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AN10808 thermal consideration of nx p flatpower mega schottky barrier rectifiers - selection criteria rev. 2 ? 12 february 2013 application note document information info content keywords flatpower mega schottky barrier re ctifiers, thermal consideration, selection criteria abstract this application note describes how to select a medium power schottky barrier rectifier from the nxp flatpower package family.
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 2 of 17 contact information for more information, please visit: http://www.nxp.com for sales office addresses, please send an email to: salesaddresses@nxp.com nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria revision history rev date description 2 20130212 section 4 ? product portfolio ? added 1 20100629 initial version
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 3 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 1. introduction nxp semiconductors offers a wide variety of me dium power schottky ba rrier rectifiers in different packages and with rated parameters like voltages, current and power capabilities. this application note has the following purposes: ? present the basics of nxp semiconductors schottky barrier rectifiers product range ? review and explain the data sheet parameters ? give design recommendation for the worst-case operating point 2. description of nxp semiconduc tors flatpower schottky barrier rectifiers 2.1 data sheet parameters the data sheet gives different parameter values. 2.1.1 limiting values v r = maximum reverse voltage the maximum allowable reverse voltage, without exceeding the given reverse currents. i f(av) = maximum average forward current the maximum allowable forward current, under a specific condition. i fsm = maximum non-repetitive peak forward current single current pulse, from t j =25 ? c before surge. after cooling down to t j =25 ? c, the next event is allowed. fig 1. pmeg nomenclature pmeg 30 20 b er nxp mega schottky barrier rectifier max. reverse voltage in v e.g. 30 = 30 v cont. forward current in a e.g. 20 = 2.0 a variant number (optional) package indicator: sod128 sot1061 sod123w p pa r internal configuration: c common cathode e single
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 4 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria p tot = total power dissipation maximum total power dissipation at 25 ? c ambient temperature on different standard nxp conditions. t j = junction temperature maximum allowable junction temperature, usually 150 ? c, for nxp discrete bipolar products. t amb = ambient temperature maximum allowable ambient temperature, usually 150 ? c, for nxp discrete bipolar products. t stg = storage temperature maximum allowable storage temperature under msl1 conditions. 2.1.2 thermal characteristics r th(j-a) = thermal resistance from junction to ambient r th(j-a) =r th(j-sp) +r th(sp?a) the r th(sp-a) value depends on the printed-circuit board (pcb) material and on the footprint, layout and surrounding environmental conditions. therefore, in the data sheets nxp semiconductors indicates on which substrate the values were measured. r th(j-sp) = thermal resistance from junction to solder point the r th(j-sp) value is essentially independent of the external component, like pcb, footprint and solder. it is sensitive to the die size, the leadframe, the die-bonding method and the mold compound of the package. the values of r th(j-sp) are measured from the cathode lead. 2.1.3 electrical characteristics v f = forward voltage typical values under different forward current conditions. i r = reverse current typical values under different reverse voltage conditions. c d = diode capacitance typical diode capacitance under diff erent reverse voltage conditions.
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 5 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 3. pmeg flatpower schottky barr ier rectifier selection criteria circuit performance and long-term reliability are affected by the tem perature of the die. electrical power dissipated in any semiconducto r device is a source of heat. this source increases the temperature of the die above the reference point of 298.15 k | 25 ? c| 77 ? f. 3.1 temperature limits the increase in temperatur e depends on the power capa bility of the device and the thermal resistance of the complete system (smd + pcb). it can be described as follow: (1) heat transfer can occur by radi ation, conduction and convection. surface-mounted devices (smd) loose most of their heat by conduction when mounted on a substrate. the heat conducts from the junction via the package leads and the soldering connections to the substrate. some heat radiates from the package into the ambient, where it disappears by convection or by active cooling air. the heat from the substrate disappears in the same way. the thermal resistance from junction to ambient can be described as follow: (2) calculating the maximum power capability, the following temper atures must be taken into account: ? maximum junction temperature t j(max) ? maximum solder point temperature t sp(max) ? ambient temperature t amb as an example, the limiting factors of the sod123w package are shown by the pmeg3020er in the following sections. p tot t jmax ?? t amb ? r th j a ? ?? ---------------------------------- - = r th j a ? ?? r th j sp ? ?? r th sp a ? ?? + =
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 6 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 3.1.1 fr4 pcb, single-sided copper, tin-plated and standard footprint ? maximum junction temperature t j(max) =150 ? c | 423.15 k ? thermal resistance from junction to ambient r th(j-a) =220k/w ? thermal resistance from ju nction to solder point r th(j-sp) =18k/w (3) (4) (5) to avoid issues, like solder cracks or degradation of the solder, nxp strongly recommends: t sp(max) ? 125 ? c 3.1.2 fr4 pcb, single-sided copper, tin-plated and mounting pad for cathode 1 cm 2 ? maximum junction temperature t j(max) =150 ? c | 423.15 k ? thermal resistance from junction to ambient r th(j-a) =130k/w ? thermal resistance from ju nction to solder point r th(j-sp) =18k/w (6) (7) (8) this behavior is shown in figure 9 and figure 10 of the data sheet pmeg3020er. to avoid issues, like solder cracks or degradation of the solder, nxp strongly recommends: t sp(max) ? 125 ? c 3.2 pulse mode in pulse mode, like in dc-to-dc converter, the thermal resistance from junction to ambient is a variable. in order to give hardware designers the opportunity for best performance design, nxp?s pmeg data sheets provide thermal impedance graphs at different footprint conditions. p tot max ?? t jmax ?? t amb ? r th j a ? ?? ---------------------------------- - 423 15k ? 298 15k ? ?? ? 220 k w ---- - ------------------------------------------------------- 057w ? == = t sp t jmax ?? p tot max ?? r th j sp ? ?? ? ?= t sp 423 15k ? 057w ? 18 k w ---- - ? ? 412 15k 139 ? c 282 2 ? f ? ?? ? == p tot max ?? t jmax ?? t amb ? r th j a ? ?? ---------------------------------- - 423 15k ? 298 15k ? ?? ? 130 k w ---- - ------------------------------------------------------- 096w ? == = t sp t jmax ?? p tot max ?? r th j sp ? ?? ? ?= t sp 423 15k ? 096w ? 18 k w ---- - ? ? 405 87k 133 ? c 271 4 ? f ? ?? ? ==
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 7 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 3.2.1 fr4 pcb, single-sided copper, tin-plated and standard footprint 3.2.2 fr4 pcb, single-sided copper, tin-plated, 1 cm 2 cathode mounting pad fr4 pcb, standard footprint fig 2. pmeg3020er: transient thermal impedance from junc tion to ambient as a function of pulse duration; typical values 006aab284 10 1 10 2 10 3 z th(j-a) (k/w) 10 ? ? ? ? fr4 pcb, mounting pad for cathode 1 cm 2 fig 3. pmeg3020er: transient thermal impedance from junction to ambient as a function of pulse duration; typical values 006aab285 10 1 10 2 10 3 z th(j-a) (k/w) 10 ? ? ? ?
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 8 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 3.2.3 example the correct use of the thermal impedance graphics is very important. in order to show how to use the z th graph the right way, the i f(av) value from the corresponding graphic i f(av) vs t amb (see figure 4 ) is verified. i f(av) is calculated as follows: (9) i m = peak current ? = duty cycle (10) t 1 = pulse duration t 2 = cycle duration fr4 pcb, standard footprint t j =150 ? c (1) ? =1; dc (2) ? = 0.5; f = 20 khz (3) ? = 0.2; f = 20 khz (4) ? = 0.1; f = 20 khz fig 4. pmeg3020er: average forward current as a function of ambient temperature; typical values t amb (c) 0 50 100 150 175 125 75 25 006aab292 1 2 3 i f(av) (a) 0 (1) (2) (3) (4) i fav ? ?? i m ?? = ? t 1 t 2 --- - =
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 9 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria for ? = 0.5 and f = 20 khz: ? t 1 =25 ? s (pulse duration) = t p (s) ? t 2 =50 ? s (cycle duration) approximate the z th(j-a) value from the graph at ? = 0.5 and calculate the maximum power dissipation with the formula: (11) so, there is an ?improvement? in p tot by factor 2 under pulsed condition. fig 5. duty cycle definition t 1 t 2 p t 006aaa812 duty cycle = t 1 t 2 fr4 pcb, standard footprint fig 6. transient thermal impedance from junction to am bient as a function of pu lse duration; typical values 006aab612 10 1 10 2 10 3 z th(j-a) (k/w) 10 ?1 t p (s) 10 ?3 10 2 10 3 10 1 10 ?2 10 ?1 duty cycle = 1 0.75 0.5 0.33 0.25 0.2 0.1 0.05 0.02 0.01 0 p tot max ?? t jmax ?? t amb ? z th j a ? ?? ---------------------------------- - 423 15k ? 298 15k ? ?? ? 100 k w ---- - ------------------------------------------------------- 125w ? == =
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 10 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria from this, i f(av) can be calculated with the equation 11 and the typical v f value taken from the data sheet: (12) (13) this result fits with the graphic i f(av) vs t amb (see figure 4 ). so thermal and electrical parameters are essential factors for the selection of the right pmeg schottky barrier rect ifier under considerations. changing the package (bigger package size, bigger silic on die, better thermal performance) fulfill easier t he requirements than increa sing the cooling pad area. 3.3 conclusion the characteristics given in the data sheet, help choosing the right pmeg schottky barrier rectifier. the most critical question in hardware design is the maximum allowable p tot capability. data sheet parameters are a good instrument to compare different products under standard conditions. the worst-case scenario of an application can be calculated from the z th graphs and r th(j-a) values. after that the right nxp pmeg schottky barrier rectifier for design can be selected. i m p tot max ?? v f --------------------- 125w ? 0 365v ? ------------------ - 34a ? === i fav ?? i m ?? 17a ? ==
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 11 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 4. product portfolio table 1. product portfolio with t j = 150 ?c type number v r i f i fsm(max) v f(max) at i f i r(max) at v r package aec-q101 pmeg2010er 20 v 1 a 50 a 340 mv 1.00 ma sod123w yes pmeg2010ber 20 v 1 a 50 a 450 mv 0.05 ma sod123w yes pmeg3010er 30 v 1 a 50 a 360 mv 1.50 ma sod123w yes pmeg3010ber 30 v 1 a 50 a 450 mv 0.05 ma sod123w yes pmeg3010ep 30 v 1 a 50 a 360 mv 1.50 ma sod128 yes pmeg3010bep 30 v 1 a 50 a 450 mv 0.05 ma sod128 yes pmeg3020er 30 v 2 a 50 a 420 mv 1.50 ma sod123w yes pmeg3020ber 30 v 2 a 50 a 520 mv 0.05 ma sod123w yes pmeg3020ep 30 v 2 a 50 a 360 mv 3.00 ma sod128 yes pmeg3020bep 30 v 2 a 50 a 450 mv 0.10 ma sod128 yes pmeg3020cep 30 v 2 a 50 a 420 mv 1.50 ma sod128 yes pmeg3020dep 30 v 2 a 50 a 520 mv 0.05 ma sod128 yes pmeg3030ep 30 v 3 a 50 a 360 mv 5.00 ma sod128 yes pmeg3030bep 30 v 3 a 50 a 450 mv 0.15 ma sod128 yes pmeg3050ep 30 v 5 a 70 a 360 mv 8.00 ma sod128 yes pmeg3050bep 30 v 5 a 70 a 450 mv 0.25 ma sod128 yes pmeg4010er 40 v 1 a 50 a 490 mv 0.05 ma sod123w yes pmeg4010ep 40 v 1 a 50 a 490 mv 0.05 ma sod128 yes pmeg4020er 40 v 2 a 50 a 490 mv 0.10 ma sod123w yes pmeg4020ep 40 v 2 a 50 a 490 mv 0.10 ma sod128 yes pmeg4030er 40 v 3 a 50 a 540 mv 0.10 ma sod123w yes pmeg4030ep 40 v 3 a 50 a 490 mv 0.20 ma sod128 yes pmeg4050ep 40 v 5 a 70 a 490 mv 0.30 ma sod128 yes pmeg6010er 60 v 1 a 50 a 530 mv 0.06 ma sod123w yes pmeg6010ep 60 v 1 a 50 a 530 mv 0.06 ma sod128 yes pmeg6020er 60 v 2 a 50 a 530 mv 0.15 ma sod123w yes pmeg6020ep 60 v 2 a 50 a 530 mv 0.15 ma sod128 yes pmeg6030ep 60 v 3 a 50 a 530 mv 0.20 ma sod128 yes table 2. product portfolio with t j = 175 ?c type number v r i f i fsm(max) v f(max) at i f i r(max) at v r package aec-q101 pmeg4010etr 40 v 1 a 50 a 490 mv 0.05 ma sod123w yes pmeg4010etp 40 v 1 a 50 a 490 mv 0.05 ma sod128 yes pmeg4020etr 40 v 2 a 50 a 490 mv 0.10 ma sod123w yes pmeg4020etp 40 v 2 a 50 a 490 mv 0.10 ma sod128 yes pmeg4030etp 40 v 3 a 70 a 490 mv 0.20 ma sod128 yes pmeg4050etp 40 v 5 a 50 a 530 mv 0.30 ma sod128 yes pmeg6010etr 60 v 1 a 50 a 530 mv 0.15 ma sod123w yes pmeg6020etr 60 v 2 a 50 a 530 mv 0.15 ma sod123w yes
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 12 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria pmeg6020etp 60 v 2 a 50 a 530 mv 0.15 ma sod128 yes pmeg6030etp 60 v 3 a 50 a 530 mv 0.20 ma sod128 yes pmeg6045etp 60 v 4.5 a 70 a 530 mv 0.40 ma sod128 yes table 2. product portfolio with t j = 175 ?c ?continued type number v r i f i fsm(max) v f(max) at i f i r(max) at v r package aec-q101
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 13 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 5. appendix 5.1 average value (14) for the given square-wave signal: (15) (16) in general, for square wave as simplification: (17) in general, for full-wave sinusoidal signal as simplification: (18) in general, for triangle signal as simplification: (19) i fav ?? 1 t -- - it ?? td 0 t ? = i fav ?? 1 t -- - it ?? t d0 + ?? 0 t2 ? ? = i fav ?? i05 ?? = i fav ?? i m ?? = i fav ?? 2i m ? ? -------------- - = i fav ?? i m ? 2 -- - ? =
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 14 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 5.2 root mean square value (20) (21) for the given square wave: (22) (23) (24) in general, for square waves: (25) in general, for full-wave sinusoidal signal as simplification: (26) in general, for triangle signal as simplification: (27) i rms i fav ?? 2 = i rms 1 t -- - it ?? 2 td 0 t ? = i rms 1 t -- - it ?? 2 t d0 + ?? 0 t2 ? ? = i rms i m 2 t 2t ------ ? = i rms i m 05 ? = i rms i m ?? = i rms i m 2 ------ - = i rms i m ? 3 -- - ? =
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 15 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 6. references [1] philips semiconductors ? power semiconductors, applications handbook 1995 [2] nxp semiconductors ? product data sheet pmeg3020er, rev. 01, 29 december 2008
AN10808 all information provided in this document is subject to legal disclaimers. ? nxp b.v. 2013. all rights reserved. application note rev. 2 ? 12 february 2013 16 of 17 nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria 7. legal information 7.1 definitions draft ? the document is a draft versi on only. the content is still under internal review and subject to formal approval, which may result in modifications or additions. nxp semiconductors does not give any representations or warranties as to the accuracy or completeness of information included herein and shall hav e no liability for the consequences of use of such information. 7.2 disclaimers limited warranty and liability ? information in this document is believed to be accurate and reliable. however, nxp semiconductors does not give any representations or warranties, expressed or implied, as to the accuracy or completeness of such information and shall have no liability for the consequences of use of such info rmation. nxp semiconductors takes no responsibility for the content in this document if provided by an information source outside of nxp semiconductors. in no event shall nxp semiconductors be liable for any indirect, incidental, punitive, special or consequential damages (including - without limitation - lost profits, lost savings, business interruption, costs related to the removal or replacement of any products or rework charges) whether or not such damages are based on tort (including negligence), warranty, breach of contract or any other legal theory. notwithstanding any damages that customer might incur for any reason whatsoever, nxp semiconductors? aggregate and cumulative liability towards customer for the products described herein shall be limited in accordance with the terms and conditions of commercial sale of nxp semiconductors. right to make changes ? nxp semiconductors reserves the right to make changes to information published in this document, including without limitation specifications and product descriptions, at any time and without notice. this document supersedes and replaces all information supplied prior to the publication hereof. suitability for use ? nxp semiconductors products are not designed, authorized or warranted to be suitable for use in life support, life-critical or safety-critical systems or equipment, nor in applications where failure or malfunction of an nxp semiconductors product can reasonably be expected to result in personal injury, death or severe property or environmental damage. nxp semiconductors and its suppliers accept no liability for inclusion and/or use of nxp semiconductors products in such equipment or applications and therefore such inclusion and/or use is at the customer?s own risk. applications ? applications that are described herein for any of these products are for illustrative purpos es only. nxp semiconductors makes no representation or warranty that such applications will be suitable for the specified use without further testing or modification. customers are responsible for the design and operation of their applications and products using nxp semiconductors products, and nxp semiconductors accepts no liability for any assistance with applications or customer product design. it is customer?s sole responsibility to determine whether the nxp semiconductors product is suitable and fit for the customer?s applications and products planned, as well as fo r the planned application and use of customer?s third party customer(s). customers should provide appropriate design and operating safeguards to minimize the risks associated with their applications and products. nxp semiconductors does not accept any liability related to any default, damage, costs or problem which is based on any weakness or default in the customer?s applications or products, or the application or use by customer?s third party customer(s). customer is responsible for doing all necessary testing for the customer?s applic ations and products using nxp semiconductors products in order to av oid a default of the applications and the products or of the application or use by customer?s third party customer(s). nxp does not accept any liability in this respect. export control ? this document as well as the item(s) described herein may be subject to export control regulations. export might require a prior authorization from competent authorities. evaluation products ? this product is provided on an ?as is? and ?with all faults? basis for evaluati on purposes only. nxp semico nductors, its affiliates and their suppliers expressly disclaim all warranties, whether express, implied or statutory, including but not limited to the implied warranties of non-infringement, merchantability and fitness for a particular purpose. the entire risk as to the quality, or arising out of the use or performance, of this product remains with customer. in no event shall nxp semiconductors, its affiliates or their suppliers be liable to customer for any special, indirect, consequential, punitive or incidental damages (including without limitation damages for loss of business, business interruption, loss of use, loss of data or information, and the like) arising out the use of or inability to use the product, whether or not based on tort (including negligence), strict liability, breach of contract, breach of warranty or any other theory, even if advised of the possibility of such damages. notwithstanding any damages that customer might incur for any reason whatsoever (including without limitat ion, all damages referenced above and all direct or general damages), the entire liability of nxp semiconductors, its affiliates and their suppliers and custom er?s exclusive remedy for all of the foregoing shall be limited to actual damages incurred by customer based on reasonable reliance up to the greater of the amount actually paid by customer for the product or five dollars (us$5.00) . the foregoing limitations, exclusions and disclaimers shall apply to the ma ximum extent permitted by applicable law, even if any remedy fails of its essential purpose. 7.3 trademarks notice: all referenced brands, produc t names, service names and trademarks are the property of their respective owners.
nxp semiconductors AN10808 nxp flatpower mega schottky rectifier - thermal selection criteria ? nxp b.v. 2013. all rights reserved. for more information, please visit: http://www.nxp.com for sales office addresses, please se nd an email to: salesaddresses@nxp.com date of release: 12 february 2013 document identifier: AN10808 please be aware that important notices concerning this document and the product(s) described herein, have been included in section ?legal information?. 8. contents 1 introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 description of nxp semiconductors flatpower schottky barrier rectifiers . . . . . . . . . . . . . . . . . 3 2.1 data sheet parameters . . . . . . . . . . . . . . . . . . . 3 2.1.1 limiting values . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 thermal characteristics. . . . . . . . . . . . . . . . . . . 4 2.1.3 electrical characteristics . . . . . . . . . . . . . . . . . . 4 3 pmeg flatpower schottky barrier rectifier selection criteria . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1 temperature limits . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 fr4 pcb, single-sided copper, tin-plated and standard footprint . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 fr4 pcb, single-sided copper, tin-plated and mounting pad for cathode 1 cm 2 . . . . . . . . . . . . 6 3.2 pulse mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2.1 fr4 pcb, single-sided copper, tin-plated and standard footprint . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.2 fr4 pcb, single-sided copper, tin-plated, 1cm 2 cathode mounting pad . . . . . . . . . . . . . . 7 3.2.3 example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 product portfolio . . . . . . . . . . . . . . . . . . . . . . . 11 5 appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.1 average value. . . . . . . . . . . . . . . . . . . . . . . . . 13 5.2 root mean square value . . . . . . . . . . . . . . . . 14 6 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 7 legal information. . . . . . . . . . . . . . . . . . . . . . . 16 7.1 definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7.2 disclaimers . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7.3 trademarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 16 8 contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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