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Unformatted text preview: MW 73 74%: Wfli Pout (it 20/! PRINTED BY: Rashaunda Henderson <[email protected]>. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. WI , $36.7, 15.12, 13.1% «t LCMLW pm We 264 Chapter 5: Impedance Matching and Tuning [3] P. Bhartia and l. J. Bahl, Millimeter Wave Engineering and Applications, Wiley Interscience, NY, 1984. [4] R. E. Collin, “The Optimum Tapered Transmission Line Matching Section,” Proc. IRE, vol. 44, pp. 539—548, April 1956. [5] R. W. Klopfenstein, "A Transmission Line Taper of Improved Design," Prov. IRE, vol. 44. pp. 31—15. January 1956. [6] M. A. Grossberg. “Extremely Rapid Computation of the Klopfenstein Impedance Taper,” Proc. IEEE, vol. 56, pp. 1629—1630. September 1968. [7] 1-1. W. Bode, Network Analysis and Feedback Amplifier Design, Van Nostrand, N.Y., 1945. [8] R. M. Fano, “Theoretical Limitations on the Broad-Band Matching of Arbitrary Impedances,“ Journal of the Franklin Institute, vol. 249, pp. 57—83, January 1950. and pp. 139-154, February 1950. PROBLEMS VDesign lossless L—section matching networks for the following normalized load impedances: (a) u = 1.5 — j2.0 (c) Q = 0.2 — j0.9 (b) u = 0.5 + j0.3 (d) :L = 20 —1'0-3 5.2 We have seen that the matching of an arbitrary load impedance requires a network with at least two degrees of freedom. Determine the types of load impedances/admittanccs that can be matched with the two single-element networks shown below. (a) (b) \ 5% A load impedance Z L = 100+ j80 Q is to be matched to a 75 S2 line using a single shunt-stub tuner. Find two solutions using open—circuited stubs. ‘ . 5 Repeat Problem 5.3 using short—circuited stubs. A load impedance Z L = 30 — j 40 $2 is to be matched to a 50 S2 line using a single series stub hitter. Find twojolutions using.open-circuitedstubs. , . . _, . , / .77 7777777, 5.6 Repeat Problem 5.5 using short—circuited stubs. ,, In the circuit shown below a Z L = 200 + j 100 Q load is to be matched to a 40 (2 line, using a length. (7., of lossless transmission line of characteristic impedance. Z 1. Find 13 and Z 1. Determine, in general. what type of load impedanccs can be matched using such a circuit. 20:40:) ZL=200+leOS2 5.8 An open-circuit tuning stub is to be made from a lossy transmission line with an attenuation constant a. What is the maximum value of normalized reactance that can be obtained with this stub? What is the maximum value of normalized reactance that can be obtained with a shorted stub of the same type of transmission line? Assume all is small. 5.9 Design a double-stub tuner using open-circuited stubs with a A/S spacing to match a load admittance YL = (0.4+jl.2)Y0. 5.10 Repeat Problem 5.9 using a double—stub tuner with short-circuited stubs and a 31/8 spacing. PRINTED BY: Rashaunda Henderson <[email protected]>. Priming is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. Problems 265 5.11 Derive the design equations for a double-stub tuner using two series stubs, spaced a distance d apart. Assume the load impedance is ZL = RL + jXL. 5.12 Consider matching a load Z L = 200 $2 to a 100 9 line, using single shunt-stub. single series stub. /and double shunt-stub tuners. with short-circuited stubs. Which tuner will give the best bandwidth? Justify your answer by calculating the reflection coefficient for all six solutions at 1.] f0. where f0 is the match frequency. or use CAD to plot the reflection coefficient versus frequency. 5.13 esign a single—section quarter-wave matching transformer to match a 350 S2 load to a 100 (2 line. What is the percent bandwidth of this transformer. for SWR 5 2? If the design frequency is 4 Gl-Iz. sketch the layout of amicrostrip circuit, includingdimensions. to implement this matching transformer. Assume the substrate is 0.159 cm thick, with a dielectric constant of 2.2. 5.14 Consider the quarter-wave transformer of Figure 5.13, with Z] = 100 $2, 22 = 150 f2, and ZL = 225 .Q. Evaluate the worst-case percent error in computing IFI from the approximate expression of (5.42), compared to the exact result. 5.15 A waveguide load with an equivalent TEIO wave impedance of 377 9 must be matched to an air-filled X-band rectangular guide at 10 61-12. A quarter-wave matching transformer is to be used, and is to consist of a section of guide filled with dielectric. Find the required dielectric constant and physical length of the matching section. What restrictions on the load impedance apply to this technique? 5.16 A four-section binomial matching transformer is to be used to match a 12.5 $2 load to a 50 9 line at a center frequency of 1 G112. (a) Design the matching transformer. and compute the bandwidth for 1‘," = 0.05. Use CAD to plot the input reflection coefficient versus frequency. (1)) Lay out the microstrip implementation ofthis circuit on an FR4 substrate having 6, = 4.2, d = 0.158 cm. tan 5 = 0.02, with copper conductors 0.5 mil thick. Use CAD to plot the insertion loss versus frequency. 5.17 Derive the exact characteristic impedance for a two-section binomial matching transformer. for a normalized load impedance ZL/Zo = 1.5. Check your results with Table 5.1. 5.18 Calculate and plot the percent bandwidth for a N = l. 2, and 4 section binomial matching transformer. versus ZL/Zo = 1.5 to 6 for 1‘," = 0.2. 5.19 Using (5.56) and trigonometric identities. verify the results of (5.60). 5.20 Design a four-section Chebyshev matching transformer to match a 40 S2 line to a 60 52 load. The maximum permissible SWR over the passband is 1.2. What is the resulting bandwidth? Use the approximate theory developed in the text, as opposed to the tables. Use CAD to plot the input reflection coefficient versus frequency. 5.21 Derive the exact characteristic impedances for a two-section Chebyshev matching transformer, for a normalized load impedance ZL/Zo = 1.5. Check your results with Table 5.2 for 1‘," = 0.05. 5.22 A load of Z L / 20 = l .5 is to be matched to a feed line using a multisection transformer, and it is desired to have a passband response with lF(8)| = A(0.1+ cos2 9). for 0 5 0 5 11'. Use the approximate theory for multisection transformers to design a two-section transformer. 5.23 A tapered matching section has d(ln Z/Zo)/dz = A sin yrz/L. Find the constant A so that Z(0) = Z0 and Z(L) = ZL. Compute 1‘, and plot ll‘l versus flL. 5.24 Design an exponentially tapered matching transformer to match a 100 S2 load to a 50 9 line. Plot lf‘l versus flL. and find the length of the matching section (at the center frequency) required to obtain 11"} 5 0.05 over a 100% bandwidth. How many sections would be required if a Chebyshev matching transformer were used to achieve the same specification-s? 5.25 An ultra wideband (UWB) radio transmitter, operating from 3.1 to 10.6 GHz, drives a parallel RC load with R = 75 $2 and C = 0.6 pF. What is the best return loss that can be obtained with an optimum matching network? 5.26 Consider a series RL load with R = 80 $2 and L = 5 nH. Design a lumped-element L-section matching network to match this load to a 50 $2 line at 2 GHz. Plot 11"] versus frequency for this network to determine the bandwidth for which 11‘ l 5 F," = 0.1. Compare this with the maximum possible bandwidth for this load. as given by the Bode-Fano criterion. (Assume a square reflection coefficient response like that of Figure 5.23:1.) 2. 3) bl C) d) 8) fl Modifications to Pozar 5.12 Design using a quarter-wave transformer, single shunt-stub, and single series stub, with short-circuited stubs. Plot 5 solutions for the reflection coefficient with center frequency of 1 GHz. Use TLIN and TLSC elements that are found in: Elements=> Transmission Lines=> Phase Design a passive matching network to match a source with impedance of 2 S2 (typical of the output impedance of a power amplifier) to a load with an impedance of 50 S2. The matching network can have a maximum of two reactive elements. You need only calculate reactances and not the capacitor and inductor values. Make the design one that allows DC to pass. A two-port matching network is shown below with a generator and a load. The generator impedance is 40 S2 and the load impedance is ZL = 50 —j20 92. Use a Smith chart to design the matching network. What is the condition for maximum power transfer from the generator? Express your answer using impedances. What is the condition for maximum power from the generator? Express your answer using reflection coefficients. What system reference impedance are you going to use to solve the problem? Plot ZL on the Smith chart and label the point. Plot ZG on the Smith chart and label the point. Design a matching network using only transmission lines. Show your work on the Smith chart. You must express the lengths ofthe line in terms of electrical length (either degrees or wavelengths long). Characteristic impedances of the lines are required. (You will have a design that consists of one stubby and one other length of transmission line.) _m SMITH® CHART FORM ZY-01-N ANALOG INSTRUMENTS COMPANY, NEW PROVIDENCE, N.J. 07974 710 NORMALIZED IMPEDANCE AN /0" ADMITTANCE COORDINATES 60W 2 b7, 0.13 OJ 0.37 4 0-38 N0|i331138 ll) 8 U, RADIALLY SCALED PARAMETERS -‘ V’ m - » o o o O _ -_ ' ‘ ‘ ' ' —- < g 3 g e 8 9 n' .- n' N“ 2 8 Z 2 _- 3o 0 3 ‘6' 6 8 8 'o g g 2 U, *__1 LLLJ K LP L—l—l—J L‘._1 A l A Av l L—L'._I_!_I_ v m g g & TOWARD GENERATOR—b -—Townno LOAD i g >- _ ,_ ED ' U) 2 g 93 8 8 '9 9 m' w' v' m‘ 38 3 144—1! ‘1 ‘ T I 1 HAM—+- Hfi‘fi—fi ‘r r‘ : H—I—I—r‘fi—w‘ 4—‘H—r" x ‘1 3 O I! ‘2’ g: 0' o’ o' 0. o, 0. 0. w. «a V. N . q 2 g < v N - n v n N _ _ _ _ _ r g :5 E CENTER - . m I COFYRIGHT I97“ BY ANALOG INSTRUMENTS COMPANV. NEW PROVIDENCE. NVJ PRINTiD IN u‘S.A. SMITH® CHART FORM ZY-01-N ANALOG INSTRUMENTS COMPANY, NEW PROVIDENCE, N.J. 07974 STANDING WAVE TRANS“. LOSS I DB RATIO DB STEPS COEFF. 82' NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES (OI) 5r” QD’JO‘Z 0‘] 0.37 ¢ 0-35 045 h Q3 0;)" \ 50 ‘2 5 046 I ' NV 0 0'0 '2. ‘ 0'” Op ,7 7 » no 0.33 ‘ u.» so , 0. b1: d n TOWARD GENERATOR ——-’ 9) 0 0‘4” 0. V ova cry 0 Q 3’ q- o- E . m" Iu~7 so: 00": "'c :2 ° ' 5 g ‘ «g x 1» *8’3’ r F“: 9. la ‘2’ s ..,o ‘3' 0 I~ i‘ <99 3 .' 306.. \ Z 5 I g I i a tub v I \ ‘ r; ‘ I ; "’ +0: m‘ e '0 “Q . w. m N v u: m‘ ‘ o" r. I o 3 I *8 ' d o' o Io o oo'; —' 4\;;‘3\ MRI,“ I'g a. oppI O O u c‘ a c m .3 g N 3~ m r .9 . w k‘ _‘ \/ ~ , . . . . a. E N r ' ' 7 '3 a o c ,4» o w l '5 ‘ ‘ I Id 1 A h m’DC «A94 oo‘j‘a I O a“; 32‘- ; ,1 \ 2‘ ‘ m% I w ., .m >.< 6°: ‘9 Z “1“; ‘%’\ Ina O 2.6;5 O A d 0 4.0. c 4.0 \ O «‘91 A C 620 “1'0 o o _ n’ N" 3 ‘3 Z ‘3 _- 9° 3 '58: A-LJI'L—UJ—Hl—I 11—1 IJ._J_T 14—11.le vmm <——T0WARD LOAD 8 i I“ ,_ .37. m ‘ I o 0 Q 0 air—0 8 9 9- as as v N' 0‘ 3g: I'I'W—v‘m‘l‘l—I'LfiH—II'ILr—Iu‘rr‘x—H 11—0 0. o. 0. 0. w. u». v. «9 Q0 qzz \n v n N — - - " " rg CENTER 7 | COPYRIGHT 1570 BY ANALOG INSTRUMENTS COMPANV, NEW PROVIDENCE, N J NAME TITLE m LEI-~14) a“; DWG.NO. SMITH® CHART FORM ZY-01-N ANALOG INSTRUMENTS COMPANY, NEW PROVIDENCE, N.J. 07974 DATE @Vobw 09 / 09M disgmw, m+ 09757)» g g a.” '00 ORMALIZED IMPEDANCE A DMITTANCE COORDINATES I ’ - u / K A AM vhf/V on?! ; 0H0” Z>i75§1 21‘; - 21'; 30 fa QZ‘WE’DRSOX‘gfi /-"' g.\0 0.33 0.35 045 @L: '0: 0A0 "mic m 1 \ ,. so 3 0.35 Q’s A} 7a 0'31 , 6% "\ ix“ ‘ er . _ 1 ‘ ' \ _‘ 0 1.: o ‘0 0 F "-xww—r‘ ‘ [V F,» . ‘7 _ [Fl/J- l m 'u Wfl» "’ U, m \ RADIALLY SCALE PARAMETERS 3 «n “- 7‘ m ' o o o 0 ' ‘ ._ '_ ' - ' V ‘ ‘ ' 1‘ 3 8 8 9 n q‘ m' N" ‘3. 2i 3 2’- L. 7 go o g g 3 g 3 8 I, g m A. |L1_1_A 4.5.1 A .|_.|_A_LT_J Iggx J._IT I'._r.L_.A’>’ 1.9—5.” .HH, ‘ " "m 2 g g & TOWARD GENERATOR—> <—‘TOWARD LOAD o ' ' 2 I“ '_ i- _ .— 3’ ' m U, u: - - » . v o q o_ q a N _ _ 50 m g m u a u: m - I =7 I’ 0 333882 3 '2 9 m' w v u opuoE: 9. I" 9000 o o b 'o o ‘0 038* 3 MH‘MHJHLHIfifiH'YHIHKJ‘—HTH LHHLr—‘fi‘H-HHJ‘HLH'fWHr—HTJY go o x ‘3 .1 — o' o' o‘ 0. 0. 0. 0. w. m. 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