Energy Harvesting on AB-Class Power Amplifier Applying Thermoelectric Generators in Push–Pull Mode

Abstract

Amplifiers are among the most commonly used circuits in electronics, performing a variety of functions in a wide range of electronic systems. Depending on the application and design, each amplifier generates waste heat. For power amplifiers that operate at low efficiency and high output power, the amount of wasted energy can be significant. This paper presents an energy harvesting system based on the application of thermoelectric generators on the output transistors of the AB-Class power amplifier. The converted electrical energy can be used in several ways, feeding the energy back into the power supply (increasing the “efficiency”) or powering surrounding sensors and sub-circuits. In this work, a comparative analysis of the successfully converted energy obtained from different generator models in various thermal configurations was carried out. All measurements are performed on an experimentally established setup. Due to the low thermoelectric efficiency of the generators as well as the realized low temperature gradient, only 0.84% of the waste heat can be converted into electrical energy in the best case scenario. Finally, a new thermal push–pull concept was presented, the main purpose of which is to generate additional energy and protect semiconductor components from overheating.

1. Introduction

Due to the good compromise between linearity and efficiency, the AB-Class power amplifier is still the most commonly used class of amplifier in high performance audio systems. The efficiency of such a class depends on the output power and can theoretically reach a value of $\pi$/4. The remaining energy that does not reach the output is considered wasted and is usually dissipated in the form of heat at the output transistors.

The main task of this work is to determine whether it is possible, by applying thermoelectric generators on the output transistors, to harvest a sufficient amount of energy that would lead to a significant increase in the “efficiency” of the amplifier.

Thermoelectric generators (TEGs) are solid-state devices that convert heat flow through the generator into usable electrical energy. Based on the temperature difference between its surfaces, thermoelectric conversion takes place according to the principles of the Seebeck effect. The basic unit of every thermoelectric generator is a thermocouple, which generates a low voltage in case of a temperature difference. To produce higher voltages, it is necessary to electrically connect a large number of thermocouples in series [1].

The main shortcoming limiting the wider application of generators is their low thermoelectric efficiency. This shortcoming is related to the properties of the thermoelectric material used. A good material for thermoelectric purposes should have a high Seebeck coefficient ($\alpha$), low thermal conductivity ($\kappa$) and low electrical resistivity ($\rho$). The above parameters are embedded in a material quality coefficient Z (figure of merit):

$$Z=\frac{{\alpha }^2}{\rho \kappa }.$$

(1)

Semiconductor materials reach the highest values of the figure of merit coefficient. In an environment where temperatures do not exceed 450 K, the material bismuth telluride $B{i}_{2}T{e}_3$ showed the best properties (in terms of the coefficient Z), and it is the most commonly used material for this temperature range [2,3,4]. Generators made of the same material are also used in this work. Calculating the exact value of a device’s thermoelectric efficiency can be a challenging task [5,6,7]. For a simplified model that does not consider the temperature variability of the parameters ($\alpha$, $\kappa$ and $\rho$), it can be assumed to be equal to:

$$\eta =\frac{\Delta T}{T_{HOT}}·\frac{\sqrt{1+Z\overline{T}}-1}{\sqrt{1+Z\overline{T}}+\frac{T_{COLD}}{T_{HOT}}},$$

(2)

where $\Delta T$ is the temperature differential at the ends of the generator, $T_{HOT}$ and $T_{COLD}$ are the temperatures of the hot side and the cold side, while $\overline{T}$ is the mean temperature of the hot and cold sides. Since the unit of measurement of the coefficient Z is reciprocal to the unit of temperature, the dimensionless parameter $Z\overline{T}$ is more often used.

Some of the most attractive features of generators are their long, maintenance-free lifespans, as they contain no moving parts and require no working gas during operation, which in turn leads to their silent operation. They are also highly scalable, meaning they can be used for heat sources of any size and generate power from µW to kW. In the scientific environment, most research has been done on the application of thermoelectric generators in the exhaust systems of internal combustion engines, as well as for powering low-power devices such as healthcare equipment or wireless sensors of IoT networks [8,9,10,11,12].

1.1. Objectives of This Work

This paper contains several tasks, and the ultimate goal is to determine the percentage of waste energy that can be converted into electrical energy. The waste energy dissipated at the output transistors of the AB-Class power amplifier is converted using thermoelectric generators. The creation of a thermoelectric setup is the first task in this work. The next task is to compare the performances of generators connected in different thermal configurations. After selecting the best configuration in terms of converted energy, a comparative analysis of the same configuration but with different generator models was carried out. The efficiency of the power amplifier used in this work, as well as the dissipated power, depends on the amount of output power. For this reason, all measurements in this work were performed for four different output powers. Finally, the thermal push–pull concept was presented, whose basic task is to protect semiconductor components from overheating while recovering an additional amount of waste energy.

1.2. Related Papers

The application of thermoelectric generators on the transistors of an RF power amplifier is shown in [13]; although no detailed analysis has been made, the authors suggested how the converted energy could be used. One of the proposals is to feed the energy back into the power supply, increasing the efficiency of the entire system. A similar study is performed in [14], where the authors used heat generated by a 1 W 2.45 GHz E-Class power amplifier in microstrip technology. In addition to the experimental measurements of harvested energy, a thermal model of the entire system was also created. The authors stated that the energy can be used to power low-power sensors and control circuits in the vicinity of the power amplifier. In [15], a fully coupled thermoelectric model is presented, and a more detailed analysis is performed on the subject of optimized pellet geometries for power generation and efficiency as a function of power amplifier transistor heat dissipation, heat sink performance and load resistance. The latest research is related to the application of generators on the output transistors of a 10 W 3.2–3.8 GHz F-Class power amplifier [16]. The experimental results showed an increase in the “efficiency” of the amplifier by 1.1% at the peak. Since the authors presented only a brief report of the academic article, several questions regarding system design and measurement techniques remained unanswered.

2. Experimental Setup

This section contains a detailed description of the components involved in the creation of the experimental setup, as well as the specifications of the measuring equipment used. The measurement procedure itself is also described in detail.

As mentioned in the objectives of this work, all measurements were performed for three different thermal configurations:

– 

single TEG,

– 

two TEGs in thermal series connection,

– 

two TEGs in thermal parallel connection.

Schematic drawings of the given configurations were created in the 3D design software SolidWorks and are shown in Figure 1a–c.

The setup consists of a 100 W AB-Class power amplifier, whose complementary pair of output transistors (Toshiba 2SC5200 and 2SA1943) is used as a heat source. They are mounted on an aluminum plate that acts as a uniform heat spreader. The material from which the heat spreader is made must have a very high thermal conductivity, which is why copper or aluminum is usually used. The dimensions of a heat spreader in the single and thermal series configuration are 65 × 49 × 5 mm, while in the thermal parallel configuration, they are 83 × 65 × 5 mm. Considering that output transistors are mounted on the heat spreader, it was necessary to use mica sheets between the collectors to ensure their electrical isolation. The generators were clamped tightly between a spreader and a heat sink according to the clamping force values given in the manufacturer’s data sheet, and all surfaces of the system were coated with thermal paste to reduce the overall thermal resistance [17,18,19].

The different models of generators used in this work were compared on the basis of the parameters listed in

Table 1. Parameters of the TEGs used according to the data sheet.

Manufacturer	Model	Dimensions (mm)	Thermocouple Number and Material	Matched Load Resistance ($\mathsf{\Omega }$)
European Thermodinamics	GM200-127-14-10	40 × 40 × 3.5	127 ($B{i}_{2}T{e}_3$)	2.28 $\pm 15$%
Kryotherm	199-1.4-0.8	40 × 40 × 3.2	199 ($B{i}_{2}T{e}_3$)	1.46 $\pm 10$%
Shenzhen Yuzens Technologies Co., Ltd.	SP1848-27145	40 × 40 × 3.4	127 ($B{i}_{2}T{e}_3$)	2.68

Matched load resistance for the temperatures: hot side $200{}^{\circ }$C, cold side $30{}^{\circ }$C.

, namely their dimensions, the material of the thermocouples and their number and the matched load resistance stated in the data sheet.

Other important parameters such as thermocouple dimensions were not known for all generators, so they are not listed in the table. Since generator models with a smaller number of thermocouples showed better results in terms of generated power, the GM200-17-14-10 model produced by European Thermodynamics was selected as the primary model and used to analyze the different thermal configurations.

The final appearance of the experimental setup is shown in Figure 2a, while Figure 2b shows the mounting method of the output transistors on the heat spreader. Styrofoam was used around the generator to avoid the occurrence of thermal bridges, i.e., heat conduction through the air from the heat spreader to the heat sink, bypassing generators.

A multimeter with a type K thermocouple was used to measure the temperature at the generator surfaces. The reading accuracy of the multimeter for the expected temperature range is ±(1% + 7 digits). The voltage generated across the load resistor and the open-circuit voltage were measured using a Hewlett-Packard 34401A benchtop digital multimeter.

Measurement Procedure

Once the experimental setup was complete, it was necessary to determine how the measurements would be made and what parameters would be observed.

The internal electrical resistance of the generator is not an exception in relation to other parameters of the generator—it is also a temperature dependent parameter. Therefore, to achieve resistance matching and generate maximum power, a DC–DC converter is usually connected to the output terminals of the generator [20,21,22]. The maximum power transfer was not achieved in this work because a fixed value resistor is connected to the output of the generator. The value of the load resistance was selected on the basis of the manufacturer’s data sheet reproduced in Table 1 and on the basis of preliminary measurements.

During the measurements, the temperatures of the hot and cold sides of the generator as well as the voltage generated at the load resistor were measured continuously, while the open-circuit voltage was measured periodically. Since the values of the generated voltage and the realized temperature gradient assume a constant value after a certain time, the graphs shown in the continuation are limited to a period of 5 and 7 min for simplicity.

The efficiency of the power amplifier used in this work depends on the output power, as can be seen in Figure 3, and it increases with increasing output power. At the amplifier’s rated output power of 100 W, the efficiency is 73.5%; at a power of 75 W, it is 62.9%; at 50 W, it is 50.9%; and at 25 W, it is 35.7%.

It is important to point out that the efficiency of the amplifier is related to the amount of power dissipation and thus to the amount of energy converted, which is the main objective of this research. One of the tasks is to observe the influence of the amplifier output power on the amount of generated energy by the generators; therefore, all measurements in this work were performed for four different amounts of output power: 25 W, 50 W, 75 W and 100 W. From the measurement results, it can be concluded that, with some exceptions, higher temperature gradients are achieved at lower output powers. Although the efficiency of the amplifier is greater at an output power of 50 W than at 25 W, the amount of waste energy is slightly greater at 50 W. This is the reason why the curves of the generated voltages for these two cases mostly overlap, although the generated power at 50 W is sometimes higher.

A thermal image of the thermoelectric assembly during operation was taken with an FLIR C3-X compact thermal imaging camera and is shown in Figure 4. It can be seen that the output transistors heat up much more than the other components of the amplifier. For this reason, the power dissipation at other components was neglected when calculating the thermoelectric efficiency, and it was assumed that the entire waste energy is dissipated at the output transistors. The amount of power dissipation is obtained as the difference of the input power received from the rectifier and the output power of the amplifier. The thermal image also shows a slight warming of the heat sink after a certain period of time.

3. Results and Discussion

The graphs of the achieved temperature gradient as well as the voltage generated at the load resistor and the open-circuit voltage for the European Thermodynamic generator model connected in all thermal configurations are shown in this section. After selecting the best configuration in terms of generated power, a comparison of the generated power of different generator models connected in the same configuration is presented.

According to the data sheet of the model used, the matched load resistance is 2.28 $\mathsf{\Omega }$ ± 15%. Since additional circuitry for tracking the maximum power point and adjusting the resistor value was not used in the experimentally established model, a fixed value resistor of 2.4 $\mathsf{\Omega }$ was used as the load resistance, as it was closest to the specified value.

3.1. Single TEG Configuration

The obtained temperature gradient for a single TEG is shown in Figure 5a. The open-circuit voltage and the voltage generated at the load resistor for the established temperature gradient are shown in Figure 5b. It can be noticed that the actual value of the internal electrical resistance is slightly lower than the value given in the data sheet.

Graphs of the realized temperature gradient and generated voltages for another sample of the generator from the same manufacturer, which was later used in other configurations, are not shown, because the generated values are comparable with those shown in Figure 5.

3.2. Thermal Series Configuration

With the thermal series connection of the generators, higher values of the temperature gradient are achievable due to the increased thermal resistance. This gradient is divided approximately equally among the generators, so that each generator produces a smaller amount of voltage compared to the single TEG configuration. In this configuration, as in the thermal parallel configuration, the parameters of the generators are observed separately, and each generator is connected to its own load resistor. For the thermal series configuration, the realized temperature gradient and the voltages generated by each generator are shown in Figure 6a–c.

The analysis of multistage thermoelectric generators has already been carried out. Their use in comparison with single-stage generators is justified at high heat source temperatures [23,24]. Therefore, factory-produced two-stage generators are not considered in this work. The thermal series configuration is similar, but not identical, to the two-stage TEG design, due to the added ceramic substrate layer, which significantly increases its thermal resistance. Maximum amounts of generated energy, thermoelectric efficiency or absorbed heat are possible with different ratios of the number of thermocouples between stages [25].

3.3. Thermal Parallel Configuration

The last observed configuration is the thermally parallel one, where the generators are physically placed side by side. This connection results in a reduction of the total thermal resistance in the system, obtaining lower values of the temperature gradient at the ends compared to other configurations. Consequently, the voltages and power generated are also lower. For the thermal parallel connection, the realized temperature gradient and the generated voltages for the individual generators are shown in Figure 7a–c.

In a large number of papers, the authors concluded, based on the results obtained with one generator, that the power generated would be multiplied if a larger number of generators was used. The above conclusions are mostly incorrect because they deal with limited heat sources, as is the case in this work. Based on the available cooling system and the waste heat source, the optimal number of thermoelectric generators should be selected both from the economic and converted energy point of view. The same conclusion was reached by the authors in [26], who analyzed the application of thermoelectric generators in the exhaust system of an internal combustion engine and concluded, on the basis of the model, that the application of a larger number of generators does not necessarily result in a larger amount of converted energy. Based on the presented graphs, the thermal series configuration proved to be the best, as it generated the highest amounts of energy.

3.4. Generated Power

After the generated voltages were measured, the generated power at the resistor with a known value was calculated. The total generated power as the sum of the generated power of each generator in the thermal series connection for different generator models is shown in Figure 8a–c. It can be seen that generator models with a smaller number of thermocouples produce larger amounts of power due to the realized larger temperature gradient. It is also noticeable that the SP1848-27145 model produces only slightly less power compared to the GM200-127-14-10 model, even though it is a much cheaper generator. As explained earlier, the thermal configuration consisting of generators with a larger number of thermocouples achieves a lower temperature gradient and a lower generated power.

By using generators with a smaller number of thermocouples, i.e., a higher thermal resistance, larger temperature gradients were achieved, which had the negative consequence that the temperatures critical for the lifetime of semiconductor components were reached in a shorter period. The solution to this problem is proposed in the form of the application of the thermal push–pull concept, which is explained in more detail in the next section.

Neglecting the power dissipation of other components in the circuit and assuming that all waste energy is dissipated at the output transistors, the thermoelectric efficiency can be calculated. The thermoelectric efficiency and the generated power of different models connected in different thermal configurations are shown in

Table 2. Thermoelectric conversion efficiency.

Output Power	TEG Model	Single TEG#1 (mW)	Single TEG#2 (mW)	Thermal Series (mW)	Thermal Parallel (mW)
25 W	GM200-127-14-10	281.6 (0.62%)	265.37 (0.59%)	379 (0.84%)	133.71 (0.3%)
	199-1.4-0.8	163.76 (0.36%)	166.95 (0.37%)	274.72 (0.61%)	73.73 (0.16%)
	SP1848-27145	268.91 (0.6%)	368.36 (0.82%)	370.29 (0.82%)	180.32 (0.4%)
50 W	GM200-127-14-10	292.57 (0.61%)	274.73 (0.57%)	387.28 (0.8%)	136.5 (0.28%)
	199-1.4-0.8	164.83 (0.34%)	170.18 (0.35%)	284.27 (0.59%)	75.91 (0.16%)
	SP1848-27145	301.72 (0.63%)	355.61 (0.74%)	352.74 (0.73%)	178.56 (0.37%)
75 W	GM200-127-14-10	215.17 (0.49%)	198 (0.45%)	276.65 (0.63%)	91.38 (0.21%)
	199-1.4-0.8	119.14 (0.27%)	119.92 (0.27%)	206.1 (0.47%)	52.81 (0.12%)
	SP1848-27145	198.59 (0.45%)	250.46 (0.57%)	243.98 (0.55%)	119.8 (0.27%)
100 W	GM200-127-14-10	125.34 (0.35%)	115.51 (0.32%)	162.54 (0.45%)	52.02 (0.14%)
	199-1.4-0.8	68.52 (0.19%)	70.81 (0.2%)	117.95 (0.33%)	29.94 (0.083%)
	SP1848-27145	99.76 (0.28%)	146.72 (0.41%)	132.36 (0.37%)	63.4 (0.18%)

For the steady state.

.

The highest thermoelectric efficiency was obtained for the thermal series configuration with generator model GM200-127-14-10, namely 0.84% for the output power of 25 W, 0.8% for 50 W, 0.63% for 75 W and 0.45% for 100 W. In terms of performances, the model SP1848-27145 follows, and finally the model 199-1.4-0.8, which has the worst performance due to the larger number of thermocouples. Since a limited heat source is used, generators with a larger number of thermocouples provide worse performance compared to those with a smaller number. This is because they are unable to reach their maximum potential of having a greater number of thermocouples.

3.5. Cost-Effectiveness Analysis

In industry, the focus is often on financial gain rather than efficiency, especially when implementing new concepts. In this part, a brief cost-effectiveness analysis is performed.

Considering the cost of a particular generator model and the corresponding power generated from Table 2, a cost-effectiveness analysis was made and is presented in

Table 3. Cost-effectiveness analysis for an amplifier output power of 25 W and 100 W.

TEG Model	Initial Cost ($/unit)	Single TEG 25–100 W ($/W)	Thermal Series 25–100 W ($/W)	Thermal Parallel 25–100 W ($/W)
GM200-127-14-10	33.73	123.33–280.1	178–415.04	504.52–1296.81
199-1.4-0.8	22.54	136.32–323.57	164.1–382.2	611.42–1505.68
SP1848-27145	2.14	6.72–17.36	11.56–32.34	23.74–67.51

For the steady state.

. Due to the relationship between the output power of the amplifier and the power dissipation, the cost-effectiveness analysis was performed only for the two extreme output power values used in this study, namely 25 W and 100 W. Based on the calculated values, it can be concluded that the implementation of a larger number of generators in thermal series and parallel configurations is not justified in terms of the initial investment and generated power. The single TEG configuration, particularly the SP1848-27145 generator model, demonstrates a superior ratio of cost to power compared to the other models.

In the existing literature, researchers have largely focused on reducing the cost to power ratio by intervening in the optimization of generator design. This is accomplished primarily by variations in fill factor, thermocouple geometry, segmentation of different materials and similar techniques. The inclusion of a heat sink presents the greatest research challenge because its price exceeds that of all other system components [27,28,29,30]. However, since the power amplifier already includes a heat sink in its original form, its cost was not considered in this analysis.

Since the generator’s lifetime is affected by several factors, including the thermal stress caused by the cyclic heating and cooling of the dynamically changing heat source [31,32], a comprehensive analysis is essential to determine the viability of using generators for these purposes. Once the system is thermally and electrically optimized, the values listed in Table 3 are likely to be further reduced. The main objective is to achieve a cost of 1 $ per Watt, which would classify generators as competitive energy conversion devices.

4. Thermal Push–Pull Concept

Since the heat sink cannot dissipate the unconverted heat energy to the same extent as it absorbs it, it begins to heat up. The voltage generated at the resistor takes a constant value after a certain time, as can be seen in Figure 5, Figure 6 and Figure 7. This means that the aluminum plate on which the output transistors are mounted heats up to the same extent as the heat sink, while the temperature gradient at the ends of the generator remains constant.

The critical temperature value for the lifetime of the output transistors used in this work is 150 ${}^{\circ }$C. The thermal series configuration reaches the critical value in a very short period of time compared to other configurations (Figure 9a). In order to protect semiconductor components from overheating, a new thermal push–pull concept is presented.

This concept is based on the fact that the configuration continues to generate power even after the amplifier is turned off, as can be seen in the graphical part of Figure 9b after the 10th minute. The power generation process continues as long as there is a temperature gradient. At the end of the cooling cycle, the following aluminum plate temperatures were measured: 55 ${}^{\circ }$C for 25 W and 50 W output power, 53 ${}^{\circ }$C for 75 W and 47 ${}^{\circ }$C for 100 W.

Based on the graph shown in Figure 9b, the areas under the generated power curve for the heating and the cooling cycle were calculated and are presented in

Table 4. Generated energy during the heating and cooling cycle.

Output Power	Heating Cycle (mWh)	Cooling Cycle (mWh)	Additional Energy
25 W	44.46	7.63	17.16%
50 W	42.35	6.68	15.77%
75 W	28.97	4.9	16.91%
100 W	15.32	2.77	18.08%

.

Comparing these amounts of generated energy, it is noticeable that a considerable amount of energy is also generated during the cooling cycle. Following the example of the push–pull operation of output transistors, a similar operating concept can be applied to generators, only in thermal form. For the realization of the concept, it is necessary to create an additional thermoelectric setup equivalent to the existing one, using another pair of output transistors as a heat source. In this way, both setups would generate energy in parallel, one in heating and the other in cooling mode. Switching between setups occurs when one of them reaches a critical temperature. By implementing this concept, additional energy can be harvested, and the output transistors can be protected from overheating.

The switching methods as well as the occurrence of additional signal distortions are not further analyzed in this paper. In order to generate maximum power, in addition to electrical matching, thermal matching of the assembly is also required [33,34,35]. Therefore, it is necessary to perform an additional analysis of the parameters and geometries of the used heat sink so that the configurations could generate even more power.

5. Conclusions

This paper presents a thermoelectric setup for harvesting waste energy dissipated at the output transistors of the AB-Class power amplifier using thermoelectric generators. Several conclusions can be drawn based on the measured values.

The parameters of the generator that were measured while it was exposed to thermal energy are the temperatures at the ends of the generator (temperature gradient), the voltage generated at the load resistor and the open-circuit voltage. Based on the measured values, the generated power of the thermoelectric generator was calculated. A comparative analysis of the above parameters was performed for three different generator models connected in different thermal configurations (single TEG, thermal series and parallel connection of TEGs) for four different amplifier output powers (25 W, 50 W, 75 W and 100 W).

The efficiency of the power amplifier in the AB-Class depends on the level of output power; at lower values, the efficiency of the amplifier is also lower, so the power dissipated on the output transistors is higher, as well as the power generated by the thermoelectric generator. The results show that generators containing a smaller number of thermocouples can achieve a higher temperature gradient at the ends and thus a higher generated power, since such generators offer a greater resistance to the heat flow. The largest temperature gradient in the system was realized when the generators were thermally connected in series due to the increased thermal resistance in the system. The temperature gradient obtained is divided almost equally between the generators, which means that the thermoelectric efficiency of this configuration is slightly higher compared to a single TEG configuration. The shortcoming of the thermal series connection is that the temperatures critical for the lifespan of the semiconductor components are quickly reached. To protect these components from overheating, a thermal push–pull concept was proposed.

Based on the cost-effectiveness analysis performed, it was concluded that the cost to power ratio does not justify using a larger number of generators for this heat source. The analysis revealed that the single TEG configuration, particularly the SP1848-27145 generator model, stood out as the superior choice. With a cost to power ratio of 6.72 $ per Watt at an amplifier output power of 25 W, it had the lowest cost to power ratio among the considered configurations and generator models.

The thermal push–pull concept aims to generate an additional amount of energy while protecting semiconductor components from overheating. This concept is based on the fact that even when the amplifier is switched off, there is still some temperature gradient at the generator ends, and the generator continues to convert energy as long as the gradient exists. In this way, energy is also harvested during the cooling cycle. If an additional setup identical to the one described in this paper were made, the energy from both setups could be harvested simultaneously, and one setup would convert energy in heating and the other in cooling mode.

Neglecting the power dissipation of other circuit components and assuming that the entire difference between the input and output power of the amplifier is dissipated by the output transistors, the total percentage of converted energy can be calculated. For the thermal series configuration of the generator model GM200-127-14-10, the percentages of converted energy at the steady state are as follows: 379 mW at an output power of 25 W (0.84% of successfully converted energy), 387.28 mW at 50 W (0.8%), 276.65 mW at 75 W (0.63%) and 162.54 mW at a nominal power of 100 W (0.45%). By applying the thermal push–pull concept and knowing the exact power dissipation of the output transistors, the percentage of converted power would be even higher than indicated.

Research is ongoing, and future focus will be on creating a simulation model for this setup including the thermal push–pull concept. This model can be used to perform various optimizations, from electrical matching to thermal matching, which tends to be neglected in the literature. Since there is an optimal number of thermoelectric generators for a given heat source, the optimal number of generators for power amplifiers with different output powers can also be determined based on the model.

Once the optimization is completed, it is necessary to wait for scientific progress in the improvement of thermoelectric materials, since the manufacturing material is the main reason for the low thermoelectric efficiency, thus representing the main obstacle to the wider application of these generators.