Why do supercapacitors have such high capacitance with such small volumes? Supercapacitor electrodes are nano porous carbon coated on a current collector substrate such as aluminium. The porous carbon has a surface area in the order of 2,500m2/gm. This gives a massive charge storage area. Supercapacitors do not have a dielectric - they are electrical double layer capacitors. Ions dissolved in an electrolyte provide charge transport. These ions nestle against the surface of the porous carbon, so the charge separation distance is effectively the molecular width of the ions. Since capacitance is proportional to charge storage area/charge separation distance, and the storage area is 1000s of square meters, and separation distance is in nanometers supercapacitors have enormous energy density. As an example, the CAP-XX HS230, which is 39mm x 17mm x 3.8mm, is 1.2F and has very low ESR, or Equivalent Series Resistance of 50mOhms, and is rated to 5.5V. This results in an energy density of ½ x 1.2F x 5.5V2/(39x17x3.8x10-6L) = 7.2KJ/L or 2Wh/L.
Since supercapacitors do not have a dielectric, their maximum operating voltage is limited by the voltage at which the electrolyte starts undergoing electrochemical reactions. There are two types of supercapacitor chemistries: those with organic electrolytes and those with aqueous electrolytes. The maximum voltage for supercapacitor cells with aqueous electrolytes is the breakdown voltage of water, ~1.1V, so these supercapacitors typically have a maximum of 0.9V/cell. Organic electrolyte supercapacitors are rated in the range 2.3V - 2.7V cell, depending on the electrolyte used and the maximum rated operating temperature. Several supercapacitor cells are connected in series to attain the working voltage needed. Although organic electrolyte supercapacitors have superior energy density because they have a higher rated voltage, they are more difficult to produce since they must be filled in a completely dry environment and hermetically sealed against moisture. Aqueous electrolyte supercapacitors, having a water based electrolyte, have no such problems. Supercapacitors have a porous separator to prevent the positive and negative electrodes from shorting against each other, but allowing ions to pass through it for charge transport.
Supercapacitors have been around for years, but were initially very low current devices such as the Panasonic gold cap, with high ESR, suitable for RTC and memory backup. The breakthrough in the last 10 years or so has to be reduce the ESR so supercapacitors can deliver high power.
When current is drawn from a supercapacitor, there is an instantaneous voltage drop = ILOAD x ESR. Hence ESR limits the amount of current that can be usefully drawn from the supercapacitor. Again, consider the CAP- XX HS230 as an example: if a 2A load is drawn from this supercapacitor, the instantaneous voltage drop will only be 2A x 50mΩ = 100mV. The maximum power transfer occurs when the load resistance = source resistance = ESR, so for an HS203 this = V2/(4 x ESR) = 5.52/200mΩ = 151.25W, so power density = 151.25W/0.0025L = 60KW/L.
An Ideal Power Buffer
The supercapacitor's high energy storage and high power delivery make it ideal to buffer a high power load from a low power energy harvesting source, as shown in Fig 1.
The source sees the average load, which with appropriate interface electronics, will be a low power constant load set at the maximum power point. The load sees a low impedance source that can deliver the power needed for the duration of the high power event. Consider a sensor that transmits data at 100mW for 1 second once an hour. If an HS230 is charged to 3.3V just prior to the transmission, then during the transmission it will only discharge to 3.27V. The average power is 0.1W/3600 = 28μW. If the circuit is 60% efficient, then the source only needs to deliver < 50μW to re-charge the supercapacitor between transmissions.
In Fig 1, the supercapacitor is placed after the Interface Electronics, so the Interface Electronics can be sized for the average power of 50μW rather than the peak power of 100mW. A discharged supercapacitor will look like a short circuit to the source, so the interface electronics must manage the inrush current when the source is first connected to a supercapacitor at 0V.
Low Leakage Current
If an energy harvesting source only provides a few μA of current, you do not want to waste a significant proportion of this on capacitor leakage current. Small supercapacitors have low leakage current, typically in the range 1μA-50μA depending on the capacitance. However, this is the equilibrium level leakage current after the supercapacitor has been held at voltage for several days. Supercapacitors, with ions migrating in and out of pores in the carbon electrode, behave like a distributed capacitor, or an RC ladder network. Immediately after a supercapacitor reached its terminal voltage, ions are still migrating further into the pores and the supercapacitor draws considerable leakage current during this phase. As the migration slows and finally reaches its end, leakage current decays until it reached its equilibrium level - see Fig 2 as an example showing leakage current over time for a population of CAP-XX GZ215 which is 75mF.
Fig 2 shows that at room temperature it has taken the supercapacitors ~4 days for the leakage current to decay to ~1μA. Another experiment has shown that the leakage current for similar supercapacitors will decay to ~0.2μA after 10 days.
Minimum Initial Charge Current
All supercapacitors have impurities. In organic electrolyte supercapacitors this will include minute amounts of water. When the supercapacitor is charged from zero volts, a minimum charge current substantially greater than the equilibrium leakage current is required, or the charge transferred to the supercapacitor will be consumed by electrochemical reactions with impurities.
Fig 3: Charging at low currents
This is shown in Fig 3, where at least 20μA is required to charge some CAP-XX GZ115 supercapacitors. The knee in the curves of Fig 3 at ~1.1V indicate that charge is being consumed reacting with water. Fig 3 also shows it takes much longer than theory predicts to charge the GZ115 to its terminal voltage of 2.3V. At 20μA, it should take 0.15F x 2.3V/20x10-6A = 17250secs = 4.8hrs, however, from Fig 3 it took over 20hrs to reach 2.3V. This can be a problem with the circuit not taking much longer than desirable to reach its operating voltage. One practical way to overcome this is to pre-charge the supercapacitor with a higher current source, either at the factory or at installation. Fig 4 shows how pre-charge at installation with a 10mA source greatly reduces charge time with a source capable of delivering only 5μA. The HZ102 supercapacitors charged at 5μA from 0V with no pre-charge took ~65hrs to charge. The straight line in Fig 4 shows the theoretical time to charge the HZ102 at 5μA constant current. Pre-charging the supercapacitors for 1 minute at 2.5V with a 10mA source reduced the charge time to ~20-25hrs, which corresponds to the theoretical time to charge. Pre-charging for 10 minutes reduces the charge time to ~15hrs. The dips seen in the voltage vs time curves for pre-charge supercapacitors is due to leakage current exceeding the 5μA charge current and then the voltage increases as the leakage current decays to < charge current.
Supercapacitor Cell Balancing
As explained above, supercapacitors are low voltage devices and several need to be strung in series to achieve a practical working voltage. In most cases, two organic electrolyte cells in series achieve the desired voltage, typically one of 5V, 4.2V, 3.6V or 3.3V. However, different cells will have slightly different leakage currents, with different VSCAP vs ILEAKAGE characteristics, but since they are in series, without any balancing circuit, they must have the same current flowing through them. In this case, the cells will re-distribute charge between themselves, i.e. adjust their voltage, to so their leakage currents will be equal. This leaves one of the cells is in danger of going over voltage. The simplest balancing circuit is a pair of resistors, one across each cell, in the range of 1KΩ - 39KΩ, depending on the operating temperature & voltage. However, this solution will draw too much current for most energy harvesting applications. The solution that draws minimal current is an active balance circuit using an ultra low current rail-rail op amp. The circuit in Fig 5 is an example of this and draws only 2 - 3μA, including supercapcitor leakage current, once the supercapacitor has reached equilibrium leakage current.
Fig 5: Low current active balance circuit
The op amp chosen draws ~750nA, supercapacitor leakage current is ~1μA, and the current drawn through R12, R11 =250nA if the supercapacitor voltage =5V, so total current ~2μA.
All supercapacitors age over time, that is, their ESR slowly increases and their capacitance slowly decreases over time. The rate of ageing depends on the supercapacitor operating voltage and temperature. The higher the voltage and/or temperature, the faster the rate of ageing. Temperature is the key driver, with the Arrhenius equation applying, so the rate of ageing approximately doubles for every 10°C increase. Therefore, the supercapacitor should be sized so that the C is large enough & ESR low enough for successful operation at end of life, given the application's expected operating profile. The operating profile is the % time at V1,T1, % of time at V2T2, ..% time at VnTn. Fig 6 shows Capacitance over time for 1 year for a CAP-XX GW214 at 3.6V, room temperature (23°C). The C loss rate is 1.4%/1000hrs.
Fig 6: Ageing, capacitance loss over time at room temperature, ambient relative humidity
Sizing the supercapacitor
Many people calculate the capacitance required by performing an energy balance:
Supercapacitor Energy, ½ C(Vinit2 - Vfinal2) = Load Energy, ELOAD =Average Load Power x Load duration,
Therefore, C = 2 x ELOAD/(Vinit2 - Vfinal2), where Vinit is the initial supercapacitor voltage and Vfinal is the minimum voltage the supercapacitor can discharge to at the end of the peak load.
However, this approach ignores ESR and is only a good approximation if the voltage drop from ILOAD x ESR << Vfinal. There are two cases to consider:
In this case the load current is constant and does not vary with voltage, so as the supercapacitor discharges, and the load voltage drops, the load current remains constant. An LED is a good example of this type of load. The final load voltage is given by:
Vfinal = Vinit - ILOAD x ESR - ILOAD x TLOAD/C
Now a supercapacitor can be selected with both C & ESR adequate to support the load for duration TLOAD.
In this case, the load power remains constant, so as the supercapacitor discharges and the load voltage drops, the load current increases to maintain the VLOAD x ILOAD product constant. The input to a DC:DC converter is a constant power load, so this will be the most common case in energy harvesting applications. You need to solve:
Fig 7: Model for solving the constant power case. Note that VSUPERCAP is not physically measureable, since C & ESR are idealized parameters within the supercapacitor.
Example Supercapacitor Interface Circuit
Consider the vibration microgenerator from Perpetuum, whose Output power vs Output voltage curve is given in Fig 8 which shows that ideally, the output voltage should be kept between 4V - 5V and that if the load is drawing little or no power (e.g. fully charged supercapacitor), the voltage could rise to ~9V.
Fig 8: Output Power vs Output Voltage for Perpetuum Microgenerator which harvests vibration energy at 100Hz or 120Hz, ideal for AC machines. Maximum power is delivered when the output voltage is between 4V - 5V. Open circuit voltage is 9.2V.
The following example circuit, shown in Fig 9 illustrates all the key features that might be needed in a circuit to interface an energy harvesting source to a supercapacitor:
- Maximum power tracking, maintaining the output voltage or current of the energy harvesting source so it delivers the maximum possible power.
- Over-voltage protection, to ensure the supercapacitor rated voltage is not exceeded
- Active balancing to maintain the supercapacitor cells at the same voltage with a low current circuit.
Fig 9: Example of a supercapacitor interface circuit
Notes on Fig 9:
i)-The coil is the microgenerator. This produces AC which is full wave rectified by diode bridge D1 - D4. D1 - D4 should be selected for low VF to maximize output power and low reverse leakage current to minimize discharge of the supercapacitor if there is no vibration to generate electrical power.
ii)-If reverse leakage from the supercapacitor to the source is an issue, then instead of using a single PFET as shown for Q1, use a pair of back-back PFETs.
iii)-C1 stores enough energy to drive U1, U2, U3 and any other low power circuits before the supercapacitor is charged. A typical value for C1 is 100μF.
iv)-An ideal IC for U1, U3 is a MAX9107 dual comparator or 2 x MAX9015. These ICs draw only ~1μA, have an internal reference, and have a push pull output to drive Q1 OFF or ON.
v)-U1 is a comparator with hysteresis that ensures the microgenerator delivers maximum power. When the microgenerator voltage < VTHRESH - VHYST, turn Q1 OFF, when the microgenerator voltage > VTHRESH+VHYST, turn Q1 ON. This limits the supercapacitor charging current to ensure the that microgenerator is output > VTHRESH and delivers maximum power. R1 and R2 set VTHRESH, which would be 4V in this example. When the supercapacitor is fully charged and only draws leakage current, U1 still attempts to leave Q1 on to supply leakage current. R5 and R6 set VHYST which would typically be 50mV - 100mV.
vi)-U3 prevents over voltage of the supercapacitor. When VSCAP > VMAX + VHYST, U3 turns Q2 ON, which turns Q1 OFF, irrespective of U1's output voltage. R4 should be as high as possible so that U1 can drive Q1 with reasonable response, and that minimum energy is dissipated in R4 when Q2 is ON but the output of U1 is low (0V). R10 and R11 set VMAX, which is typically 4.5V, 5V or 5.5V depending on the application and the supercapacitor type. In this case, with a CAP-XX H series supercapacitor, VMAX would be set in the range 5V - 5.5V. R8 and R9 set VHYST.
vii)-U2 and its associated circuit is the active balance circuit. The MAX4470 is an ideal op amp for this application since t draws < 1μA supply current but can source or sink over 10mA if required.
viii) If the open circuit voltage of the energy harvesting unit < supercapacitor rated voltage, then U3, Q2 and associated circuits are not required.
ix) If a single cell supercapacitor is used e.g. energy harvester open circuit voltage < 2.7V, or U3 used to keep max voltage < 2.7V, then U2 and associated circuit is not required.
x) The energy harvester needs to provide >- 1.8V in order for U1, Q1 to operate and charge the supercapacitor, otherwise a boost converter is needed.
Supercapacitors offer an important benefit for energy harvesting applications - the ability to buffer a high power load from a low power source in a small form factor, but they do not behave like classical capacitors. This article has explored some of the key properties of supercapacitors that engineers should be aware of when designing energy harvesting circuits and culminated with an example circuit that can be used as a reference design and modified for other applications.
About the Author
Pierre Mars is the VP of Applications Engineering for CAP-XX Ltd. He jointly holds three patents on supercapacitor applications. Mr. Mars has a BE electrical (1st class hons) and an MEng Sc from the University of NSW, Australia, in addition to an MBA from INSEAD, France. He is also a member of the IEEE. Based in Sydney, Australia; the company can be reached at email@example.com. Design tools, application notes and other details are available at http://www.cap-xx.com.
Top image: example of a supercapacitor from Cap XX