I E C 63 ® Edition 201 7-06 I N TE RN ATI ON AL S TAN D ARD colour i n sid e Wi re l ess power tran sfe r – Ai rfu e l al l i an ce res on an t base l i n e s ys te m s pe ci fi cati on IEC 63028:201 7-06(en) (B S S ) T H I S P U B L I C AT I O N I S C O P YRI G H T P RO T E C T E D C o p yri g h t © I E C , G e n e v a , S wi tz e rl a n d All rights reserved Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either IEC or IEC's member National Committee in the country of the requester If you have any questions about I EC copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or your local I EC member National Committee for further information IEC Central Office 3, rue de Varembé CH-1 21 Geneva 20 Switzerland Tel.: +41 22 91 02 1 Fax: +41 22 91 03 00 info@iec.ch www.iec.ch Ab ou t th e I E C The I nternational Electrotechnical Commission (I EC) is the leading global organization that prepares and publishes I nternational Standards for all electrical, electronic and related technologies Ab o u t I E C p u b l i ca ti o n s The technical content of IEC publications is kept under constant review by the IEC Please make sure that you have the latest edition, a corrigenda or an amendment might have been published I E C Catal og u e - webstore i ec ch /catal og u e The stand-alone application for consulting the entire bibliographical information on IEC International Standards, Technical Specifications, Technical Reports and other documents Available for PC, Mac OS, Android Tablets and iPad I E C pu bl i cati on s s earch - www i ec ch /search pu b The advanced search enables to find IEC publications by a variety of criteria (reference number, text, technical committee,…) It also gives information on projects, replaced and withdrawn publications E l ectroped i a - www el ectroped i a org The world's leading online dictionary of electronic and electrical terms containing 20 000 terms and definitions in English and French, with equivalent terms in additional languages Also known as the International Electrotechnical Vocabulary (IEV) online I E C G l os sary - s td i ec ch /g l oss ary 65 000 electrotechnical terminology entries in English and French extracted from the Terms and Definitions clause of IEC publications issued since 2002 Some entries have been collected from earlier publications of IEC TC 37, 77, 86 and CISPR I E C J u st Pu bl i s h ed - webstore i ec ch /j u stpu bl i sh ed Stay up to date on all new IEC publications Just Published details all new publications released Available online and also once a month by email I E C C u stom er S ervi ce C en tre - webstore i ec ch /csc If you wish to give us your feedback on this publication or need further assistance, please contact the Customer Service Centre: csc@iec.ch I E C 63 ® Edition 201 7-06 I N TE RN ATI ON AL S TAN D ARD colour i n sid e Wi rel ess power tran sfe r – Ai rfu el al l i an ce res on an t basel i n e s ys tem s peci fi cati on (B S S ) INTERNATIONAL ELECTROTECHNICAL COMMISSION ICS 29.240.99; 33.1 60.99; 35.200 ISBN 978-2-8322-4429-6 Warn i n g ! M ake s u re th a t you ob tai n ed th i s p u b l i cati on from an au th ori zed d i stri b u tor ® Registered trademark of the International Electrotechnical Commission –2– I EC 63028: 201 I EC:201 CONTENTS FOREWORD I NTRODUCTI ON Scope Norm ative references Terms, definitions, symbols and abbreviated term s Terms and definitions Sym bols and abbreviated terms 3 Symbols 3 2 Abbreviated term s System description Conform ance and backwards com patibility Device types PTU classification PRU category 20 Power transfer specifications 20 System equivalent circuit and reference param eters 20 General system requirem ents 21 Operating frequency 21 2 ZTX_I N relationship to R RECT 21 Power stability 21 PTU co-location protection 21 PRU self-protection (inform ative) 21 Resonator requirem ents 21 Resonator coupling efficiency (RCE) 21 PTU resonator requirem ents 22 3 PRU resonator requirem ents 24 Load parameters 25 Load param eters introduction 25 Minim um load resistance 26 Maxim um allowable d ynamic load 26 4 Maxim um load capacitance 26 Power control specifications 26 Control objectives 26 PTU specifications 26 PTU state 26 2 General state requirem ents 27 PTU power save state 28 PTU Low Power state 30 PTU Power Transfer state 31 PTU Configuration state 33 PTU Local Fault state 34 8 PTU latching fault state 34 PTU state transitions 35 PTU Test Mode 38 PRU specifications 38 PRU general requirements 38 I EC 63028: 201 I EC: 201 –3– PRU state model 41 8 3 Null state 42 PRU boot 42 PRU On state 42 PRU System Error state 43 PRU state transitions 44 Signaling specifications 45 Architecture and state diagrams 45 Architecture 45 Overall charge process 46 Charge procedure and requirements 48 Removing PRU from WPT network 48 2 Power Sharing mode 48 Bluetooth low energy requirements 49 Bluetooth low energ y requirements introduction 49 Bluetooth low energ y obj ectives 49 3 PTU hardware requirement 49 PRU hardware requirement 49 Basic network structure 49 RF requirem ents 49 Timing and sequencing requirem ents 50 Profile structure 53 BLE profile definition 53 GATT sub-procedure 53 Configuration 53 PRU requirements 54 4 PTU requirem ents 55 Connection establishm ent 55 Security considerations 57 Charge com pletion 57 WPT service characteristics 58 WPT service characteristics introduction 58 PRU advertising payload 58 WPT service 60 PRU control 62 5 PTU static param eter 64 PRU static parameter characteristic 69 PRU d ynamic parameter characteristic 72 PRU alert characteristic 76 Cross connection algorithm 78 Cross connection algorithm introduction 78 Definitions 78 Acceptance of advertisem ent 78 I m pedance shift sensing 78 Reboot bit handling 79 6 Time set handling 79 Mode transition 80 Mode transition introduction 80 Mode transition procedure 80 –4– I EC 63028: 201 I EC:201 BLE reconnection procedure 81 PTU resonators 83 1 PTU resonators introduction 83 Class n design template 83 Class n design tem plate introduction 83 2 Table of specifications 83 PTU resonator structure 83 Approved PTU resonators 83 Annex A (informative) Reference PRU for PTU acceptance testing 84 A Category 84 A Category 84 A Category 84 A 3.1 PRU design 3-1 84 A 3.2 Geometry 84 A Category 87 A Category 87 Annex B (informative) Lost power 88 B Overview 88 B General 88 B Cross connection issues 88 B Handoff issues 88 B Power noise issues 89 B PTU lost power calculation 89 B 6.1 Lost power detection threshold 89 B 6.2 Lost power detection speed 89 B 6.3 PTU lost power calculation 89 B 6.4 PTU power transmission detection accuracy 89 B 6.5 PRU lost power reports 89 B 6.6 Accuracy of reported power 90 B 6.7 Other PRU lost power reports 90 Annex C (norm ative) User experience requirem ents 91 C General 91 C User indication 91 C PRU user indication 91 C 2 PTU user indication 91 Annex D (inform ative) RCE calculations 92 D RCE calculation (using S-param eters) 92 D RCE calculation (using Z-param eters) 93 D Series tuned case 94 D 2 Other RCE calculations 94 D Conversion between S-param eters and Z-param eters 94 Figure Figure Figure Figure Figure – Wireless power transfer system – PTU-PRU resonator PTX_I N – PTU-PRU resonator P RX_OUT 20 – Equivalent circuit and system param eters 20 – PTU resonator-load considerations 24 I EC 63028: 201 I EC: 201 –5– Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure – PTU state model 27 – Beacon sequences 29 – Load variation detection 29 – Discovery 30 – PTU ITX transition responses 31 1 – PRU state m odel 41 – VRECT operating regions 42 – Basic architecture of WPT system 45 – Basic state procedure (inform ative) 47 – Registration period tim eline exam ple (inform ative) 52 – PTU/PRU services/characteristics comm unication 54 – PRU mode transition – Device Address field set to a non-zero value 81 – PRU mode transition – Device Address field set to all zeros 82 A – PRU design block diagram 84 A – Front view 85 A – Back view 85 A – Side view 86 A – Front view, coil onl y 86 A – Side view, coil onl y 86 Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table – PTU classification – PRU category 20 – Minim um RCE (percent and dB) between PRU and PTU 22 – Maxim um load capacitance 26 – Tim e requirement to enter PTU Power Transfer state 28 – Sub-state of PTU Power Transfer 32 – PTU latching faults 37 – Exam ple of accuracy of reported current 41 – PRU system errors 45 – RF budget (informative) 50 1 – Timing constraints 52 – BLE profile characteristics 53 – GATT sub-procedure 53 – PRU advertising payload 58 – I m pedance shift bit 60 – WPT service UU I D 60 – WPT service 61 – GAP service 62 – GATT service 62 20 – PRU Control Characteristic 63 21 – Detail: bit field for enables 63 22 – Detail: bit field for perm ission 64 23 – Detail: bit field for time set 64 –6– Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table I EC 63028: 201 I EC:201 24 – PTU reporting static values to PRU 65 25 – Detail: bit field for optional fields validity 65 26 – PTU power 66 27 – Max source impedance 67 28 – Max load resistance 68 29 – AirFuel protocol revision field 69 30 – PTU number of devices 69 31 – PRU reporting static values to the PTU 70 32 – Detail: bit field for optional fields validity 70 33 – Detail: bit field for PRU inform ati on 71 34 – PRU d ynam ic param eter characteristic 73 35 – Detail: bit field for optional fields validity 73 36 – Detail: bit field for PRU alert 75 37 – Detail: bit field for PRU alert 76 38 – Test mode commands 76 39 – PRU alert fields 77 40 – Detail: bit field for PRU alert notification 77 41 – Mode transition 78 A – PRU table of specifications 84 I EC 63028: 201 I EC: 201 –7– INTERNATI ONAL ELECTROTECHNI CAL COMMISSI ON WI RE L E S S P O WE R T R AN S F E R – AI RF U E L AL L I AN C E RE S O N AN T B AS E L I N E S YS T E M S P E C I F I C AT I O N (B S S ) FOREWORD ) The I nternati on al Electrotechni cal Comm ission (I EC) is a worl d wid e organization for stan dardization com prisin g all n ation al el ectrotechnical comm ittees (I EC National Comm ittees) The object of I EC is to prom ote internati onal co-operation on all questions concerni ng stand ardi zati on in the el ectrical an d electronic fields To this end and in additi on to other acti vities, I EC publish es I nternational Stan dards, Techn ical Specifications, Technical Reports, Publicly Avail abl e Specifications (PAS) an d Gui des (hereafter referred to as "I EC Publication(s)") Thei r preparation is entrusted to technical comm ittees; any I EC Nati on al Comm ittee interested in the subj ect dealt with m ay partici pate in this preparatory work I nternational, governm ental an d n on governm ental organ izations l iaising with th e I EC also participate i n this preparation I EC collaborates closel y with the I ntern ational Organi zation for Stand ardization (I SO) in accordance with ditions determ ined by agreem ent between th e two organi zati ons 2) The form al decisions or ag reem ents of I EC on tech nical m atters express, as n early as possible, an i nternati onal consensus of opi nion on the rel evant subjects since each technical com m ittee has representati on from all interested I EC N ational Com m ittees 3) I EC Publications have the form of recomm endations for intern ational use an d are accepted by I EC National Com m ittees in that sense While all reasonable efforts are m ade to ensure that the tech nical content of I EC Publications is accu rate, I EC cann ot be h eld responsi ble for th e way in which th ey are used or for an y m isinterpretation by an y en d u ser 4) I n order to prom ote intern ational uniform ity, I EC National Com m ittees und ertake to apply I EC Publications transparentl y to the m axim um extent possible i n their national an d regi on al publicati ons Any d ivergence between an y I EC Publication and the correspondi ng national or regi on al publicati on sh all be clearl y in dicated in the latter 5) I EC itself d oes n ot provi de an y attestation of conform ity I n dependent certificati on bodies provi de conform ity assessm ent services and, in som e areas, access to I EC m arks of conform ity I EC is not responsi ble for an y services carri ed out by ind ependent certification bodi es 6) All users shou ld ensure that th ey have the l atest editi on of thi s publicati on 7) No liability shall attach to I EC or its directors, em ployees, servants or ag ents inclu din g in divi dual experts an d m em bers of its technical com m ittees and I EC Nati on al Com m ittees for any person al i njury, property d am age or other dam age of any nature whatsoever, wheth er di rect or indirect, or for costs (includ i ng leg al fees) and expenses arisi ng out of the publ ication, use of, or relian ce upon, this I EC Publicati on or any other I EC Publications 8) Attention is drawn to th e N orm ative references cited in th is publ ication Use of the referenced publ ications is indispensable for the correct applicati on of this publication 9) Attention is drawn to the possibility that som e of the elem ents of this I EC Publication m ay be the su bject of patent rig hts I EC shall not be held responsibl e for identifyi ng any or all such patent ri ghts I nternational Standard I EC 63028 has been prepared by technical area 5: Wireless power transfer, of I EC technical comm ittee 00: Audio, video and multimedia systems and equipm ent The text of this I nternational Standard is based on the following documents: FDI S Report on votin g 00/2901 /FDI S 00/2941 /RVD Full information on the voting for the approval of this I nternational Standard can be found in the report on voting indicated in the above table This document has been drafted in accordance with the I SO/I EC Directives, Part –8– I EC 63028: 201 I EC:201 The com mittee has decided that the contents of this docum ent will rem ain unchanged until the stability date indicated on the I EC website under "http://webstore iec.ch " in the data related to the specific document At this date, the document will be • • • • reconfirmed, withdrawn, replaced by a revised edition, or am ended A bilingual version of this publication m ay be issued at a later date I M P O R T AN T th a t it – Th e ' co l ou r i n s i d e' tai n s u n d e rs t a n d i n g c o l o u r p ri n t e r of c o l o u rs i ts wh i ch c o n te n ts logo a re U s e rs on th e co ve r p ag e o f th i s c o n s i d e re d sh ou l d to t h e re fo re be p ri n t p u b l i c ati o n u s e fu l th i s fo r i n d i c ate s th e d o cu m en t c o rre c t u sin g a – 84 – I EC 63028: 201 I EC:201 Annex A (informative) Reference PRU for PTU acceptance testing NOTE See for PRU categ ori es A.1 Category For further stud y A.2 Category See the RI T 3-2 design in AirFuel Resonant PTU Resonator and Resonator I nterface Acceptance Test A.3 A.3.1 Category PRU design 3-1 Table A and Figure A provide RI T 3-2 specific parameters and block diagram Table A.1 – PRU table of specifications Parameter Value Units VRX_OC_BOOT 5, Volts VRX_OC_M I N 8, Volts VRX_OC_H I G H 3, Volts VRX_OC_M AX 18 Volts R RX_M I N 2, Ohm s Min im um clearance from charg er area surface 0, m illim etres Z21 + Candidate PTU Resonator Golden PRU Resonator (N) VRX_OC C ilter and Rectifier Load IEC Figure A.1 – PRU design block diagram A.3.2 Geometry Figures A through A provide RI T 3-2 specific geometry I EC: 201 – 85 – Dim ensions in m illim etres 48, 65, 28, 45, IEC Fi g u re A – Fron t vi ew Dim ensions in m illim etres 40 I EC 63028: 201 57 IEC Fig u re A – Back vi ew – 86 – I EC 63028: 201 I EC:201 , 41 0, 69 2, 41 0, Dim ensions in m illim etres IEC Fi gu re A – Sid e vi ew Dim ensions in m illim etres 61 , 01 3, 09 (3X EQ SP) 44, 01 IEC NOTE "3X EQ SP" m eans "Th ree equ al spaces" Fi gu re A – Fron t vi ew, coil on l y Dim ensions in m illim etres 0, 51 , 51 IEC Figu re A – Sid e vi ew, coi l on l y I EC 63028: 201 A.4 I EC: 201 Category For further stud y A.5 Category For further stud y – 87 – – 88 – I EC 63028: 201 I EC:201 Annex B (informative) Lost power B.1 Overview Annex B provides considerations for the developm ent of lost power procedures and lost power calculations B.2 General Lost power is defined as the power that cannot be accounted for by the system System power losses include: • • • • • • • efficiency losses in the PTU power section; losses in the PTU resonator; radiated losses; losses in the PRU resonator; efficiency losses in the PRU power section ; losses caused by induction heating of the bod y of the PRU ; losses caused by induction heating of other obj ects in the vicinity Generall y, the PTU will have the ability to measure power in and the PRU will have the ability to m easure and report power out There will always be a difference between these two caused by the losses listed above Som e of the losses (such as PTU and PRU resonator losses, and PRU induction heating losses) can be estim ated and accounted for fairl y accurately Som e of the losses (such as induction heating of other objects) are unknowns Since induction heating of other objects is undesirable, PTU designers will often wish to estimate the amount of lost power assignable to induction heating of other obj ects Sim ulation and empirical testing demonstrates that this can be done with an accuracy of a few watts I f an unaccountable amount of lost power is detected, PTU designers might elect to shut down the PTU to prevent potential heating of other objects Annex B lists some of the issues surrounding lost power detection B.3 Cross connection issues When a device is cross-connected, it will be reporting its power to the "wrong" PTU and will generall y cause a significant am ount of lost power error This can be used to help rem ed y cross connection issues, since a shutdown will tend to reset all BLE links on that PTU and allow the cross-connected device to "try again" B.4 Handoff issues I n some cases, a device m ight need to "hand off", i e., to transfer control from one BLE link to another, or from one BLE radio to another During this tim e, there will often be a transient in unreported power, and PTU designers need to ensure that this does not cause an undesired lost power detection shutdown I EC 63028: 201 B I EC: 201 – 89 – Power noi se i ssu es The "spectrum " of power draw of a phone in current lim it (i e., drawing maxim um power during charge) is relatively quiet since m ost phone inputs are current-regulated However, once full y charged or close to fully charged, the power drawn becomes very noisy and thus hard to measure accuratel y System designers can overcom e this by implementing filters with a time constant much longer than the 250 ms sam pling interval for PRU power, but this is som ewhat difficult to implement Thus, m easurement of lost power during periods other than full power might be difficult or impossible B PTU l ost power cal cul ati on B Lost power detection th resh old The PTU detects when PLOST ≥ n W for at least six seconds, where n is an implem entation specific value B Lost power detection speed I f lost power exceeds, and then stays above the im plementation threshold, the PTU shall shut down within six seconds measured from the m om ent that the im plementation threshold was first exceeded B PTU l ost power cal cu l ation The PTU can implement the calculation PLOST = PTX_OUT – PACK where PTX_OUT PACK is the power output of the PTU resonator; is the power consum ption acknowledged by PRU s PTX_OUT = P TX – PTX_RESONATOR_DI SSI PATI ON where PTX_RESONATOR_DI SSI PATI ON is the power dissipated in the PTU resonator PACK = ( PAC1 + P RXCOI L1 + PI N DU CTI ON ) +… + ( PAC_N + PRXCOI L_ N + PI NDU CTI ON_ N) where is the power into the rectifier of PRU ; PAC1 is the power dissipated in the coil of PRU ; PRXCOI L1 PI NDUCTI ON1 is the power consum ed by the induction heating of PRU B PTU power tran smi ssion d etection accu racy The PTU detects the am ount of power transm itted to within n W, where n is an implem entation specific value B PRU lost power reports NOTE The PRU reports are used to calcul ate a total val ue of power consum ption and dissipation that is acknowl edg ed by the PRU ( P ACK ) The param eters VRECT , IRECT , R RX_I N , η RECT , and Delta R1 can be used to com pute the total of power d el ivered to the load, power consum ed by an y PRU circuitry, power consum ed by th e resonator, and power consum ed by an y in duction heating effects – 90 – B 6 I EC 63028: 201 I EC:201 Accu racy of reported power The total error of the power acknowledged by each PRU , ( PACK ), is less than 0, 75 W B None Oth er PRU l ost power reports I EC 63028: 201 I EC: 201 – 91 – Annex C (normative) User experience requirements C.1 General Annex C defines the requirem ents that AirFuel Resonant PTUs and PRUs should meet to achieve a satisfactory overall user experience C.2 User indication A user indication is a PTU and/or PRU capability to convey inform ation to the user regarding the state of wireless power transfer Use case and form factor m ay limit the capability of some devices to provide a user indication See for additional inform ation on PRU charge permission C.2.1 PRU user indication The PRU , if it has the capability as declared by the PRU vendor, shall provide the following user indications for wireless power transfer a) The PRU is charging (for initial conditions, this can also m ean preparing or permitted to charge) b) The PRU is not charging ) The PRU is denied charge 2) The PRU is waiting to charge (i e , there is limited charging available) 3) An error condition is preventing the PRU from charging C.2.2 PTU user indication The PTU, if it has the capability, shall provide the following user indications for wireless power transfer a) The PTU is charging one or more PRUs b) The PTU is not charging an y PRUs ) A PRU is denied charge 2) Charging is available, no PRUs are charging or present 3) An error condition is preventing one or more PRU from charging – 92 – I EC 63028: 201 I EC:201 Annex D (informative) RCE calculations D.1 RCE calculation (using S-parameters) Delete this test equation: ∆ = det( S ) = S1 S22 − S1 S21 Optim um resonator coupling efficiency can be determined from the S-parameters This method rem oves the effect of an y m atching network used in the measurement Define the following constants, which depend only on the S-parameters: Δ = det(푆 ) = 푆11 푆22 − 푆12 푆21 퐵1 = + | 푆11 | − | 푆22 | − | Δ| 퐵2 = + | 푆22 | − | 푆11 | − | Δ| ∗ 퐶1 = 푆11 − Δ 푆22 ∗ 퐶2 = 푆22 − Δ 푆11 (D.1 ) The reflection coefficients for the generator and load at optimal efficiency are then given by: Γ퐺표 표표 = Γ퐿표표표 = 퐵1 − sign(퐵1 ) �퐵12 − 4| 퐶1 | 2 퐶1 퐵2 − sign(퐵2 ) �퐵22 − 4| 퐶2 | 2 퐶2 (D.2) The expression for the optimal efficiency in term s of the S-param eters is obtained by 표표 표 ∗ substituting in the values for Γ퐿표표표 and Γ푖표표표 푖 = ( Γ퐺 ) in Equation (D 2) into: 푅 퐶푅 = |푆 |2 표 표 표 21 − � Γ푖푖 � − � Γ퐿표표 표 � �� − 푆22 Γ퐿표 표 표 � � (D.3) The optim al loads can be found using the following expressions, where Z_0 = 50 Ω is the port im pedance used in the S-parameter measurement: 푍퐺 푍퐿 1+Γ = 푍0 − Γ퐺 퐺 1+Γ = 푍0 − Γ퐿 퐿 (D.4) I EC 63028: 201 D.2 I EC: 201 – 93 – RCE calculation (using Z-parameters) Optim um resonator coupling efficiency can also be determ ined from the Z param eters General case: Given the x matrix of Z-param eters, we can determ ine the impedances seen at the input and output ports of the 2-port network with load impedance 푍퐿 and generator impedance 푍퐺 : 푍퐼 푍푂 푍 푍 푂 (D.5) = 푍11 − 푍 12+ 21푍 퐼 퐿 22 푂 푍 푍 (D.6) = 푍2 − 푍 12+ 21푍 11 퐺 For perfect conjugate m atching, we want 푍퐼퐼 = 푍퐺∗ and 푍푂 푂푂 = 푍퐿∗ Solving these two equations for the optim um 푍퐿 and 푍퐺 we find: 푍퐿 ,표 표 표 = −푗푋2 = −푗 22 푋 + 푗 +푗 퐼퐼 [푍12 푍21 ] 퐼퐼 [푍12 푍21 ] 푍12 푍21 � + 푅 � + 푗 22 푅11 푅11 푅2 � − 푅11 푅 22 퐼퐼 [푍12 푍21 ] 푅푅 [푍12 푍21 ] 퐼퐼 [푍12 푍21 ] + 푅 22 �1 − � � − 푅11 푅11 푅 22 푅11 푅 22 (D.7) ) 푍퐺 , 표표표 = 퐼퐼 [푍12 푍2 ] 퐼퐼 [푍12 푍21 ] 푍12 푍21 � − 푗 푋11 + 푗 푅22 + 푅11 � + 푗 푅11 푅2 � − 푅11 푅 2 = − 푗 푋11 + 푗 퐼퐼 [푍12 푍2 ] 퐼퐼 [푍12 푍21 ] 푅 푅 [ 푍12 푍21 ] � 푅22 + 푅11 − � 푅11 푅 22 � − 푅11 푅 22 (D.8) where 푅11 = 푅푅 [푍11 ] , 푅 2 = 푅푅 [푍22 ] , 푋11 = 퐼퐼 [푍11 ] and 푋22 = 퐼퐼 [푍22 ] We can determine the optim um efficiency using 푅 퐶푅 = � | 푍21 | 2 푅 퐿 , 표표표 / 푅 퐼 퐼 푍2 + 푍퐿 , 표표표 (D.9) � where 푅 퐿 ,표표표 = 푅푅 [푍퐿 ,표표표 ] and 푅 퐼퐼 = 푅푅 [푍퐼퐼 ] evaluated with 푍퐿 = 푍퐿 ,표표표 U nder optimum loadin g conditions, 푅 퐿 , 표표표 푅 퐼퐼 and 푅퐶푅 can be expressed as = 푅푅 �푍퐿 , 표표표 � 푅푅 �푍퐺 , 표표표 � 푅 = 푅2 11 (D.1 0) – 94 – 푅 퐶푅 = I EC:201 | 푍21 | 푅11 푅 22 퐼 [푍 푍 ] � + �1 − � 푅 12푅 � 퐼 11 D.2.1 I EC 63028: 201 22 2 푅 푅 [푍12 푍21 ] 퐼 퐼 [ 푍12 푍21 ] − � + � � 푅11 푅 22 푅11 푅 22 (D.1 ) Series tuned case I n the special case of coils with onl y series matching elements, 푍21 = 푍12 = 푗푗 퐼 and then 푍퐿 , 표 표 표 푗 퐼2 = − 푗 푋22 + 푅2 �1 + 푅 푅 (D.1 2) 푍퐺 , 표 표표 푗 퐼2 = − 푗 푋11 + 푅11 �1 + 푅 푅 (D.1 3) 11 22 and 11 22 푅 퐶푅 sim plifies to: 푅 퐶푅 = 푄푀 �1 + �1 + 푄푀2 � (D.1 4) where 푄푀 = 푗퐼 �푅11 푅 22 (D.1 5) Note that in this case 푅11 = 푅1 and 푅 22 = 푅 , where 푅1 and 푅 are the resistances of coils and plus series m atching capacitors, respectivel y D.2.2 Other RCE calculations None D.3 Conversion between S-parameters and Z-parameters S-parameters can be converted to Z-parameters and vice-versa 푍0 = 50 I EC 63028: 201 I EC:201 – 95 – S to Z Parameters 푍11 = 푍12 = 푍21 = 푍22 = � (1 + 푆11 )(1 − 푆2 ) + 푆12 푆2 � 푆12 ∆푠 Z to S Parameters 푍0 푍 ∆푠 푆21 푍 ∆푠 � (1 − 푆11 )(1 + 푆22 ) + 푆12 푆21 � ∆푠 푍0 푆11 = 푆12 = 푆21 = 푆22 = (푍11 − 푍0 )(푍22 + 푍0 ) − 푍12 푍21 푍12 푍0 ∆푍 푍21 푍0 ∆푍 (푍11 + 푍0 )(푍2 − 푍0 ) − 푍12 푍21 ∆ 푍 = (푍11 ∆푠 = � (1 − 푆11 )(1 − 푆22 ) − 푆12 푆21 � _ ∆푍 ∆푍 + 푍0 )(푍22 + 푍0 ) − 푍12 푍21 INTERNATIONAL ELECTROTECHNICAL COMMISSI ON 3, rue de Varembé PO Box 31 CH-1 21 Geneva 20 Switzerland Tel: + 41 22 91 02 1 Fax: + 41 22 91 03 00 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