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TECHNICAL REPORT IEC TR 62152 First edition 2004-08 LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Background of terms and definitions of cascaded two-ports Reference number IEC/TR 62152:2004(E) Publication numbering As from January 1997 all IEC publications are issued with a designation in the 60000 series For example, IEC 34-1 is now referred to as IEC 60034-1 Consolidated editions The IEC is now publishing consolidated versions of its publications For example, edition numbers 1.0, 1.1 and 1.2 refer, respectively, to the base publication, the base publication incorporating amendment and the base publication incorporating amendments and Further information on IEC publications • IEC Web Site (www.iec.ch) • Catalogue of IEC publications The on-line catalogue on the IEC web site (www.iec.ch/searchpub) enables you to search by a variety of criteria including text searches, technical committees and date of publication On-line information is also available on recently issued publications, withdrawn and replaced publications, as well as corrigenda • IEC Just Published This summary of recently issued publications (www.iec.ch/online_news/ justpub) is also available by email Please contact the Customer Service Centre (see below) for further information • Customer Service Centre If you have any questions regarding this publication or need further assistance, please contact the Customer Service Centre: Email: custserv@iec.ch Tel: +41 22 919 02 11 Fax: +41 22 919 03 00 LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU The technical content of IEC publications is kept under constant review by the IEC, thus ensuring that the content reflects current technology Information relating to this publication, including its validity, is available in the IEC Catalogue of publications (see below) in addition to new editions, amendments and corrigenda Information on the subjects under consideration and work in progress undertaken by the technical committee which has prepared this publication, as well as the list of publications issued, is also available from the following: TECHNICAL REPORT IEC TR 62152 First edition 2004-08 LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Background of terms and definitions of cascaded two-ports IEC 2004 Copyright - all rights reserved 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 the publisher International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch Com mission Electrotechnique Internationale International Electrotechnical Com m ission Ɇɟɠɞɭɧɚɪɨɞɧɚɹ ɗɥɟɤɬɪɨɬɟɯɧɢɱɟɫɤɚɹ Ʉɨɦɢɫɫɢɹ PRICE CODE X For price, see current catalogue –2– TR 62152 IEC:2004(E) CONTENTS FOREWORD .4 General Operational, image and insertion transfer functions and complex attenuations or losses Terms and definitions .7 Annex A (normative) Concepts of normalized voltage waves, square root of power waves and operational attenuation and losses A.1 General A.2 Complex operational attenuation or operational propagation coefficient * B .9 A.4 Operational reflection coefficient 10 A.5 Return loss 10 A.6 General coupling transfer function .11 A.7 Benefits of the concept of operational quantities 12 Annex B (normative) Two-port transmission technique – Terms 13 Annex C (normative) Two-port theory and fundamental concepts in transmission engineering 14 C.1 General 14 C.2 Transfer equations for a passive two-port 14 C.3 Chain matrix 15 C.4 The symmetries and impedances of a two-port 19 C.5 Impedance matching 21 C.6 Level concepts .23 C.7 Attenuation and gain concepts 24 C.8 Concepts related to return loss and matching 28 C.9 Scattering parameter 35 C.9.1 Scattering parameter of a one-port 35 C.9.2 Scattering parameters and scattering matrix of a two-port 38 C.10 Examples 43 C.10.1 Example 43 C.10.2 Example 45 C.11 Reference documents 46 Figure – Defining the transfer functions of a two-port Figure – Constant value A s and A r curves on a complex plane z = x + jy .8 Figure A.1 – Coupling between two systems 12 Figure C.1 – A quadripole or two-port 14 Figure C.2 – An impedance-unsymmetrical two-port (a) with its equivalent circuit (b) 16 Figure C.3 – Two chained two-ports 17 Figure C.4 – An impedance-symmetrical two-port 19 Figure C.5 – An impedance-unsymmetrical two-port for which Z z Z when Z A = Z B 19 Figure C.6 – A two-port terminated with an impedance Z B 20 Figure C.7 – Reflection less matching 22 LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU A.3 Impedance 10 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) –3– Figure C.8 – Power matching for maximizing the effective power 22 Figure C.9 – Absolute and nominal level in a system 24 Figure C.10 – Definition of the complex image attenuation * of a two-port 24 Figure C.11 – Definition of the complex operational attenuation of a two-port .25 Figure C.12 – Definition of residual attenuation 27 Figure C.13 – Measurement of the sending reference equivalent 27 Figure C.14 – Measurement of the receiving reference equivalent 28 Figure C.15 – Definition of the complex return loss 28 Figure C.16 – Apollonius’ circle 29 Figure C.17 – Return loss 30 Figure C.19 – Curves for constant values of A s or A r in the complex plane 33 Figure C.20 – Smith chart for transmission lines 34 Figure C.21 – One-port .35 Figure C.22 – Homogenous transmission line 36 Figure C.23 – One-port fed from a generator with source impedance Zg 37 Figure C.24 – Two-port .39 Figure C.25 – Termination Z B by virtue of the stray parameters of the two-port 40 Figure C.26 – Ideal transformer 43 Figure C.27 – Determination of a scattering matrix of a passive reciprocal two-port 45 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Figure C.18 – Curves for constant values of A s or A r in the complex plane 32 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) –4– INTERNATIONAL ELECTROTECHNICAL COMMISSION BACKGROUND OF TERMS AND DEFINITIONS OF CASCADED TWO-PORTS FOREWORD 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees 3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter 5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment declared to be in conformity with an IEC Publication 6) All users should ensure that they have the latest edition of this publication 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications 8) Attention is drawn to the Normative references cited in this publication Use of the referenced publications is indispensable for the correct application of this publication 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights IEC shall not be held responsible for identifying any or all such patent rights The main task of IEC technical committees is to prepare International Standards However, a technical committee may propose the publication of a technical report when it has collected data of a different kind from that which is normally published as an International Standard, for example "state of the art" IEC 62152, which is a technical report, has been prepared by IEC technical committee 46: Cables, wires, waveguides, r.f connectors, r.f and microwave passive components and accessories The text of this technical report is based on the following documents: Enquiry draft Report on voting 46/129/DTR 46/133/RVC Full information on the voting for the approval of this technical report can be found in the report on voting indicated in the above table This publication has been drafted in accordance with the ISO/IEC Directives, Part Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees) The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”) Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work International, governmental and nongovernmental organizations liaising with the IEC also participate in this preparation IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) –5– The committee has decided that the contents of this publication will remain unchanged until the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to the specific publication At this date, the publication will be • • • • reconfirmed; withdrawn; replaced by a revised edition, or amended A bilingual edition of this document may be issued at a later date LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) –6– BACKGROUND OF TERMS AND DEFINITIONS OF CASCADED TWO-PORTS General It is important and practical that components of a transmission chain can be separated and tested separately This means well-defined interfaces and measuring techniques including agreed terms and definitions It is advantageous to operate, by the square root of a reference impedance (normally application impedance of the system), with normalized voltage waves corresponding to the square root of power waves The quadripole theory was originally developed for voice- and carrier-frequency technologies and transmission, and later for microwaves, but both can be used through the whole frequency range Operational, image and insertion transfer functions and complex attenuations or losses a) Operational transfer function T B is defined as the square root of the power wave into the load (equal to reference P2 compared with an unreflected square root of power impedance R ) of a two-port wave P0 from the generator with a source impedance equal to the reference impedance R1 R1 P2 Z01 U1 E0 Z02 U2 R2 P02 R1 E0 E0 U0 R1 P0 IEC 1181/04 Figure – Defining the transfer functions of a two-port Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU This technical report has two main goals It lays the foundation for agreement on the fundamental terms and definitions to be used world wide in describing the transmission properties of a two-port or quadripole end and builds a bridge between the classical quadripole theory and the scattering matrix presentation which is based on incident and reflecting square root of power waves at the input and output of a two-port Finally, it is shown that the two concepts are bound together through simple equations and are fundamentally identical C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) TB –7– P2 U2 R2 P0 U0 R1 P2 S21 P0 (1) P02 which is equal to the forward transfer scattering parameter S 21 The operational transfer function becomes b) the image transfer function T when the reference impedance becomes equal to the input and output characteristic impedances Z 01 and Z 02 of the two-port; and c) the insertion transfer function T’ B when R = R = R Correspondingly, the complex attenuations or losses are as follows Complex operational attenuation AB jBB ln TB 20 log TB in >dB@ j arg(TB ) in >rad@ (2) Complex image attenuation * A jB ln T 20 log T in >dB@ j arg(T ) in >rad @ (3) Complex insertion attenuation or loss *B' R1 R2 R AB' jBB' ln TB' 20 log TB' in >dB@ j arg(TB' ) in >rad@ (4) Terms and definitions For the purposes of this document, the following terms and definitions apply 3.1 operational attenuation quotient of the unreflected square root of the power wave fed into the reference impedance of the input of the two-port and the square root of the power wave consumed by the load of the two-port expressed in dB and radians NOTE By defining a new quantity operational insertion loss in the same way as the operational attenuation, at least when the reference impedances on both sides of the two-port are the same, the problem of insertion loss and operational attenuation is solved 3.2 operational insertion loss quotient of the unreflected square root of the power wave fed into the reference impedance of the input of the two-port and the square root of the power wave consumed by the load of the two-port expressed in dB and radians Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU *B C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) –8– r 0,5 1,0 0,5 20 0 2,0 1,5 2,0 1,0 15 0,5 10 Ar 1,0 1,5 2,5 2,5 5,0 2,0 1,5 As 1,0 0,5 1,0 jx 2,5 IEC 1182/04 Reflection loss As 20 log zN [dB] zN Return loss Ar 20 log zN [dB] zN zN Z2 Z1 (= normalized impedance) = r + jx Figure – Constant value A s and A r curves on a complex plane z = x + jy 3.3 operational attenuation and insertion loss quotient of the unreflected square root of the power wave fed into the reference impedance of the input of the two-port and the square root of the power wave consumed by the load of the two-port expressed in dB and radians NOTE In the IEV, insertion loss is understood as the loss produced by inserting a two-port into a separated point of the transmission chain Because of varying terminating impedances of the two-port, this leads to insertion loss or operational attenuation deviation, that is, depending on where, in the chain, the two-port is inserted It is obvious that the insertion of a two-port with a certain operational attenuation or operational insertion loss causes different attenuation increases (or decreases) in separate circuit points of different impedances This is called the Insertion Loss Deviation (ILD) ILD has proved to be a very important subject of discussion in the standardization of a data channel Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU 0,5 2,0 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) C.9 – 35 – Scattering parameter C.9.1 Scattering parameter of a one-port We can characterize a port, as shown in Figure C.21, by incident (i) and reflected (r) voltage, current and square-root of power waves I Vi U Vr b) IEC 1204/04 Figure C.21 – One-port U Ui Ur I Ii Ir (C.71) Ui Ur R0 R0 (C.72) Ui (U R0 I ) (C.73) Ur (U R0 I ) (C.74) U and I are respectively the voltage and current at the terminals of the one-port and R can be regarded as the image impedance of the one-port Compare with the characteristic impedance of the homogenous transmission line in Figure C.22 For practical applications, it is advantageous to choose for the characteristic impedance nominal values, for example, 50 :, 75 :, 100 :, 120 :, 150 : This impedance is also used as reference impedance for measurements This impedance does not necessarily correspond to the image impedance of the one-port, because V i is defined as the unreflected square root of the power entering into the one-port and the square root of the fictive power, which is calculated or measured by matching the generator with this impedance Recalling that the square-root of power is P Pi UI Vi U R0 Ui R0 R0 I V U ( R0 I ) R0 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn (C.75) (C.76) LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU a) C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an – 36 – Pr Ur Vr TR 62152 IEC:2004(E) U ( R0 I ) R0 R0 Z1 (C.77) I (Z) U (Z) E Z0, J Z Z2 IEC 1205/04 The relation between the incident and the reflected wave can be expressed by means of the scattering parameter S: Vr S Vi (C.78) The parameter S is here identical to the reflection coefficient U , which equally represents the ratio of the reflected voltage to the incident voltage at the reflection plane (see Clause C.8) From the definition for V i and V r , it follows that U R0 R0 I S( U R0 R0 I ) (C.79) the solution of which gives S Z R0 Z R0 (C.80) where Z = U I is the input impedance of the one-port If Z = R , the voltage of the reflected wave is V r = The inverse value of S, when expressed in dB or Np and radians, is called the complex return loss * r (compare with equation C.61): īr 20 lg S >dB@ j arg S >rad@ or (C.81) ln S >Np@ j arg >rad@ S V i at a one-port, which is fed from a generator with an internal impedance Z g equal to the image impedance of the one-port Z , is: Vi E (C.82) Zg Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Figure C.22 – Homogenous transmission line C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 37 – By definition Vi U ( R0 I ) R0 (C.83a) Figure C.23 yields U E IZ g (C.83b) and (C.83c) When U and I are substituted into equation (C.83), expression (C.82) is obtained: R0 Vi ª E Zg RE º ) » «( E Zg Z Z g Z ằẳ ôơ R Zg E (1 ) Zg Z R0 E Zg (C.83d) Z g Ro Z1 E U Z IEC 1206/04 Figure C.23 – One-port fed from a generator with source impedance Zg The reflected wave vanishes, if Z = R On the other hand, there are no reflections between the generator and the load, if their impedance is equal, i.e if Z g = Z This condition is equivalent to a properly matched generator and the load impedance The maximum effective power is transmitted to the load, when Z g = Z * (see Clause C.5), whereas the maximum complex power is reached when Z g = Z In accordance with equations (C.76) and (C.82), the maximum complex power is P' Vi E2 4Z g (C.84a) From the expressions (C.74) and (C.75) we obtain U (Vi Vr ) R0 and I (Vi Vr ) / R0 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn (C.84b and C.84c) LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU E Zg Z I C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an – 38 – TR 62152 IEC:2004(E) This yields the expression for the complex power absorbed by the one-port, which is represented by the load: P UI Vi Vr 2 (C.85) Substitution of equation (C.79) and (C.80) yields ê ĐZ Z g P Vi (1 S ) Vi ô1 ă ă ô â Z Zg 2 Ã á º » » ¼ (C.86a) P’ = V i (C.86b) We obtain then the ratio between the complex power absorbed in the one-port and the actual complex power if the one-port is represented by the reference impedance Z: P' P Đ (Z Z g ) à ă ă 4Z Z g â 1 S (C.87) Compare to equations (C.65) and (C.66) Expressed in logarithmic units, this is called the complex reflection loss s C.9.2 Đ Z Zg à >rad @ j arg ă ă2 Z Z Z Zg g â 10 lg S >dB@ j arg (1 S ) >rad@ 1 ln S >Np@ j arg (1 S ) >rad @ 2 20 lg Z Zg >dB@ (C.88) Scattering parameters and scattering matrix of a two-port A two-port, shown in Figure C.24, can be treated as two individual one-ports, face to face For both one-ports, the incident and reflected waves are characterized by Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU If the impedance Z g of the generator, that feeds the one-port, is taken as reference impedance then the maximum complex power at the load is C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 39 – Vi 1 U1 R01 I1 ) ( R01 Vr1 U1 R01 I1 ) ( R01 Vi2 U2 R02 I ) ( R02 Vr2 U2 R02 I ) ( R02 I1 U1 E1 Z1 ZB I2 Two-port Z2 U2 Vi1 Vi2 Vr1 Vr2 E2 IEC 1207/04 Figure C.24 – Two-port Where R 01 and R 02 is the reference impedance at input and output, respectively, V i1 and V r1 are represented by the square roots of incident (unreflected) and reflected complex powers (see note) at port 1, and V i2 and V r2 are those at port NOTE Complex power is the product = UI Apparent power is the product UI * , which is used in electrical power technique, where the angle between the voltage and current is of interest current I I* is the complex conjugate of the The scattering parameters S mn of a two-port are defined as follows: Vr1 S11Vï S12Vi2 Vr S 21Vi1 S 22Vi2 (C.91) or in a matrix form ªVr ôV ằ r2 ẳ ê S11 ôS 21 S12 êVi1 S 22 ằẳ ôơVi2 ằẳ (C.92) where the matrix >S@ ê S11 ôS 21 S12 º S 22 »¼ is called the scattering matrix [4] It has the elements: Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn (C.93) LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU ZA (C.90) C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 40 – S11 Vr Vi1 Vi2 Z1 Z A Z1 Z A S12 Vr Vi2 Vi1 2U1 E2 S 21 Vr2 Vi1 S 22 Vr2 Vi2 īB 20 lg ZB ZA 2U E1 Vi2 U B11 ZA ZB Z2 ZB Z2 ZB Vi1 H B12 (C.94a) H B21 U B22 with >dB@ (C.94b) The above refers to the quantities under operational conditions, i.e to the complex operational reflection coefficient U B and to the operational transfer function H B (see equation (C.53) They are directly derived from the condition that V i2 and V i1 are zero, a condition which is satisfied, in accordance with equation C.90) as soon as the terminal impedances Z A and Z B are equal to the reference impedance R 01 and R 02 , respectively Hence, S 11 or U B11 is the complex operational reflection coefficient at the input; S 22 or U B22 is the complex operational reflection coefficient at the output; S 21 or H B21 is the operational transfer function in the forward direction; S 12 or H B12 is the operational transfer function in the backward direction The scattering matrix can thus be written in the form >S@ ê U B11 ôH B21 S11 Vr1 Vi1 H B12 º U B22 »¼ (C.95a) (C.95b) Vi2 The connection between the scattering parameters and the above-mentioned working quantities can be derived as follows: the condition V i2 = and its impact on the reflection factor at the input of the two-port is considered first Vi2 Two-port ZB Vr2 S2 IEC 1208/04 Figure C.25 – Termination Z B by virtue of the stray parameters of the two-port Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU HB C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 41 – Let us consider the influence of the termination Z B on the parameters V i2 and V r2 of the twoport The scattering parameter of the termination is S2 Z B R02 Z B R02 (C.95c) where R 02 is the reference impedance at the output of the two-port The connection between V i2 and V r2 is obtained by the relation Vi2 S Vr2 (C.95d) Hence, we can conclude that, if the terminal impedances Z A and Z B are selected to be equal as reference impedances, the parameters V i1 and V i2 are equivalent to zero The input and output impedances of the two-port are Z1 U1 I1 Z2 U2 I2 (C.96) When R 01 = Z A , we have S11 º ª U1 Z A I1 ằ ô ơô Z A ẳằ ê U1 Z A I1 ằ ô ơô Z A ¼» Z1 Z A Z 1 Z A UB11 (C.97a) Similarly, when R 02 = Z B , we have S 22 Z2 ZB Z2 ZB U B22 (C.97b) By definition, then, S 21 Vr2 Vi1 (C.97c) Vi2 As derived above, we have V i2 = for R 02 = Z B If an e.m.f E with an internal impedance equal to the reference impedance R 01 is connected to the input terminals, then equation (C.82) yields Vi1 E1 ZA (C.98) Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU If the reference impedance is chosen to be equal to the impedance Z B of the termination, then S = and V i2 = Similarly, it can be shown that V i1 = 0, when R 01 = Z A C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an – 42 – TR 62152 IEC:2004(E) with Vi2 U2 ( ZB I2 ) ZB (C.99a) It follows that U2 ZB ZB I2 (C.99b) By substituting this into the expression U2 ( ZB I2 ) ZB (C.99c) we obtain Vr2 U2 ZB S 21 2U E1 (C.100) and ZA ZB H B21 (C.101) H B12 (C.102) Correspondingly we have: S12 2U E2 ZB ZA We note that S 21 and S 12 are voltage ratios corrected to the terminal impedances and they describe under operating conditions the transfer function of the two-port Therefore, we have the name composite transfer function The complex composite loss of the two-port in the forward and the backward direction, respectively, is ī B21 20 lg E1 2U ZB ZA 20 lg | S 21 | >dB@ j arg S 21 >rad@ (C.103) ī B12 20 lg E2 2U ZA ZB 20 lg | S12 | >dB@ j arg S12 >rad @ In the passive transfer-balanced case i.e if the two-port is reciprocal, S 21 is equal to S 12 The usefulness of the scattering matrix in determining the transmission properties of the twoport is based on the direct measurements of composite reflection and composite loss coefficients at the input and output of the two-port, when it is terminated with a reference impedance Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Vr2 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 43 – It follows from the above that, in the matched case, V i and V r are square roots of the complex power at the input and output at the two-port, when the reference impedance is chosen to be Z A E ’ is the internal electromotive-force at port of the two-port V i2 and V r2 are obtained by changing the sub-index o and impedance Z A o Z B Vi1 E1 ZA U Z A I1 ZA (C.104) Vr1 E1c U1 Z A I1 ZA ZA In this case, we have S11 Z1 Z A Z1 Z A S 21 2U E1 * (C.105a) Re Z A Re Z B (C.105b) ZB These expressions are identical to (C.97) and (C.101) only when Z A and Z B are resistive In line transmission, it is generally not wise to use the so-called available power matching, because there will always remain reflections (see Clause C.5) It is worthwhile to mention the available power matching, which is deployed in lump loaded line, but, also in this case, consideration is given to reflectionless matching at the ends of the line Another example of available power matching is required for matching a transmitter to an antenna C.10 Examples C.10.1 Example Consider an ideal transformer with a turns ratio n:1 (Figure C.26) Then, U1 nU I1 I2 n (C.106) ZA E1 I1 n:1 U1 ZB I2 U2 E2 IEC 1209/04 Figure C.26 – Ideal transformer Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU In the literature [5], parameters V i and V r are defined utilizing the so-called available power The results are identical to those previously mentioned, but only when the reference impedances are purely resistive C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an – 44 – TR 62152 IEC:2004(E) Let us choose terminal impedances as reference impedance Then n2ZB ZA n2ZB ZA S 22 ZA ZB n2 ZA ZB n2 S 21 2U E1 ZA n2ZB ZA n2ZB ZA ZB 2nZ B ZA n2ZB S12 2U E1 ZB ZA (C.107a) (C.107b) E1 n Z B ( Z A n Z B )nE1 ZA ZB ZA ZB 2nZ A ZA n2ZB ZB ZA (C.108a) (C.108b) Therefore, the scattering matrix of the ideal transformer is >S@ êA B ôC D ằ ẳ A n2Z B Z A n2 Z B Z A B 2nZ A Z A n2 Z B (C.108c) where ZB ZA (C.108d) C 2nZ B Z A n2 Z B D ZA n2Z% Z A n2Z B ZA ZB If Z A = n Z B , then >S@ ê0 ô1 ằ ẳ (C.108e) Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU S11 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 45 – Hence, both ports are reflectionless, and attenuation is = dB, i.e the transfer function is equal to one C.10.2 Example Let us determine the scattering matrix of a passive, reciprocal two-port terminated by Z A and Z B The image impedances of the two-port are Z 01 and Z 02 , the complex image attenuation is * and input impedances are Z and Z ZA I1 ZB I2 * U1 E1 Z1 Z01 Z02 Z2 U2 E2 Figure C.27 – Determination of a scattering matrix of a passive reciprocal two-port From expression (C.94) we obtain S 11 and S 22 S11 S 22 Z1 Z A Z1 Z A (C.109a) Z2 ZB Z2 ZB (C.109b) We find the voltage U to be U2 Z 01 E1 Z A Z 01 Z 02 * 2Z B e Z 01 Z B Z 02 Z 01 E1 Z A Z 01 Z 02 * Z B Z 02 e Z 01 Z B Z 02 Z 01 * Z A Z 01 e Z 02 Z A Z 01 Z 02 * Z B e Z 01 Z B Z 02 Z 01 E1 Z A Z 01 Z 02 * Z B Z 02 e Z 01 Z B Z 02 Z 01 * Z A Z 01 e Z 02 Z A Z 01 Z 02 * e Z 01 Z B Z 02 Z B Z 02 U2 Z 01 * Z A Z 01 e Z 02 Z A Z 01 Z 01 E1 Z A Z 01 Z 02 * 2Z B e Z 01 Z B Z 01 (C.110a) Z 02 2Z B e * Z 01 Z B Z 02 ª Z Z 02 Z A Z 01 * º Z Z 02 Z A Z 01 * e ( B e ) » «1 B Z B Z 02 Z A Z 01 ¬ Z A Z 02 Z A Z 01 ¼ Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn (C.110b) LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU IEC 1210/04 C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an TR 62152 IEC:2004(E) – 46 – U2 Z 01E1 2Z B Z A Z 01 Z B Z 02 Z 02 * e Z Z 01 Z B Z 02 * Z 01 1 A e Z A Z 01 Z B Z 02 (C.110c) By substituting this into expression (C.94), we get S 21 2U E1 ZA ZB Z A Z 01 Z B Z 02 Z A Z 01 Z B Z 02 e * 1 Z A Z 01 Z A Z 01 Z B Z 02 2* e Z B Z 02 (C.111) S12 2U E1 Z B Z 02 Z A Z 01 ZB ZA Z B Z 02 Z A Z 01 e * Z B Z 02 Z A Z 01 2* 1 e Z B Z 02 Z A Z 01 (C.112a) By substituting expressions (C.109), (C.111) and (C.112) into the matrix (C.93), we get >S@ ª S11 ôS 21 S12 S 22 ằẳ (C.112b) we obtain the scattering matrix of the two-port shown in Figure C.27 C.11 Reference documents [1] Goubau, G., Design of Surface-Wave Transmission Lines, Electronics, vol 27, April 1954 [2] Reference Data for Radio Engineers Howard W Sams & Co., Inc, Indianapolis/Kansas City/New York, 1972 [3] Idlingmaier, M., Haag, A., Kühnemann, K., Einheiten-Grundbegriffe-Messverfahren der Nachrichten-übertragungstechnik, Siemens Aktiengesellschaft München, 1973 [4] Kuo, F.F., Network Analysis and Synthesis, John Wiley & Sons, Inc., New York/ London, 1962 [5] Tekniikan käsikirja, osa K.J Gummerus Oy, Jyväskylä 1973 _ Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Correspondingly S 12: C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Standards Survey The IEC would like to offer you the best quality standards possible To make sure that we continue to meet your needs, your feedback is essential Would you please take a minute to answer the questions overleaf and fax them to us at +41 22 919 03 00 or mail them to the address below Thank you! 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