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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] 11. W. Bode, Network Analysis and Feedback Ampliﬁer Design, Van Nostrand, N.Y., 1945. [8] R. M. Fano, “Theoretical Limitations on the BroadBand Matching of Arbitrary Impedances,“ Journal
of the Franklin Institute, vol. 249, pp. 57—83, January 1950. and pp. 139154, 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 —1'03 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 singleelement 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 shuntstub 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.opencircuitedstubs. , . . _, . , / .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 opencircuit 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 doublestub tuner using opencircuited 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 shortcircuited 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 doublestub 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 shuntstub. single series stub.
/and double shuntstub tuners. with shortcircuited 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 quarterwave 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 GlIz.
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 quarterwave transformer of Figure 5.13, with Z] = 100 $2, 22 = 150 f2, and ZL =
225 .Q. Evaluate the worstcase 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 airﬁlled
Xband rectangular guide at 10 6112. A quarterwave 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 foursection 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 twosection 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 foursection 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 twosection 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 twosection 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 speciﬁcations? 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 lumpedelement Lsection
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 BodeFano 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 quarterwave transformer, single shuntstub, and single series
stub, with shortcircuited 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 twoport 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
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