Switched-capacitor-convertors based on fractal design for output power management of triboelectric nanogenerator

Owing to the advantages of integration and being magnet-free and light-weight, the switched-capacitor-convertor plays an increasing role compared to traditional transformer in some specific power supply systems. However, the high output impedance and switching loss largely reduces its power efficiency, due to imperfect topology and transistors. Herein, we propose a fractal-design based switched-capacitor-convertors with characteristics including high conversion efficiency, minimum output impedance, and electrostatic voltage applicability. As a double-function output power management system for triboelectric nanogenerators, it delivers over 67 times charge boosting and 954 W m−2 power density in pulse mode, and achieves over 94% total energy transfer efficiency in constant mode. The establishment of the fractal-design switched-capacitor-convertors provides significant guidance for the development of power management toward multi-functional output for numerous applications. The successful demonstration in triboelectric nanogenerators also declares its great potential in electric vehicles, DC micro-grids etc.


Point-to-Point Response to the Reviewer's Comments (Comments in black, response in blue，corrections in yellow background)
Dear reviewers: Thank you for your detailed and useful comments and suggestions on our manuscript. We have revised the manuscript accordingly and the detailed corrections are listed below point by point.

Reviewer #1 (Remarks to the Author):
This manuscript showed the fractal design based switched-capacitor-converters as power management circuit for triboelectric nanogenerator. With using this circuit, the pulsed power density was elevated by 192 times than without this circuit and 94.5% of an energy transfer efficiency was achieved. However, some modification needs to be conducted for accepting to this Nature Communications.
Response: We highly appreciate the reviewer's positive comments and good suggestions on our work. And we also thank the reviewer's detailed and responsible reviewing of our work.
1. There is no analysis or discussion of Fig 3e, f in the results part. Response: Thanks for your valuable suggestion. Figure 3e and 3f show the maximum pulsed current density and pulsed power density curve with optimum FSCC (6=2×3) power management system, and 807 times and 192 times enhancement of current density and pulsed power density are reached respectively compared with that of TENG without any power management. Here, owning to the multifold increase in output charges achieved by FSCC and super-short discharging time (< 1ms) controlled by contact switch, 14.3 A m -2 pulsed current density and 954 W m -2 pulsed power density are realized for the first time. The result is almost twice larger than that of the previously highest record (500 W m -2 , Adv. Mater. 2014, 26, 3788-3796). Besides, the matching impedance decreases from 20 MΩ to 2.4 KΩ with FSCC, which is more suitable for driving common electric devices (Inner impedance:1~100 KΩ). To obtain the maximum current density, some works for optimizing parameters are also carried out, including the investigation in influence of total voltage drop, charge quantity of TENG, types of the integrated substrate, capacitance of charge storage capacitor and different orders on current density, as shown in Supplementary  Figure 13 and Note 4. It is clear that FSCC makes TENG have the characteristics of high current density, high power density, small matching impedance and large charge output, leading TENG closer to practical application. The revised discussions of Fig.  3e and 3f in manuscript are listed below: Besides, when the charge quantity of TENG is 291 nC at frequency of 1 Hz and the energy storage capacitor is 1 nF, the short-circuit pulsed current density of FSCC power management system reaches 14.3 A m -2 as shown in Fig. 3e. Owning to the multifold increase in output charges and super-short discharging time (< 1ms), the current density is boosted by 807 times compared with 17.7 mA m -2 of TENG (Supplementary Figure 12b). The pulse power density reaches 954 W m -2 for the first time on 2.4 kΩ load (Fig. 3f), which is elevated by 192 times as that of 4.97 W m -2 of TENG on 20 MΩ (Supplementary Figure 12c). almost twice larger than that of the previous highest record (500 W m -2 ) 9 . The matching impedance is effectively reduced after the power management, which is more suitable for driving common electric devices (1~100 KΩ). With the increase of frequency, the pulse power density on 3 kΩ load increases from 403 W m -2 at 0.1 Hz to 960 W m -2 at 2 Hz, which is illustrated by Supplementary Figure 12d. To reach the maximum pulse power output, some preliminary researches are carried out to discuss the influence of total voltage drop, types of the integrated substrate, capacitance of charge storage capacitor and different orders on current density to get optimum parameter, as shown in Supplementary Figure 13 and Note 4.

E =
For the Q-V curve in this work, two testing equipment are used to measure voltage and charge at the same time. Here, an electrostatic voltmeter (TREK 370-3) which has ±3 kV measuring range is used to test the voltage over 200V ( Fig. 3g and 3i), and a Keithley 6514 is used to measure the voltage below 200 V (Fig. 3h). Another Keithley 6514 is used to measure the charge quantity. In brief, Q-V curve was acquired by 6514 to measure charge and TREK 370-3 (or 6514) to measure voltage at the same time through dual channel testing system with the same sampling rate of 1000 data per second. The grounding terminal of the measuring line of the two testing equipment should be connected together, to gain the accurate data. Especially, smoothing or filtering the test data may cause serious distortion of the waveform, therefore, filtering or smoothing should not be used when testing Q-V curve. We can draw the Q-V curve in Origin software by setting Q as X-axis and V as Y-axis, and the energy value is the area surrounded by Q-V curve. In addition, we have added this information in the method part.
The contact-separation process of TENG was driven by a linear motor (LINMOT E1200-P01) under sinusoidal motion in an acrylic glove box with 5% relative humidity. The voltage was measured by an electrostatic voltmeter (TREK 370-3, voltage over 200 V) and electrometer (Keithley 6514, voltage below 200 V), the current and charge were measured by electrometer (Keithley 6514), the voltage 3 driving electric devices was measured by electrometer as well. A programmable power supply (Keithley 2230G) was used to drive the electric devices to test the driving current and turn-on voltage drop with electrometer. Q-V curve ( Fig. 3g and 3i) was measured by Keithley 6514 (charge) and TREK 370-3 (voltage) at the same time through dual channel testing system, with the same sampling rate of 1000 data per second and no filtering or smoothing processing. Q-V curve (Fig. 3h) was measured by two 6514 at the same time through dual channel testing system which measured Q and V, respectively. The grounding terminal of the measuring line of the two testing devices were connected together to gain accurate data. Figure 12, there is no reason why 1 nF capacitor showed highest output. In Supplementary Figure 13, here also no discussion of this figure. Response: Thank the reviewer for the detailed and valuable comments. The discharging process of FSCC is equivalent to the discharging process of a big capacitor, which can be described by equation as follow: The discharging process of FSCC is equivalent to discharging process of a big capacitor, which can be described by equation below:

Supplementary
Where C and is respectively the capacitance and the voltage of capacitor. So the discharging process of FSCC can be conducted according to Equation 4 ( = ) and 6 ( = • ).

= (13)
In the equation above, as ∈ (1~0) is a decay factor the maximum value of current is: Therefore, the maximum current is inversely proportional to the capacitance of charge storage capacitor. Preliminary researches are carried out with TENG of 200 nC charge quantity for quantitative characterization. Firstly, the influence of voltage drop is discussed in Supplementary Figure 13a, and total voltage drop could reduce output current linearly. Supplementary Figure 13b shows that small (1 nF) charge storage capacitor is suitable to obtain high current in experimental aspect, which is consistent to theoretical analysis for the influence of voltage drop. The current output under different units indicates that TENG with 5-unit FSCC has a maximum current output (Supplementary Figure 13c). Supplementary Figure 13d  In addition, when charging a 100 µF capacitor with FSCC on PCB, the voltage of capacitor can reach 8.76 V from 0 V within 85 seconds. Meanwhile, the output voltage of FSCC increases from 9.9 V to 14.3 V as shown in Fig. 3c, which indicates a unique voltage cumulative effect and better output stability compared with works based on inductance transducer. And the voltage cumulative effect is caused by the accumulated residual charge of charge storage capacitors (V=Q/C) in each discharge cycle, and the residual charge is owning to that the external load is too large to release all the charge. 5. There are many punctuation errors and some commas should be changed to periods. Response: Thanks the reviewer for the good suggestion. In the revised manuscript, we have carefully checked the contents, and there are 16 places where commas were changed to periods. After the related punctuation errors are revised, it is easier to read and understand this paper.
Reviewer #2 (Remarks to the Author): Nowadays, large energy output and energy transfer efficiency are two key factors for TENG toward actual applications. In this manuscript, authors put forward a fractal design based switched-capacitor-convertors (FSCC), by which, the highest record of peak power density and over 94% total energy transfer efficiency of TENG are achieved. This is an interesting work with enough innovation, and the manuscript is well-organized with a lot of supporting information for readers. Therefore, it is good enough to be published in Nature Communication. However, there are a few minor questions that need to be addressed before this manuscript accepted.
Response: We highly appreciate the reviewer's positive and valuable comments on our work as "enough innovation". And we also thank the reviewer's detailed and responsible reviewing of our work. 1. A power management system with stable output is necessary for the actual applications of TENG, so the time curve is suggested to demonstrate the reliability issue. Response: Thanks for your instructive suggestion. Stable output is important in actual 6 applications, and we have tested the stability performance of the power management circuit in the revised manuscript. Because output charge is accumulated in one direction, so, the charge quantity would beyond the measuring range. Therefore, output voltage is chosen to characterize the stability performance of FSCC power management system at 1 Hz. Power management circuit of 96=2×2×2×2×2×3 FSCC integrated on PCB is used, the corresponding data figure is shown below. After more than 30000 cycles, the output voltage finally maintains at 8.8 V from the initial 9.4 V, which is a quite good result and can meet the requirements of actual applications.

Supplementary Figure 19 | The stability performance of 96=2×2×2×2×2×3 FSCC.
In addition, the stability performance of 96-unit FSCC is also tested (Supplementary  Figure 19), and after more than 30000 cycles at 1 Hz, the output voltage finally maintains at 8.8 V from the initial 9.4 V. It is believed that FSCC with such a quite stable output can meet the requirements of practical applications.
2. The concepts of total energy transfer efficiency and energy conversion efficiency in manuscripts are confusing, authors should clarify these concepts for readers. Response: Thanks for your good suggestion. The total energy transfer efficiency is used to describe the efficiency of the energy transfer process from TENG to load through FSCC power management system, which belongs to efficiency of whole energy system. As for the energy conversion efficiency, it is used to describe the efficiency of FSCC itself only and belongs to efficiency of part.
3. The fractal design based switched-capacitor-convertors is interesting, is there a limitation of the orders for this design? What would happen if the orders is too large? Response: Thanks for the valuable question. The detailed structure of FSCC is described with expanded form below: Where is the total basic unit number of FSCC, and is the unit number of per order. When the basic unit number is given, it is obvious that the expansion of has a finite number of terms, meaning that there is a limitation of orders with given . (Response to "is there a limitation of the orders for this design"). There are two cases existing when the order is too large. One is that the output charge, current and energy conversion efficiency all increase toward the beneficial side with the increase in order when basic unit number is given. The other is that the total basic unit number will increase and the output voltage will decrease along with the order increase when is not limited. And the output voltage would be too low to drive electric devices if order number is too large. (Response to "What would happen if the orders is too large?"). Therefore, the basic unit number is decided by the desired output voltage and voltage of TENG, and the large order is expectedwhen is determined.
4. The combination of this FSCC design and contact-separation mode TENG shows a quite good result, is it a must to combine FSCC design and contact-separation mode TENG? Can other modes of TENG have a good power management characteristic with this FSCC? Response: Thanks for your valuable question. Previous work has proved that the TENG has extremely low energy utilization efficiency when directly driving electric devices (Nat. Commun. 2015, 6, 8975). The basic working principle of FSCC is charging the charge storage capacitors of FSCC in series state and the capacitors discharge in parallel, so that the FSCC can decrease the output voltage and increase the output charge of TENG. Besides, fractal design is used to effectively decrease the total voltage drop to achieve maximum output. Here, the TENG is equal to a voltage/charge source, and FSCC is equal to a transformer to output energy matching common device, thus, it is a must to combine FSCC design and TENG for achieving effectively energy usage in common electric devices (Response to "is it a must to combine FSCC design and contact-separation mode TENG"). The output performance after power management is fully depended on the power management circuit when the charge and voltage of TENG keep constant. Therefore, other modes TENG also can have a good power management characteristic with suitable structure FSCC power management system (Response to "Can other modes of TENG have a good power management characteristic with this FSCC?"). This work reports switched-capacitor-convertors for dual-function output power management of triboelectric nanogenerator (TENG), where the fractal designed configurations were proposed. This power management circuit show attractive features of high conversion efficiency, minimum output impedance, electrostatic voltage applicability, and high step-down ratio. After the comprehensive study, the developed circuit achieved higher than 94% total energy transfer efficiency. The research topic of this work is very interesting, the proposed method is innovative, and the manuscript is well organized. Thus, it is recommended to the acceptance.
Answer: We highly appreciate the reviewer's positive comments on our work as "innovative". And we also thank the reviewer's detailed and responsible reviewing of our work.
1. Fig. 1 could be improved better. It is suggested to remove Fig. 1(b) to the Supplementary file. Response: Thanks reviewer for the valuable suggestion. According to this suggestion, we have removed Fig. 1b to the Supplementary file as Supplementary Figure 1. We also checked the content and revised the related part to match the revised Figure. The revised Figure 1 is as follow: repeatedly with 2=2 SCC unit.
2. It is suggested to replace Fig. 2(g) with the photograph of the fabricated TENG. Response: Thanks for your helpful suggestion. We replaced Fig. 2g with the photograph of the fabricated TENG in the revised manuscript for intuitive understanding of TENG itself, and the original Fig. 2g with each layer structure of TENG has been removed to the Supplementary file as Supplementary Figure 5b. The revised Fig. 2g is as follows. The FSCC can achieve multifold charge output through the auto-switch of capacitors from serial to parallel connection. d, The equivalent diagram of discharging process of FSCC in c. The turn-on voltage drop of diode has a significant influence on charge output. e, The output voltage and f, the output charge of 24-unit FSCC with different orders. 1st order FSCC has the largest turn-on voltage drop and the output charge increases rapidly with multi-order FSCC. g, Photograph of triboelectric nanogenerator (TENG) with a contact switch in this work. h, Schematic diagram of the power management system, which consists of a TENG, half-rectifier circuit, contact switch and FSCC, and there are two output modes in pulse and constant after power management.
3. Why the current curve in Fig. 3(e) is dissymmetric? Response: Thanks for your detailed comment. The output current of the FSCC power management system is rectified by a half-wave rectifier, therefore, the current curve is asymmetric in up and down direction. As for the -asymmetric output current in left and right direction, the discharging process of FSCC is equivalent to discharging process of a big capacitor, which can be described by equation below: = The current will decrease from maximum to zero during the discharge process, therefore, the current curve in Fig. 3e is asymmetric in left and right direction.
4. The photographs in Fig. 5(d, e) should be enlarged to show more details. Response: Thanks for your good suggestion. In order to show more details, we have reorganized Figure 5d, e, and the photographs have been enlarged. The revised Figure is as follows.