Paradigm shift In lithium battery SoC measurements.

1. 31-4: Diamagnetic Measurements in Lead Acid Batteries to Estimate State of
Charge
Jörn A. Tinnemeyer
Vice President – Research & Development
Cadex Electronics Inc.
22000 Fraserwood Way, Richmond BC, Canada V6W 1J6
Joern.Tinnemeyer@cadex.com or www.cadex.com
Abstract: With the development of start/stop technology to entertainment systems and start-stop technologies (micro
improve fuel economy and a larger prevalence of electronic hybridization) to name two [1]. Recent technological
loads in standard automobiles, the accurate determination developments promise to use battery power for critical
of State of Charge (SoC) is highly desirable. The market is safety features of the vehicle - such as, electrical steering
already experiencing a paradigm shift away from handheld (drive by wire) and braking systems. In such instances
diagnostic equipment to onboard sensors in high end when critical operations of the automobile depend on
automobiles. Concurrently, the adoption has also battery power, accurate knowledge of the state of the
stagnated in the last few years due to inaccuracies of these battery is not a nicety, it is paramount.
sensors. Specifically, all sensors on the market today
employ voltage, current and temperature sensing to
estimate the SoC. Although these methods are reasonable As our demands for battery sensor technologies have
(defined as having a +/- 15% accuracy to relative state of increased, so too have the types of sensor technologies that
charge) when the battery is new, the errors increase are available. Initial automotive battery sensors consisted
dramatically with age. The reason for this is that different of a primitive shunt style system that assessed the cranking
failure modes resulting from varying operating conditions capacity of the battery. Now, battery sensor systems have
will have independent effects on battery health. In order to been placed in mid-level and luxury automobiles that
make a more direct assessment, Cadex Electronics Inc. is monitor the current of the battery from a few milliamps to
developing a sensor based on measuring the change in hundreds of amperes. These modern battery sensors rely,
magnetic susceptibility of lead / lead sulphate as the almost exclusively, on mathematical models. The sensors
battery changes SoC. Measurements of the diamagnetic take in a number of parameters from the battery - voltage,
field changes have demonstrated improved predictive current, and temperature - and then an algorithm estimates
capability (+/- 7%) within a challenging automotive the battery’s SoC. The computational models are dynamic
environment. and are based on the parameters of a new battery plus an
aging model. Not surprisingly, these models work
reasonably well (+/-15% SoC) when the battery is new,
Keywords: state of charge; lead acid; diamagnetic; charged, and left standing for a prolonged period of time
magnetic susceptibility (allows voltage to be directly correlated to SoC). However,
if the battery is not new, is or has been recently polarized,
then these estimation techniques become less accurate
Introduction (+/-30% SoC or worse). The greatest hurdle that these
In our portable world, we use batteries to keep our estimation techniques face is the ability to obtain an
electronic devices functioning and we monitor the state of accurate measure the battery’s capacity. The capacity of
the battery to assure that the equipment will operate as we the battery decreases as the battery ages. Importantly, the
expect. Realtime battery monitoring is commonplace in speed of this aging processes is modified by a host of
devices, which use the battery as the primary source of different environmental conditions (e.g., outside
power - such as, cellular phones, laptop computers, etc. By temperature, usage rate, degree of charge-discharge cycles)
contrast, battery monitoring is less frequent in electronic [2], which thwart the meaningful development of a
systems that place fewer demands on the battery. computational estimation system.
Automobiles and other vehicles provide a good example of
this later trend. Traditionally, automobiles used the
onboard battery system to start the engine; thus, realtime Unfortunately, this roadblock to effective battery
battery monitoring was not required or implemented. monitoring occurs at the same time as the demand for a
reliable, realtime measure of SoC grows: the ADAC reports
that 40% of roadside automotive failures are battery-related
This trend is changing. The last two decades have brought [3]. More importantly there is an increasing trend towards
many advances in automobile technologies, which place these failures (36% in 2007 for example) [4]. It is time to
more demands on the automobile’s battery: onboard consider a novel approach.

2. Concept Description we can determine the magnetic field absorption. The
The modern lead acid battery primarily consists of the degree of penetration into the metal, or skin depth, is given
following reactions: by δ. The permeability of the material is represented by µ
and the conductivity by σ. The frequency, f, reflects the
depth of the material being sampled. Since equation 1 is
inversely proportional, we know that deeper penetration of
the material occurs at lower frequencies. The skin depth of
pure lead is 29 mm at 60 Hz to 0.73 mm at 10kHz [6].
The magnetic field produced by a coil follows Biot-
Savart’s Law,
Thus, the voltage of the battery is a direct response of the
∧ ..2
µ IdI × r
materials used at the cathode and anode poles. Changes in dB = 0
4π r 2
the SoC of the battery are accompanied by physical
changes in the material properties of the cathode and anode
poles that we can measure.
in which...
dB represents the vector quantity that describes the
magnetic field at the desired point;
I is the current;
Table 1 - Magnetic susceptibilities of electrode
species [5] dl is a vector quantity of an infinitesimal current element in
the direction of the field potential;
As evidenced in Table 1, the magnetic susceptibility of
negative electrode changes from -23 xm/10-6cm3mol-1 when µ0 is the magnetic susceptibility dependent on the material;
the battery is fully charged to -69.7 xm/10-6cm3mol-1 when ∧
the battery is discharged. To measure this three fold change r is the unit vector in the direction to where the magnetic
in magnetic susceptibility, an excitation field is needed to field is to be calculated; and
stimulate the metals and a sensor is needed that is capable
of registering these minute changes in the magnetic field. r is the distance to the calculation point.
To create an excitation field, a coil is used to generate eddy If we consider a current loop with a radius of R, and we
currents. These eddy currents produce magnetic fields that wish to measure the field at a particular point x, the
are countered by the diamagnetic response of the to-be- equation can be simplified to:
measured material. The extent of this reduction depends on
the strength of the diamagnetic response - more reduction
is registered when the diamagnetic response is greater. In µ0 nIR 2 ..3
the case of lead acid batteries, the greater the diamagnetic B(x) = 3
response reveals a greater contribution of lead sulphate or, 2(R + x )
2 2 2
in layman’s terms, the battery is more fully charged. The
field may be a regular DC field or an AC field. which allows us to easily assess the material properties of
the negative electrode.
By using the definition,
A sensor is then used to measure these changes in the
magnetic field. Magnetic field sensor technology has
changed significantly over the last decade, driven mainly
by hard drive read head development. Magnetic tunneling
1 ..1 junction sensors are, currently, the state of the art. The
δ= sensors are built by separating two metals, CoFeB, by an
πµϑ f insulator of MgO that is only a few atoms thick. A biasing
voltage is created between the metals, by allowing current

3. to flow across the insulator. The likelihood of quantum obtained at the same time, as evidenced in Figure 2.
tunneling is directly related to electron spin alignment, Typical errors between actual SoC and estimated SoC are
which can be manipulated and controlled by introducing on the order of ± 7%.
external magnetic fields, with the following consequence:
as the strength of the magnetic field increases, the electron
spin alignment increases, and more electrons may tunnel
across the insulator. As more electrons tunnel across the
insulator, the resistance of the device falls [7]. Accordingly,
the magnetoresistance of the sensor is the first indication of
its performance: for example, anisotropic sensors have
2-3% magnetoresistance, whereas giant sensors have
15-20% magnetoresistance. By contrast, sensors that
implement magnetic tunnel junctions have a
magnetoresistance of 200% [7].
Finally, a fuzzy logic algorithm is applied to the outputs
from the sensor to provide an estimate of the state of charge
of the battery.
Figure 2 - Model estimation compared to actual SoC
Results within vehicle.
Figure 1 highlights how these diamagnetic measurements
can be used to track a typical discharge/charge profile of a
lead acid battery. As evidenced in this figure, a systematic
increase in Estimated SoC (blue triangles) is measured
from the sensor that accompanies charging the battery. Two important points about the functioning of this
diamagnetic sensor technique require explicit mention.
First, the data shown in Figures 1 and 2 were collected
within the electromagnetically noisy environment of the
automobile; thus, represent data that one can expect from
the field. Second, this technique has been tested on
different batteries (flooded and AGM) of different ages, and
has yielded identical results (within ± 7% of actual SoC);
therefore, this diamagnetic method provides a very accurate
measure of SoC for batteries of all ages.
It is often possible to create technologies that function well,
but are impractical by virtue of price and ease of
implementation (or use) - if the price is too high or the
device is too large or cumbersome, then it will not be
adopted by industry.
Figure 1 - Discharge/charge profile of a standard SLI Current battery sensors, which depend on mathematical
(starting lighting ignition) battery modeling, cost automotive manufacturers approximately
$15 per unit. Our diamagnetic sensor technology can be
In this example, the battery was subjected to a 20A built a similar price level.
discharge, followed by a constant current (9A) constant
voltage (14.4V) charge. The data set contains both Moreover, our diamagnetic sensor easily adjusts to all
polarized and float data; however, the voltage was makes and models of lead-acid batteries, as illustrated in
subjected to float levels after 5 minutes of rest. Figure 3. Thus, it is easy to use.
Importantly, this pattern is independent of voltage changes
that accompany the charging of the battery, as evidenced by
comparing the Estimated SOC (blue triangles) with the
voltage (green circles).
More important, this diamagnetic measure of SoC
corresponds closely to actual measures of SoC that were

4. the automotive industry to implement drive-by-wire
technologies, which will improve the efficiency of
automobiles at the same time as reducing manufacturing
costs.
Taken together, at a time when consumers, governments,
and industry ubiquitously demand more of the automotive
battery, and at the time when 40% of roadside problems
originate from battery-related failures, we have created a
simple, accurate, and effective realtime battery monitoring
system.
Figure 3 - Simple overview of sensor and required References
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Accuracy: +/-15% SoC +/-7% SoC
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Conclusions
for Testing and Failure Analysis,2006.
Our diamagnetic sensor affords the benefits of substantially
better accuracy that is largely independent of the age or
condition of the battery, but is equally easy to implement
and costs approximately the same amount of money per
unit.
Now consider the following issues: (a) 40 % of all roadside
failures originate from the (lack of) functioning of the
battery, (b) the ever increasing demands for electric loads
placed on the automotive battery originating from
consumer desires for entertainment devices, governmental
requirements for the implementation of start-stop
technologies to help protect the environment, and desires of