“In power backup or maintenance systems, energy storage media may account for most of the total material cost (BOM) and occupy most of the space. The key to optimizing the solution lies in carefully selecting components to achieve the required hold time without overdesigning the system. In other words, it is necessary to calculate the energy storage required to meet the retention/backup time requirements during the application lifespan without excessive energy storage.
“
Author: Markus Holtkamp, Director of Strategic Marketing, ADI;
Gabino Alonso, ADI Field Application Engineer
Question: Can a simple energy calculation method be used when selecting a super capacitor for a backup power system?
Answer: Simple electric energy calculation methods may not meet the requirements, unless you take into account all the factors that affect the energy storage performance of the entire life cycle of the supercapacitor.
Introduction
In power backup or maintenance systems, energy storage media may account for most of the total material cost (BOM) and occupy most of the space. The key to optimizing the solution lies in carefully selecting components to achieve the required hold time without overdesigning the system. In other words, it is necessary to calculate the energy storage required to meet the retention/backup time requirements during the application lifespan without excessive energy storage.
This article introduces the strategy of selecting super capacitors and backup controllers under a given holding time and power considering the changes of super capacitors during their service life.
Electrostatic doublelayer capacitors (EDLC) or supercaps (supercaps) are effective energy storage devices that can bridge the functional gap between larger and heavier battery systems and largecapacity capacitors. Compared to rechargeable batteries, supercapacitors can withstand faster charge and discharge cycles. Therefore, in relatively lowenergy backup power systems, shortterm charging systems, buffer peak load current systems, and energy recovery systems, supercapacitors are better for shortterm energy storage than batteries (refer to Table 1). In the existing batterysupercapacitor hybrid system, the high current and shortterm power supply function of the supercapacitor is an effective supplement to the battery’s longduration and compact energy storage function.
Table 1. Comparison between EDLC and Liion battery
characteristic 
Super capacitor 
Lithium Ion Battery 
Charge/discharge time 
10 s 
30 minutes to 600 minutes 
Terminal electrode/overcharge 
― 
Yes 
Charge/discharge efficiency 
85% to 98% 
70% to 85% 
life cycle 
100,000+ 
500+ 
Lowest to highest battery voltage (V) 
0 to 2.3* 
3 to 4.2 
Specific energy (Wh/kg) 
1 to 5 
100 to 240 
Specific power (W/kg) 
10,000+ 
1000 to 3000 
Temperature(℃) 
C40°C to +45°C* 
0°C to +45°C charging* 
Selfdischarge rate 
high 
Low 
Intrinsically safe 
high 
Low 
*In order to maintain a reasonable service life
It should be noted that the high temperature and high battery voltage of the super capacitor will shorten the service life of the super capacitor. It must be ensured that the battery voltage does not exceed the temperature and voltage ratings. In applications where supercapacitors need to be stacked or the input voltage cannot be effectively adjusted, these parameters meet the working specifications (see Figure 1).
Figure 1. An example of excessively simple design that leads to risks in supercapacitor charging schemes
It is difficult to build a reliable and efficient solution using discrete components. In contrast, integrated supercapacitor charger/backup controller solutions are easy to use and generally provide most or all of the following functions:
► Regardless of how the input voltage changes, the battery voltage can be regulated stably
► Each stacked battery can achieve voltage balance to ensure that no matter whether the batteries are mismatched or not, they can provide matching voltages under all operating conditions
► The battery voltage maintains low conduction loss and low dropout voltage to ensure that the system can obtain the maximum power from a given super capacitor
► Surge current limiting, support live insertion into the circuit board
► Communication with host controller
Choose the right integrated solution
ADI provides a series of integrated solutions, all of which use all the necessary circuits to provide all the basic functions of the backup system through a single IC. Table 2 summarizes the functions of some ADI’s supercapacitor chargers.
For applications using 3.3 V or 5 V rails, consider:
► LTC3110: 2 A bidirectional buckboost DCDC regulator and charger/balancer
► LTC4041: 2.5 A super capacitor backup power manager
For applications that use 12 V or 24 V rails, or if a backup power supply higher than 10 W is required, consider:
► LTC3350: Highcurrent super capacitor backup controller and system monitor
► LTC3351: Hotswappable super capacitor charger, backup controller and system monitor
If your system needs to use the main buck regulator to regulate the 3.3 V or 5 V power supply rail, use the builtin boost converter for backup, use a single super capacitor or other energy source for temporary backup or emergency operation of power failure, you should consider :
► LTC3355: 20 V, 1 A stepdown DCDC system with integrated super capacitor charger and backup regulator
ADI also offers many other constant current/constant voltage (CC/CV) solutions that can be used to charge a single supercapacitor, electrolytic capacitor, lithiumion battery, or NiMH battery. For more information on supercapacitor solutions, please visit analog.com.
For more information about other solutions, please contact your local FAE or regional support team.
Calculate retention or backup time
When designing a supercapacitor energy storage solution, how big is enough? In order to limit the scope of the discussion and analysis, we will focus on the classic retention/backup applications used in highend consumer electronics, portable industrial equipment, energy metering, and military applications.
Table 2. Overview of the features of the integrated supercapacitor charger solution

LTC3110 
LTC4041 
LTC3350 
LTC3351 
LTC3355 
V_{IN} (V) 
1.8 to 5.25 
2.9 to 5.5 (60 V OVP) 
4.5 to 35 
4.5 to 35 
3 to 20 
Charger (V_{IN} → V_{CAP}) 
2 A buckboost 
2.5 A stepdown 
10+ A stepdown controller 
10+ A stepdown controller 
1 A buck 
Number of batteries 
2 
1 to 2 
1 to 4* 
1 to 4* 
1 
Cell balance 
Yes 
Yes 
Yes 
Yes 
― 
V_{CAP} (V) 
0.1 to 5.5 
0.8 to 5.4 
1.2 to 20 
1.2 to 20 
0.5 to 5 
DCDC(V_{CAP} → V_{OUT}) 
2 A buckboost 
2.5 A boost 
10+ A boost controller 
10+ A boost controller 
5 A boost 
V_{OUT}Range (V) 
1.8 to 5.25 
2.7 to 5.5 
4.5 to 35 
4.5 to 35 
2.7 to 5 
PowerPath 
Internal FET 
External FET 
External FET 
External FET 
Single boost 
Inrush current limit 
― 
― 
― 
Yes 
― 
System monitoring 
― 
PWR power rail, PG 
V, I, cap, ESR 
V, I, cap, ESR 
V_{IN}, V_{OUT}, V_{CAP} 
Encapsulation 
24pin TSSOP, 24pin QFN 
4 mm × 5 mm, 24pin QFN 
5 mm × 7 mm, 38pin QFN 
5 mm × 7 mm, 38pin QFN 
4 mm × 4 mm, 20pin QFN 
*Can be configured for more than four capacitors
This design task is equivalent to determining how much water a hiker needs to bring for a day of hiking. Bringing a small amount of water on the mountain must be easy at first, but he may drink up the water prematurely, especially during difficult hikes. With a large bottle of water, hikers need to carry extra weight, but they can maintain adequate drinking water throughout the journey. In addition, hikers also need to consider the weather conditions: bring more water when it is hot, and less water when it is cold.
Choosing a supercapacitor is very similar; the holding time and load are the same as the ambient temperature, which are very important. In addition, the lifetime degradation of the nominal capacitor must also be considered, as well as the ESR of the supercapacitor itself. Generally speaking, the endoflife (EOL) parameters of supercapacitors are defined as:
► The rated (initial) capacitance is reduced to 70% of the nominal capacitance.
► ESR has reached twice the rated initial value.
These two parameters are very important in the following calculations.
To determine the size of the power supply components, you need to understand the retention/backup load specifications. For example, in the event of a power failure, the system may disable noncritical loads in order to transfer power to critical circuits, such as those that save data from volatile memory to nonvolatile memory.
There are many forms of power failure, but the backup/maintain power supply usually must support the system to shut down smoothly in the event of a continuous failure, or continue to operate in the event of a brief power failure.
In both cases, the component size must be determined based on the total amount of load that needs to be supported during the backup/retention period and the time that these loads must be supported.
Energy required to maintain or backup the system:
The electric energy stored in the capacitor:
According to design common sense and experience, the electrical energy stored in the capacitor must be greater than the electrical energy required for maintenance or backup:
This can give a rough estimate of the size of the capacitor, but it is not enough to determine the size required for a truly reliable system. It is necessary to determine the key details, such as the various reasons for the power loss, which may eventually lead to the need for larger capacitors. Power loss is divided into two categories: the loss caused by the efficiency of the DCDC converter, and the loss caused by the capacitor itself.
If the load is powered by the super capacitor during the hold or backup period, the efficiency of the DCDC converter must also be known. The efficiency depends on the duty cycle (line and load) conditions and can be obtained from the controller data sheet. The peak efficiency of the device in Table 2 ranges from 85% to 95%, which varies with the load current and duty cycle during the hold or backup period.
The amount of electrical energy loss in a super capacitor is equivalent to the amount of electrical energy that we cannot extract from the super capacitor. This loss is determined by the minimum input operating voltage of the DCDC converter and depends on the topology of the DCDC converter, which is called the differential pressure. This is an important parameter to consider when comparing integrated solutions.
Using the previous calculation method of capacitive energy, subtract less than V_{Dropout}The electric energy that cannot be obtained at the time can be obtained:
Well, V_{Capacitor}Woolen cloth? Obviously, the V_{Capacitor}Setting it close to its maximum rating will increase the stored electrical energy, but this strategy has serious drawbacks. Generally, the absolute maximum rated voltage of a super capacitor is 2.7 V, but the typical value is 2.5 V or less. This takes into account the service life of the application and the rated operating ambient temperature (see Figure 2). Use higher V at higher ambient temperature_{Capacitor}, It will reduce the service life of supercapacitors. For robust applications that require a long service life or operate at relatively high ambient temperatures, a lower V is recommended_{Capacitor}. Supercapacitor suppliers usually provide characteristic curves for estimated service life based on clamping voltage and temperature.
Figure 2. The relationship between service life and clamping voltage (with temperature as the key parameter)
Maximum power transfer theorem
The third influencing factor that must be considered is not particularly obvious: the maximum power transfer theorem. In order to obtain the maximum external power from a supercapacitor source with equivalent series resistance (see Figure 3), the load resistance must be equal to the source resistance. This article uses the expressions depletion, backup, or load interchangeably, where they all mean the same thing.
Figure 3. Power from a capacitor stack with series resistance
If we take the schematic diagram in Figure 3 as the Thevenin equivalent circuit, the following formula can be used to easily calculate the power consumption of the load:
In order to calculate the maximum power transfer, we can take the derivative of the previous formula and find the condition when it is zero. R_{STK} = R_{LOAD}This is the case at times.
Let R_{STK} = R_{LOAD}, We can get:
This can also be understood intuitively. In other words, if the load resistance is greater than the source resistance, the load power will decrease due to the increase in the total circuit resistance. Similarly, if the load resistance is lower than the source resistance, since the total resistance is reduced, most of the power consumption is in the capacitive source; similarly, the power consumed in the load is also reduced. Therefore, for a given capacitor voltage and a given stack resistance (ESR of the super capacitor), when the source impedance matches the load impedance, the maximum power can be transmitted.
Figure 4. The relationship between available power and stack current
There are some hints about the available electrical energy in the design. Since the ESR of the stacked supercapacitor is fixed, the only value that changes during the backup operation is the stack voltage, which of course also includes the stack current.
In order to meet the requirements of the backup load, as the stack voltage decreases, the current required to support the load increases. Unfortunately, when the current increases beyond the defined optimal level, the ESR loss of the supercapacitor will increase, resulting in a decrease in the available backup power. If this happens before the DCDC converter reaches its minimum input voltage, it will be converted into additional usable power loss.
Figure 5. This figure shows the minimum V required for some output power_{IN}Derivation process
Figure 5 shows the available power and V_{STK}Assuming that the optimal resistance matches the load, the standby power is 25 W. This graph can also be regarded as a unitless time base: when the super capacitor meets the required 25 W backup power, the super capacitor discharges to the load, and the stack voltage decreases accordingly. At 3 V, there is an inflection point when the load current is higher than the optimal level, resulting in a decrease in the available backup power of the load. This is the maximum output power point of the system, at this point, the ESR loss of the supercapacitor increases. In this example, 3 V is significantly higher than the voltage difference of the DCDC converter, so the unusable electric energy is completely caused by the super capacitor, causing the regulator to be underutilized. Ideally, the supercapacitor achieves the pressure difference, which makes the system power supply capacity reach the highest.
P before use_{BACKUP}Equation, we can solve for V_{STK(MIN)}Similarly, we can also consider the efficiency of the boost converter and add it to this formula:
Boost operation:
Use this lower limit V_{STK(MIN)}, We can get the capacitance utilization rate α from the maximum and minimum battery voltage_{B}:
When determining the backup time, not only the capacitance value of the supercapacitor is important, but the ESR of the capacitor is also important. The ESR of the supercapacitor determines how much stack voltage can be used to back up the load, that is, the utilization.
Since the backup process is a dynamic process in terms of input voltage, output current, and duty cycle, the complete formula for calculating the required stack capacitance will not be as simple as the previous version. It can be seen that the final formula is:
Where η = the efficiency of the DCDC converter.
Design Method of Super Capacitor Backup System
According to the concepts and calculations introduced above, the design method of the super capacitor backup system is summarized as follows:
► Confirm P_{Backup}And t_{Backup}Backup requirements.
► Determine the maximum battery voltage V according to the required service life of the capacitor_{STK(MAX)}.
► Select the number of stacked capacitors (n).
► Select the required utilization rate α for the super capacitor_{B}(For example, 80% to 90%).
► Solve the capacitance C_{SC}:
► Find enough C_{SC}Supercapacitors and verify that they meet the minimum R_{SC}formula:
Figure 6. 36 W, 4 second hold time system with 25 F capacitor and calculation result of LTC3350/LTC3351
Figure 7. Calculation results using 45 F capacitor system and LTC3350/LTC3351
If there is no suitable capacitance, you can choose higher capacitance, higher battery voltage, more stacked capacitance or lower utilization rate for iteration.
Consider the endoflife factors of supercapacitors
For systems that must reach a certain service life, corresponding changes must be made when using the aforementioned method and considering the EOL value, generally 70% C is used_{NOM}, 200% ESR_{NOM}. This complicates the calculations, but most ADI supercapacitor managers can use the existing spreadsheet tools on the product page to perform calculations.
Let’s take LTC3350 as an example to use the simplified method:
► The required standby power is 36 W and the duration is 4 seconds.
► In order to achieve a longer service life/support a higher ambient temperature, the V_{CELL(MAX)}Set to 2.4 V.
► Four capacitors are stacked together in series.
► The DCDC efficiency (ŋ) is 90%.
► Using the initially estimated 25 F capacitor, the result can be obtained through the spreadsheet tool, as shown in Figure 6.
Based on the initially estimated 25 F capacitor, we used the nominal value to get the required 4 second backup time (with 25% extra margin). However, if we consider the ESR and the EOL value of the capacitor, our backup time is almost reduced by half. To use the EOL value of the capacitor to obtain a 4 second backup time, we must modify at least one of the input parameters. Since they are mostly fixed values, capacitance is the easiest parameter to increase.
► Increase the capacitance to 45 F and use the spreadsheet tool to get the result, as shown in Figure 7.
When using 45 F, since the nominal value provides a backup time of up to 9 seconds, the increase seems to be large. However, by adding CAP_{EOL}And ESR_{EOL}After the parameter and the lowest stack voltage of 6.2 V are obtained, the backup time when EOL is taken into account is slashed by half. However, this still meets our requirement of 4 seconds of backup time and has an extra margin of 5%.
Extra super capacitor manager function
The LTC3350 and LTC3351 provide additional telemetry functions through an integrated ADC. These components can measure the system voltage, current, capacitance and ESR of the supercapacitor stack. When making capacitance and ESR measurements, the impact on the online system is also minimal. Device configuration and measurement pass I^{2}C/SMBus communicates. Therefore, the system processor can monitor important parameters during the life cycle of the application to ensure that the available backup power meets the system requirements.
LTC3350 and LTC3351 can measure the capacitance and ESR of the supercapacitor stack in real time, and can reduce the clamping voltage when using new capacitors, thereby easily meeting the backup requirements. The processor receiving the telemetry data can be programmed to perform the above calculations. Therefore, the system can calculate the minimum clamping voltage required to meet the backup time in real time, and consider the realtime capacitance and ESR. This algorithm will further increase the service life of the super capacitor backup system. As shown in Figure 2, under high temperature conditions, even if the clamping voltage is slightly reduced, the service life of the super capacitor will be significantly extended.
Finally, LTC3351 has a hotswappable controller to provide protection. The hotswap controller uses backtoback Nchannel MOSFETs to provide a foldback current limit function, which can reduce inrush current and shortcircuit protection in highavailability applications.
in conclusion
Using the basic knowledge of power transmission under the nominal value, the calculation of the capacitance value required to meet the backup specification can be converted into a simple calculation of the required power, and the problem of storage power. Unfortunately, when you consider the effects of maximum power transfer, EOL capacitance and ESR of capacitors, this simple method cannot meet the requirements. These factors will greatly affect the available electrical energy of the system throughout its life cycle. Utilizing ADI’s integrated supercapacitor solution and a large number of available backup time calculation tools, analog engineers can design and build a reliable supercapacitor backup/retention solution with confidence, not only to meet the design requirements during the life of the application, but also to the cost The impact is minimal.
About the Author
Markus Holtkamp received his degree from Bochum University, Germany in 1993. He joined Linear Technology (now part of ADI) in October 2010 as a Field Application Engineer (FAE), providing technical support for customers in China and Europe. Markus worked as an IC designer (highspeed and mixedsignal ASIC) for a German design company for 14 years. He also worked at Arrow Electronics for three and a half years as an analog field application engineer.
Gabino Alonso is currently the director of strategic marketing for the Power by Linear™ division. Before joining ADI, Gabino held multiple positions in marketing, engineering, operations, and lecturer at Linear Technology, Texas Instruments, and California Polytechnic State University. He holds a master’s degree in electrical and computer engineering from the University of California, Santa Barbara.
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