Module 2 : Transmission LinesLecture 15 : Impedance Matching using Transmission Line Objectives In this course you willlearn about the followingImpedance matching techniques.Quater wavelength transformer matching its advantages and limitations.Single stub matching technique and its special features.Module 2 : Transmission LinesLecture 15 : Impedance Matching using Transmission LineImpedance Matching Impedance matching is one of the important aspects of high frequency circuit analysis. To avoid reflections andfor maximum power transfer the circuits have to be impedance matched. Transmission line sections can be used for the purpose of impedance matching. There are various impedance matching techniques which are discussed in the following : Quarter Wavelength Transformer Thistechniqueisgenerallyusedformatchingaresistiveloadtoatransmissionline(a), for matching tworesistive loads(b),or for matching two transmission lines with unequal characteristic impedances (c) (see Figure).All cases are identicalin principle as allrequire matching between two purely resistive impedances. Principle Introduce a section of a transmission line(called transformer) between two resistances to be matched, such thatthe transformed impedances perfectly match at either end of the transformer section. That is, in Figure (a) say,the impedance seen towards right at A should be, and impedance seen towards left at B should be R. Sowhen seen from transmission line side it appears to be terminated in, and when seen from load resistanceside it appears to be connected to a conjugately matched load R. Similar is true for Figure (b,c). For the transformer we have two parameters to control, characteristic impedance of the transformer section, andthe length of the transformer section. Letusassumethatthecharacteristicimpedanceofthetransformersection is.Forlength,thetransformer inverts the normalized impedance. Therefore the impedance seen at A towards right in Figure (a)would beFor matching at A, should be equal to, i.e.ConclusionTwo resistive impedances can be matched by a section of a transmission line which is quarter-wavelength longand has characteristic impedance equal to the geometric mean of the two resistances.Thequarterwavelengthtransferiscommonlyusedatthejunctionoftwotransmissionlinesof unequalcharacteristic impedances. DrawbackThis technique needs special line of characteristics impedance for every pair of resistances to bematched.Module 2 : Transmission LinesLecture 15 : Impedance Matching using Transmission Line Single-Stub Matching TechniqueA stub is a short-circuited section of a transmission line connected in parallel to the main transmission line.Astubofappropriatelengthisplacedatsomedistancefromtheloadsuch that the impedance seenbeyond the stub is equal to the characteristic impedance.Suppose we have a load impedance connected to a transmission line with characteristic impedance (Figurea).Theobjectivehereisthatnoreflectionshould be seen by the generator. In other words,even if there are standing waves in the vicinity of the load,thestandingwaves must vanish beyondcertain distance from the load.Conceptually this can be achieved by adding a stub to the main line such that the reflected wave from theshort-circuit end of the stub and the reflected wave from the load on the main line completely cancel eachother at point B to give no net reflected wave beyond point B towards the generator.We make use of Smith chart for this purposeSince we have a parallel connection of transmission lines, it is more convenient to solve the problem usingadmittances rather than impedances. To convert the impedance into admittance also we make use of theSmith chart and avoid any analyticalcalculation.Now onwards treat the Smith chart as the admittance chartMatching ProcedureFirstmark the load admittance on the admittance smith chart (A).Plot the constant circleonthesmithchart.Move on the constant circletillyouintersecttheconstant circle this point of intersection corresponds to point(B). The distance traversedon the constant circle is . This is the location of placing the stub on the transmission line from theload end . Find constant suseptance circle.Find mirror image of the circle to get circle.Mark on the outer most circle (D).From (D) move circular clockwise upto s.c point (E) to get the stub length . AdvantageThe single-stub matching technique is superior to the quarter wavelength transformer as it makesuse of only one type of transmission line for the main line as well as the stub. This technique alsoinprincipleiscapableofmatchinganycomplex load to the characteristic impedance/admittance.Thesinglestubmatchingtechniqueisquitepopularin matching fixed impedances at microwavefrequencies. DrawbackThesinglestubmatchingtechniquealthoughhasovercomethedrawbackofthe quarterwavelengthtransformertechnique,itstillisnotsuitableformatching variable impedances. Achange in load impedance results in a change in the length as well as the location of the stub. Evenif changing length of a stub is a simpler task, changing the location of a stub may not be easy incertaintransmissionlineconfigurations.Forexample,ifthetransmission line is a co-axial cable,the connection of a stub would need drilling of a hole in the outer conductor.Module 2 : Transmission LinesLecture 15 : Impedance Matching using Transmission Line Recap In this course you have learntthe followingImpedance matching techniques.Quater wavelength transformer matching its advantages and limitations.Single stub matching technique and its special features.