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Subelement E9
ANTENNAS AND TRANSMISSION LINES
Section E9G
The Smith chart
Which of the following can be calculated using a Smith chart?
  • Correct Answer
    Impedance along transmission lines
  • Radiation resistance
  • Antenna radiation pattern
  • Radio propagation

The Smith chart, invented by Phillip H. Smith (1905-1987),[1][2] is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits.

  1. ^ Smith, P. H.; Transmission Line Calculator; Electronics, Vol. 12, No. 1, pp 29-31, January 1939
  2. ^ Smith, P. H.; An Improved Transmission Line Calculator; Electronics, Vol. 17, No. 1, p 130, January 1944

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What type of coordinate system is used in a Smith chart?
  • Voltage circles and current arcs
  • Correct Answer
    Resistance circles and reactance arcs
  • Voltage lines and current chords
  • Resistance lines and reactance chords

Smith charts have to do with Impedance matching (Resistance). The coordinate system used is resistance circles, and curves.

See: https://en.wikipedia.org/wiki/Smith_chart

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Which of the following is often determined using a Smith chart?
  • Beam headings and radiation patterns
  • Satellite azimuth and elevation bearings
  • Correct Answer
    Impedance and SWR values in transmission lines
  • Trigonometric functions

The Smith chart, invented by Phillip H. Smith (1905-1987) http://en.wikipedia.org/wiki/Smith_chart#cite_note-0

http://en.wikipedia.org/wiki/Smith_chart#cite_note-1 is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits.

  1. ^ Smith, P. H.; Transmission Line Calculator; Electronics, Vol. 12, No. 1, pp 29-31, January 1939
  2. ^ Smith, P. H.; An Improved Transmission Line Calculator; Electronics, Vol. 17, No. 1, p 130, January 1944

Transmission lines, and matching circuits have all to do about matching impedence (resistance).

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What are the two families of circles and arcs that make up a Smith chart?
  • Resistance and voltage
  • Reactance and voltage
  • Correct Answer
    Resistance and reactance
  • Voltage and impedance

remember: smith chart uses R & R, resistance and reactance. Also remember complex impedance is \(R + jX\) with R being resistance and X being reactance.

See wikipedia article for more information

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What type of chart is shown in Figure E9-3?
  • Correct Answer
    Smith chart
  • Free space radiation directivity chart
  • Elevation angle radiation pattern chart
  • Azimuth angle radiation pattern chart

This is a Smith Chart.

The circles, all tangent to each other, represent different resistances. The one closest to the tangent represents an infinite resistance, and the one furthest out (largest circle) represents zero resistance. The curved lines represent reactances, from zero (the straight line) to shorter curved lines, the ones representing larger reactances.

The Smith Chart is used to do antenna calculations by drawing lines rather than using formulas.

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On the Smith chart shown in Figure E9-3, what is the name for the large outer circle on which the reactance arcs terminate?
  • Prime axis
  • Correct Answer
    Reactance axis
  • Impedance axis
  • Polar axis

The key word here is "REACTANCE".

Reactance arcs terminate at the "REACTANCE" axis!

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On the Smith chart shown in Figure E9-3, what is the only straight line shown?
  • The reactance axis
  • The current axis
  • The voltage axis
  • Correct Answer
    The resistance axis

The straight line (the ONLY straight line) in a Smith Chart is the resistance axis. -K4AGO

Stick trick: The only line that resists bending. - N7ELC

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What is the process of normalization with regard to a Smith chart?
  • Reassigning resistance values with regard to the reactance axis
  • Reassigning reactance values with regard to the resistance axis
  • Correct Answer
    Reassigning impedance values with regard to the prime center
  • Reassigning prime center with regard to the reactance axis

The Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance (the most common), normalised admittance or both, using different colours to distinguish between them. These are often known as the Z, Y and YZ Smith charts respectively.[7] Normalised scaling allows the Smith chart to be used for problems involving any characteristic or system impedance which is represented by the center point of the chart. The most commonly used normalization impedance is 50 ohms. Once an answer is obtained through the graphical constructions described below, it is straightforward to convert between normalised impedance (or normalised admittance) and the corresponding unnormalized value by multiplying by the characteristic impedance (admittance). Reflection coefficients can be read directly from the chart as they are unit-less parameters. Wikipedia.org https://en.wikipedia.org/wiki/Smith_chart

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What third family of circles is often added to a Smith chart during the process of solving problems?
  • Correct Answer
    Standing wave ratio circles
  • Antenna-length circles
  • Coaxial-length circles
  • Radiation-pattern circles

The circles already present on the Smith chart include those for the resistive and reactive components of the normalized load impedance. One would normally use the intersection of these circles to identify the magnitude and angle of gamma, the voltage reflection coefficient.

By maintaining a gamma of constant magnitude about the origin, one can draw a third group of circles. Because standing wave ratio only depends on this magnitude, these circles define the standing wave ratio.

Thus, the correct answer is Standing-wave ratio circles.

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What do the arcs on a Smith chart represent?
  • Frequency
  • SWR
  • Points with constant resistance
  • Correct Answer
    Points with constant reactance

In the days of slide rules, the Smith chart was packed with lines, curves, grids and nomographs.

In the ARRL Extra class manual a Smith chart is introduced as an XY coordinate graph where the top and bottom of the Y axis is bent to the right to touch the X axis at the infinite resistance point. THESE ARE NOT the arcs the test is asking about. Those are the constant resistance circles. The "arcs" are the lines that intersect these bent Y axis lines, coming from the infinite resistance point out to the edge of the circle.

The arcs represent points with constant reactance. To interpret impedance on the Smith chart, it is necessary to understand constant resistance circles and constant reactance arcs.

A very comprehensive and in depth depiction of Smith Charts can be found at Wikipedia

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How are the wavelength scales on a Smith chart calibrated?
  • In fractions of transmission line electrical frequency
  • Correct Answer
    In fractions of transmission line electrical wavelength
  • In fractions of antenna electrical wavelength
  • In fractions of antenna electrical frequency

The wavelength scales on a Smith chart are calibrated in fractions of transmission line electrical wavelength.


The outer ring of a Smith Chart defines fractional electrical wavelength of feedline starting at zero and ending at 0.5 (half the electrical wavelength). It also defines the direction toward the generator. This is a hint, indicating that this is a feedline length and not antenna length.

Smith Charts are useful to determine feedline line length required to match a load to a radio transmitter.

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