1 Introduction

As low-power technology advances, electronic components are becoming indispensable across a broad spectrum of industries. Energy harvesting is an essential field of research for obtaining sustainable energy sources for low-power electronic components [1,2,3]. Among the various energy harvesting technologies, a triboelectric nanogenerator (TENG) directly converts input energy into electrical energy through triboelectric and electrostatic induction [4,5,6]. As an effect of direct conversion, when converting small amounts of ambient energy into electricity, TENGs are more efficient than conventional electromagnetic induction generators [7, 8]. Furthermore, miniaturization and efficient maintenance can provide flexibility in various applications, such as providing a sustainable power source for active sensors [9, 10], biomedical applications [11, 12], and building off-grid networks in hard to manage locations [13, 14].

The output of electrical energy devices can be quantified by two key parameters: current, which is the amount of moving charge, and voltage, which is the difference in the potential energy of these moving charges. For this reason, the output performance of an electrical energy device is evaluated in terms of the open-circuit voltage (VOC), which refers to the maximum voltage a device can produce, and the short-circuit current (ISC), which refers to the maximum current that a device can support. Conventional energy devices have a fixed intrinsic output impedance, which renders a single VOC and ISC. In the case of TENGs, the device has a variable output impedance depending on the motion, resulting in an electrostatic displacement current between the facing two conducting plates. The TENG output generated by impedance change can exhibit asymmetrical characteristics [15,16,17]. In order to understand the output characteristics of the TENG, it is necessary to consider the changing output impedance. Many studies have reported enhancing the output of TENGs by optimizing the output impedance [18,19,20].

In this study, we analyzed the two distinct VOCs generated at the two extreme output impedances of the maximum and minimum states. Experimental and circuit simulations confirmed the existence of these two VOCs. Circuit simulation revealed that these two VOCs were measured differently depending on the input capacitance of the high-impedance measurement system. This paper presents an analysis of the methods and principles of operation for exploiting the variable output impedance effects of TENGs. Our findings will provide insights into the accurate measurement of the output of the variable impedance energy device of a TENG, which is crucial for the optimization of the device to maximize its power utilization in real-world applications.

2 Experimental

2.1 Fabrication of the CS-TENG

In the experimental procedure, a contact-separate TENG (CS-TENG) was fabricated with a contact area defined by adhering a 2 × 2 cm2 polymethyl methacrylate (PMMA) plate to a 4 × 4 cm2 PMMA substrate. The 50 μm-thick aluminum tape was used as the electrode on both sides of the two facing contact areas, while the 50 μm-thick layer of polyimide tape was adhered on the side of the aluminum electrode to serve as the dielectric layer. The charge density of the TENG was enhanced using the prior charge injection method, which utilizes an electric field formed by a high-voltage source [21]. Following exposure to an electric field for a duration, the surface voltage of the dielectric remains constant even after the electric field is removed. The output voltage was maintained at 93% after 500 s of exposure to air (Fig. S1). The experiment was conducted at 22 °C and 46% RH.

2.2 Output measurement of the TENG

The contact-separation process of the CS-TENG was repeated using a solenoid (Shindengen, M080117SS). A force sensor (Marveldex, RA18) was positioned beneath the CS-TENG to detect consistent force application. There are two ways to measure open-circuit voltage: (1) a voltmeter (contact method) and (2) an electrostatic field meter (noncontact method). The VOC is measured as the voltage without a connected load between the device and the voltmeter. An ideal voltmeter should remain open-circuited; it should not draw any current. To minimize the current flowing through the measuring device, an electrometer with a high impedance is necessary. The electrical output characteristics of the TENG with initial charge balancing were measured using an electrometer (Keithley, 6514). The value of 370 pF was measured in the electrometer and probe measurement system (CMeas) using a capacitance meter (FLUKE, 289). An electrostatic field meter has the advantages of virtually zero input capacitance and infinite impedance. We used an electrostatic field meter (SIMCO, FMX-004) for noncontact voltage measurements. For the two methods, the analog output was connected to an oscilloscope (Keysight, DSO-2014A) to obtain the waveform. Figure 1a shows the experimental setup. Figure 1b illustrates the structure of the CS-TENG and a schematic of the VOC measurement.

Fig. 1
figure 1

a Photograph of the TENG and the VOC measurement system. b Schematics of the CS-TENG and equivalent model of the VOC measurement system

Full size image

2.3 Equivalent circuit simulation

The Multisim program (National Instruments Inc.) was used as the Simulation Program with Integrated Circuit Emphasis (SPICE) to model the behavior of the TENG. Figure 1b shows the lumped-parameter equivalent model of the TENG and measurement system, which consists of three components: constant surface voltage (VSurface), intrinsic output series impedance (CImpedance), and measurement system impedance (CMeas). Many studies have used this model to understand the output of TENGs [22,23,24]. The VSurface of the TENG formed by the dielectric layer determines the output of the TENG according to the change in the CImpedance of the TENG during the contact-separation process. The electrical output characteristics were measured by connecting the HI and LO probes of an electrometer. This process connects the input capacitance of the electrometer (CMeas) to the TENG. The SPICE was used with an equivalent model to simulate the output of the TENG. The values used in the simulation were set as follows. The capacitance of the TENG in the contact separation process was obtained via calculations. The contact capacitance is 233.7 pF, and the isolation capacitance is 0.554 pF. The value of VSurface was set to 134 V, which is the saturation voltage from the experiment. We confirmed that the saturation voltage determines the VSurface of the lumped parameter model of the TENG when a half-wave rectifier is used [25]. The ideal device models used in the SPICE simulation were as follows: the diode has no reverse breakdown voltage, the forward threshold voltage is 1 V, and there was no leakage and infinite conductance in the wire. The parameters used in the SPICE model (Table S1) and the measured VSurface can be found in Fig. S2.

3 Results and discussion

3.1 Dual polarity open circuit voltage in TENG

In the idealized state of an open circuit, the output voltage produced by the VSurface and CImpedance should be the same as the VSurface. However, under actual measuring conditions, the CImpedance of the TENG and CMeas of the measurement system are connected in series, dividing the VSurface to a certain voltage that is less than the VSurface. When measuring voltage with an electrometer, an initial voltage reference of 0 V must be set initially, which is called a zero check. In this process, an internal shunt resistor of 10 MΩ of our electrometer (Keithley 6514) is connected between the measuring probes to equilibrate (zero-check), which is a charge balancing between the TENG and the measurement system; the shunt resistance value is referenced from the zero-check section of the manual [26]. This phenomenon can be replicated with a shunting wire instead of an internal wire of 10 MΩ. The amount of charge stored in the CMeas will balance the source voltage with the voltage reference. There are two types of balancing processes: the separate balancing process (SBP), in which the capacitors of the measurement system are charged and balanced while the TENG is separated, and the contact balancing process (CBP), in which the capacitors of the measurement system are charged and balanced while the TENG is in contact. It should be noted that these SBP and CBP states have two distinctive CImpedance conditions.

In the initial condition with SBP, the output capacitance is minimum (Cmin, Fig. 2a). We measure the VOC when the output capacitance is maximum (Cmax, Fig. 2b). In the initial condition with the CBP, the output capacitance is maximum (Cmax, Fig. 2c). We measure VOC when the output capacitance is minimum (Cmin, Fig. 2d). Figure 2e shows the measured voltage starting from the reference voltage of zero volt depending on the initial CBP and SBP conditions. When the dielectric layer, which is the friction layer of the TENG, bears a positive surface voltage, the output voltage of the TENG would be larger than the voltage at the separate state (Cmin). It has a maximum voltage at the contact state (Cmax) regardless of the initial balancing process. Thus, the polarity of the output voltage is positive after SBP and negative after CBP, and the magnitude of the VOC is 82 V with CBP, which is approximately 1.6 times larger than that of 52 V with SBP. This resulted in two measured VOCs with different magnitudes and different polarities depending only on the initial balancing process, i.e., setting the initial reference voltage.

Fig. 2
figure 2

Illustration of the initial impedance state of the TENG for setting the reference voltage and charge depiction during measurement. a Setting the reference voltage at Cmin (SBP) and b measuring at Cmax. c Setting the reference voltage at Cmax (CBP) and d measuring at Cmin. e Voltage measurement results depending on the initial conditions

Full size image

A circuit simulation was performed based on the equivalent circuit model parameters using the SPICE to understand the difference in VOC depending on the initial condition of charge balancing. In Fig. 3a, CMeas has an initial voltage condition (IC) to model the initial charge stored during the initial balancing process. When the CMeas has an initial voltage (VIC) of zero, there are no initially stored charges at CMeas, which means that there are almost zero bound charges at the electrodes of the TENG. Thus, VSuface will be divided by the CImpedance and CMeas rendering output voltages. This is the case for the SBP with the minimum capacitance of the TENG (i.e., a voltage of zero under separate condition). If initially stored charges exist in CMeas, the output voltage can be interpreted as a superposition of two sources: the VSurface and initial stored charges at CMeas. The stored charges in CMeas will be divided by the CImpedance and CMeas. Thus, the measured voltage will be modified (shifted) from the SBP case depending on the amount of stored charges in CMeas (i.e., VIC) (Fig. 3b). For an initial voltage (VIC) of 0 V, the output voltage is 52 Vpk-pk; for − 50 V, it is 71 Vpk-pk; for − 80 V, it is 83 Vpk-pk; and for − 150 V, it is 110 Vpk-pk. Among them, there is a unique state where the voltage generated from the VSurface is complemented by the voltage generated from charge redistribution originating from the VIC. In this state, the output will be zero. Thus, the voltage swing of the measurement result will be from the VIC to zero. Zero output will occur at the maximum charge redistribution state. If we start from the contact state, the maximum charge redistribution will occur in the separate state and vice versa. Because we want to simulate the CBP condition (i.e., a voltage of zero at the contact condition), we must choose the voltage minimum (i.e., VIC) under separate condition. Thus, we know that the initial separate state with zero VIC causes SBP, and the initial separate state with a certain negative VIC can cause CBP. In the simulation, this condition corresponds to a voltage condition of VIC = −82 V. With the aid of a negative VIC, we successfully simulated SBP and CBP by the motion of separate or contact in a unified form, which is consistent with the experimental results (VOC at SBP: 52 V, VOC at CBP: − 82 V).

Fig. 3
figure 3

a SPICE model according to the initial voltage condition (VIC) of CMeas. b Output voltage for each initial voltage condition. The first lower state represents the initial voltage at the separate state (Cmin). The ascending peak indicates the voltage at the contact state (Cmax)

Full size image

3.2 Model of repeated charge balancing with diode

It is difficult to set an initial condition in which the charges in CImpedance and CMeas are balanced to produce a reference voltage of 0 V in the CBP condition in the SPICE. When a diode, which is an active element, is connected to both ends of the TENG, the potential difference between the two nodes becomes the forward voltage of the diode (VF = 1 V). It can be treated as a zero volt (compared to the high voltage output of the TENG). Due to the diode being turned on in the forward voltage direction, we set the reference voltage in this turn-on period, and the reverse voltage can be maintained referenced from the diode turn-on condition. The TENG with a positive output voltage referenced from zero volt (Cmin) can be simulated with Fig. 4a. Similarly, a TENG with a negative output voltage referenced from zero volt (Cmax) can be simulated with Fig. 4b. With the same SPICE parameters used in Fig. 3, we can obtain the same results for SBP and CBP, even under different VIC conditions. If we choose the initial condition above the VIC of − 82 V, we can obtain consistent results, as shown in Fig. 4c. When the VIC is lower than − 82 V, the voltage generated from the maximum charge redistribution will be larger than that generated from the VSurface. Therefore, the overall voltage output will be negative in this case (e.g., VIC = −150 V), and the balancing process cannot be simulated. For this reason, we can safely and conveniently choose zero VIC conditions in all CBP and SBP cases. In the simulation, diodes were connected to replicate the initial balancing effect. Regardless of the initial voltage conditions of CMeas, the occurrence of SBP and CBP is solely based on the direction of the diodes, which can be interpreted as repeated charge balancing in each cycle. To verify the repeated charge balancing, we removed the initial charge balancing effect by setting CMeas = 0 pF, i.e., no measurement system. Even at this time, two different VOCs were observed, indicating that any form of charge balancing effect still existed, as confirmed in Fig. 4d, e. When the diode turn on in each cycle, the two electrodes became the same potential, which is a charge balancing effect as previously described in Sect. 3.1. Additionally, the charge dividing effect caused by CMeas is eliminated, resulting in an increased voltage.

Fig. 4
figure 4

SPICE model with initial reference voltage conditions using a diode connection. a TENG with SBP condition. b TENG with CBP condition. (c) Output voltage depending on the initial reference voltage conditions with different initial charged CMeas voltages (VIC). Output of the TENG in the absence of a measurement system (CMeas = 0 pF) under d SBP and e CBP conditions

Full size image

3.3 Open-circuit voltages of the TENG with a capacitive load

Since it was confirmed that CMeas reduces VOC due to the charge dividing effect, VOC was analyzed by varying CMeas to systematically investigate this phenomenon. Depending on the type of balancing process, a TENG with a specific balancing condition can be represented as shown in Fig. 5a, b. The polarity of the voltage output can be chosen according to the direction of the diode. To simulate the input impedance of the voltage measurement system, we add CMeas to the ideal voltage probe of the SPICE. Figure 5c–e shows the results of varying VSurface while keeping Cmax and Cmin fixed. The positive voltage (SBP), VOC_L, follows the VSurface when CMeas is small enough. As the CMeas increases, impedance matching occurs at the point where CMeas equals the series output impedance Cmax, reducing the voltage to 1/2 of the original VSurface. If CMeas becomes large enough, VOC_L rolls off (Fig. 5c). In the case of the CBP, we obtain a negative VOC_H. The absolute value of VOC_H is larger than that of VSurface. The increased output voltage is maintained if the CMeas is small enough (Fig. 5d). The dependency on CMeas is equal to that of VOC_L. Impedance matching occurs when CMeas is equal to Cmin, which is the output impedance of the TENG under measurement conditions (Fig. 2d). The ratio of VOC_H to VOC_L is constant regardless of the VSurface, which is the value of Cmax/Cmin when CMeas is small enough (Fig. 5e), but this ratio steadily decreases as CMeas becomes larger than Cmin. This ratio can be termed the amplification ratio.

Fig. 5
figure 5

VOC with different CMeas in the repeated charge balancing. TENG with a SBP and b CBP conditions connected to the measurement system. The VOCs of the TENG with changes in surface voltage (VSurface). c Lower VOC (VOC_L), d higher VOC (VOC_H), and e the ratio of VOC_H to VOC_L at fixed values of Cmin = 1 pF and Cmax = 100 pF when VSurface is varied. At a constant VSurface of 100 V with a fixed Cmax, the changes in (f) VOC_L, g VOC_H, and h the ratio of VOC_H to VOC_L are shown as a function of CMeas. The effect of varying the magnitude of Cmax and Cmin while maintaining the ratio of Cmax to Cmin fixed to 100 with a VSurface of 100 V, i VOC_L, j VOC_H, and k the ratio of VOC_H to VOC_L as a function of CMeas

Full size image

Only Cmin was varied to verify this amplification ratio, while VSuface and Cmax were fixed, as shown in Fig. 5f–h. The output voltage is constant with the value of the VSurface, and the role of the point is also fixed at the corresponding series impedance of Cmax (Fig. 5f). We can see that VOC_L is independent of Cmin. On the other hand, by varying Cmin, it was observed that three different values of VOC_H were obtained by three different Cmin at small enough CMeas, and the impedance matching point followed each Cmin value (Fig. 5g). Each VOC_H can be obtained by VSurface × Cmax/Cmin. Thus, the ratio of VOC_H to VOC_L follows the Cmax/Cmin ratio precisely as before (Fig. 5h).

As shown in Fig. 5i–k, the Cmax and Cmin varied simultaneously at the same rate but with a fixed ratio of Cmax/Cmin = 100. We can see that VOC_L and VOC_H are fixed at constant values at sufficiently small CMeas and impedance matching with each Cmin and Cmax (Fig. 5i, j). The VOC_H/VOC_L ratio follows the CImpedance ratio of Cmax/Cmin when the CMeas is less than Cmin (Fig. 5k).

When the influence of CMeas is very small, the two VOC_L and VOC_H values converge to constant values, indicating that these are intrinsic characteristics of the TENG. Under SBP conditions, the amount of charge accumulated during the charge balancing process facilitated by the diode is determined by Cmin and VSurface.

$$\begin{array}{*{20}c} {Q_{SBP} = C_{min} \times V_{Surface} } \\ \end{array}$$
(1)

When the charged TENG with the QSBP transit to a contact state, the output voltage is the sum of the voltage generated by the QSBP and the VSurface.

$$\begin{array}{*{20}c} {V_{OC\_L} = \frac{{Q_{SBP} }}{{C_{max} }} + V_{Surface} = \frac{{C_{min} \times V_{Surface} }}{{C_{max} }} + V_{Surface} } \\ \end{array}$$
(2)

When Cmin/Cmax is negligible in Eq. (2), VOC_L can be expressed as follows:

$$\begin{array}{*{20}c} {V_{OC\_L} = \left( {\frac{{C_{min} }}{{C_{max} }} + 1} \right) \times V_{Surface} \cong V_{Surface}\qquad\left( {C_{min} /C_{max} \ll 1} \right) } \\ \end{array}$$
(3)

Under CBP conditions, the amount of charge accumulated during the charge balancing process facilitated by the diode is as follows:

$$\begin{array}{*{20}c} {Q_{CBP} = C_{max} \times V_{Surface} } \\ \end{array}$$
(4)

The output generated by QCBP and VSurface is as follows:

$$\begin{array}{*{20}c} {V_{OC\_H} = \frac{{Q_{CBP} }}{{C_{min} }} + V_{Surface} = \left( {\frac{{C_{max} }}{{C_{min} }} + 1} \right) \times V_{Surface} } \\ \end{array}$$
(5)

When Cmax/Cmin is very large, the output voltage can be expressed as follows:

$$\begin{array}{*{20}c} {V_{OC\_H} \cong \frac{{C_{max} }}{{C_{min} }} \times V_{Surface} \qquad\left( {1 \ll C_{max} /C_{min} } \right)} \\ \end{array}$$
(6)

When the balancing process occurs under CBP conditions facilitated by the diode, a charge corresponding to the VSurface is stored in Cmax. Subsequently, as the impedance changes to Cmin, an additional voltage is generated by the previously stored charge, resulting in a higher output voltage than that of the VSurface.

3.4 Experimental verification of diode balancing

We can see that VOC_L is determined by VSurface, and its series impedance is Cmax, while VOC_H has a value of Cmax/Cmin × VSurface, and its series impedance is Cmin. The output properties of TENG are determined by its two impedances, and to achieve a high output voltage, a balancing diode must be connected. To fulfill these two conditions, two characteristic impedances, Cmin and Cmax, must include the balancing diode effect. To verify this, the Cmin and Cmax of the TENG with a diode were measured (Fig. S3). Using these parameters (VSurface = 138 V, Cmin = 4 pF, and Cmax = 118 pF), the changes in VOC with varying CMeas were measured and compared with circuit simulations. We minimized the measurement capacitance by using a noncontact voltage measurement device such as an electrostatic fieldmeter, and we added an additional capacitor to simulate the CMeas. In the circuits used for the experiment shown in Fig. 5a, b, the voltage of the TENG was measured (Fig. 6a). Figure 6b shows the measurement and simulation results. The experimental outputs of VOC_L and VOC_H are consistent with the simulation results. However, VOC_H slightly decreases compared with the simulation results. This can be originated from the decreased voltage, as shown by the sawtooth shape at CMeas = 0 pF (Fig. 6a). In the SPICE simulation, the parameter of the RSHUNT represents the leakage of the DC path between the circuit and the ground. The output (Fig. S4) replicates a sawtooth shape with this finite leakage parameter. Due to leakage, it can be expected that the observed voltage would be lower than the ideal simulation results without leakage. When we conducted initial charge balancing with CMeas, the outputs of SBP and CBP converged to a value between that of CBP and SBP over time. In contrast, when we apply repeated charge balancing with a diode, the output voltage decreases in each cycle but remains constant across the repeating cycles. The maintenance of the reference voltage level came from the recovery charge originated from the ground.

Fig. 6
figure 6

a VOC_L and VOC_H were measured using an electrostatic field meter with an additional capacitor as CMeas. b Measurement and simulation results. The SPICE parameters were modified by including the diode effect

Full size image

3.5 TENG power curve for the resistive load

In order to verify that VOC_H has a physical meaning, we calculated the power curve for the resistive load. To observe the power curve, we drive the TENG in a sinusoidal shape at 1 Hz with a corresponding sinusoidal change in the series output impedance with a maximum value of 100 pF and a minimum value of 1 pF. The circuits in Fig. 7a, b have a resistive load without or with (dashed line) CMeas of the measurement system. For the two different resistive loads without CMeas, a half-wave sinusoidal voltage appears across the resistive load depending on the SBP and CBP conditions (Fig. 7c). The output voltage and current were used to determine the output power of the TENG (Fig. 7d, e). From the behavior of the same TENG, the maximum output power is observed at different points depending on the orientation of the diode. The difference between these maximum power outputs is approximately 320 times when CMeas is zero (Fig. 7d). When measured using CMeas of 370 pF with a resistive load, the output power lines almost coincide, as shown in the two lower output lines in Fig. 7d. With an ideal voltage measurement system with a very small CMeas = 0 pF, all the internal power of the TENG is delivered to the resistive load. However, in the real world, when the voltage measurement system has infinite resistance but finite capacitance, the impedance of the instrument system affects the circuit, as shown in Fig. 5. The output characteristics under the CBP condition severely deteriorate. The charge transfer during the operation of the TENG at the point of maximum power output was obtained, as shown in the Q–V plot in Fig. 7e. The Q–V plot also shows a large output of CBP (4.84 mW) and SBP (7.38 μW) in the ideal situation of CMeas = 0 pF. In the case of CMeas = 370 pF, we can see that both the CBP (1.85 μW) and SBP (1.31 μW) in the zoomed Q–V plot are heavily deteriorated and almost similar sized circular shape output characteristics as in the case of the lower power curves of Fig. 7d. If we do not deteriorate the output of the TENG with significantly smaller CMeas (i.e., parasitic capacitive load in a without measurement system), we can effectively use the maximum power output by selecting an appropriate initial/repeated balancing process.

Fig. 7
figure 7

SPICE models of a TENG under resistive load conditions with a SBP and b CBP reference voltage settings. The CImpedance varies sinusoidally at 1 Hz between Cmax = 100 pF and Cmin = 1 pF. c Output voltage waveform with two different resistive loads. d The power curve as a function of resistive load. e Q–V plot at the maximum power output point of d, where the numerals represent the area of the curve, indicating the output power

Full size image

4 Conclusions

In our experiments, two distinctive VOCs were observed, which were dependent on the initial voltage setting method. This behavior was replicated in circuit simulations, where the output voltage depended on the initial voltage setting method. Furthermore, we successfully achieved two independent VOCs in the simulation and measurement by employing diode connections, irrespective of the initial voltage settings. The diode connection can be interpreted as repeated charge balancing.

When the measurement system capacitance was lower than the minimum series capacitance, the VOC_L was equivalent to the VSurface. Meanwhile, the VOC_H was amplified by the product of the VSurface and the ratio of the TENG's characteristic impedance (Cmax/Cmin). However, as the measurement system impedance increased, the difference between the two VOCs decreased, and their absolute magnitudes also fell below the VSurface.

The system exhibited two distinct power characteristics when a resistive load was connected. To maximize the output power, it is essential to utilize the amplified VOC. This necessitates precise reference voltage settings and minimizing the capacitive load of the measurement system or parasitic component to less than the Cmin of the TENG.

This study highlights the critical influence of the capacitance of the system on the performance of the TENG. This finding underscores the necessity of proper reference voltage settings (initial/repeated charge balancing) to fully leverage the potential of TENGs for various applications.