Concept of an efficient self-startup voltage converter with dynamic maximum power point tracking for microscale thermoelectric generators

Microscale Thermoelectric Generators (microTEGs) have a high application potential for energy harvesting for autonomous microsystems. In contrast to conventional thermoelectric generators, microTEGs can only supply small output-voltages. Therefore, voltage converters are required to provide supply-voltages that are sufficiently high to power microelectronics. However, for high conversion efficiency, voltage converters need to be optimized for the limited input voltage range and the typically high internal resistance of microTEGs. To overcome the limitations of conventional voltage converters we present an optimized self-startup voltage converter with dynamic maximum power point tracking. The performance potential of our concept is theoretically and experimentally analyzed. The voltage conversion interface demonstrates energy harvesting from open-circuit voltages as low as 30.7 mV, and enables independent and full start-up from 131 mV. No additional external power supply is required at any time during operation. It can be operated with a wide range of internal resistances from 20.6 to − 4 kΩ with a conversation efficiency between η = 68–79%.


Introduction
Thermoelectric generators (TEGs) used as energy harvesters have several advantages for autonomous systems such as low maintenance, long operating lifetime as well as vibration-and pollution-free operation [1,2]. While conventional macroscale thermoelectric generators are only found in niche applications due to their limited powerefficiency [3], recent advances in micro- [4] and nanotechnology [5][6][7] combined with the use of low-dimensional materials [8] paved the way towards micro-and nanoscale TEGs with much higher power-efficiency and even opened-up new application ranges. For instance, the integration of TEGs in microelectronics enables harvesting of waste heat from hotspots [9,10] for potential applications involving autonomous sensors [11], wireless systems [1] or for increasing battery life [6]. Microscale TEGs (micro-TEGs) have been fabricated for operation with in-plane [12] or cross-plane heat-flux configurations [13][14][15][16], and can be integrated on a wide range of substrates, including silicon [17] and flexible polymers [13,18]. Due to their geometric constrains, microTEGs typically show relatively large internal resistances in a range of 10 1 -10 3 Ω and can only provide small open-circuit voltages of typically V TEG = 30 mV -300 mV [13,17,19,20]. The load-resistance of microelectronic devices is often not matching such large internal resistances and/or require higher supply-voltages. Therefore, voltage converters that are compatible with the limitations of microTEGs are required to provide sufficiently high supply-voltages to power microelectronics [21]. However, voltage converters reported in literature do either not provide high efficiency, for example < 60% [22][23][24][25][26], or often require external power supplies or signals for startup [24,[27][28][29]. These disadvantages make most voltage converters not compatible with the limitations of microTEGs and application in autonomous systems, which require full and independent self-startup functionality.
In this study we report on a two-stage voltage converter with full self-startup functionality from an open-circuit source voltage as low as 131 mV, which corresponds to a minimum converter input voltage of V in = 65.5 mV. No additional external power supply is required at any time during operation.
The converter can be operated at high efficiency > 68% with a large range of source impedances ranging from 20.6 Ω to 4 kΩ, which is a much larger impedance range compared to concept reported so far. After self-startup, the converter achieves a maximum conversion efficiency of between 68 and 79% over the entire impedance range by using a novel dynamic maximum power point tracking concept.
The outline of the manuscript is as follows: at first, stateof-the-art voltage converters as well as the limitations of microTEGs are shortly introduced. Next, the proposed concept of a two-stage voltage converter with full selfstartup functionality and dynamic maximum power point tracking is introduced. Section 4 summarizes the experimental details of the printed circuit board prototype and the simulation details. The experimental and simulation results are shown and discussed in Sect. 5 followed by a short conclusion.

State-of-the-art voltage converters for microTEGs
In the simplest case, the equivalent circuit of a microTEG is composed of a series connection of the actual thermoelectric open-circuit voltage source V TEG and an internal resistance R TEG (Fig. 1). The input voltage V in of an external circuit with a load resistance connected to the micro-TEG, i.e. here a converter circuit, is given by V TEG and the voltage drop V R across R TEG . When the load resistance is much larger than R TEG it follows V in ≈ V TEG . Typical ranges for R TEG and V TEG are 10 1 -10 3 Ω and 30 mV -300 mV, respectively [13,17,19,20]. It should be noted that this equivalent circuit is appropriate for approximation of the steady-state operation of a microTEG on which we mainly focus in this study. To simulate the dynamic operation such as fluctuating internal resistance or generated voltage, a more complex equivalent circuit is required. Such an equivalent circuit may account for the microTEG's time constants determined by its thermal mass. In addition, external parameters such as convection or radiation may also affect the microTEG's Seebeck coefficients, and thermal and electrical impedances. Advanced microTEGs provide maximum power-densities of some mW/cm 2 [14]. For comparison modern microelectronics have a heat power dissipation density of up to 1000 W/cm 2 [30]. Typical supply-voltages for embedded microelectronics or ultra-low-power microcontrollers range from 1.8 to 3.3 V [31]. Therefore, dedicated voltage converters that are compatible with the performance limitations of microTEGs are required to provide sufficiently high supply-voltages for microelectronics.
The following design criteria need to be fulfilled by a microTEG-compatible voltage converter [32]: • Full and independent self-startup functionality, that is no requirement for external power supplies and control-signals for autonomous applications. • Compatibility to low input voltages V TEG = 30 mV 300 mV and relatively high generator internal resistances R TEG = 10 1 10 3 Ω. • High conversion efficiency to prevent further decrease of the already small thermoelectric conversion efficiency.
Most voltage converters are based on either Meissner oscillators (Fig. 1a), boost converters ( Fig. 1b), flyback converters ( Fig. 1c), or a combination of these circuits. The operation principle of each converter is here only shortly introduced. Further details of the converter concepts can be found in Refs. [21,33,34].
In the Meissner oscillator, T M1 , C M2 and the coupled inductors N P and N S , which are typically realized by a transformer with opposite windings, form a self-triggered oscillator. C M1 is an input buffer-capacitor. Voltage conversion from an input voltage V in to an output voltage V M,out is achieved by self-oscillated electromagnetic charging and discharging of the coupled inductors. V M,out drives an output current I M,out when an external load R L is connected. Note, although N P and N S are part of the oscillator, they determine the transient increase of the output-voltage, and its amplitude is only slightly affected by the winding resistances. Thus, the magnitude of V M,out is almost independent on the selected transformer. V M,out can be fixed to a maximum output voltage by e.g. using a Zener diode (not shown here).
In boost converts, which belong to the class of switched-mode power supplies [35], an external control signal ~ S TB is required for charging and discharging of an inductor L B . A rectifying diode D B is used to allow the output current I B,out only to be driven in one direction. Here, the output voltage is V B,out , and C B1 and C B2 are input and output buffer-capacitors, respectively.
In a flyback converter, charging and discharging is also achieved using a control signal ~ S TF . Similar to a Meissner oscillator coupled inductors, which are usually realized by a transformer with opposite windings as well, are used. Compared to a boost converter, the flyback converter has typically slightly smaller efficiencies due to the non-ideal coupling of both inductors. In contrast to the Meissner oscillator, the output voltage V F,out depends on the ratio between the windings of N P and N S . A flyback converter allows in principle for galvanic insulation between V in and V F,out . C F1 and C F2 are input and output buffer-capacitors. D F is required to allow the output current I F,out only to be driven in one direction.
The performance of voltage converters can be compared by the relative efficiency , that is given by the converter's in-and output-power P in and P out , respectively: Boost and flyback converters have high efficiencies typically above 70%. However, they require control signals for voltage conversion and therefore an external power supply for startup. In contrast, Meissner oscillators do not require any external power supply nor signals but have significantly lower efficiencies < 60% than boost and flyback converters [29,36]. A straightforward method is to combine a Meissner oscillator with a boost converter for example to provide a voltage converter with self-startup functionality and high conversion efficiency. Additional efficiency improvement is achieved using maximum power point tracking (MPPT). This allows to obtain a good impedance matching between the microTEG power source and the voltage converter [37,38]. However, most concepts reported in literature are still suffering from poor efficiency [22][23][24][25][26], or require external signals or even power supplies for startup [24,[27][28][29]. Very recently, Dillersberger et al. reported on an integrated bipolar voltage converter with full self-startup functionality and high efficiency of 85% [39]. A Meissner oscillator is used for startup while a flyback converter is used for normal operation. However, the authors report on a limited source impedance range of 0 < R TEG ≤ 60 Ω, which is much smaller compared to typical source impedances of up to 10 3 Ω of microTEGs. The study by Dillersberger et al. does not report whether the converter is compatible with the limitations of micro-TEGs. In addition, the output voltage depends on N P :N S , thus, one may not be flexible in using transformers with different footprints and windings

Concept of a high efficiency voltage converter for microTEGs
We propose a two-stage voltage converter with full and independent self-startup functionality. Although the converter has been designed for microTEGs, it is high flexibility. The concept is compatible to a large range of source impedances while simultaneously maintaining a high efficiency between 65 and 79%. This makes it possible to use the converter for bulk TEGs and many other energy harvesters as well. The complete circuitry is shown in Fig. 2. Upon startup, the Meissner oscillator (first stage) generates an internal voltage V CC to supply the pulse generator. As soon as the pulse generator is in operation, a boost converter (second stage) with dynamic MPPT generates the output voltage with high conversion efficiency. In this case, T M2 is switched off and the pulse-generator is then also only supplied by the boost converter. The Meissner oscillator is then operating in open circuit condition. Thus, after startup the contribution of the Meissner oscillator's poor efficiency to the overall converter efficiency is small. Note, the whole circuitry, including the pulse-generator, operation amplifiers and inverters are only operated using a single input voltage V in . No additional control, clock or reference signals are required.

Working principle of the dynamic maximum power point tracking
Since the performance of the microTEGs can change over time, e.g. by change of the heat flux, dynamic impedance matching is required to operate the converter with maximum efficiency. In the work by Dillersberger et al. this is achieved by setting up an appropriate switching frequency, which controls the converter's input resistance [40]. Hence, the frequency needs to re-programmed in case of performance variation of the microTEG for impedance matching. In the paper by Im et al. a similar MPPT circuitry like here is used, which, however, requires external control signals [32].
In the concept shown here flexible impedance matching is achieved using dynamic maximum power point tracking. The internal reference voltage for MPPT is V MPP+ . A conventional MPPT compares the converter's input voltage with a reference voltage that corresponds to the voltage for perfect impedance matching. Impedance matching is then provided by the MPPT setting up and appropriate switching frequency of T B1 . Here, instead of using a fixed reference-voltage for MPPT, a Sample & Hold (S&H) circuit continuously generates a variable reference voltage V MPP− . The S&H circuit [28,32] is controlled by an internal pulse generator. When V P is high and consequently the inverted signal ~ V P is low, T SH1 is switched off and insulates the S&H from the boost converter. C SH2 is then discharged, and the voltage drop across C SH1 is equal to the open-circuit voltage of the microTEG. When V P is low, the microTEG is connected to the boost converter.

Experimental and Simulation Details
We prepared a prototype PCB-board for experimental verification of the operation principle and self-startup functionality of the proposed voltage converter. The voltage signals were probed using a Tektronix TDS 1001B oscilloscope with a bandwidth 40 MHz. Quasi-static voltages were measured using an Escort 3136 A multimeter. V TEG was provided by an external precision power supply (S160, Knick GmbH, Germany) and R TEG was varied between 12 and 4 kΩ using a potentiometer in series to V TEG . The MPPT, pulse generator and boost converter circuit were additionally simulated by LT Spice using a constant output of the Meissner oscillator of 3 V. Table 1 shows a list of the circuit components.
For operation of the Meissner oscillator, a p-JFET is required (the capacitive gate-input of a MOSFET would not lead to an oscillation). The transformer is based on a WE-EHPI (Würth Elektronik, Germany) with an inductivity of 7 µH on the primary side and 70 mH on the secondary side. The parasitic resistances on the primary and secondary side are 0.085 Ω and 205 Ω, respectively. Note, for simulation an ideal coupling-factor of 1 is assumed between the primary and secondary side. Schottky diodes D B , D S1 and D S2 are used due to their low forward voltage drop. The pulse generator uses a fast switchingsignal diode and is optimized for a frequency range of some hundreds of Hz and short pulse peaks (length some hundreds of µs). A TLV7031 for OP1 and OP2 is chosen, which has a quiescent supply current of 315 nA. An inverting buffer with 900 nA max. static current has been selected due to its low power consumption. The nand p-MOSFET types were used due to their low on-state resistance, respectively. D BZ limits V Out to 6.8 V. Here, for R L ≥ 100 kΩ the output voltage is limited by the load resistance. A picture of the printed circuit board of the voltage-converter is shown in Fig. 3. Figure 4 depicts experimental results of the voltage converter prototype for V TEG = 300 mV, R TEG = 98 Ω. In Fig. 4a the output voltages V P and ~ V P of the pulse generator are shown. The pulse generator frequency f P ≈ 20 Hz and pulse length (duty cycle) set by C P , R P1 and R P2 . Here, the length is ≈ 385 µs, which equals a duty cycle of 0.019. The pulse generator controls the S&H circuit, which generates a dynamic reference voltage V MPP− = V TEG ∕2 . As can be seen, the dynamic maximum power point tracking automatically regulates the internal boost converter's input voltage to V B,in ≈ V TEG ∕2 . The peaks (A) correspond to events when V P = high, in which C SH1 is charged to V TEG and C SH2 is discharged. When V P = low, the charge is equally distributed to C SH1 and C SH2 resulting in a voltage drop of V TEG ∕2 . The dynamic maximum power point tracking results in a ripple on V B,in of ± 13 mV as can be seen in the zoom in V B,in in Fig. 4c. The switching signals of the charging transistor T B1 determine the ripple frequency ≈ 3.85 kHz and are shown for comparison in Fig. 4c as well. The simulation reveals a power consumption of the pulse generator of 4.7 µW and of the MPPT of 7.2 µW. Thus, the total power consumption of the dynamic impedance matching is 11.9 µW. Figure 4d shows the results of the voltage conversion. As discussed above, the Meissner oscillator is used during startup to act as a power supply for the pulse-generator and the MPPT. The oscillation generates an internal output The operation principle has been also experimentally verified by variation of R TEG from 12 Ω to 4 kΩ and V TEG between 30.7 and 1148 mV. Note, the performance demonstrated in most studies in literature [32,[41][42][43][44] are specified for a given input voltage V in rather than for the opencircuit voltage V TEG . Thus, due to the voltage-drop across R TEG the open-circuit voltage for the microTEG needs to be higher than the input voltage specified in most studies. Here, the voltage converter can convert voltages from as low as V TEG = 30.7 mV, i.e. V in = 15.35 mV. However, a larger voltage is required for full self-startup. For 51 Ω we found a minimum self-startup voltage of V TEG = 202 mV, i.e. V in = 100.5 mV, and for 660 Ω we found V TEG = 726 mV, i.e. V in = 363 mV. The smallest self-startup voltage of V TEG = 131 mV, i.e. V in = 65.5 mV, was found for R TEG = 21.6 Ω with an efficiency of 68%.

Performance and potential of further improvements
The overall goal in this study is to develop a voltage converter concept that fulfills the requirements for autonomous microTEG applications listed in Sect. 2. Table 2 shows a list of commercially available voltage converters (LTC 3108, LTC 3109, ECT 310, BQ25504) and research concepts.
The experimental results of our prototype demonstrate full and independent self-startup functionality from V TEG as low as 131 mV for R TEG = 21.6 Ω, since apart from the microTEG no additional voltage supply or signal sources are required for operation. LT Spice simulations were done to analyze the performance of the proposed voltage converter for R TEG between 5 Ω to 4 kΩ and V TEG between 30.7 mV and 1790 mV. The same or at least similar components/ models have been used for simulation and design of the experimental prototype. Figure 5a depicts the converter efficiency (equ. (1)) by variation of the input power P in and R TEG . Note, P in can be found without knowing I TEG : A simple model for a theoretical total loss balance is discussed in Supplementary Information S1. Theoretically, an efficiency of 85% is found in the ideal case, which is as expected larger than what is found in the simulations and experimentally. However, it is difficult to estimate a theoretical total loss balance or a limit of the efficiency of the proposed voltage converter since the performance and efficiency of the individual electriconic components is important. For example, the efficiency depends on the On resistance of the transistors, the transformer coupling factor, and the power consumption of the operation amplifier. Our simulation data already accounts for these parameters with the exception of the coupling factor of the transformer, for which we assume the ideal case of 1. Note, a smaller coupling factor is limiting the Meissner oscillator performance mainly during startup. In steady-state operation the output voltage is generated by the boost conveter and the loss contribution of the Meissner osciallator depends on the leakage current of T M1 , T M2 and D MZ .
The experimental and simulation results reveal that the fundamental design criteria for voltage converters for autonomous microTEG applications are fulfilled. In particular, the voltage converter can be operated with relatively high microTEG impedances and a low input voltage. However, a minimum voltage of at least V in = 65.5 mV is required for full self-startup. The overall efficiency of the converter is between 68% and 79%, which is competitive to values for power-efficient voltage converters reported in literature, see Table 2. It should be noted that this efficiency is achieved for a large range of source impedances R TEG = 20.6 Ω -4 kΩ (for P in > 180 µW and full self-startup functionality, see Fig. 5a), while for example an efficiency of up 85% of the converter reported by Dillersberger et al. is specified for only R TEG = 0-60 Ω [39]. A similar large range of compatible source impedances has been reported by Bautista et al. [28]. However, their concept requires a much higher input voltage for self-startup 900 mV vs. 65.5 m V in this work, and shows a smaller efficiency of max. 61.15% vs. 68-79%. Nevertheless, there is still potential for further improvement. For a proof-of-concept we designed a printed circuit board with discrete electronics as shown in Fig. 3. Obviously, this is not the ideal solution for a TEG application with microscale dimensions. However, all components can be in general integrated in an application specific circuit (ASIC) apart from the inductivity L B , the transformer N P :N S as well as C B1 and C B2 . Usually in studies reporting on integrated voltage converters, these or similar components are externally connected to the voltage converter's integrated circuit. C M1 , and C M2 are also relatively large but are only used for the Meissner osciallator and may be optimized when the circuit, including the buffer inverters and comparators, are fully integrated on a single-low-power chip. A disadvantage of our converter is the external circuitry overhead by using a separate transformer and inductor L B . This could be overcome by reusing the inductivity of the transformer's secondary side. Such a concept reduces the external circuitry and footprint, and has been reported by Dillersberger et al. for example [39]. However, for the flyback converter by Dillersberger et al. the ratio of N P :N S is critical for the output voltage amplitude. By adjusting the switching frequency of the boost converter, our concept has a higher flexibility in choosing an inductor L B with small footprint. Therefore, the proposed voltage converter has a high potential for further improvement and area efficiency when the circuitry is modified for reusing the secondary side of the transformer.
Funding Open Access funding enabled and organized by Projekt DEAL. The authors have not disclosed any funding.

Data Availability
The data that support the findings of this study are available on request from the corresponding author.

Conflict of interest
The authors have no conflict to disclose.
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