 So welcome everybody, welcome to our discussion on lithium ion battery management. I'm John Johnson from ST Microelectronics. Let's start out with a little bit of a poll. Let's find out how much experience our attendees have and what their level of interest in this topic is. Go ahead and fill those out and we'll review the results in just a minute. Today we'll be discussing battery management. In our chat it'll take less than an hour. We'll spend about a third of our time talking about battery basics. Now we're not going to discuss battery components like the anode, the cathode, the electrolyte, etc. Rather we're going to highlight various battery chemistries, their characteristics and their use cases. Then we'll zero in on lithium ion battery technology. We'll talk about lithium ion battery characteristics as well as different battery management architectures. Then we'll round out our talk by briefly introducing you to battery management solutions from ST Microelectronics. So first let's examine some foundational concepts. So according to Wikipedia, a battery is a device consisting of one or more electrochemical cells with external connections for powering electric devices like flashlights, mobile phones, electric cars, etc. Historically the term quote-unquote battery specifically referred to a device composed of multiple cells, however the usage is evolved to include devices composed of a single cell. Primary or single use or disposable batteries are used once and then discarded as the electrode materials are irreversibly changed during discharge. The common example is an alkaline battery used in flashlights and a multitude of portable electronic devices. Secondary or rechargeable batteries can be discharged and recharged multiple times using an applied electric current. The original composition of the electrode can be restored by reverse current. Examples include lead acid batteries used in vehicles, in lithium ion batteries used for portable electronic devices such as laptops and mobile phones. Batteries come in many shapes and sizes from miniature cells used to power hearing aids and wristwatches to small thin cells used in smartphones to large lead acid batteries or lithium ion battery packs in vehicles and at the largest extremes huge banks of batteries the size of rooms that provide standby emergency power for telephone exchanges and data centers and whatnot. So in-product requirements greatly influence the characteristics of the battery employed if a battery is incorporated at all. If energy storage is required then several factors or even many factors come into play when choosing battery technology. These parameters include physical, electrical, environmental and commercial aspects shown here is a list of battery selection criteria. Obviously the breadth of in-use applications necessitates various battery selection criteria as is evidence just by the length of this list. So here's what we're looking at as far as our polls concerned. It looks like that we have a lot of people that have some knowledge and hobbyists. There's a couple of experts out there. I hope I don't disappoint you experts, but this is a good topic for all of you given this knowledge level. So let's get trudging on with some of our other topics here, our other slides. So let's look at some simple comparisons of a few rechargeable that is secondary battery types. We're going to forget about primary batteries from now on. We're going to only talk about rechargeables. The graph on the left is related to a parameter called energy density, which we'll discuss in more detail a little bit later. For a given volume, different chemistries afford different energy storage capacity. The graph on the right considers specific power, again, which we'll discuss a little later, and specific energy. From this graph, we'll get an indication of which battery can deliver the most current for the longest period of time. If longer service time at higher current is desired, lithium ion appears to be the best choice. And it's used as prevalent in many applications, including vehicle electrification, tools, and consumer products. So how significant are battery parameters? How do these battery parameters, let's call them figures of merit, how do they factor into the end product and how it performs? So tabulated below are some of these important figures of merit, as well as their units, and how they affect the end product. So energy density is probably the big one, especially for electric vehicles. The unit is watt hours per liter. So how much oomph do you get and how much space does it occupy? And that gives you an indication of compactness. But also, if it's like a vehicle or a tool, how much time will it operate or run? How much energy can you take with you? Specific power is in watts per kilogram. That's an indication of how much power and how much weight do you incur when you store that power? There's charge time, and that's obvious in hours. It's time, and it's basically an indication of utility. How long does it take to recharge if a recharge is possible and required? Service life is stated in cycles, can be charged, discharged cycles, or in years. It gives an indication of reliability, obviously, but also long term costs. If it's a vehicle or something like that or a tool, you're going to have to go, perhaps, purchase a new battery pack toward the end of the service life of the battery. And then finally, cost itself, which is in currency, and that's acquisition costs or replacement costs. So these are all significant figures of merit that we look at when we consider different batteries. So let's examine how traditional alkaline batteries, which we talked about earlier, compare to various rechargeable choices for a few parameters of interest. These graphs evaluate things like weight and volume, shelf life, reliability, operating temperature, and cost. From a size and a weight perspective, the only rechargeable battery that rivals an alkaline battery is lithium ion. Alkaline batteries are by far the cheapest choice, and they exhibit very long shelf life. But the primary showstopper is that alkaline batteries are simply not rechargeable. If cost is no object, then lithium ion is a front runner. And as I mentioned before, it rivals alkaline batteries in terms of energy performance and demonstrates decent longevity. We're going to talk about the pros and cons of lithium ion battery technology in the next few slides. First of all, let's look at some transportation use cases. This is kind of interesting because it kind of underscores that lithium ion is not necessarily chosen every time. So these are different transportation applications. The specific applications requirements for each use case warrants the use of an appropriate battery chemistry. There are specific trade-offs and optimizations that must be achieved for each use case that we'll explore in a little bit more depth. But it seems like lead acid batteries might be a leading candidate because of its cost effectiveness, and that is dollars per kilowatt hour. But there are other considerations, including power density, how big is that battery going to be as well as specific power, which is how much is that thing going away to make lithium ion a more appropriate choice depending on the application. So in 2019, the Nobel Prize in Chemistry was awarded to John Gunanot, Stanley Willingham, and Akira Yoshino for their work associated with lithium ion batteries. So in honor of their accomplishments, let's talk a little bit about some characteristics of lithium ion batteries. First of all, let's talk a little bit about the number of charge and discharge cycles. Actually, this poll question is a little off, I think, because we probably need a choice that says less than 1,000. But why don't you enter in, for your product, how many charge and discharge cycles are you targeting or would you expect to be reasonable for lithium ion battery design? Anyway, let's go ahead and enter your answers and we'll look at the results in just a second. So lithium ion batteries have many advantages and it's no accident their use is now prevalent in rechargeable applications. Nonetheless, lithium ion has drawbacks. Lithium ion is finicky to charge. Moreover, it is difficult to gauge a lithium ion packed state of charge. Lithium ion cells can be tricky as thermal runaway issues and consumer products like hoverboards have demonstrated. And finally, lithium ion is an expensive technology, not just because of the exotic materials comprising the cells, but also because of the complexity of the battery and thermal management systems that must be present to optimize performance, safety, and battery life. Lithium ion cells are sensitive to operating conditions including temperature, over voltage, overcharging, and under discharging to name a few. And we'll explore this in a little bit more detail. So when we say lithium ion batteries cost a lot, what do we mean? Here's an example of an electric vehicle and many other products have the same characteristic and that is the battery system is the most expensive component comprising the bill of materials. For this reason, batteries must be able to impact performance and functionality in a big way, commensurate with its relative cost. So the care and feeding of the battery pack is a big focus to ensure that it delivers the performance and longevity that justifies its cost. Now, while I showed one of these on an earlier side, a Rogoni plot compares energy density of different energy storage devices. Often lithium ion cells, manufacturers publish these plots as they provide a way to read the runtime in minutes and hours presented on the diagonal lines of the graph. In this case, the vertical axis plots power in watts and the horizontal axis plots energy in watt hours. The diagonal lines represent the length of time that the cell can deliver energy under specific loading conditions. This graph actually contemplates, provides data for three different lithium ion cell types. There's lithium ion phosphate, which is the magenta line. There's lithium manganese oxide, which is the violet and blue plots on the graph. And then nickel manganese cobalt, which is the cyan plot on the graph. The Rogoni plot assists with battery selection by illustrating how different cells perform. Engineers can examine how much cells, how much power each cell is capable of delivering for a specific runtime. Let's give an example. The lithium ion phosphate cell, the magenta line, is capable of providing 40 watts for 3.3 minutes. The nickel manganese cobalt cell, the cyan plot, can provide 36 watts for that same period of time. So the operating time is significantly longer instead of like 3.3 minutes. Let's talk about 33 minutes, which is an ordinary magnitude longer. The power delivery performance relationship is reversed. The lithium ion phosphate cell delivers 5.8 watts, while the nickel manganese cobalt cell delivers 17 watts for the same period of time. Now that we understand how different lithium ion battery types are selected, let's briefly go over lithium ion cell charge and discharge characteristics. Consider these graphs, which depict the charge and discharge characteristics for a typical lithium ion cell. Once the cell reaches saturation during charging or even when discharging, the cell voltage remains nearly constant for most of the operational envelope. You see how flat the cell voltage curve is. This flat discharge curve makes it very attractive as an energy source because the battery provides nearly constant energy over a wide operational range. But this characteristic, along with other intrinsic qualities, presents battery management challenges, and these largely determine the operating time per charge, battery service life, safety, and the usability of the product. And what I mean by that is knowing how much battery capacity is available at any point in time. I also call this term kind of like fuel gauging. Filling a martini glass is often used to illustrate the charging curve for a lithium ion cell. If your martini is poured into the glass at a constant rate, the glass fills quickly initially. As the glass fill level reaches the midpoint, it takes more and more time to raise the level in the glass. And so it is with the charge curve of a lithium ion cell. Let's examine charging a little bit closer. There are different stages to charging, the charging process for a lithium ion cell. So after discharge, when charging the cell undergoes a constant current charging phase, the charge current is controlled and limited by the charger itself. During this initial phase, the level of charge raises quickly. Remember our martini glass analogy from the previous slide. While raising the charge current does not affect the total charge time, that is the time to reach the ready state, it can accelerate the time to reach the plateau of around 70% capacity. And this method is what the so-called superchargers employ. The maximum current allowed in constant current mode for a given battery is set by the battery manufacturer. The next stage of charging is called the saturation charge. For this stage, the charger delivers constant voltage and the charge current is limited by cell impedance. This phase takes substantially longer to reach the ready phase, which is the third phase. Different materials comprise the anode and cathode, which impact cell characteristics. For example, lithium ion cells charge from about 3.8 to 4.2 volts with the tolerance of just plus or minus 50 millivolts, depending on the anode cathode materials employed. The cells considered fully charged when charge current falls below about 3% of the cell's ampere hour rating. Charging the cell to something less than 100% is desirable to extend service life as lithium ion cells cannot accept an overcharge without some cell damage and or compromised safety. Prolonged overcharging leads to plating of metallic lithium on the anode. However, undercharging, the cell obviously diminishes the capacity of the cell to deliver power to the appliance. You've got less capacity there. Therefore, charging is sort of a balancing act between capacity, cell longevity, and charge time. In describing batteries, current is often expressed as a C-rate in order to normalize against battery capacity, which is often very different between batteries. A C-rate is a measure of the rate at which the battery is discharged relative to its maximum capacity. So one C-rate means that the discharge current will discharge the entire battery in one hour. For a battery with a capacity of 100 amp hours, this equates to a discharge current of 100 amps. A 5C-rate for this battery would be 500 amps and a C-over-2 rate would be 50 amps. Similarly, an E-rate describes a discharge power. A 1E-rate is the discharge power to discharge the entire battery in one hour. So let's talk about service life factors here. From the time a brand new lithium ion cell is installed in a product to the time that its capacity diminishes to the point at which the battery must be replaced or discarded, the cell undergoes several changes that impact its capacity to store energy. Now these changes are brought about by either abuse of the cell, either by accident or because of poorly designed battery management, or by natural processes associated with aging. Now as it turns out, most of these factors can either be eliminated or mitigated by incorporating a properly designed battery management system. Abuses to the cell include exposing the cells to overcharging or deep discharging for extended periods of time. Most rechargeable batteries can be overloaded briefly, but this must be kept short. Short deep discharge does not damage the cell, however, leaving the battery discharged for prolonged periods of time damages internal protective layers. The voltage level that a cell is exposed to during the charging phase can have a dramatic impact on cell capacity. Finally, one of the biggest culprits to diminishing cell capacity is exposure to high temperatures. While lithium ion cells do not readily take a charge when it's cold, exposure to high temperatures is the primary culprit for cell damage. This is why many high-end systems employ thermal management as part of the battery management system. The secondary category of factors that impact battery surface life is associated with aging. The number of charged discharge cycles that a cell undergoes can slowly damage the anode cathode of the cell as well as cause lithium plating. Lithium plating occurs during charging and has a couple of root causes. Higher charge currents force the lithium ions to move faster at a faster reaction rate and thereby accumulate on the anode if charging occurs at low temperatures. The reaction rate slows impacting the inner calculation of lithium ions, also causing lithium ion plating on the anode. Materials comprising the cell also degrade with age and this is called calendar aging. The electrolyte can oxidize over time and structures like the passivation layer can degrade as well. Obviously, most of our people attending today have a realistic view of how many charged and discharged cycles they'd expected. I would expect that if we had something in the under-thousand category we'd probably have a distribution down there as well, probably most of you. In commercial applications, lithium ion batteries require protection mechanisms in circuits to ensure safety of the battery. They're well-documented instances of thermal runaway that they've been observed recall the hoverboard products propensity to catch fire. Now, IEC 62133 defines the safety requirements for lithium ion battery packs. The energy density of lithium ion batteries roughly twice that of a NICAD. The battery comprises an anode, a cathode, and a liquid electrolyte that is dissolving in lithium salts. There is an ultra-thin permeable separator and made of polyethylene that is approximately about 10 microns thick. A breached separator causes a short circuit that initiates thermal runaway. A shortened cell can eventually achieve temperatures exceeding 500 Celsius. The electrolyte can ignite and even become explosive when it's exposed to oxygen. So as more and more cells become hot they either short out due to the separator degradation or they can be taken offline by the BMU, causing the rest of the cells to take the load current. If left unchecked the battery will undergo what's called a thermal runaway in which the load current is shouldered by fewer and fewer cells causing the cells remain online and the ones that are online heat up and that in turn causes some of them to go offline which causes fewer and fewer of them to shoulder the burden. So to avoid the cell temperatures as well as current need to be constantly monitored and the battery needs to be controlled accordingly. So we've learned a lot about the characteristics of batteries in lithium ion cells and some of the challenges managing the batteries comprising lithium ion. Now let's look at how lithium ion cells can be managed looking at BMU architectures. First it should be obvious at this point the managing lithium ion batteries involves trade-offs and these trade-offs present a challenging balancing act where parameters associated with service life cost charging and operating time and safety comes and works against each other. For example charging the battery faster can affect service life and maybe cause damage that impacts safety. Employing extensive monitoring and control facilities better management that can optimize service life and operating time and that adds line items to build materials and obviously cost as well. So with the aforementioned trade-offs in mind there are certain key functions that a battery management system can and should provide. Some functions are obvious like measuring the cell voltage the currents and temperature while others may be new concepts to some of you like cell equalization or balancing for example we're going to dig into all of these a little bit more next. This chart kind of gives you a few methods of gauging battery capacity and performance as well as some basic pros and cons for each approach. Now intuitively monitoring the cell voltage to track the charge and discharge and hence the capacity seems like the simplest approach to implement however there are potential pitfalls first mid-charge lithium ion discharge curves that are flat as we talked about before so what makes it a very good energy source makes it difficult to gauge because you have to have very high resolution signal path to quantify changes in the battery state or through measuring the voltage. In difference in addition cell voltage is impacted by load current as well as temperature variation further complicating this issue and even most papers that address lithium ion chemistry suggest that the battery be unloaded for a relatively long period of time before cell voltages are sampled and so obviously this is perhaps impractical for some implementations where you can unload your battery let it sit and then measure it to know how much energy is left to do fuel gauging. Hydrometers is a way to measure capacity as well it's employed on chemistries where you have access to the fluid let us as a good example if you've ever taken your car battery to a battery shop to use a hydrometer so for lead acid chemistry sulfuric acid density increases as lead acid battery changes charges and this is measured using a hydrometer which is basically measurement of specific gravity if the fluid level changes the ability to accurately estimate state of charge can also be affected but also there are instances where you really can't get into any fluid to measure specific gravity or density of the fluid anyway then the third method that I'm going to talk about is something called coulomb counting and what this is is basically measuring amp seconds in and amp seconds out of the battery packet integrating that so it's really effective means of fuel gauging but it's not without its drawbacks it entails keeping a rolling tally of these things there's no battery chemistry that's 100% efficient in terms of charge and discharge and by the way the other thing is that gauging this on a per cell level is impractical if you have a stack of batteries typically what happens with coulomb counting is you have one since resistor and you're measuring the current out of the entire stack so a fundamental component of battery management is something that we're calling a cell measurement unit CMU it contains control and instrumentation that helps monitor the state of charge on a cell by cell basis for the entire battery stack these include the ability to measure cell voltage on a cell by cell basis as well as stack current battery temperature must also carefully be monitored to ensure efficient charging battery longevity and battery safety the measurement signal path of the CMU shown here must deliver a requisite precision to estimate state of charge now this is critical if parameters like operating time charge time, battery life are to be optimized specifically cell voltage and stack current measurement precision are critical due to the flatness of the charge and discharge curves as we've already discussed in battery management solutions sometimes incorporate coulomb counting which is the amp seconds in and out that I talked about before to estimate state of charge of the entire stack to gain an understanding and some insight into how these parameters factor into battery management consider something called JIDA guidelines for lithium-ion battery charging JIDA which is an acronym that stands for Japan electronics and information technology industries association this was a voluntary group that was formed in reaction to battery fires that occurred in the mid-1990s and since this time battery construction and manufacturing has improved considerably however these scenarios provide some insight into how monitoring and controlling critical parameters like voltage current and temperature play a role in battery management what JIDA recommends is to vary the charge rate depending on the battery temperature to prevent cell damage these graphs provide an intuitive example of how battery management is used to control the charging process so in 2007 JIDA battery charging safety guidelines that stressed the need to avoid high charge currents and voltages outside of certain cell temperature ranges these recommendations noted that thermal runaway could occur if the cell temperature reached 175 degrees with the cell voltage of 4.3 volts it also noted that safe charging could be implemented at temperatures up to 60 degrees and charging voltage was limited and tightly controlled so as we discussed earlier the objective is to ensure that charging and discharging the battery is carefully managed and this is not to manage the range of the operating time and the product per se the efficiency optimization but it's also to maximize battery longevity if an entire battery is charged to 50% yet a single cell is at 80% the results of charging the entire battery 80% would result in cell damage for a single cell in the stack so cell balancing or cell equalization provides a mechanism to force all the cells to nearly identical levels of charge thereby maximizing battery longevity as well as efficiency of the product as the chart shows without proper cell balancing the longevity of the battery is impossible to maintain the power of charge and discharge cycles in addition to carefully monitoring and in some cases controlling battery temperature controlling charge levels can have a dramatic impact on battery life consider the chart on the left that plots battery capacity as a percentage of original capacity versus charge discharge cycles for different charge levels you can see we're plotting a percentage of original capacity and a degradation of capacity over charge and discharge cycles and as you can see as we charge and discharge more and more of the entire range of the battery the battery lasts for fewer and fewer cycles so if you wanted a battery to last for a long, long time you'd obviously want to use less of the entire range of the battery which shows how capacity degrades when the battery management continuously charges the battery to 100% and then permits the battery to be discharged to 25% nearly using the battery rail to rail the magenta plot shows the result of charging the cells to 85% instead of 100% and you can see that has an improvement on the actual overall life of the battery in terms of its capacity to store energy in a lot of cases what a product will do is over the life of the product it will use more and more of the entire range of the battery as the cells degrade but in order to extend the life of the battery they won't use the entire range in terms of charging it all the way up or letting it discharge all the way down initially from the onset to let the battery last and you can think about it if the battery pack for an electric vehicle costs $12000 which means its replacement cost is close to $20,000 you really don't want that battery to fail over the life of the product so I've already introduced you to the cell measurement unit the CMU but it's worth touching on it a little bit some more in the context of how it interfaces with the balance of the other components in the BMU the cell monitoring unit sometimes called a cell supervisor circuit or collectively a data acquisition unit the CMU monitors cell voltage temperature and other cell level parameters it also includes circuitry necessary for cell balancing the CMU must measure several cell level and stack level parameters accurately recall the cell voltage during discharge is relatively flat therefore high resolution is required for accurate state of charge estimation this ensures that the battery is charged and discharged safely and efficiently and also prolongs battery life remember our last slide we talked about charging and discharging the battery over a very specific amount of its capacity well this is how you do that ideally cell voltage measurement should be taken simultaneously in other words all cells in the stack at once to ensure that the algorithms have a true picture of the condition of the stack some CMU implementations multiplex the cell voltages into a single A to D and by the way this can be particularly problematic if you have hundreds of cells like an electric vehicle however this assumes that all cells are stable over this entire sampling window and that the sampling itself does not affect measurement accuracy whatsoever so the module management unit or MMU manages and monitors collections of CMU typically between 8 and 16 cells the MMU groups cells into a module and perform cell balancing across the module it aggregates cell data and communicates with what we call a PMU which is a pack management unit the PMU is also sometimes called the central management unit so it performs functions and its scope is typically battery pack wide it monitors pack parameters including voltage and peak current it controls and monitors safety devices including switches and breakers and it communicates with both the battery pack elements as well as the product as a whole it also typically controls battery pack heating and cooling if there are thermal management mechanisms there generally a PMU employs a microcontroller while the MMU does not necessarily contain a microcontroller depending on the number of cells in the stack and their proximity to one another, BMUs are implemented using one of three architectures a centralized a modular or a distributed a centralized architecture combines cell monitoring as well as module and pack monitoring into one current circuit board assembly this might be a tool, a toy or even a small scooter or what not where all the cells are in cloaks proximity to one another this obviously saves cost this implementation is commonly used to support small numbers of cells low capacity battery packs etc a typical use cases in electric bicycle or power tool modular BMU architectures employ multiple instances of a module management unit these are near the battery cells and greatly reduce the complexity of the wiring MMU share control and parametric data with the PMU via communications interface it can be can or anything and this means that the PMU requires the MMU as a proxy for the state of the individual cells distributed architecture incorporates more than one pack management unit that supervises a specific subset of modules or cells in the battery pack by the way the communications interface is an electric vehicle or going wireless between PMUs PMUs can work independently or can coordinate activities depending on the use case and other requirements this architecture affords the most scalability and flexibility but it's also the costliest and most complex this approach is sometimes called the smart battery in that clusters have cells that have their own dedicated MPU getting close to the end and then we can get to some maybe some Q&A time that would be good so to wrap things up let's take a quick look at the BMU solutions from ST Microelectronics here's a typical bill materials for a BMU that implements a distributed architecture that we just talked about that has one CMU and then multiple MMUs and PMUs aside from the CMU, MMU and PMU blocks that bill materials combines the cooling fan control as well one particular component that I want to highlight here is the L9963 which we'll show in more detail later that particular product combines a cell measurement unit and a module measurement unit into one chip and it's pretty cool we'll talk about it next so let's talk about a high level block diagram of how this would all look connected together to form a system next here's how the L9963 is used as part of the BMU chip set so the L9963 includes the CMU and MMU functions and is used to monitor up to 14 cells per 9963 it can use stand alone for something as simple as a power tool or you can cascade up to 15 of them in a 900 volt lithium-ion battery stack in this case ST Microelectronics also offers an isolated transceiver so the stack can communicate to the MCU as shown so let's briefly describe what the L9963 does in the BMU system so for every connected cell the L9963 acquire cell voltages and temperatures and communicates this via galvanically isolated interface to the main processing unit in addition the L9963 measures stack data via galvanically isolated interface but it provides current and also cool and counting to better estimate the state of charge as well as cell voltage the CMU directly affects the KPI parameters of the whole battery and the more accurately it can determine cell voltages the better it can utilize available cell capacity the more precisely it can drive higher level application parameters such as state of charge so to achieve effective charge balancing between cells there's a passive balancing method that can be applied the switchable load is placed in parallel to each cell so that during the charge phase cell level of individual cells can be kept constant or slightly decreased in the case of the switch conducting this balances the level of charge throughout the entire stack has cells with the non-conducting balancing bypass continue to raise their charge level so the L9963 simplifies this passive balancing as it provides integrated MOSFETS such that only the externally balanced load is needed furthermore the device offers several configuration options that facilitate autonomous and simplified control of this balancing process so the acquired sensor data and diagnostic information must be transferred to a CPU using a galvanically isolated interface to properly separate the high voltage domains from the conventional bus and supply so the L9963 supports both a transformer or capacitor based coupling to increase galvanic isolation fast communication is key and the L9963 allows data rates up to 2.66 megabits per second which translates to an update interval of less than 4 milliseconds for a complete 400 volt battery stack in this example the battery consists of 96 cells with 7 of the L9963 managing those devices all these aspects from acquisition to sensor data the integrity test of the measurements to transfer simple sample data as well as the permanent supervision of cells are safely critical for both operation of the product in a lot of cases for instance this product is used as a vehicle so it has to comply with ISO 26262 AISLD requirements and this product actually has that built in you'll notice by the way that in terms of cell voltage accuracy the accuracy is plus or minus 2 millivolts and it samples the entire stack current for a coulomb counting at an error rate of 0.5 percent so these are the kinds of accuracies that you need to be able to gauge and extend the service life of the battery and maximize charge time and whatnot so anyway I appreciate your time thanks for listening let's see if we've got any questions here that we can answer real quick and