2Review Input impedance for finite length line Quarter wavelength line Half wavelength lineSmith chartA graphical tool to solve transmission line problemsUse for measuring reflection coefficient, VSWR, input impedance, load impedance, the locations of Vmax and Vmin
3Ex1 ZL = 25+j50 , given Z0 = 50 and the line length is 60 cm, the wavelength is 2 m, find Zin. Ex2 A 0.334 long TL with Z0 = 50 is terminated in a load ZL = 100-j100 . Use the Smith chart to find a) L b) VSWR c) Zin d) the distance from load to the first voltage minimum
4Ex3 ZL = 80-j100 is located at z = 0 on a lossless 50 line, given the signal wavelength = 2 m, find a) If the line is 0.8 m in length, find Zin.b) VSWRc) What is the distance from load to the nearest voltagemaximumd) what is the distance from the input to the nearest point atwhich the remainder of the line could be replaced by a pureresistance?
5Ex4 A 0.269- long lossless line with Z0 = 50 is terminated in a load ZL = 60+j40 . Use the Smith chart to finda) Lb) VSWRc) Zind) the distance from the load to the first voltage maximum
6Impedance matching To minimize power reflection from load Zin = Z0 Matching techniques1. Quarter - wave transformers for real load2. single - stub tuners3. lumped – element tunersThe capability of tuning is desired by having variable reactive elements or stub length.
7Simple matching by adding reactive elements (1) EX5, a load 10-j25 is terminated in a 50 line. In order for 100% of power to reach a load, ZLoad must match with Z0, that means ZLoad = Z0 = 50 .Distance d WTG = ( ) = to point 1+ j2.3. Therefore cut TL and insert a reactive element that has a normalized reactance of -j2.3.The normalized input impedance becomes1+ j2.3 - j2.3 = 1which corresponds to the center or the Smith chart.
8Simple matching by adding reactive elements (2) The value of capacitance can be evaluated by known frequency, for example, 1 GHz is given.
9Single stub tunersWorking with admittance (Y) since it is more convenientto add shunt elements than series elementsStub tuning is the method to add purely reactive elementsWhere is the location of y on Smith chart?We can easily find the admittance on the Smith chart bymoving 180 from the location of z.Ex6 let z = 2+j2, what is the admittance?
10Stub tuners on Y-chart (Admittance chart) (1) There are two types of stub tunersShorted end, y = (the rightmost of the Y chart)opened end, y = 0 (the leftmost of the Y chart)Short-circuited shunt stubOpen-circuited shunt stub
11Stub tuners on Y-chart (Admittance chart) (2) ProcedureLocate zL and then yL. From yL, move clockwise to1 jb circle, at which point the admittance yd = 1 jb.On the WTG scale, this represents length d.2. For a short-circuited shunt stub, locate the short end at0.250 then move to jb, the length of stub is thenl and then yl = jb.3. For an open-circuit shunt stub, locate the open end at 0,then move to jb.4. Total normalized admittance ytot = yd+yl = 1.
13Microstrip (1)The most popular transmission line since it can be fabricated using printed circuit techniques and it is convenient to connect lumped elements and transistor devices.By definition, it is a transmission line that consists of a strip conductor and a grounded plane separated by a dielectric medium
14Microstrip (2)The EM field is not contained entirely in dielectric so it is not pure TEM mode but a quasi-TEM mode that is valid at lower microwave frequency.The effective relative dielectric constant of the microstrip is related to the relative dielectric constant r of the dielectric and also takes into account the effect of the external EM field.Typical electric field linesField lines where the air anddielectric have been replaced bya medium of effective relativepermittivity, eff
15Microstrip (2.1)Some typical dielectric substrates are RT/Duroid® (a trademark of Rogers Corporation, Chandler, Arizona), which is available with several values of εr (e.g. ε = 2.23εo, ε = 6εo, ε = 10.5εo, etc.); quartz (ε = 3.7εo); alumina (ε = 9εo) and Epsilam-109® (ε = 10εo).Various substrate materials are available for the construction of microstrip lines, with practical values of εr ranging from 2 to 10. The substrate material comes plated on both sides with copper, and an additional layer of gold plating on top of the copper is usually added after the ckt pattern is etched in order to prevent oxidation. Typical plating thickness of copper is from ½ mils to 2 mils (1 inch = 1000 mils).The value of εr and the dielectric thickness (h) determine the width of the microstrip line for a given Zo. These parameters also determine the speed of propagation in the line, and consequently its length. Typical thickness are 25, 30, 40, 50 and 100 mils.
16Microstrip (3) Therefore in this case and and The evaluation of up, Zo and λ in microstrip line requires the evaluation of εeff and C. There are different methods for determining εeff and C and, of course, closed-form expressions are of great importance in microstrip-line design. The evaluation of εeff and C based on a quasi-TEM mode is accurate for design purposes at lower microwave freq. However, at higher microwave freq, the longitudinal components of the EM fields are significant and the quasi-TEM assumption is no longer valid.
17Evaluation of the microstrip configuration (1) Consider t/h < and assume no dependence of frequency, the ratio of w/h and r are known, we can calculate Z0 as
18Evaluation of the microstrip configuration (2) Assume t is negligible, if Z0 and r are known, the ratio w/h can be calculated asThe value of r and the dielectric thickness (h) determines thewidth (w) of the microstrip for a given Z0.
19Characteristic impedance of the microstrip line versus w/h
20Normalized wavelength of the microstrip line versus w/h
21Ex8 A microstrip material with r = 10 and h = 1 Ex8 A microstrip material with r = 10 and h = mm is used to build a TL. Determine the width for the microstrip TL to have a Z0 = 50 . Also determine the wavelength and the effective relative dielectric constant of the microstrip line.
22Wavelength in the microstrip line Assume t/h 0.005,