# Coupling a supercapacitor with a small energy-harvesting source

Pierre Mars, CAP-XX Ltd -June 07, 2012

Small wireless sensors are becoming ubiquitous. Applications for sensors include building control, industrial control, security, location tracking, and RFID. It is much more convenient and cost-effective to autonomously power these sensors with a small energy-harvesting source without expensive wires or batteries that need repeated replacement.

The environment provides infinite ambient energy, including piezoelectric, thermal, vibration, and photovoltaic energy, but at low power, which falls short of the peak power necessary for transmitting data across wireless networks such as IEEE 802.15.4 (Zigbee), 802.11 (WLAN), or GSM/GPRS. A battery or a supercapacitor acts as a power buffer to store enough energy to provide the power bursts needed to acquire and transmit data. These energy-storage devices charge at low power and deliver the burst power when necessary.

Sizing the supercapacitor

Supercapacitor cells typically operate at 2.3 to 2.8V. The most efficient and cost-effective strategy is to limit the supercapacitor’s charge voltage to less than the cell-rated voltage and store enough energy for your application.

A simple approach to sizing the supercapacitor is to calculate the energy necessary to support the peak power of the application, P, and set this value equal to ½C(V2INITIAL− V2FINAL), where C is the capacitance, V2INITIAL is the square of the supercapacitor’s voltage just before the peak-power burst, and V2FINAL is the square of the final voltage. However, this equation does not allow for any losses in the supercapacitor’s ESR (equivalent series resistance). The load sees a voltage of VINITIAL−ESR×ILOAD, where ILOAD is the load current. Because the load voltage decreases, the load current increases to achieve the load power. Referring to Figure 1, designers can model supercapacitor discharge as

where VSCAP is the supercapacitor’s voltage.

This equation yields the equation for the load current:

Supercapacitor discharge can then be simply modeled in Excel as

This calculation is important if the load current times ESR is significant compared with the supercapacitor’s final voltage. In this case, a simple energy-balance approach would make the supercapacitor’s value too small. This undersizing is likely to be the case at low temperatures, when ESR is typically two to three times higher than at room temperature.

The supercapacitor capacitance and ESR should also allow for aging. Supercapacitors slowly lose capacitance and increase ESR over time. The aging rate depends on cell voltage and temperature. Designers should select initial capacitance and ESR so that the end-of-life capacitance and ESR can support the applications.

Supercapacitor charging

A discharged supercapacitor looks like a short circuit to an energy source. Fortunately, many energy-harvesting sources, such as solar cells and microgenerators, can drive into a short circuit and directly charge a supercapacitor from 0V. ICs to interface energy sources, such as piezoelectric or thermoelectric energy, must be able to drive into a short circuit to charge a supercapacitor.

The industry has invested much effort in MPPT (maximum-peak-power tracking) to most efficiently draw power from energy-harvesting sources. This approach is applicable when charging a battery that must charge at constant voltage. The battery charger is typically a dc/dc converter that is a constant-power load to the energy source, so it makes sense to draw that power at the most efficient point using MPPT.

In contrast to a battery, a supercapacitor need not charge at a constant voltage but charges most efficiently by drawing the maximum current the source can supply. Figure 2 shows a simple and effective charging circuit for cases in which the open-circuit voltage of a solar-cell array is less than the supercapacitor’s rated voltage. The diode prevents the supercapacitor from discharging back through the solar cell if it goes dark. If the energy source’s open-circuit voltage is greater than the supercapacitor’s voltage, then the supercapacitor requires overvoltage protection using a shunt regulator (Figure 3). A shunt regulator is an inexpensive and simple approach to overvoltage protection, and, once the supercapacitor fully charges, it does not matter whether the excess energy dissipates.

The energy harvester is like a hose with an endless supply of water filling a barrel, which is analogous to a supercapacitor. If the hose is still running once the barrel is full, the water may overflow. This situation differs from that of a battery, which has a limited energy supply and thus would require a series regulator.

In the circuit in Figure 2, the supercapacitor, at 0V, draws short-circuit current from a solar cell. As the supercapacitor charges, the current decreases, depending on the solar cell’s voltage/current characteristic. The supercapacitor always draws the maximum current it can, however, so it charges at the highest possible rate. The circuit in Figure 3 uses the TLV3011 solar cell because it integrates a voltage reference, draws only approximately 3-μA quiescent current, and is an open-drain cell so that the output is open-circuit when the regulator is off. This circuit uses the BAT54 diode because it has a low forward voltage at low currents—that is, the forward voltage is less than 0.1V at a forward current of less than 10 μA.

Microgenerators are ideal for industrial-control applications, such as monitoring rotating machinery, because by definition they will vibrate when they are operating. Figure 4 shows the voltage-current characteristic of a microgenerator, which is similar to that of a solar cell and which delivers maximum current into a short circuit. A microgenerator also includes a diode bridge, which prevents the supercapacitor from discharging back into the generator, leading to a simple charging circuit (Figure 5).

Click image to enlarge

The open-circuit voltage is 8.5V, requiring a dual-cell supercapacitor, such as the CAP-XX HZ202, which operates at 5.5V. A shunt regulator provides overvoltage protection, and a lowcurrent active-balance circuit ensures even distribution between the cells. Linear Technology, with its LT3652, LTC3108, and LTC3625 ICs, and Texas Instruments, with its BQ25504, charge supercapacitors from energy-harvesting sources.