**The efficiency profile of the charger used to extract energy from the thermal energy harvester plays a big role in determining the optimal input regulation point to maximize the energy delivered.**

Thermoelectric harvesters are a preferred medium to harvest electrical energy from ambient heat energy. Applications for these harvesters can be found in industrial and residential settings, along with the emerging wearable sensors market. While it is well-known that operating the thermoelectric harvesters at half their open-circuit voltage maximizes their output power, this operating point may not be optimal when used in a charging system.

The deficiencies of the charging system, especially at the low output voltage levels of the thermoelectric harvester, require a system level approach to maximize the usable power into the storage element.

**Thermoelectric Harvester Model**

The basic construction unit of a thermal harvester is a thermocouple, which is composed of an N-type thermoelectric material electrically in series with a P-type thermoelectric material (**Figure 1**). When a temperature difference is applied across this material, heat begins to flow from the hotter to the cooler side. In the process, energy from the applied heat allows the free electrons and holes to move and form an electric potential. Commonly used thermal harvesters for power generation consist of P- and N-doped legs, each of which generates around 0.2 mV/K of temperature difference between the hot and cold sides.

To boost the output voltage and get more power, many of these legs are connected electrically in series and thermally in parallel to form a thermopile (**Figure 2**). Electrically, the thermal harvester can be modeled as a voltage source in series with a resistance where the open-circuit voltage (OCV) can be expressed as S∆T, where S is the Seebeck coefficient of the material. The electrical resistance RT models the losses within the material due to thermal flow and electrical interconnections. It can be easily deduced from the equivalent circuit that the maximum power available from the thermal harvester is:

P_{max} = V_{T}^{2}/4R_{T} = (S∆T)^{2}/4R_{T}

**Figure 3** shows the voltage and power characteristics of a micromachined thermoelectric device from Micropelt called the MPG-D751^{2}. This device has 540 P-N legs connected in series that gives it a Seebeck coefficient of 140 mV/K and an electrical resistance of 300 Ω. The OCV is proportional to the temperature difference, while the maximum power output by the device follows a parabolic shape with change in temperature as described in equation 1. For applications where 2-3 K of temperature difference is possible, the thermal element only outputs ~300 mV of open-circuit voltage with its maximum power point at 150 mV. The low output voltage poses a challenge to circuit designers to extract power efficiently from the harvester.

**Extracting Energy from the Harvester**

The thermal harvester needs dedicated circuits to extract the energy from the harvester and power the load electronics while smoothing out the variations in input power and output load currents. **Figure 4** shows a thermoelectric charging system using the bq25505 as the energy management IC. The bq25505 is an ultra-low quiescent current charger IC designed to perform maximum power point tracking (MPPT) of the attached energy harvester.^{3} The power extracted from the harvester is accumulated in the storage medium on VBAT_SEC, which can either be a rechargeable battery or a supercapacitor.

The resistors ROV1 and ROV2 are used to set the over-voltage threshold of the storage element and the under-voltage level is internally set. The resistors ROK1, ROK2, and ROK3 are used to set the upper and lower thresholds of the VBAT_OK signal, which can be used to indicate state of charge of the rechargeable element. The thermal harvester is connected to the VIN_DC pin.

To get the maximum power out of the harvester, the voltage at the output of the harvester needs to be regulated at its maximum power point. This voltage has to be tracked as the OCV of the harvester changes with temperature shifts. To perform MPPT, the energy management IC periodically shuts off charging and samples and holds a fraction of the OCV as dictated by the resistors RMPP1 and RMPP2. This reference is used to regulate the input voltage during the remainder of the charging cycle. Based on the discussion from the earlier section, it is evident that the resistor ratio needs to be set to 50 percent to get the maximum power out of the harvester. While this maximizes the power out of the harvester from a system perspective, the important thing is to maximize the power into the storage element, which is determined by the power coming out of the harvester, as well as by the efficiency of the charger.

For an ideal 100 percent efficient charger, operating at half the OCV also maximizes power into the storage element, but looking at **Figure 5a**, which shows the efficiency plot of the interface IC, the efficiency increases linearly at low input voltages where the thermal harvester operates. When the overall energy transfer is taken into account, the true MPP is not really at half the OCV. Assuming that the thermal harvester output is regulated at a fraction k of the OCV and the efficiency of the charger is linearly related to its input voltage by the term α, the power delivered to the storage element is given by:

P_{out }≈ kV_{oc}^{2}(1-k)/RT *Charger Effeciency ≈ kV_{oc}^{2}(1-k)αkV_{oc}/RT

dP_{out}/dk = O ⇒ k = 2/3

From equations 2 and 3, it is clear that in the voltage regime where the efficiency of the charger is almost linearly related to the input voltage, operating the thermal harvester at two-thirds of its OCV maximizes the overall power delivered to the storage element. The theoretical output power improvement over operating at half the OCV can be calculated from equation 2 to be 18.5 percent. As the input voltage increases further, the dependence of efficiency on the input voltage flattens out. The optimal ratio then shifts towards k = 0.5. **Figure 5b** shows that power into the storage element is improved compared to the power obtained with k = 0.5. This plot takes into account charger efficiency at the voltages output by the MPG-D751 harvester. At low temperature differences where OCV is lower, the ratio k = 0.66 is optimal. Above a temperature difference of 3K, the optimal ratio slowly shifts towards k = 0.5.

In summary, the efficiency profile of the charger used to extract energy from the thermal energy harvester plays a big role in determining the optimal input regulation point to maximize the energy delivered to the storage element. The linear dependence of efficiency with voltage at the low-voltage levels output by the TEG makes it optimal to operate the harvester at two-thirds its OCV. This can deliver close to 20 percent more output power than the conventional operating point of half the OCV.

**Reference**

- G. Snyder et al., “Thermoelectric microdevice fabricated by a MEMS-like electrochemical process,” Nature Materials, July 2003
- MPG-D751 Thin Film Thermogenerator and Sensing Device, Preliminary Datasheet (0025DSPG70313c2e), Micropelt Harvesting: http://www.micropelt.com/down/datasheet_mpg_d751.pdf [1]
- For more information, download this datasheet: www.ti.com/bq25505-ca [2]

This article originally appeared in the November/December print issue. Click here to read the full issue [3].

Thermoelectric harvesters are a preferred medium to harvest electrical energy from ambient heat energy. Applications for these harvesters can be found in industrial and residential settings, along with the emerging wearable sensors market. While it is well-known that operating the...