Electronic Applications of the Smith Chart
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This is the second edition of Electronic Applications of the Smith Chart, written by Phillip H. Smith, the originator of the Smith Chart. It covers the history, development and applications of the Smith Chart. This classic reference book describes how the chart is used for designing lumped element and transmission line circuits. The text provides tutorial material on transmission line theory and behavior, circuit representation on the chart, matching networks, network transformations and broadband matching. This edition includes a new chapter with example designs and description of the winSMITH software accessory.
Other keywords: graphical determination; complex transmission coefficients; transmission lines; data plotting; admittance; sampling current; impedance matching; radial scales; complex parameters; normalized impedance coordinates; negative resistance loads; lumped Lcircuits; slotted line section; impedance measurement; sampling voltage; electronic applications; linear parameters; electromagnetic wave propagation; equivalent circuit representations; antiresonant line sections; Smith Chart; peripheral scales; resonant line sections
 Book DOI: 10.1049/SBEW003E
 ISBN: 9781884932397
 eISBN: 9781613530665
 Format: PDF

Front Matter
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0 Introduction
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This introductory chapter discusses graphical vs. mathematical representations; the rectangular transmission line chart; the circular transmission line chart; orientation of impedance coordinates; and overlays for the Smith Chart.

1 Guided Wave Propagation
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The Smith chart is, fundamentally, a graphical representation of the interrelationships between electrical parameters of a uniform waveguide. Accordingly, its design and many of its applications can best be described in accordance with principles of guided wave propagation. The qualitative descriptions of the electrical behavior of a waveguide, as presented in this chapter, will provide a background for better understanding the significance of various interrelated electrical parameters which are more quantitatively described in the following chapter. As will be seen, many of these parameters are represented directly by the coordinates and associated scales of a Smith chart, and their relationships are basic to its construction.

2 Waveguide Electrical Parameters
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Two fundamental waveguide constants, the characteristic impedance and the propagation constant, will next be discussed in terms of traveling voltage and current waves, as well as in terms of primary circuit elements. The relationship of these two waveguide constants to the normalized input impedance characteristics of a waveguide will be shown. This relationship is the basis for the coordinate arrangement of the SMITH CHART. Following this, the use of the SMITH CHART coordinates in converting from normalized impedances to normalized admittances will be described.

3 Smith Chart Construction
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This chapter describes the construction of the basic coordinates of the SMITH CHART and then discusses some of the more important waveguide electrical parameters related thereto. All of these related parameters may be graphically portrayed as either radial or peripheral scales. The construction of the basic series impedance or parallel admittance coordinates of the SMITH CHART is shown.

4 Losses, and VoltageCurrent Representations
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In Chap. 3 it was shown that entry and exit to the coordinates of the SMITH CHART are conveniently accomplished through the use of appropriately graduated peripheral and radial scales. The peripheral scales (which were described in Chap. 3) relate all angular positions on the chart coordinates, as measured from its center, to corresponding physical positions along a waveguide. These scales include two linear length scales, one progressing clockwise and the other counterclockwise, from zero to onehalf wavelength around the chart circumference. A third peripheral scale measures the phase angle of the voltage reflection coefficient in relation to chart coordinates. Each point along each of the three peripheral scales was shown to apply to all chart positions radially in line therewith.

5 Waveguide Phase Representations
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In this chapter some fundamental waveguide phase conventions will first be reviewed. Following this, more generalized uses of the peripheral scale labeled 'angle of reflection coefficient' will be presented. Next, a discussion of the voltage, current, and power transmission coefficient, with generalized SMITH CHART overlays therefore, will be given. Finally, some additional waveguide voltage and waveguide current phase relationships will be discussed and presented in the form of generalpurpose overlays for the SMITH CHART. These latter phase relationships are of fundamental importance in the design of waveguide components and antennas employing phased radiating elements excited through waveguide feed systems.

6 Equivalent Circuit Representations of Impedance and Admitance
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This book chapter presents the following: the concept of waveguide input impedance (and admittance); impedanceadmittance relationships of a waveguide to those of simple series and parallel circuits which present equivalent impedance (or admittance) at a given frequency; seriescircuit representations of impedance and equivalent parallelcircuit representations of admittance on conventional Smith chart coordinates; parallelcircuit representations of impedance and series circuit representations of admittance on an alternate form of the Smith chart; Smith chart overlay for converting a seriescircuit impedance to an equivalent parallelcircuit impedance, and a parallel circuit admittance to an equivalent seriescircuit admittance; impedance or admittance magnitude and angle overlay for the Smith chart; and graphical combination of normalized polar impedance vectors.

7 Expanded Smith Chart
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In this chapter, enlargements of the more frequently used regions of the SMITH CHART will be presented and discussed, and special applications for these will be given. The graphical representation of the properties of stub sections of waveguide which are operated near their resonant or antiresonant frequency, as may be readily portrayed on two of these expanded charts, will be discussed in some detail.

8 Waveguide Transmission Coefficientτ
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Numerous attempts have been made to find simpler grids than that of the SMITH CHART on which waveguide transmission and reflection functions could be displayed. This chapter presents one solution to the problem which does not alter the basic SMITH CHART coordinates and which because of its inherent simplicity has certain practical advantages.

9 Waveguide Impedance and Admittance Matching
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Several commonly used devices for obtaining a match at the load end of a transmission line will be described in this chapter. These include the single and the dual matching stub, and the single and the dual matching slug transformers. Matching stubs or buildingout sections, as they are sometimes called, are sections of transmission line, frequently of the same characteristic impedance (or characteristic admittance) as that of the main line, and either open or shortcircuited at their far end, connected in shunt with the main line at any one of several permissible positions in the general location where it is desired to provide the match. Slug transformers, on the other hand, are sections of line of appropriate characteristic impedance (or characteristic admittance) and length connected in series with, and forming a continuation of, the main line. These devices are described in some detail herein since it is through its terminations alone that the transmission characteristics of waves along any given waveguide can be controlled. Furthermore, the SMITH CHART provides the ideal medium for visualization of the principle of operation of such transformers and for quantitatively determining their specific design constants.

10 Network Impedance Transformations
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This chapter discusses impedance matching. The author elaborates the following topics : Ltype matching circuits; Ttype matching circuits; and balanced L or balanced Ttype circuits.

11 Measurements of Standing Waves
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At radio frequencies where slotted waveguide or transmission line sections would be excessively long, probe measurements of the relative current (or relative voltage) amplitudes at discrete sampling points along the waveguide provide a convenient and practical technique for measuring the complex impedance and related parameters. The SMITH CHART is useful for interpreting and evaluating data obtained from such measurements as will be described herein. The principle is made use of in the SMITH CHART plotting board shown.

12 Negative Smith Chart
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In all passive waveguide structures, the primary circuit elements resistance and conductance act like absorbers of electromagnetic wave energy. As such, their mathematical sign is, by convention, positive. However, certain active electrical devices exist whose equivalent circuit can most conveniently be represented by negative resistance or negative conductance elements. Negative resistance and negative conductance circuit elements act more like sources than absorbers of electromagnetic wave energy.

13 Special Uses of Smith Charts
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The many uses of the Smith chart may conveniently be classified as 'basic,' 'specific,' and 'special.' The more common uses in the first two categories, in which procedures for solving problems will be evident from the material which has been presented in previous chapters, are listed below. These lists are followed by descriptions of some of the more important 'special' uses of this chart.

14 Smith Chart Instruments
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This book chapter presents Smith chart instruments which are purely mechanical in operation, and are thus more analogous to the ordinary logarithmicscaled slide rule.The following topics are also highlighted: radio transmission line calculator; improved transmission line calculator; calculator with spiral cursor; impedance transferring; MegaRule; examples of application; and MegaCharts.

15 Examples Using winSMITH
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This chapter demonstrate the use of winSmith. winSmith is a computer program which operates under Microsoft Windows 3.1, Windows 95, 98, 2000 and NT. winSmith automates the graphical solution of transmission line and simple matching problems and serves as an excellent training aid. This chapter uses the program to illustrate key SMITH CHART concepts with examples that illustrate common matching problems. Because the pertinent screen displays are included in this chapter, a copy of winSmith is not required to learn from these examples.

Appendix A: Transmission Line Formulas
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The mathematical relationships of the various parameters involved in guided wave propagation are basic to the construction of the SMITH CHART, or any other chart which portrays these relationships. Accordingly, the applicable transmission line equations are included herein for those who may desire this background information without the necessity of referring to other sources. Also, these relationships serve to provide more exact solutions to specific problems in cases where graphical solutions cannot provide the desired accuracy or when, for example, a computer is available.

Appendix B :Coordinate Transformation
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A conformal transformation can be applied to the curves on the rectangular transmission line chart in Fig. 1.2 in order to obtain the more convenient circular form shown in Fig. 1.3.

Back Matter
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Supplementary material

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