_.
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`x
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`“SFIPR
`
`INTEL 1012
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`

`

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`

`

`DN&82>naSFDob=a=.
`
`me=3oO
`
`

`

`Editor-in-Chief
`Dr. Frank Toolenaar
`Philips Research Laboratories, Eindhoven, The Netherlands
`
`SCOPE TO THE ‘PHILIPS RESEARCH BOOK SERIES’
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`This ‘Philips Research Book Series’ has been set up as a wayfor Philips researchers to
`contribute to the scientific community by publishing their comprehensive results and
`theories in bookform.
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`Philips Research
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`VOLUME1
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`Ad Huijser
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`

`

`
`
`
`Battery Management Systems
`Design by Modelling ©
`
`
`
`
`
`
`
`
`
`
`
`
`by
`
`Henk Jan Bergveld
`WandaS. Kruijt
`Peter H.L. Notten
`
`Philips Research Laboratories,
`Eindhoven, The Netherlands
`
`
`
`r n
`
`, The Netherlands
`
`ES’
`
`lishments in the world, Philips
`ons that meet peoples’ needs and
`fits of these inventions end up on
`and technological basis usually
`
`1a wayfor Philips researchersto
`their comprehensive results and
`
`
`
`
`
`
`
`KLUWER ACADEMIC PUBLISHERS
`DORDRECHT / BOSTON / LONDON
`
`
`
`

`

`
`
`he Library of Congress.
`
`lishers,
`letherlands.
`
`South America
`ts,
`L, U.S.A.
`
`ributed
`ition Center,
`Netherlands.
`
`inagement Systems
`
`ustration of the use
`
`shers
`
`rieval system,or transmitted
`
`yhotocopying, microfilming,
`on from the Publisher,
`ically for the purpose of
`2m, for exclusive use
`kK
`
`To Peggy, Bert and Pascalle
`
`
`
`
`
`
`
`

`

`A C.LP. Cataloguerécord for hispeokisavailable from the Library of Congress.
`
`as
`
`tani “2
`Ger SU
`
`ISBN 1-4020-0832-5
`
`Published by Kluwer Academic Publishers,
`P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
`
`Sold and distributed in North, Central and South America
`by Kluwer Academic Publishers,
`101 Philip Drive, Norwell, MA 02061, U.S.A.
`
`In all other countries, sold and distributed
`by Kluwer Academic Publishers, Distribution Center,
`PO. Box 322, 3300 AH Dordrecht, The Netherlands.
`
`Printed on acid-free paper
`
`Explanation of cover:
`The cover showsa transparent battery as an illustration of the use
`of battery models for the design of Battery Management Systems
`designed by Hennie Alblas
`
`All Rights Reserved
`© 2002 Kluwer Academic Publishers
`No part of this work may be reproduced, stored in a retrieval system, or transmitted
`in any form or by any means, electronic, mechanical, photocopying, microfilming, .
`recording or otherwise, without written permission from the Publisher,
`with the exception of any material supplied specifically for the purpose of
`being entered and executed on a computer system, for exclusive use
`by the purchaser of the work.
`
`Printed in the Netherlands.
`
`200232F69
`
`

`

`Table of contents
`
`List of abbreviations
`
`List of symbols
`
`Series preface
`
`Preface
`
`1. Introduction
`
`1.1 The energy chain
`1.2 Definition of a Battery Management System
`1.3 Motivation of the research described in this book
`1.4 Scope ofthis book
`1.5 References
`
`Battery Management Systems
`
`2.1 A general Battery Management System
`2.2 Battery Management System parts
`2.2.1.
`The Power Module (PM)
`2.2.2
`The battery
`2.2.3.
`The DC/DC converter
`2.2.4
`The load
`2.2.5
`The communication channel
`2.3 Examples of Battery Management Systems
`2.3.1
`Introduction
`2.3.2 Comparison of BMS in a low-end and
`high-end shaver
`Comparison of BMS in two typesofcellular
`phones
`2.4 References
`
`2.3.3
`
`Basic information on batteries
`
`3.1 Historical overview
`3.2 Battery systems
`3.2.1
`Definitions
`3.2.2
`Battery design
`3.2.3.
`Battery characteristics
`
`Vil
`
`Xill
`
`Xxi
`
`XXill
`
`NnBWre
`
`10
`10
`14
`
`18
`19
`19
`22
`
`22
`
`22
`
`25
`29
`
`31
`
`31
`33
`33
`35
`36
`
`

`

`Vitl
`
`3.3 General operational mechanism ofbatteries
`3.3.1
`Introduction
`3.3.2
`Basic thermodynamics
`3.3.3. Kinetic and diffusion overpotentials
`3.3.4 Double-layer capacitance
`3.3.5
`Battery voltage
`3.4 References
`
`Battery modelling
`
`4.1 General approach to modelling batteries
`4.1.1
`Chemical and electrochemical potential
`4.1.2 Modelling chemical and electrochemicalreactions
`4.1.3 Modelling mass transport
`4.1.4 Modelling thermal behaviour
`4.2 A simulation model of a rechargeable NiCd battery
`4.2.1
`Introduction
`4.2.2
`The nickel reaction
`4.2.3.
`The cadmium reactions
`4.2.4
`The oxygen reactions
`4.2.5
`Temperature dependence of the reactions
`4.2.6
`The model
`4.3 A simulation model of a rechargeable Li-ion battery
`4.3.1
`Introduction
`43.2
`The LiCoO,electrode reaction
`4.3.3
`The LiC, electrode reaction
`4.3.4
`The electrolyte solution
`4.3.5
`Temperature dependence of the reactions
`4.3.6
`The model
`4.4 Parameterization of the NiCd battery model
`4.4.1
`Introduction
`44.2 Mathematical parameter optimization
`4.4.3
`Results and discussion
`4.4.4 Quality of the parameter set presented in section
`4.4.3 underdifferent charging conditions
`Results obtained with a modified NiCd battery
`model anddiscussion
`4.5 Simulation examples
`4.5.1
`Simulations using the NiCd model presented in
`section 4.2
`Simulations using the Li-ion model presented in
`section 4.3
`4.6 Conclusions
`4.7 References
`
`4.5.2
`
`44.5
`
`43
`
`43
`44
`
`45
`50
`52
`52
`
`55
`
`55
`
`59
`67
`
`82
`86
`86
`89
`92
`97
`102
`103
`107
`107
`108
`113
`117
`118
`118
`
`124
`124
`126
`131
`
`138
`
`144
`149
`
`149
`
`155
`162
`165
`
`

`

`5. Battery charging algorithms
`
`5.1.3.
`
`5.1 Charging algorithms for NiCd and NiMHbatteries
`5.1.1
`Charging modes, end-of-charge triggers and
`chargerfeatures
`5.1.2 Differences between charging algorithms
`for NiCd and NiMHbatteries
`Simulation example: an alternative charging
`algorithm for NiCd batteries
`5.2 Charging algorithm for Li-ion batteries
`5.2.1.
`The basic principle
`5.2.2
`The influence of charge voltage on the
`charging process
`The influence of charge current on the
`charging process
`Simulation example: fast charging of a
`Li-ion battery
`5.3 Conclusions
`5.4 References
`
`5.2.3
`
`5.2.4
`
`169
`
`169
`
`169
`
`175
`
`177
`184
`184
`
`186
`
`187
`
`188
`191
`192
`
`193
`
`6. Battery State-of-Charge indication
`
`193
`6.1 Possible State-of-Charge indication methods
`193
`6.1.1
`Definitions
`195
`6.1.2 Direct measurements
`199
`6.1.3
`Book-keeping systems
`202
`6.1.4 Adaptive systems
`203
`6.1.5
`Some remarks on accuracy andreliability
`204
`6.2 Experimental tests using the bq2050
`204
`6.2.1
`Operation of the bq2050
`206
`6.2.2
`Set-up of the experiments
`208
`6.2.3
`Results and discussion
`211
`6.2.4
`Conclusions of the experiments
`6.3 Direct measurements for Li-ion batteries: the EMF method 212
`6.3.1
`Introduction
`212
`6.3.2
`EMF measurement methods
`212
`6.3.3. Measured and simulated EMF curves for the
`214
`CGR17500 Li-ion battery
`219
`Conclusions
`6.3.4
`6.4 A simple mathematical model for overpotential description 219
`6.5 Proposed set-up for State-of-Charge system
`225
`6.5.1
`The algorithm
`225
`6.5.2
`Comparison with the bq2050 system
`229
`6.5.3.
`Comparison with systems found in the literature
`230
`
`

`

`6.6 Experimentaltests with the system proposed in section 6.5 231
`6.6.1
`Introduction
`231
`6.6.2
`Set-up of the experiments
`231
`6.6.3.
`Experimental results
`232
`6.6.4 Discussion of the results
`235
`6.6.5
`Conclusions of the experiments
`237
`6.7 Conclusions
`238
`6.8 References
`239
`
`. Optimum supply strategies for Power Amplifiers
`in cellular phones
`241
`
`241
`245
`246
`250
`251
`252
`253
`255
`
`267
`
`269
`
`7.1 Trends in cellular systems
`7.2 The efficiency control concept
`7.2.1
`Basic information on Power Amplifiers
`7.2.2 Optimum supply voltage for optimum efficiency
`7.3 DC/DC conversion principles
`7.3.1
`Linear voltage regulators
`7.3.2
`Capacitive voltage converters
`7.3.3
`Inductive voltage converters
`7.3.4
`EMI problems involved in capacitive and
`258
`inductive voltage converters
`Inductive voltage conversion for efficiency control 258
`7.3.5
`7.4 Simulation model derivation
`258
`7.4.1.
`DC/DC down-converter
`258
`74.2
`Power Amplifier
`260
`7.5 Theoretical benefits of efficiency control
`261
`7.5.1
`Sinnulation set-up
`262
`7.5.2
`Results and discussion
`263
`7.5.3.
`Conclusions
`265
`7.6 Experimental results obtained with a CDMA PA
`266
`7.6.1. Measurementset-up
`266
`7.6.2 Measurementresults and discussion ofpart 1:
`no DC/DC converter
`7.6.3. Measurementresults and discussion of part 2:
`with DC/DC converter
`Estimation of talk time increaseina
`complete CDMAcellular phone
`7.7 Application ofefficiency control in a GSM cellular phone
`7.7.1.
`GSM powercontrol protocol
`7.7.2 Modifications in the Spark GSM phone
`7.7.3 Measurementresults and discussion
`7.7.4
`Conclusions of the experiments
`7.8 Conclusions
`7.9 References
`
`7.6.4
`
`271
`274
`274
`276
`279
`281
`281
`282
`
`

`

`8. General conclusions
`
`About the authors
`
`Index
`
`Xl
`
`285
`
`289
`
`291
`
`

`

`Optimum supply strategies for Power Amplifiers in cellular phones
`
`251
`
`e
`
`only has to take a limited range of supply voltages into account during the
`design, as opposed to a whole range of supply voltages when the PA is
`connecteddirectly to the battery. This advantage already holds when a DC/DC
`converter with a fixed output voltage is used.
`The PA designer can choose the optimum nominal supply voltage when a
`DC/DCconverter is present in the system anyway. Impedance transformationis
`neededto be able to transmit at the desired output power, as was explainedin
`section 7.2.1.
`(7.2) shows that
`the higher the nominal supply voltage for
`maximum output power is chosento be, the higher the load observed by the PA
`will be allowedto be andthe lowerthe ratio of the 50 Q antenna impedance and
`the impedance Riga observed at the PA side will become. This lowers the losses
`in the impedance transformation network, because the parasitic resistances in
`this network are now smallerrelative to Rigag.
`
`The implementation ofefficiency control in a cellular phone does not imply drastic
`changesto the transmit architecture. An example for a GSM phonewill be given in
`section 7.7.
`The transmit path needs to be sufficiently linear when the cellular system
`employs non-constant envelope modulation; see section 7.1. Full swing RF signals
`at the output of the PA are then not allowed, because saturation of the output
`transistor will
`lead to an unacceptable level of non-linearity.
`In that case, a
`somewhat higher value than that found from (7.6) and (7.7) has to be chosen for
`Vsupop This will
`lead to a smaller improvement
`in efficiency. A quantitative
`example will be given in section 7.6, which showsthat a considerable improvement
`can still be realized in practice.
`
`7.3. DC/DC conversion principles
`In general, two approaches exist for converting one voltage into another. Thefirst
`approachinvolves a time-continuouscircuit with a dissipative element, whereas the
`second approach involves a time-discrete circuit with an energy-storage element.
`The first approach is only suitable for converting a higher voltage into a lower
`voltage, which is down-conversion, whereas the second approach enables up- and
`down-conversion. The two approaches are illustrated in Figure 7.5, in which the
`battery voltage V;,, is converted into V,,,.
`
`Leaci
`
`Vv in
`
`I
`
`Vout
`
`Energy-
`storage
`element
`
`Figure 7.5: Two approaches to convert a battery voltage into another voltage. (a): Time-
`continuous with dissipative element (Vi, > Vo. only) (b) Time-discrete with energy-storage
`element
`
`

`

`252
`
`Chapter 7
`
`The dissipative element in Figure 7.5a remains connected between the battery and
`the load. The efficiency of the voltage conversion will always be lower than 100%,
`because of its dissipative nature. The energy-storage element in Figure 7.5b is first
`connected to the battery to store energy, after whichit is connected to the load to
`supply this energy. The efficiency ofthe voltage conversion process 1s 100% in the
`theoretical case in which no energy is lost
`in the energy-storage element and
`switches. The type of time-discrete voltage converter employed and the char-
`acteristics of the employed componentswill determine the efficiency in practice. An
`energy buffer C;,/ is necessary, because of the time-discrete nature of converters of
`this type.
`
`Linear voltage regulators
`7.3.1
`The configuration of Figure 7.5a is commonly knownas a linear voltage regulator
`[8]. A more detailed schematic representation ofa linear voltage regulator is shown
`in Figure 7.6. It consists of a transistor, which may be of any type, controlled by a
`regulator, which compares a fraction of Vo, with a reference voltage V,.. Linear
`regulators vary in the used type of transistor and its drive circuit. The transistor is
`operated in the saturation region in the case of FETs and the linear region in the case
`of bipolar transistors. This means that the output current /,,,, and hence Vous Will
`hardly change whenV,, changes. However, a certain minimum voltage difference
`Vin-Vous Which is the dropout voltage, hastobe present for proper operation. A
`simple resistor represents the load in Figure 7.6.
`Figure 7.6 illustrates that the maximum efficiency 77 is the ratio of V4, and Vin.
`A decrease from this maximumvalue is caused by the current consumptionof the
`linear voltage regulator itself, including the opamp, voltage reference and current
`through R; and R2. Hence, Jou, is smaller than lin. The efficiency of the linear voltage
`regulator will be higher in the case of smaller differences between V;, and Vou, as
`can be understood from theratio. Therefore, the term Low DropOut regulator (LDQ)
`is often encountered in practice when a low voltage drop can be accommodated, the:
`term ‘low’ being a relative term.
`
`'i1tt'‘‘'''1't'1tl‘
`
`
`enaLe
`‘Linear voltage
`
`regulator
`
`
`
`
`
`
`
`Vout
`
`Vin > Vout
`
`1 = Pout/PinS Vout/Vin
`(Vin — Vout)min = dropout voltage
`
`Load
`
`i lout
`
`Figure 7.6: Basic schematic representation of a linear voltage regulator
`
`Linear voltage regulators are encountered in portable devices whenthe difference
`between the battery and load supply voltages is not toohigh, because the efficiency
`will then still be acceptable. An advantage oflinear regulators is that they are cheap
`and small because they do not need an energy-storage element, which usually takes
`
`

`

`Optimumsupply strategies for Power Amplifters in cellular phones
`
`253
`
`up quite some volume. Linear regulators are often used as filters, because variations
`in V,, are suppressed in V,,,. Although not included in Figure 7.6, small capacitors
`with values specified in the data sheet are added to the input and output ofa linear
`voltage regulator in practice. The output capacitor improves the response to load
`changes and usually implements regulator loop frequency compensation.
`
`Capacitive voltage converters
`7.3.2
`A converter as shown in Figure 7.5b has to be used whenthere is a large difference
`between the battery voltage and the voltage needed by the load, or when the load
`voltage should be higher than the battery voltage. The energy-storage elements can
`either be capacitive or
`inductive. The basic principle of a capacitive voltage
`converter is shown in Figure 7.7. Such a configuration is commonly referred to as a
`charge pump. The switches are operated from a non-overlapping clock signal with
`periods ®, and ®,. The capacitors are connected in parallel to the battery for the up-
`converter for period @®, and each capacitor is charged to the battery voltage. The
`capacitors are connected in series for period @,, added to the battery voltage, and
`connected. to the output buffer capacitor C,,,. At no load, this leads to an output
`voltage Vic=(n+1} Vin, where n is the numberof capacitors.
`
`"<VoutVout
`
`Yo,
`
`Load
`
`eSH
`
`g
`
`<3
`
`
`
` | |
`
`
`
`(b)
`
`Figure 7.7: Basic schematic representation of a capacitive voltage converter: (a) Voltage up-
`converter (b) Voltage down-converter
`
`The capacitors are connected in series for the down-converter for period @; and the
`total
`series connection is charged to the battery voltage. The capacitors are
`connected in parallel for period ®, and connected to the output buffer capacitor Co.
`This leads to an output voltage V,,,=V;,/n at zero load, with n being the number of
`
`

`

`254
`
`Chapter 7
`
`capacitors. By combining parallel and series connections for periods ©, and @,,
`non-integer conversionfactors can berealized.
`
`Efficiency considerations
`Considerthe charging of an ideal capacitor by a voltage source V through a switch S
`with an on-resistance Rs. Thisis illustrated in Figure 7.8, from which the following
`equation can be derived for the energy E¢(t) stored in C as a function of timet:
`
`Ee) = [Vc(t)I(t)dt = CV" e* —Zet +1
`
`-2r
`
`-t
`
`t
`
`0
`
`Andfor the energy Ex(t) dissipated in Rs as a function oftimet:
`
`E,(t) = [V,()1@)dt = 5cv as
`
`t
`
`0
`
`ot
`
`(7.8)
`
`(7.9)
`
`+ Vr (t) -
`Rs
`Te
`
`C==
`
`+
`Ve (t)
`
`+
`
`tL
`
`4
`I(t) = ae er
`Va(t) =Vre*
`Volt) =V- (1 -e°)
`t=RsC
`
`Figure 7.8: Charging a capacitor C by a voltage source V through a switch S$ with an on-
`resistance Rs
`
`E({t) and Ep(t) both become Emar= %CV’ when t approaches infinity. This means
`that,
`irrespective of the value of Rs, equal amounts of energy are stored and
`dissipated. This also holds when Rs is zero or is not constant. Thelatter case occurs,
`when the capacitor C is charged througha transistor. Table 7.3 shows the course in
`time of E¢(t) and E,(t). For clarity,
`these energies have been normalized to the
`maximum energy Ejnay.
`
`Table 7.3: Normalized energies E(t) and Eg(t) and normalized voltage V;(t)/V at normalized
`times t/t
`
`3
`
`Ve(tYV [%]
`
`Ec(t)/Emax [%]
`5
`
`Ep(t)/Emax [%]
`
`Table 7.3 showsthat storing the first 5% of Emax Causes an energy loss of 39.7% of
`Emax in Rs. However, when the same amount ofenergy is stored starting at 90%
`(90% —>95% of Emax), the energy loss is only 0.2% of Exma,. Hence, although the
`
`

`

`Optimum supplystrategies for Power Amplifiers in cellular phones
`
`255
`
`energy storage occurs fast at the beginning of charging, because it only takes 0.25t
`to store the first 5% of E,,o,, it is rather inefficient. Theefficiency is 5/(5+39.7) =
`11.2%. The efficiency increases to 5/(5+0.2)=96.2% when Vc approaches its end
`value of V, but it takes 0.711 to store 5% of E,,., from 90% to 95%. This meansthat
`the capacitors should be charged (almost) to the source voltage V in order to have a
`high efficiency and the capacitance should be high, so that the voltage drop is
`minimalin the discharge period. Hence, only a fraction of the stored energy is active
`in the transfer process.
`The frequency at which the energy is transferred or the amountof the energy
`that is transferred each cycle need to increase when the required output powerof the
`charge pumpis high. The combination of high efficiency and high power leads to
`very large capacitance values, because storing energy takes more timeat the end of
`the charging process. These large capacitors cannot be integrated with the switches
`and control circuitry on a single IC in practice. External capacitors should be used
`instead. Whenefficiency is not a big issue and/or the load current is small, smaller
`capacitors can be used, which creates the possibility of integrating them.
`
`Inductive voltage converters
`7.3.3
`The basic principle of using an inductive voltage converter is depicted in Figure 7.9.
`This type of converter is generally referred to as a DC/DC converter. As with ca-
`pacitive converters, up-conversion and down-conversion of the battery voltage are
`possible. The time-discrete nature of the two converters can be clearly recognized by
`the switches.
`
`Vin < Vout
`
`S2
`
`Vin
`
`
`:
`L
`TIL )
`°
`|
`Cou1g
`|
`
`Si
`
`Vout
`
`| Load
`
`Vin > Vout
`
`Vout
`
`
`
`Load
`
`(a)
`
`(b)
`
`Figure 7.9: Basic schematic representation of an inductive voltage converter: (a) Voltage up-
`converter (b) Voltage down-converter
`
`Switch S, is closed first and energy is stored in the inductor for both the up- and the
`down-converters. The inductor current ramps up linearly in the ideal case of zero
`series resistance. Switch S; is opened at a certain moment, depending on the desired
`ratio of V;, and V,,, and the value of the load. The current will flow through the
`diode D, because the inductor current cannot change instantly, and the polarity of
`the voltage across the inductor changes, which leads to a decrease in the energy
`stored in the inductor and the current will ramp down accordingly. The energy that
`wasstored in the inductor for the period when S, conducted will now be transferred
`to the output buffer capacitor C,,,. Switch Sz is not strictly necessary in either case.
`
`

`

`256
`
`Chapter 7
`
`Whenit conducts in the second phase,the efficiency will be higher than without the
`switch, since the voltage across diode D will be lower than without the bypass
`switch. Bypassing the diode by switch Sz is commonly referred to as synchronous
`rectification.
`The waveform of the current through the inductor is shown in Figure 7.10 for
`both the up- and the down-converter. For simplicity, it is assumed that the inductor
`current is never zero. This is called continuous conduction mode, as opposed to
`discontinuous conduction mode, in whichthe inductor current decreases to zero each
`switching cycle. The depicted waveform is valid for a high-efficiency converter, in
`which the voltage drop across the switches during current conduction can be
`neglected.
`
`
`
`Figure 7.10: Inductor current J, for the converters of Figure 7.9 in continuous conduction
`mode with ideal switches
`
`The conduction period of S; is 6T. The duty cycle dis defined as the ratio of the
`time for which S, conducts and the total switching time T and has a value 0<d<].
`As a consequence, S, conducts for a period (J-6)-T. In steady-state, in which case the
`input voltage, load current and duty cycle are fixed, all the energy that was stored in
`the inductor for the period &T will be transferred to C,,, during (1-6):T. This means
`that
`the Voltsecond product
`for
`the coil
`is
`equal
`in both periods, or
`V,(6T) & T=V,((1-5)T)(1-6) T. For the up-converter, this leads to:
`
`]
`V
`Vor =V.-V, Yl-6FTa= 7.10
`
`in
`
`( out
`
`un X
`
`i
`
`Vi
`
`l= 6
`
`(
`
`)
`
`whereas for the down-converterit leadsto:
`
`Wa
`(V,, -V,,, OT = Vout (-éV=> V =6
`in
`
`(7.11)
`
`(7.10) and (7.11) illustrate that the ratio of V,, and V,,, can be controlled by
`controlling the duty cycle 6. The ratio of the output and input voltages is greater than
`unity in the case of the up-converter and smaller than unity in the case of the down-
`converter, because 0<d<1. An up/down-converter can be constructed by combining
`the configurations of Figure 7.9a and b. Four switches are necessary in that case and
`
`

`

`Optimum supply strategies for Power Amplifiers in cellular phones
`
`257
`
`two conducting switches are always present in the current path. This leads to an
`efficiency that is poorer than that of single up- or down-converters, because then
`only one conducting switch is present in the current path.
`The number of components needed to achieve a certain ratio of V;, and Vog is
`much smaller than in the case of capacitive converters. Only the inductor and diode
`are realized with external componentsin practice and the switches andthe controller
`can be integrated. Another difference is that the ratio of V,, and V,,, in inductive
`converters can be changed by controlling 6. In the case of a capacitive converter, the
`circuit topology has to be changed to achieve this or additional losses must be
`introduced in the form of an additional
`linear voltage regulator. Moreover, an
`essential difference between capacitive and inductive voltage converters is the effi-
`ciency of energy storage.
`
`Efficiency considerations
`Consider the storage of energy in an ideal inductor L from a voltage source V
`through a switch S with an on-resistance Rs. A voltage source is again to be
`considered, because this book deals with batteries as power sources and a battery
`can be regardedas a voltage source. This is shownin Figure 7.11.
`
`—___-
`
`Va
`
`()—-
`
`pa
`Te
`
`LS
`
`7
`v(t
`J
`
`at
`
`+t
`
`My = (1 -e*)
`Va(t) =V «(1 -e*)
`Vii) =V-ie*
`i=
`
`z
`vG
`7
`
`Figure 7.11: Charging an inductor L by a voltage source V through a switch S with an on-
`resistance Rs
`
`The energy E,(t) stored in L as a function oftime ¢ can be obtained from:
`
`E,(t)=[V,lat = Sur. et —2e* +1
`
`a
`
`=
`
`ft
`
`0
`
`(7.12)
`
`where J=V/Rs. When t approachesinfinity, the energy stored equals Emax= LP. The
`energy Ep(t) dissipated in R as a function oftimetis obtained from:
`
`Eq (t) = [Ve (t)I(t)dt = 1°Rs - 1-427 ae z
`
`0
`
`-t
`
`-2¢t
`
`(7.13)
`
`An important difference with respect to a capacitive converter is that E(t) can be
`made zero when Ry is made zero. Hence, energy can bestored in an inductor from a
`voltage source with 100% efficiency in the ideal case when Rs is zero, as opposed to
`storing energy in a capacitor from a voltage source, in which case a certain amount
`of energy of “2CV’ is alwayslost, irrespective of the value of Rs, when the capacitor
`is charged from 0 V to a voltage V. This meansthat inductive voltage converters can
`
`

`

`258
`
`Chapter 7
`
`achieve a 100% efficiency with ideal components. Thisis not the case for capacitive
`converters. This holds for a voltage source as input, which is the case in battery-
`powered equipment. Inductive voltage converters are for this reason found in many
`portable products.
`Although an efficiency of 100% is theoretically possible with an inductive
`voltage converter,
`losses will occur in practice, resistive and capacitive losses.
`Resistive losses are caused by series resistance in the current path, for example an
`Equivalent Series Resistance (ESR) of the inductor and on-resistances of the
`switches. Moreover, each switch has a parasitic capacitance, which leads to
`capacitive switching losses in practice.
`
`EMI problemsinvolvedin capacitive and inductive voltage converters
`7.3.4
`The time-discrete voltage converters can cause Electro-Magnetic Interference
`(EMI), for example, due to voltage ripple on the output buffer capacitor caused by
`the ESR,or due to current loops with varying currents that span a significant area.
`These problems can be avoided bycarefully choosing the components,filtering and
`Printed-Circuit Board (PCB) layout. An output voltage control scheme with a fixed
`switching frequency outside the frequency bands of interest could also be
`considered. A linear regulator often follows an inductive voltage converter when the
`load is highly sensitive to EMI, as in RFcircuitry in cellular phones. The voltage
`difference across the linear regulator should be kept low for efficiency reasons, as
`discussed earlier. However,
`the linear regulator has the advantage of offering
`additional filtering [9]. Moreover, the addition of a linear voltage regulator to the
`output of an inductive voltage up-converter implies the possibility of realizing a
`voltage up/down-converter [10]. Finally, one should realize that the output spectrum
`of a down-converter will be more favourable than that of an up-converter. The
`reason is the difference in shape and frequency content of the current that flows
`through the output capacitor for both converter types.
`
`Inductive voltage conversion forefficiency control
`7.3.5
`The battery voltage has to be converted into a variable PA supply voltage for
`efficiency control; see section 7.2. An inductive voltage converter is most suitable
`for this from an efficiency point of view. Moreover, the ratio of Vin and Vy, can be
`_ controlled relatively easily. This makes it easy to change from one converter output
`voltage to another. However,the influence of voltage ripple at the converter output
`on the PA’s RF behaviour should be carefully investigated. This will be discussed in
`sections 7.6 and 7.7.
`
`7.4 Simulation model derivation
`
`Simple simulation models for a DC/DC down-converter and a PA will be derivedin
`this section. Both models will be used in section 7.5 to compare different supply
`Strategies of a PA by meansofsimulation.
`
`7.4.1.
`
`DC/DC down-converter
`
`The efficiency of a DC/DC converteris obtained from:
`
`

`

`781 063 A
`
`|l| iwi
`
`781402°008320
`
`ISBN 1-4020-0832~5
`
`Win
`
`