Scheduling battery usage in mobile systems

1136 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 11, NO. 6, DECEMBER 2003

Transactions Briefs__________________________________________________________________

Scheduling Battery Usage in Mobile Systems

Luca Benini, Alberto Macii, Enrico Macii, Massimo Poncino, andRiccardo Scarsi

Abstract—The use of multibattery power supplies is becoming commonpractice in electronic appliances of the latest generations. Economical andmanufacturing constraints are at the basis of this choice. Unfortunately,a partitioned battery subsystem is not able to deliver the same amount ofcharge as a monolithic battery with the same total capacity. In this paper, wedefine the concept of battery scheduling, we investigate several policies forsolving the problem of optimal charge delivery, and we study the relation-ship of such policies with different configurations of the battery subsystem.Experimental results, obtained for different kinds of current workloads,demonstrate that the choice of the proper scheduling can make system life-time as close as 1% of the theoretical upper bound, that is, a monolithicpower supply of equal capacity.

Index Terms—Battery optimization, low-power design, low-powerdissipation.

I. INTRODUCTION

Many portable electronic systems of the latest generations utilizepower supplies made of multiple batteries. This is done primarily toincrease user’s flexibility in exploiting the existing tradeoff betweenweight and capacity of the battery subsystem. As an example, it iscommon practice plugging into the secondary module bay of a note-book computer an additional battery pack before starting a long, in-tercontinental flight, while a light-weight, plastic place holder is usedinstead when a short, domestic flight is taken.

Flexibility in modifying the configuration of the battery subsystemaccording to the user’s specific needs is not the only motivation foradopting a partitioned power supply. Fabrication constraints for boththe battery cells (custom-designed battery packs withadhocsize andcapacity are used only in high-end electronic appliances, low-cost prod-ucts normally utilize batteries with standard shape and capacity) and theapplication (battery packs need to adapt to shape and size of the case)are equally important factors that may hamper the choice of a mono-lithic battery cell.

Supporting multibattery power supplies is thus becoming a major re-quirement for current electronic products, and significant advances inthe technologies that enable the realization of multibattery devices havebeen achieved very recently. Among others, smart batteries (i.e., bat-teries equipped with specialized hardware that provides present state,calculated, and predicted information under software control), dedi-cated battery-to-bus interfaces (e.g., Intel SMBUS [1], an ACPI-com-pliant [2], two-wire interface similar to PhilipsI2C [3] that enablesthe exchange of information between smart batteries and the system),

Manuscript received October 30, 2000; revised August 1, 2002.L. Benini is with Dipartimento di Elettronica, Informatica e Sistemistica, Uni-

versità di Bologna, Bologna, 40136 Italy.A. Macii, E. Macii, and R. Scarsi are with Dipartimento di Automatica e

Informatica, Politecnico di Torino, Torino, 10129 Italy.M. Poncino is with Dipartimento di Informatica, Università di Verona,

Verona, 37134 Italy.Digital Object Identifier 10.1109/TVLSI.2003.817555

and battery selector circuits (e.g., theIntelligent Chargerby O2Micro[4] and theGeneral-Purpose Smart Battery Charger/Selector ICbyMitsubishi Semiconductors [5]) play an increasingly important role inthe multibattery electronics scenario.

Unfortunately, the choice of distributing the total amount of capacityto different battery packs has some penalizing effects on the total chargethat can be extracted from the battery subsystem. This is due to the factthat a battery is not an ideal capacitor; therefore, under a fixed systemworkload, the lifetime guaranteed by a battery does not scale linearlywith its capacity [6]. For example, if a monolithic battery of capacityC guarantees a lifetime ofLT time units, two batteries of capacityC=2which are discharged one after the other ensure a lifetime smaller thanLT. An additional drawback of multibattery power supplies is that, usu-ally, several small batteries tend to weigh more than a monolithic bat-tery with the same total capacity, due to the additional packaging over-head and replication of the battery control circuitry which is aboardeach pack.

Weight increase can only be faced by battery manufacturers. On theother hand, the problem of decreased usable battery capacity in multi-battery applications can be viewed as a system-level design problem,and can, thus, be solved by adopting smart management policies forcharge extraction from the battery power supply.

In this transactions brief, we introduce the concept ofbattery sched-uling and we explore the impact of different scheduling policies onthe achievable lifetime increase. More formally, we investigate the fol-lowing problem. Given a partitioned battery subsystem (i.e.,N batterypacks, each of which is characterized by its own nominal capacity) anda system workload, find the optimal scheduling policy that maximizesbattery lifetime for such a workload. To the best of our knowledge, thisis the first time the battery scheduling problem is formulated and solvedin the context of system-level design.

The basis for battery scheduling is the fact that the amount of chargethat can be extracted from a battery depends on how the current is drawnover time [7]–[11]. The idea is to utilize the various battery packs in analternate fashion, instead of following a strict, sequential scheme, asit is done in most appliances now available on the market. The ratio-nale behind this choice is that electro-chemical cells can recover someamount of deliverable charge if they are allowed to rest after a periodof high-current discharge.

We investigate two classes of scheduling algorithms with increasinggenerality, complexity, and performance, and present the results ofextensive experimentation we have run on power supply subsystemswith different configurations and containing up to four battery packsof varying capacities. This choice was made in accordance with theSMBUS specification [1], which states that partitioning a battery intomore than four packs may not payoff due to the intrinsic managementoverhead this solution does introduce. Eight current waveforms withdifferent characteristics and profiles (over time) have been used assystem workloads. The results we have obtained demonstrate thatscheduling schemes allow to fully recover the loss in deliverablecharge caused by the adoption of a partitioned battery supply sub-system. In fact, the difference in lifetime with respect to the monolithiccase can be as small as 1%.

The rest of this article is organized as follows. In Section II, we re-view two of the macroscopic phenomena that differentiate a battery

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 11, NO. 6, DECEMBER 2003 1137

Fig. 1. Capacity variation as a function of load current.

from an ideal power supply and that are at the basis of the scheduling al-gorithms we propose to optimize charge extraction from the partitionedbattery power supply. In Section III, we illustrate with the aid of experi-mental data, the main limitation of currently adopted policies for chargeextraction from partitioned power supplies and we introduce the con-cept of battery scheduling. Section IV presents the first class of sched-uling algorithms (i.e.,static scheduling) we have devised and showshow such algorithms help in increasing system lifetime. Section V de-scribesdynamicscheduling. This solution is more flexible than staticscheduling, although, more complex to implement in practice, becauseit takes into account the actual conditions of each pack (i.e., the state ofcharge) to decide whether a new battery should go in use. Results re-ported in the same section confirm the claim that dynamic schedulingoutperforms static algorithms for battery subsystems of heterogeneousnature. The paper concludes in Section VI, by directing the reader toopen issues and possible future research topics in the area of batterymanagement for portable applications.

II. BATTERY PROPERTIES

From the system designer’s point of view, there are two physicalproperties of interest in a battery: 1) output voltage and 2) battery ca-pacity. In an ideal battery, the voltage is constant over a complete dis-charge cycle, and it drops to zero when the battery is fully discharged.In practice, however, voltage decreases as the time of discharge in-creases. As a matter of fact, a battery is considered exhausted whenits output voltage falls below a given voltage threshold (e.g., 80% ofthe nominal voltage). This behavior motivates the adoption of dc–dcconverters for voltage stabilization when batteries are used to powerup digital systems.

Beside this intuitive and very well-known fact, there are two addi-tional factors that differentiate real batteries from ideal power suppliesand that are at the basis of the battery scheduling policies we discussin this paper:

• the capacity of a battery depends on the discharge current;• a battery can recover some of its deliverable charge when it is

given some rest.

We illustrate these two effects through experimental evidence, ratherthan by rigorous construction and derivation of mathematical modelsrepresenting chemical phenomena. Studying and justifying the phys-ical behavior of battery cells is, in fact, beyond the scope of this paper;the interested reader may refer to the vast, specialized literature forfully worked out theories.

The data we present in the sequel have been obtained throughevent-driven simulation of the system-level discrete-time model ofa Lithium-Ion battery that we have presented in [11]. Such modelguarantees an average error in estimated lifetime of 0.52% withrespect to a circuit-level, continuous-time model, derived from thosedescribed in [12] and [13]; the latter, in their turn have proven tobe within 15% from measured data under a large variety of loadingconditions. The accuracy of output voltage estimation provided by thesystem-level model is also very high, the average root mean squarerelative error (RMSRE) over different workloads being around 0.7%.

A. Capacity Versus Discharge Current

At higher currents, a battery is less efficient in converting its chem-ically stored energy into available electrical energy. This fact is picto-rially shown in the diagram of Fig. 1, where the capacity of the batteryis plotted as a function of the average current load. The plot is relativeto a battery of nominal capacitance of 1.35 Ah (solid line). We observethat, for increasing load currents, the battery capacity progressively de-viates from the nominal value (dashed line).

B. Charge Recovery

A battery can recover some of its deliverable charge if periods ofdischarge are interleaved with rest periods, i.e., periods in which nocurrent is drawn. This fact is pictorially shown in Fig. 2, where theoutput voltage of the battery is plotted under two discharge profiles:A constant current load (solid line) and an intermittent current load(dashed line).

Both the constant current and the intermittent current, while on, havethe same discharge rate. In addition, the off-time of the intermittentdischarge is not shown in the plot. Then, thex axis represents the actual


Fig. 2. Continuous versus intermittent discharge.

elapsed time of discharge, and it is proportional to the actual usablecapacity of the battery.

Note that in the plot, the constant line at 3.3 V represents the voltagelevel under which the battery is regarded as exhausted.

III. PARTITIONED POWER SUPPLIES: THE BATTERY

SCHEDULING PROBLEM

In existing multibattery systems, the presence of several batterypacks in the power supply is managed in the simplest and mostintuitive way, that is, batteries are discharged in sequential order,one after the other. In other words, the battery currently in use isdisconnected from the load only when it is totally empty.

In order to quantify the performance of a conventional, sequentialdischarging policy, we have run a set of experiments under differentload conditions and for battery subsystems characterized by differentconfigurations.

Regarding the current drawn from the power supply, for our exper-iments, we have chosen four pairs of workloads with different shapesand temporal profiles.

The first three pairs (CC, SW , andPW ) are artificial workloads:

1) CC: constant current load of 0.5 A forCCa and 1.0 A forCCb.2) SW : square wave with 50% duty-cycle, average current value

of 0.5 A and discharge rates of (0.3 A, 0.7 A) forSWa, averagecurrent value of 1.0 A and discharge rates of (0.8 A, 1.2 A) forSWb.

3) PW : periodic current pulses with period of 6 s, duration of thepulse of 5 s and discharge rate of 0.7 A forPWa, period of 25 s,duration of the pulse of 20 s and discharge rate of 1.2 A forPWb.

The fourth pair of workloads (RL) refers to a real-life example; currentprofiles have been obtained by monitoring the activity of a personaldigital assistant (PDA) over a few hours of operation (the interestedreader may refer to [11] for a description of the PDA and its modeof operation). For this example, the temporal waveforms of the currentdrawn by the system from the power supply do not have the same shape;

TABLE IBATTERY LIFETIME FOR SEQUENTIAL DISCHARGE

the mean value of workload namedRLa is 0.45 A, and it is lower thanthat of workload namedRLb (1.1 A).

Concerning the architecture of the battery subsystem, we haveexperimented with four configurations (denoted, in the sequel, byBS1–BS4). All of them respect the constraints set by the SMBUSspecification [1] (e.g., at most four batteries).

The sum of the capacity of all packs in the partitioned power supplyis chosen to be the same for all configurations (i.e.,CTOT = 1:35Ahr).This is also the capacity of the monolithic battery we use as the baselinefor comparison.

All the battery packs in the power supply have the same nominaloutput voltage of 4.1 V, independently of their capacities. As for theexperiments in Section II, a battery pack is regarded as completely dis-charged after its output voltage drops below 3.3 V.

The details of the various configurations we consider are thefollowing:

• BS1: two battery packs of capacityCTOT=2 each.• BS2: four battery packs of capacityCTOT=4 each.• BS3: four battery packs, one of which hasback-uppurposes

(thus, has a very small capacity, i.e.,Cbackup = CTOT=20),and the remaining three have the same capacity of(CTOT �

Cbackup)=3.• BS4: four battery packs, all with different capacities:CTOT=3,CTOT=4, CTOT=5, and13 � CTOT=60.

Table I quantifies the lifetime (defined as the time in which a fully-charged battery gets completely exhausted and expressed, here andin the sequel, in seconds) achieved when sequential discharge is used


Fig. 3. Capacity variation for different batteries.

under the various loading conditions and for all the four battery subsys-tems. lifetime decreases from 7.0% (best case) to 32.3% (worst case).

Notice, that in general for a battery subsystem consisting ofN

packs, there is a total ofN ! different ways of performing sequentialdischarging. However, the order of discharge is relevant only forpartitioned power supplies containing packs of different capacitiesand nonconstant load profiles. For these cases, the table reports thebest lifetime results we have obtained after considering all possiblecombinations.

From the data of the experiments, we observe that sequential dis-charge is a highly suboptimal solution from the lifetime point of viewif compared to the achievable lifetime guaranteed by the monolithicbattery. The explanation for this fact can be found in the diagram ofFig. 3, where the variation of battery capacity for increasing load cur-rents is plotted for a battery of capacity 1.35 Ah (top curve) and for abattery of capacity 0.675 Ah (bottom curve). If we consider a given loadcurrent, for example, 0.5 A, the usable capacity corresponding to thebattery of 1.35 Ah is 1.138 Ah. On the other hand, the usable capacitycorresponding to the battery of 0.675 Ah, at the same load current, is0.528 Ah. Therefore, the usable capacity of two batteries of 0.675Ah,when discharged sequentially, is: 2� 0.528 Ah= 1.056 Ah, whichis approximately 7% smaller than the corresponding usable capacityof the monolithic battery. The intuitive explanation for this behavior isthat, for a given value of the load, a battery with smaller nominal ca-pacity is subject to a capacity loss which is higher than for a batterywith higher nominal capacity. For example, in the case of the 0.5 Acurrent, the ratio between the nominal and the usable capacity of the0.675 Ah battery is 1.28, while it is smaller (i.e., 1.18) for the 1.35 Ahbattery.

We observe that sequential discharging does not take advantage atall of the fact that a battery can recover some of its charge if it is givensome rest time, as shown in the diagram of Fig. 2.

Therefore, the problem we address in this paper is that of deciding,given a multibattery subsystem, how rest times can be scheduled for thevarious packs such that the recovery effect can be maximally exploited.In other words, we are interested in finding which battery pack shouldbe connected to the load at any point in time, and for how long, during

TABLE IISTATIC SCHEDULING LIFE-TIME RESULTS(10 s TIME SLICE)

TABLE IIISTATIC SCHEDULING LIFE-TIME RESULTS(2 s TIME SLICE)

system operation in order to make the overall power supply lastinglonger. We define this problem as thebattery schedulingproblem.

A more abstract formulation of the problem amounts to that of clas-sical scheduling problems, and consists of viewing the set of batterypacks as divided into two subsets: 1) consists of one battery only (theone connected to the load) and 2) includes all the batteries “ready” tobe connected to the load. Scheduling implies a decision on when to re-place the discharging battery and which battery to connect to the load.

In the following, we introduce two battery scheduling solutions thatconsiderably improve the simple (and inefficient) sequential dischargescheme. The two solutions manage the alternance of idle and activetimes of each battery using different criteria.

IV. STATIC SCHEDULING

The first category of scheduling algorithms we propose uses time asthe criterion that drives the decision on which battery must be selectedfor replacement. This implies detaching a battery from the load after agiven time has elapsed, and replacing it with the battery that has rested


(a)

(b)

Fig. 4. Battery lifetime versus switching frequency.

for the longest period of time. We call this policystatic scheduling; theterm “static” emphasizes the fact that no physical quantity related tothe battery subsystem is involved in the choice.

In static scheduling, batteries are discharged following around-robinscheme. Each battery stays connected to the load for a fixed amount oftime, then it is disconnected. It will be used again after all other batterieshave been discharged for their assigned period of time.

Policies of this class are characterized by two parameters: the orderin which batteries are discharged and the time period (ortime slice)during which each battery is connected to the load. AssumingN batterypacks andM time slices each pack can be assigned, there is a total ofN ! � M

N possible static schedulings that should be explored. Some

pruning of the search space must then be adopted, the simplest beingthe choice of a single time slice for all batteries. In this case, the numberof schedulings to be explored reduces toN !.

In order to evaluate the performance of static scheduling, we haverun a set of experiments using the same battery subsystems and cur-rent workloads as in Section III. Table II shows the lifetime resultsfor the case of a time slice of 10 s for all the packs in each batterysubsystem. For each combination of power supply configuration andworkload, only the best result is shown (out of theN ! that have been ex-plored). Data show sensible improvements over sequential discharging(see Table I), due to the exploitation of the rest times. The gap with re-spect to the lifetime provided by the monolithic battery is in the range


(c)

(d)

Fig. 4. (Continued). Battery lifetime versus switching frequency.

[3.1%–31.1%], and it is notably smaller than what we observed for se-quential discharging.

The choice of a time slice of 10 s for the previous experiment wastotally arbitrary. Therefore, in order to acquire some further insight onhow the choice of the frequency at which the various battery packs mustbe connected/disconnected from the load, we have run the same exper-iment with a shorter time slice, namely 2 s. Table III collects the resultsof the exploration. We notice that lifetime degradation with respect tothe monolithic battery has further decreased with the reduction of thetime slice, and it is now in the range of 1.1%–24.5%. This consistentlifetime increase over all battery systems and load profiles suggeststhat further decreasing the time slice value may improve lifetime ac-

cordingly. We have therefore completed this analysis by determiningthe lifetimes for the four battery configurations as a function of the in-verse of the time slice (i.e., the switching frequency,fsw). The plots ofFig. 4(a)–(d) show the corresponding results for the case of a constantcurrent of 0.5 A (i.e., workloadCCa).

All the curves exhibit the same trend: whenfsw is very low, thebatteries are discharged in sequence and lifetime is minimum. Thiscorresponds to sequential discharging. Asfsw increases, lifetimeincreases as well, and it asymptotically tends to the lifetime pro-vided by a monolithic battery with double capacity (i.e., 1.35 Ahrin the plots). This behavior is consistently observed for all the fourbattery subsystems.


The bottom line of this exploration is that, in principle, a multibatterysystem using a static scheduling policy where batteries are switchedwith an ideally infinite frequency will perform as if an equivalent (i.e.,with equal total capacity) monolithic battery is attached to the load. Nobetter solution can be found, no matter what type of current load orcomposition of the battery subsystem.

To support a static scheduling scheme with a high-switchingfrequency, a high-switching battery selector is required. Commerciallyavailable battery selectors are used for the sequential dischargingpolicies of Section III: that is, they connect a load to a battery withswitching periods in the order of the lifetime of a single battery. Batteryselectors working at high switching frequencies can be built quiteeasily, and their use introduces negligible overheads in performanceand power; yet, commercial implementations of these kinds of devicesare not very wide-spread, and should be customarily designed.

V. DYNAMIC SCHEDULING

The second category of scheduling policies we propose uses specificbattery information to drive battery selection. This information can berelated to the physical state of the batteries, and can be expressed bythe output voltage, the state-of-charge, or the elapsed discharge time.Clearly, the chosen representative quantity should be observable at thebattery interface to allow the practical implementation of the policy.

We classify this class of policies asdynamic scheduling. Dynamicscheduling no longer assumes a unique time slice being assigned toeach battery pack. Rather, each battery is discharged for a differentamount of time depending on the quantity that is observed.

We note that in principle, there is no guarantee that dynamic sched-uling outperforms the static approach. However, the former holds theadvantage of adapting the rest time which is given to each battery packto the actual conditions of the various batteries. Therefore, it is likelyto provide a finer tuning of the times in which charge recovery cantake place, and may then be more effective for battery subsystems con-taining packs of different capacities.

For our experiments, we use the output voltage of each battery asthe quantity to be monitored. Then, disconnection from the load of thecurrently active pack takes place as soon as its voltage drops below agiven threshold.

The selection of the next battery to be discharged allows several de-grees of freedoms. Possible strategies can be based on either the actualstate of charge of the various battery packs or the rest time each packhas been given at any point in time. The value of the threshold, whichis specified as a percentage of the output voltage the battery pack holdsat the time it is connected to the load and starts delivering the current,may also be critical, and should then be chosen with care.

After a battery pack is disconnected, it must be given some rest timein order to let it recover some of its charge, and then it must be resched-uled. A strategy is then needed for choosing the next battery pack tobe connected to the load. We have experimented with the followingpolicies:

• Vmax: select the battery pack with highest state of charge.• Vmin: select the battery pack with lowest state of charge.• Tmax: select the battery pack that has been unused for the longest

time.• Tmin: select the battery that has been unused for the shortest time.

If more than one battery is eligible for selection, the initial capacityof the pack is used as first-level tie-breaker (i.e., the battery with largercapacity is chosen), while random selection is used if further ties occur.

Independently of the chosen policy, once the next battery pack isselected, a check is performed to make sure that a minimum rest timehas elapsed for such battery. If this is not the case, the next battery

TABLE IVRESULTS: DYNAMIC SCHEDULING

in the schedule is selected, and the one that missed its turn will bereconsidered when a new selection will take place.

We observe that the dynamic policyTmax is, in practice, very similarto static scheduling, with the difference that disconnection from theload of the active battery pack is voltage-driven rather than time-driven.

As already mentioned, the dynamic selection policies automaticallyprevent the scheduling of a battery if a rest time greater than or equalto a given value has not elapsed. Then, if a threshold voltage very closeto 100% is chosen, dead-lock conditions may occur (i.e., none of thebatteries can be selected), because switching between batteries maytake place too often. The choice of the threshold voltage is then critical.

For our experiments, a threshold of 95% of the voltage of the cur-rently active battery has been used for all the packs. This value waschosen because it was the highest value in the range (90%–99%) thatavoided the occurrence of dead-lock situations for all the workloads andall the power supply configurations. Table IV reports all the results.

The data tell that policyVmax is generally better than the others, ex-cept for one case whereTmax gives the same result (battery systemBS2 with workloadCCa). In general, we notice that the lifetime de-crease with respect to the case of a monolithic power supply is in therange of [2.5%–30.4%]. By comparing these values to those providedby static scheduling we observe that, in some cases, the latter are better.This happens primarily for battery systems in which all packs have thesame capacity; in these cases, switching at constant times helps in op-timizing charge extraction.

On the other hand, dynamic scheduling is more flexible and it is thusmore appropriate in providing the best performance in the case of het-erogeneous battery subsystems and highly irregular current profiles, asthose occurring in power-managed applications. This can be observed,for example, for battery systemBS4, where lifetimes obtained withdynamic scheduling are in almost all cases longer than those of staticscheduling.

We also note that, for the two-battery configuration (i.e.,BS1), allpolicies yield exactly the same scheduling. This is due to the fact thata battery pack cannot be scheduled as the next battery of itself, since aminimum rest time is imposed.

VI. CONCLUSION

Manufacturing and cost constraints force the producers of modernelectronic appliances to adopt multipack batteries as power supplies. Ithas been shown that a partitioned battery in which the components areconnected in sequence to the load (i.e., a new pack comes in use onlyafter the active one is exhausted), as done in commercially availablesystems, is sensibly suboptimal with respect to the lifetime obtainedwith a monolithic battery of equal total capacity.

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 11, NO.6, DECEMBER 2003 1143

Some preliminary experiments have proven that a proper manage-ment of the partitioned power supply may help in recovering part ofthe usable capacity which is lost because of the splitting.

We have, therefore, introduced the concept of battery scheduling(i.e., the policy used to connect and disconnect the packs of a multi-battery power supply to the current load during system operation), andproposed two alternative scheduling algorithms, characterized by in-creasing efficiency and complexity.

On average, we have observed that static and dynamic schedulingallow system lifetime to increase significantly with respect to conven-tional sequential discharging, and to close the gap between partitionedand monolithic power supplies down to 1% in the best case. Regardingthe pros and cons of the two scheduling approaches (i.e., static versusdynamic), experiments have shown that static is preferable when thebattery system is more homogeneous (that is, battery packs have sim-ilar capacities), while dynamic works better in the case of battery sys-tems containing asymmetric cells and nonuniform workloads.

REFERENCES

[1] Intel. System management bus. [Online]. Available: http://www.smbus.org.

[2] Compaq, Intel, Microsoft, Phoenix, and Toshiba. Advanced configura-tion and power interface. [Online]. Available: http://www.teleport.com/acpi.

[3] Philips. Inter-IC (I C) bus. [Online]. Available: http://www-us.semi-conductors.com/i2c.

[4] O2Micro. Intelligent charger. [Online]. Available: http://www.o2micro.com/products.

[5] Mitsubishi Semiconductors. General-purpose smart battery charger/selector IC. [Online]. Available: http://www.mitsubishichips.com/prod-ucts/assps/assp.htm.

[6] T. L. Martin, “Balancing batteries, power and performance: System is-sues in CPU speed-setting for mobile computing,” Ph.D. dissertation,Dept. Elect. Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, Aug.1999.

[7] M. Doyle, T. F. Fuller, and J. Newmann, “Modeling of galvanostaticcharge and discharge of the lithium/polymer/insertion cell,”J. Electro-chemical Society, vol. 140, no. 6, pp. 1526–1533, June 1993.

[8] T. Martin and D. Sewiorek, “A power metric for mobile systems,”in Proc.: ACM/IEEE Int. Symp. Low-Power Electronics and Design(ISLPED), Monterey, CA, Aug. 1996, pp. 37–42.

[9] M. Pedram and Q. Wu, “Battery-powered digital CMOS design,” inProc. IEEE Design Automation and Test (DATE), Munich, Germany,Mar. 1999, pp. 72–76.

[10] M. Pedram and Q. Wu, “Design considerations for battery-powered elec-tronics,” inProc. ACM/IEEE Design Automation Conf. (DAC), New Or-leans, LA, June 1999, pp. 861–866.

[11] L. Benini, G. Castelli, A. Macii, E. Macii, M. Poncino, and R. Scarsi,“Discrete-time battery models for system-level low-power design,”IEEE Trans. VLSI Syst., vol. 9, pp. 630–640, Oct. 2001.

[12] S. C. Hageman, “Simple PSpice models let you simulate common bat-tery types,”EDN, pp. 117–132, Oct. 1993.

[13] S. Gold, “A PSPICE macromodel for lithium-ion batteries,” inProc.12th Ann. Battery Conf. Applications and Advances, Jan. 1997, pp.215–222.

A Clock Interconnect Extractor for MultigigahertzFrequencies Incorporating Inductance Effect

M. A. Azadpour and T. S. Kalkur

Abstract—Due to decreasing device sizes and increasing clock speed, in-terconnect inductance is becoming an important factor in the on-chip delayanalysis of deep submicrometer technologies. This delay has been repre-sented as anRCmodel in the available electric design automation tools. Inthis paper, we model the on-chip interconnect as aRLC for systems run-ning at multigigahertz frequencies. A static-extraction analysis method op-timized for ASICs is detailed. It considers all the lines within the vicinity ofthe target signal line as return paths.

Index Terms—Delay, extraction software, static analysis, VLSI intercon-nect.

I. INTRODUCTION

The increase in complexity of integrated circuits (ICs) and the emer-gence of system on chips (SoCs) in the recent years has led to a needfor smaller device sizes and more densely packed ICs [1]. On-chip in-terconnects have become the dominant factor in determining the max-imum speed of a system. This fact has complicated the clock distribu-tion design methodologies more than any other signal in an IC today.It is more important than ever before to model and analyze the clockdistribution trees accurately for VLSI systems running at over 1 GHz[2]. This need is the driving force for the analysis presented here. Asa result, most of the discussion presented here focuses on clock in-terconnects. However, the same principle can be applied to any tar-geted signal line in order to accurately analyze the corresponding signalinterconnect.

The clock wireload has been traditionally modeled as anRCinterconnect by computer-aided design (CAD) extraction tools.As system-wide clock frequencies increase beyond 1 GHz, lineinductance begins to influence the performance of clock distributionnetworks [3]–[5]. This on-chip inductance affects both the clocksignal delay and power dissipation. The other effects of interconnectinductance include signal ringing, signal reflection, and additionalinductance crosstalk under fast slew rate [6]. Therefore, it is importantto include the effects of inductance in multigigahertz clock distributiontree analysis.

A clock distribution tree can be constructed from a combination ofinterconnect wires and buffers. Various papers, such as [4] explore theplacement of buffers to balance the clock load seen at the source. Sincethere is extensive literature on the placement of buffers, here the focusis on clock trees made of interconnecting wires. However, the analysiscan easily be extended to include buffers. First, each interconnectingsection between two buffers is modeled by the extracted values fromthe presented analysis. Next, cell models of the buffers are added to theextracted netlist and the complete netlist is analyzed for delay calcula-tion purposes.

First, we will focus on the available inductance extraction tools.Then, we will concentrate on extracting the “L” element of intercon-nectRLCparasitic. Finally, we will perform analysis on the extracteddata.

Manuscript received August 15, 2002; revised January 23, 2003.M. A. Azadpour is with the Vitesse Semiconductor Corporation, Colorado

Springs, CO 80907 USA (e-mail: [email protected]).T. S. Kalkur is with the Department of Electrical and Computer Engineering,

University of Colorado, Colorado Springs, CO 80933 USA.Digital Object Identifier 10.1109/TVLSI.2003.817544

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Scheduling battery usage in mobile systems