage of the L_EH can be derived using volt-second balance. According to KVL and CEC, the capacitors’ voltage in this interval can be expressed as

$$v_{C2i(i=1,2\dots n)}^{M\_off}=v_{C2i-1(i=1,2\dots n)}^{M\_off}+v_A^{M\_off}-V_D$$

(5)

$$v_{C2i-1(i=2,3\dots n)}^{M\_off}=v_{C2i-1(i=2,3\dots n)}^{M\_on}-\frac{\Delta Q_{Boost}}{C_{2i-1(i=2,3\dots n)}}$$

(6)

where $v_A^{M\_off}$ is the voltage across L_EH and R_EH when M is off.

As shown in Figure 7a, when M is on in the DT_s interval, C₁ charges L_EH with ΔQ_LEH. Simultaneously, C₁ and C₂ charge C₃ through D₃ with ΔQ_Boost, and C₁ and C₄ charge C₅ through D₅ with ΔQ_Boost, as do C₁ and C_{2i−2(i = 2,3…n)}. Hence, ΔQ_LEH equals to nΔQ_BoostD/(1 − D). According to KVL and CEC, the capacitors’ voltage in this interval can be expressed as

$$v_{C2i-1(i=2,3\dots n)}^{M\_on}=v_{C2i-2(i=2,3\dots n)}^{M\_off}-v_A^{M\_on}-V_D$$

(7)

$$v_{C2i(i=1,2\dots n)}^{M\_on}=v_{C2i(i=1,2\dots n)}^{M\_off}-\frac{\mathsf{\Delta }{Q}_{Boost}}{C_{2i(i=1,2\dots n)}}$$

(8)

where $v_A^{M\_on}$ is the voltage across L_EH and R_EH when M is on.

Assuming that the voltage across C₁ does not change in one switching period—e.g., $v_{C1}^{M\_on}=v_{C1}^{M\_off}=V_{C1}$—V_{O_boost} can be expressed according to (5)–(8):

$$V_{\mathrm{O}\_\mathrm{boost}}=\frac{v_{2n}^{M\_on}+v_{2n}^{M\_off}}{2}=\frac{n\frac{V_{C1}}{1-D}-(2n-1)V_D}{1+\frac{n^2{R}_{\mathrm{EH}}}{R_{\mathrm{O}}{(1-D)}^2}+\frac{X_{C\_\mathrm{s}}}{R_{\mathrm{O}}}}$$

(9)

where $X_{C\_\mathrm{s}}=\frac{1}{f_s}({\displaystyle \sum _{i=1}^{2n-1}\frac{1}{C_i}}+\frac{1}{2C_{2n}})$.

4. PWM Regulation for Boost Mode

A PI-based PWM regulation is adopted for output control under boost mode, as shown in Figure 8 and Figure 9. The PI output is compared with the sawtooth wave (V_saw) to generate the PWM signal for the gate driver of GaN HEMT devices (M). The sawtooth generator is composed of series resistor R_s, capacitor C_s, two voltage comparators, a RS trigger, and switch S₂, as shown in Figure 9. The two voltage thresholds are set as V_High and V_Low (V_High > V_Low). If V_saw is higher than V_High or lower than V_Low, the status of the RS trigger changes to control the on and off of S₂. According to the RC charging theorem, the frequency of the sawtooth wave can be expressed as

$$f_s=\frac{1}{R_s{C}_s\ln \frac{V_{\mathrm{CC}}-V_{\mathrm{Low}}}{V_{\mathrm{CC}}-V_{\mathrm{High}}}}$$

(10)

To avoid the mode oscillations during mode switch, S₁ is closed in order to maintain the output of the PI regulator at a low level under VM mode, as shown in Figure 8.

5. Key Parameters and Analysis

As can be seen from (3) and (9), the output voltage of the proposed hybrid converter is dependent on the number of stages and the design of the super-capacitor. In order to realize sufficient voltage amplification at VM mode and ensure a long operation duration (t_boost) in boost mode, these two parameters are fully studied in this section. In the meantime, the loss distributions of VM mode are analyzed, which also leads to the optimum design of the number of VM stages.

5.1. Selection of the Number of Stages

For VM mode, the VM converter needs to tolerate the variations of the load resistors (R_O) and R_EH. Assuming that C₁ = C₂ = … = C_2n = C, the minimum required number of stages can be derived through (3), as

$$n_{\min }=\frac{-V_{\mathrm{O}\_\mathrm{V}\mathrm{M}}+\frac{R_{\mathrm{O}}}{X}(V_p-V_D)\pm \sqrt{{(\frac{R_{\mathrm{E}\mathrm{H}}}{X})}^2{(V_p-V_D)}^2+2\frac{R_{\mathrm{O}}}{X}{V}_{\mathrm{O}\_\mathrm{V}\mathrm{M}}(V_p-V_D)+V_{\mathrm{O}\_\mathrm{VM}}^2[(4-4\frac{R_{\mathrm{O}}}{X}-2\frac{C_i}{C_{2n}})\frac{R_{\mathrm{EH}}}{X}+1]}}{4\frac{R_{\mathrm{EH}}}{X}{V}_{\mathrm{O}\_\mathrm{VM}}}$$

(11)

where $X=\frac{1}{C{f}_{\mathrm{vib}}}$.

V_{O_VM} increases first, then decreases with the increase of the number of stages. n_max is defined as the number of stages when the output voltage reaches its maximum value under a certain input. The n_max for the peak output voltage at a certain load resistor can be deduced from $\mathrm{d}{V}_{\mathrm{O}\_\mathrm{VM}}/\mathrm{d}n=0$, as

$$n_{\max }=\frac{\sqrt{2C_{2n}\frac{R_{\mathrm{EH}}}{X}(2C_{2n}\frac{R_{\mathrm{O}}}{X}+C_i-2C_{2n})}}{4C_{2n}\frac{R_{\mathrm{EH}}}{X}}$$

(12)

Hence, with an LDO post-regulation, the possible number of stages for a certain V_{O_VM} should be chosen as

$$n_{\min }\le n\le n_{\max }$$

(13)

Figure 10a describes the relationship between the number of stages and V_{O_VM} with different R_O at an R_EH of 100 Ω. The higher R_O is, the smaller the number of stages required for a certain V_{O_VM}. Figure 10b describes the relationship between the number of stages and V_{O_VM} with different R_EH at R_O of 10 kΩ. The higher R_EH is, the larger the number of stages required for a certain V_{O_VM}. According to (1), the minimum R_O for a certain output V_{O_VM} can be derived as

$$R_{\mathrm{O}(\min )}=\frac{V_{\mathrm{O}\_\mathrm{VM}}(4R_{\mathrm{EH}}{n}^2+X_{C\_\mathrm{vib}})}{2n(V_p-V_D)-V_{\mathrm{O}\_\mathrm{VM}}}$$

(14)

If R_O ≤ R_O(min), the converter can’t stabilize to V_{O_VM}. If the load R_O > R_O(min), the LDO module is required to further stabilize the output to V_{O_VM}.

For boost mode, the main target is to provide a stable output as long as possible when vibration disappears. Considering that C₁ reaches a steady state before vibration disappears, the total energy stored in C₁ will be divided into three parts in boost mode, as shown in Figure 11: E_load is the energy transferred to the output; E_loss is the energy dissipated in the circuit, and E_left represents the energy leftover in C₁ when the output fails to be regulated to V_{O_boost}. Therefore, E_{total_C1} = E_left + E_load + E_loss. In order to extend the duration for a stable output when vibration disappears, E_{total_C1} should be large and the proportion of E_load should be as large as possible for a certain E_{total_C1}.

The initial voltage across the super-capacitor C₁ in boost mode (V_{C1_max}) can be derived by (4). The larger V_{C1_max} is, the larger E_{total_C1} will be. V_{C1_max} decreases with the increase of n.

When the converter operates at maximum duty cycle D_max, C₁ reaches to its minimum voltage level to be capable to provide a well-regulated V_{O_boost}. D_max can be obtained by forcing dV_{O_boost}/dD = 0. Therefore, the minimum V_C1 to maintain V_{O_boost} becomes:

$$V_{C1\_\min }=\frac{2\sqrt{R_{\mathrm{EH}}{V}_{\mathrm{O}\_\mathrm{boost}}(R_{\mathrm{O}}{V}_{\mathrm{O}\_\mathrm{boost}}-R_{\mathrm{O}}{V}_D+X_{C\_\mathrm{s}}{V}_{\mathrm{O}\_\mathrm{boost}}+2n{R}_{\mathrm{O}}{V}_D)}}{R_{\mathrm{O}}}$$

(15)

The lower V_{C1_min} is, the lower E_left will be. As V_{C1_min} increases with the increase of n, the more number of stages adopted, the more proportion of E_left will be.

The total transferred charge of C₁ (Q_{C1_output}) is directly related with E_load + E_loss in one boost period, as

$$Q_{C1\_\mathrm{output}}=[(n-1)\mathsf{\Delta }Q+\mathsf{\Delta }Q]f_s{t}_{\mathrm{boost}}+{\displaystyle \underset{0}{\overset{t_{\mathrm{boost}}}{\int }}\mathsf{\Delta }{Q}_{\mathrm{LEH}}{f}_{s}dt}=n{I}_O{t}_{\mathrm{boost}}+n{I}_O{\displaystyle \underset{0}{\overset{t_{\mathrm{boost}}}{\int }}\frac{D(t)}{1-D(t)}dt}$$

(16)

It can be seen that the more number of stages will be, the more charges are required from C₁ to power the output for a certain t_boost under the same load and output voltage. It can be concluded that E_load is reversely proportional to the number of stages under certain E_{total_C1}. Hence, combing the two aspects for both with (VM mode) and without (Boost mode) vibration, the minimum feasible number of stages (n_min) should be selected.

5.2. Design of Super-Capacitor C₁

In order to ensure that the selected C₁ can provide sufficient energy during required t_boost time interval, C₁ is designed under the most extreme condition where maximum duty ratio is always applied. It is the situation when the discharge rate of C₁ is highest. According to (16), C₁ can be chosen as

$$C_1=\frac{n{I}_O{t}_{\mathrm{boost}}(1+\frac{D_{\max }}{1-D_{\max }})}{V_{C1\_\max }-V_{C1\_\min }}$$

(17)

5.3. Loss Analysis

As the VM mode is the main circuit processing EH power, the power consumptions of VM mode are discussed in this section. In EVEH, R_EH is usually much larger than the impedance of winding inductance of jωL_EH, so that L_EH is ignored the loss analysis. The charging current of capacitor is shown in Figure 12, where I_VM(t) is the current of EH source. Capacitors are only charged during the intervals of t₁~t₂ and (T − t₂~T − t₁) in one vibration period.

In negative half period, odd number capacitors C_{2i−1(i =1, 2…n)} in Figure 5 are charged by EH source with the following relationships satisfied:

$$\begin{gathered} V_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-I_{\mathrm{VM}}(t)R_{\mathrm{EH}}>V_{C1} \\ {V}_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-I_{\mathrm{VM}}(t)R_{\mathrm{EH}}>V_{C2i-1(i=2\dots n)}-V_{C2i-2(i=2\dots n)} \end{gathered}$$

(18)

In positive half period, even number capacitors C_{2i(i =1, 2…n)} in Figure 5 are charged with the following formula satisfied:

$$\begin{gathered} V_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-I_{\mathrm{VM}}(t)R_{\mathrm{EH}}>V_{C2}-V_{C1} \\ {V}_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-I_{\mathrm{VM}}(t)R_{\mathrm{EH}}>V_{C2i(i=2\dots n)}-V_{C2i-1(i=1,2\dots n)} \end{gathered}$$

(19)

Ignoring the voltage variations in C₁ as it is quite large, I_VM(t) can be calculated as

$$I_{\mathrm{VM}}(t)=\left\{\begin{array}{l}\frac{V_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-V_{C1}}{R_{\mathrm{EH}}} t\in (t_1~t_2)\\ -\frac{V_p\sin (2\pi f_{\mathrm{vib}}t)-V_D-V_{C1}}{R_{\mathrm{EH}}} t\in (T-t_1~T-t_2)\\ 0 t\in other\end{array}\right.$$

(20)

where $t_1=\frac{1}{2\pi f_{\mathrm{vib}}}{\sin }^{-1}(\frac{V_{C1}+V_D}{V_P})$ and $t_2=\frac{1}{2\pi f_{\mathrm{vib}}}[\pi -{\sin }^{-1}(\frac{V_{C1}+V_D}{V_P})]$.

5.3.1. Loss of R_EH

R_EH is the output resistance of the EVEH source and its power loss can be expressed as

$$P_{loss\_REH}=2f_{\mathrm{vib}}{\displaystyle \underset{t_1}{\overset{t_2}{\int }}{I}_{\mathrm{VM}}^2(t)R_{EH}}dt$$

(21)

5.3.2. Loss of Capacitors’ Charge Transfer

When the charge $\Delta Q_{AB}$ is transferred from capacitor A (C_A) with initial voltage u_A to capacitor B (C_B) with initial voltage u_B, according to CEC, the loss of charge transfer is:

$$P_{loss\_CAB}=(u_A-u_B)\Delta Q_{AB}-\frac{1}{2}\Delta Q_{AB}^2(\frac{1}{C_A}+\frac{1}{C_B})$$

(22)

In each vibration period, ΔQ_VM is transferred between the C_{i(i = 1,2…2n)} and C_{i+1(i = 1,2…2n−1)}. Assuming that C_{i(i = 2…2n)} is large enough with ignorable voltage ripples, the loss of C_{i(i = 1,2…2n)} in the process of charge transfer can be expressed as

$$P_{loss\_{\displaystyle \sum C}}=(2n-1)f_{\mathrm{vib}}\Delta Q_{VM}{V}_{C1}-\frac{1}{2}{f}_{\mathrm{vib}}\Delta Q_{{}_{\mathrm{VM}}}^2(2{\displaystyle \sum _{i=1}^{2n-1}\frac{1}{C_i}}+\frac{1}{C_{2n}})$$

(23)

5.3.3. Loss of Diodes

Diode D_{i(i = 1,3…2n − 1)} and D_{i(i = 2,4…2n)} turns on during time intervals (t₁~t₂) and (T − t₂~T − t₁) respectively in each EM period. Hence, diodes’ conduction losses can be described as

$$P_{loss\_Don}=2n{f}_{\mathrm{vib}}{\displaystyle \underset{t_1}{\overset{t_2}{\int }}\frac{I_{\mathrm{VM}}(t)V_D}{n}}dt$$

(24)

When diodes are off, leakage current will also induce loss, as

$$P_{loss\_Doff}=2n{f}_{\mathrm{vib}}{I}_{leak}\left.\left\{2{\displaystyle \underset{t_2}{\overset{T-t_2}{\int }}[V_{C1}+V_p\sin (2\pi f_{\mathrm{vib}}t)]dt}+(t_2-t_1)[V_{C1}+V_p\sin (2\pi f_{\mathrm{vib}}{t}_1)]\right.\right\}$$

(25)

where I_leak is the reverse leakage current of diodes. Therefore, the overall losses of diodes can be expressed as

$$P_{loss\_{\displaystyle \sum D}}=P_{loss\_Don}+P_{loss\_Doff}$$

(26)

5.3.4. Loss of Super-Capacitor

Super-capacitors have large series resistors in the order to tens of ohms. The power consumptions on the parasitic resistor (R_C1) can be expressed as

$$P_{loss\_R_{C1}}=2f_{\mathrm{vib}}{\displaystyle \underset{t_1}{\overset{t_2}{\int }}(\frac{I_{\mathrm{VM}}(t)}{n}}{)}^2{R}_{C1}dt$$

(27)

In order to evaluate the loss contributions in the VM mode of the proposed circuit, the circuit parameters are given in

Table 1. The circuit parameters of VM mode used in the loss analysis.

Name	Value	Name	Value
n	2	VD	0.3 V
Vp	1.8 V	Ileak	0.05 mA
fvib	100 Hz	REH	105 Ω
C1	100 mF	RC1	20 Ω
C2, C3	10 μF	RO	10 kΩ
C4	100 μF

. As shown in Figure 13, the charge transfer loss is the major loss contributor, which is 75.8% of the total losses. The second largest loss contributor is diode conduction loss, which accounts for 20.8% of the total losses. Both the charge transfer loss and diode conductor loss increase with the increase of the number of stages (n). The power losses on EVEH’s internal resistor and parasitic resistor at the super capacitor are negligible. Therefore, the minimum number of stages to provide sufficient output voltage level should be used. This conclusion is also consistent with the discussions in Section 5.1.

6. Prototype Design and Measurement Results

A cylindrical EVEH [22] is employed in this experiment as the source for the proposed dual-mode converter. As shown in Figure 14a, it is designed with a cylindrical magnet, two planar springs connected to the top and bottom of the magnet, and two sets of windings. The measured winding resistance R_EH and inductance L_EH are 105 Ω and 5.1 mH, respectively. The designed EVEH has a 4.2-cm height and a 2-cm diameter. At a vibration resonance frequency of 100 Hz and an acceleration of 0.7 g, the AC output amplitude (V_p) reaches 1.8 V. The prototype of the dual-mode hybrid step-up circuit is shown in Figure 14b. A Schokky diode (VS-10BQ015HM3) with a low forward conduction voltage of 0.3 V is used. A GaN HEMT EPC2015C (40 V/53 A) is employed as the main switching transistor. V_com, V_hys, V_hys+ and V_hys− are set to 3.4 V, 2.25 V, 3.6 V and 0.6 V, respectively. V_ref for the boost mode output is set to 3.3 V. According to (11), the number of stages should be chosen as two. The key parameters used in this design are summarized in

Table 2. The key components used in this design.

Name	Component	Value
RO	Load	10 kΩ
C1	Super-capacitor	FM0H104ZF (0.1 F)
C2, C3	Flying capacitors	10 μF
C4	Filter capacitor	100 μF
Di(i = 1~4)	Schottky diode	VS-10BQ015HM3
M	N-channel GaN HEMT	EPC2015C
Udriver	Gate driver	UCC27525

.

Figure 15 shows the waveforms of VM mode operation under vibration. The output voltage of the VM circuit and voltage across the supercapacitor are maintained at 4.05 V and 1.23 V, respectively. Figure 16 shows the circuit efficiency (η) of the VM circuit when n = 2 with different load resistors and the same V_p, where the peak efficiency reaches 60.7%.

Figure 17 reveals the different cases of the operation modes transitions from the existence (①) of vibration to the disappearance of vibration (②) and the resumption of vibration (③). Four different cases are studied:

Case 1: In Figure 17a, the vibration is resumed after 700 ms of disappearance. v_O is stabilized to 3.3 V during the disappearance period. V_C1 drops to 1.19 V from 1.23 V. v_O and V_C1 rise to 3.3 V and 1.23 V after vibration is resumed, respectively.

Case 2: In Figure 17b, the vibration is resumed after a 14.7-s disappearance. v_O is stabilized to V_{O_boost} (3.3 V), and V_C1 drops to 1.0 V from 1.23 V in the first 13 s. After 13 s, the boost mode cannot keep v_O to V_{O_boost}, and v_O begins to decrease. At 14.7 s, v_O drops to 3 V and V_C1 drops to 0.95 V. v_O and V_C1 rise to 3.3 V and 1.23 V after vibration is resumed, respectively.

Case 3: As shown in Figure 17c, v_O is stabilized to 3.3 V for 13 s and drops after the vibration’s disappearance. The vibration is resumed after a 24.6-s disappearance, and the output rises again. However, the boost mode-enabled signal switches between high and low within a short time, starting from the time that v_O rises near to V_com. This is caused by the output voltage fluctuating around V_com in the process of rising.

Case 4: As shown in Figure 17d, after the first 13 s of well regulation, v_O begins to drop. At 75 s, v_O drops to 0.5 V, which is lower than V_hys−, and the boost mode is shutdown. The vibration is resumed after 79.8 s disappearance, and the converter is restarted.

As depicted in Figure 17b–d, the time of voltage stabilization of the circuit is 13 s, which is 30% lower than the calculation results. This is because the large ESR (50 Ohms) of the selected super-capacitor consumes lots of stored energy in C₁.

Figure 18 shows the operation mode switches with the changes of external vibration. When the vibration disappears (e.g., region ②④⑥⑧), the boost-enabled signal becomes high. The circuit works under boost mode and the supercapacitor starts to discharge. v_O is stabilized at V_{O_boost} (3.3 V). When external vibration resumes (e.g., region ①③⑤⑦⑨), the output v_O starts to increase above V_com and the boost-enabled signal becomes low. The circuit switches back to VM mode and the supercapacitor voltage starts to rise. This shows that the circuit has a strong capability to maintain a stable output when the vibration is unstable. With an extra LDO stage, the output voltage can be better regulated.

Table 3. Performance comparisons with state-of-art power conversions for vibration energy harvesting.

Topology	Stages of Converter	Output Voltage	Output Power	Maximum Efficiency	Control Mode	Uninterrupted Output ①	Extra Start-Up Circuit
Active Voltage-multiplier (n = 4) [23]	One	3.3 V	294 μW	80%	N/A	No	Yes
Cross-connected Active Voltage-multiplier (n = 1) [24]	One	2.68 V	960 μW	87% (Simulation)	N/A	No	Yes
Dual polarity Boost circuit [25]	One	3.3 V	50 mW	50%	Polarity detection + PWM	No	Yes
Dual Boost full-wave converter [14]	One	2.1 V	900 μW	65%	Burst + PWM	No	Yes
Dual Boost full-wave converter [26]	One	N/A	600 μW	89%	MPPT	No	Yes
Dual Boost split-capacitor converter [12]	One	3.3 V	21.8 mW	82.4%	COT	No	Yes
Voltage-multiplier + buck [18]	Two	2.57 V	500 μW	60%	MPPT	No	Yes
Full-wave Rectifier + step-down converter [16]	Two	3.3 V	104 mW	49%	N/A	Yes	Yes
Voltage-multiplier + boost [27]	Two	1 V	100 μW	85% (Simulation)	PWM	Yes	Yes
Dual Boost + Bi-directional Buck/Boost converter [19]	Two	3.3 V	10 mW	Not mentioned	MPPT + PWM	Yes	Yes
This work (n = 2)	One	4.05 V	1.64 mW	60.7%	Mode switch + PWM	Yes	No
Previous work [21] (n = 1)	One	3.8 V	1.44 mW	85.9%	Mode switch + PWM	Yes	No

^① An energy storage element is included and can continue to supply power to the load when the source is disappeared.

summarizes the performance of the proposed dual-mode hybrid step-up converter and compares it with state-of-art power converters in EVEH applications. Compared with active VM circuits [23,24] and direct AC~DC dual boost converters [12,14,25,26] where energy storages were not included, the proposed work has the advantage of continuously providing energy when the vibration disappears in a simple hybrid topology. In the meantime, it can achieve almost the same efficiency as a dual boost circuit with a much simpler control method. Some studies [16,18,27] adopted energy storage as the intermediate stage, as shown in Figure 2. The efficiencies of the topology given in [16,18] were lower than the proposed circuit due to the two-level transformation. One study [27] reported a high conversion efficiency of 85% and a stable output when the vibration source disappeared, but only simulation results were presented, and the output power was tens of orders lower than the proposed work. One study [19] described a three-port converter with additional battery as the energy storage. A microcontroller was employed for MPPT control, which is quite power consuming and is not suitable for milli-power applications. The total efficiency was not reported in [19]. Furthermore, the state-of-arts in Table 3 all require extra start-up circuits, which may induce high energy loss with discrete components. Hence, the proposed dual-mode hybrid converter has been demonstrated to achieve a decent efficiency for EH energy conversion, and provides continuous output under unstable vibrations in a simple system architecture.

7. Conclusions

A dual-mode hybrid step-up circuit with stable output for vibration energy harvesting (EH) was proposed in this paper. The converter operates as a multi-stage voltage multiplier when vibration exists, with the supercapacitor and output load both powered. Once vibration disappears, it will switch to boost mode, and the supercapacitor is employed as a power supply. The selections of the number of stages and supercapacitor are based on the voltage gain characteristics under different input and output impedance and the system’s energy utilization. A GaN HEMT-based dual-mode prototype was designed and tested with an in-house-designed EVEH device. Different operation modes were fully verified. When n = 2, the output voltage of the prototype reaches 4.05 V/1.64 mW in the existence of a vibration of 0.7 g and 100 Hz. The proposed converter is able to stabilize to 3.3 V in the absence of vibration for 13 s. The peak output efficiency of a hybrid circuit reaches 60.7%. The proposed hybrid converter has been demonstrated to achieve a descent efficiency for EH energy conversion, and provides continuous output under unstable vibrations in a simple system architecture without the need for an extra start-up circuit. It is a premium solution for a low-voltage, low-power EVEH system with unstable vibrations.

Future work will focus on the following two aspects. One is the low-voltage integration of the converter to reduce the loss brought about by discrete devices and parasitic interconnection. For example, the discrete Schottky diodes adopted in this paper suffer from high forward conduction because diodes with a voltage rating of 15 V and a current rating of 1 A are employed, which are far beyond the actual voltage and current requirements in the proposed application. Voltage/current-suitable devices will be available through IC integration, which will further improve the overall efficiency. The other focus is to apply the design of the energy harvester and hybrid step-up converter considering the specific vibration environment and load characteristics.