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Electronic Applications of the Smith Chart
Introduction
1.1 Graphical vs. Mathematical Representations
The physical laws governing natural phenomena can generally be
represented either mathematically or graphically. Usually the more
complex the law the more useful is its graphical representation.
For example, a simple physical relationship such as that expressed
by Ohm's law does not require a graphical representation for its
comprehension or use, whereas laws of spherical geometry which must
be applied in solving navigational problems may be sufficiently
complicated to justify the use of charts for their more rapid evaluation.
The ancient astrolabe, a Renaissance version of which is shown in
Fig. 1.1, provides an interesting example of a chart which was used
by mariners and astronomers for over 20 centuries, even though the
mathematics was well understood.
The laws governing the propagation of electromagnetic waves along
transmission lines are basically simple; however, their mathematical
representation and application involves hyperbolic and exponential
functions (see Appendix A) which are not readily evaluated without
the aid of charts or tables. Hence these physical phenomena lend
themselves quite naturally to graphical representation.
Tables of hyperbolic functions published by A. E. Kennelly [3]
in 1914 simplified the mathematical evaluation of problems relating
to guided wave propagation in that period, but did not carry the
solutions completely into the graphical realm.
Fig. I.1. A Renaissance version of the oldest scientific instrument
in the world. (Danti des Renaldi, 1940.)
I.2 The Rectangular Transmission Line Chart
The progenitor of the circular transmission line chart was rectangular
in shape. The original rectangular chart devised by the writer in
1931 is shown in Fig. 1.2. This particular chart was intended only
to assist in the solution of the mathematics which applied to transmission
line problems inherent in the design of directional shortwave antennas
for Bell System applications of that period; its broader application
was hardly envisioned at that time.
The chart in Fig. I.2 is a graphical plot of a modified form
of J. A. Fleming's 1911 "telephone" equation [2], as given in Chap.
2 and in Appendix A, which expresses the impedance characteristics
of high-frequency transmission lines in terms of measurable effects
of electromagnetic waves propagating thereon, namely, the standing-wave
amplitude ratio and wave position. Since this chart displays impedances
whose complex components are "normalized," i.e., expressed as a
fraction of the characteristic impedance of the transmission line
under consideration, it is applicable to all types of waveguides,
including open-wire and coaxial transmission lines, independent
of their characteristic impedances. In fact, it is this impedance
normalizing concept which makes such a general plot possible.
Although larger and more accurate rectangular charts have subsequently
been drawn, their uses have been relatively limited because of the
limited range of normalized impedance values and standing-wave amplitude
ratios which can be represented thereon. This stimulated several
attempts by the writer to transform the curves into a more useful
arrangement, among them the chart shown in Fig. 7.7 which was constructed
in 1936.
I.3 The Circular Transmission Line Chart
The initial clue to the fact that a conformal transformation
of the circular orthogonal curves of Fig. I.2 might be possible
was provided by the realization that these two families of circles
correspond exactly to the lines of force and the equipotentials
surrounding a pair of equal and opposite parallel line charges,
as seen in Fig. I.1. It was then a simple matter to show that a
bilinear conformal transformation [55,109] would, in fact, produce
the desired results (see Appendix B), and the circular form of chart
shown in Fig. I.3, which retained the normalizing feature of the
rectangular chart of Fig. I.2, was subsequently devised and constructed.
All possible impedance values are representable within the periphery
of this later chart. An article describing the impedance chart of
Fig. I.3 was published in January, 1939 [101].
During World War II at the Radiation Laboratory of the Massachusetts
Institute of Technology, in the environment of a flourishing microwave
development program, the chart first gained widespread acceptance
and publicity, and first became generally referred to as the Smith
Chart.
Descriptive names have in a few instances been applied to the
Smith Chart (see glossary) by other writers; these include "Reflection
Chart," "Circle Diagram (of Impedance)," "Immittance Chart," and
"Z-plane Chart." However, none of these are in themselves sufficiently
definitive to be used unambiguously when comparing the Smith Chart
with similar charts or with its overlay charts as discussed in this
text. For these reasons, without wishing to appear immodest, the
writer has decided to use the more generally accepted name in the
interest of both clarity and brevity.
Imped. Along Trans. Line vs. Standing Wave Ratio (r) and Distance
(D), in Wavelengths, to Adjacent Current (or voltage) Min. or Max.
Point
R
Dist. to Following Imin or Emax
R/Z0
Dist. to Following Imax or Emin
- (jX/Z0)
Normalized Reactance
+ (jX/Z0)
Fig. I.2. The original rectangular transmission line chart.
Fig. I.3. Transmission line calculator. (Electronics, January,
1939.)
Drafting refinements in the layout of the impedance coordinates
were subsequently made and additional scales were added showing
the relation of the reflection coefficient to the impedance coordinates,
which increased the utility of the chart. These changes are shown
in Fig. I.4. A second article published in 1944 incorporated these
improvements [102]. This later article also described the dual use
of the chart coordinates for impedances and/or admittances, and
for converting series components of impedance to their equivalent
parallel component values.
In 1949 the labeling of the chart impedance coordinates was changed
so that the chart would display directly either normalized impedance
or normalized admittance. This change is shown in the chart of Fig.
2.3. On this later chart the specific values assigned to each of
the coordinate curves apply, optionally, to either the impedance
or to the admittance notations.
In 1966 additional radial and peripheral scales were added to
portray the fixed relationship of the complex transmission coefficients
to the chart coordinates, as shown in Fig. 8.6.
I.4 Orientation of Impedance Coordinates
The charts in Figs. I.2 and I.3 as originally plotted have their
resistance axes vertical. It became apparent shortly after publication
of Fig. I.3, as thus oriented, that a horizontal representation
of the resistance axis was preferable since this conformed to the
accepted convention represented by the Argand diagram in which complex
numbers (x ± iy) are graphically represented with the real
(x) component horizontal and the imaginary (y) component vertical.
Therefore, subsequently published Smith Charts have generally
been shown, and are shown throughout the remainder of this book,
with the resistance (R) axis horizontal, and the reactance (±
jX) axis vertical; inductive reactance (+ jX) is plotted above,
and capacitive reactance (- jX) below the resistance axis.
I.5 Overlays for the Smith Chart
Axially symmetric overlays for the Smith Chart were inherent
in the first chart, as represented by the peripheral and radial
scales for the chart coordinates. These overlays include position
and amplitude ratio of the standing waves, and magnitude and phase
angle of the reflection coefficients. Additionally, overlays showing
attenuation and reflection functions were represented by radial
scales alone (see Fig. I.4).
Fig. I.4. Improved transmission line calculator (Electronics,
January, 1944.)
In the present text 26 additional general-purpose overlays (both
symmetrical and asymmetrical) for which useful applications exist
and which have been devised for the Smith Chart are presented.
Fig. 3.1. Construction of normalized resistance circles
for Smith Chart of unit radius.
Fig. 3.2. Construction of normalized reactance circles for
Smith Chart of unit radius.
Vector Convention
Legend
i - Incident
r - Reflected
R - Resultant
Fig. 5.1. Vector representation of phase relations for voltages
on impedance coordinates, or currents on admittance coordinates,
Smith Chart when SWR = 3.0 (refer to Table 5.1).
A relative phase lag of one vector over another is indicated
by a negative sign (-) on the lagging vector, whereas a relative
phase lead of one vector over another is indicated by a positive
sign (+).
In accordance with the above convention, Fig. 5.1 shows a Smith
Chart upon which eight specific vector representations of the voltage
or current on the impedance or admittance coordinates, respectively,
are plotted.
Network Impedance Transformations
Fig. 10.2. Impedances in unshaded areas of Smith Charts, represented
by eight circular boundaries, are transformable to a pure resistance
Z0 with specific L·type circuits indicated (transforming
effect of each circuit element is indicated by a heavy line with
arrows).
...for erasable chalk marking are also commercially available
[20]. (See Fig. 14.12.) These are printed with white characters
and can be rolled up and down on a curtain roller. The blackboard
chart is intended for basic instruction in a large classroom, and
consequently designations are in a bold type and a coarse coordinate
grid is employed. This chart is not suitable for accurate solution
of specific problems.
Fig. 14.12. Blackboard Smith Chart for classroom use [20].
14.11 Mega-Charts
14.11.1 Paper Smith Charts
Regular size (8 1/2 x 11 in.) Smith Charts in the following several
forms, each of which is described herein, are commercially available
[14]. These "Mega-Chart" forms are printed in red ink on 151b. (approximately
7lbs/ 1,000 sheets) translucent master paper, and packaged in clear
plastic envelopes of 100 sheets each, either padded or loose:
1. Standard Smith Chart - Form 82-BSPR (9-66) (see Fig.
8.6).
2. Expanded Center Smith Charts Form 82-SPR (2-49) (see Fig.
7.2).
3.Highly Expanded Center Smith Charts - Form 82-ASPR (see Fig.
7.3).
Also, Smith Charts with coordinates having negative real parts
(negative Smith Charts) are available in the same paper packaging,
printed in green ink, in the following form:
1. Negative Smith Chart - Form 82-CSPR (see Fig. 12.3).
14.11.2 Plastic Laminated Smith Charts
All of the above chart forms (except -the negative Smith Chart)
are available [14] laminated to a thickness of 0.025 in., with a
matte finish on the front for erasable pen marking. Abbreviated
instructions for use of Smith Charts are printed on the back.
14.11.3 Instructions for Smith Charts
Abbreviated sets of instructions for use the Smith Chart, containing
an explanation of the chart coordinates and radial scales and printed
on single sheets, are available commercially [14] printed on 50
lb offset paper. These may be used for classroom instruction.
Glossary - Smith Chart Terms
The terms which appear on Smith Charts as coordinate designations,
radially scaled parameters, peripheral scale captions, etc., are
individually defined and reviewed in this glossary. A more complete
discussion of these terms is found in applicable sections of the
text.
Although relevant to all Smith Charts, these terms are specifically
associated with the basic chart forms printed in Chaps. 6, 8 and
12, and enlarged chart forms described in Chap. 7. Other Smith Charts
with which these terms are specifically associated include the normalized
current and voltage overlay in Chap. 4, and the charts with dual
(polar and rectangular) coordinate transmission and reflection coefficients
in Chap. 8.
In the definitions which follow, certain qualifying words and
phrases are omitted when, in the context in which the terms are
used, these words and phrases will be understood to apply. For example,
the phrase "at a specified frequency" will apply to many of the
definitions, and the phrases "normalized input impedance of a uniform
waveguide" and "normalized input admittance of a uniform waveguide"
will generally be understood to be meant by the shorter terms, "waveguide
impedance" and "waveguide admittance," respectively.
This glossary supplements definitions which have been formulated
and published by the Institute of Radio Engineers (IRE) [11] (presently
the Institute of Electrical and Electronics Engineers, IEEE), and
by the American Standards Association (ASA-C42.65-1957) (presently
the United States of America Standards Institute, USASI), and upon
which usage of such terms in this text is based.
Angle of Reflection Coefficient, Degrees
At a specified point in a waveguide, the phase angle of the reflected
voltage or current wave relative to that of the corresponding incident
wave. The relative phase angle of the reflection coefficient; i.e.,
the total angle reduced to a value less than ± 180°, is generally
indicated by this term. This relative phase angle has a fixed relationship
to a specific combination of waveguide impedances or admittances
and, accordingly, to a specific locus on the impedance or admittance
coordinates of a Smith Chart, this locus being a radial line.
Note: The angles of both the voltage and the current reflection
coefficients are represented on Smith Charts by a single linear
peripheral scale, with designated values ranging between 0 and ±
180°. The angle of the voltage reflection coefficient is directly
obtainable for any point on the impedance coordinates by projecting
the point radially outward to this peripheral scale, labeled "Angle
of Reflection Coefficient, Degrees." Similarly, the angle of the
current reflection coefficient is directly obtainable for any point
on the admittance coordinates. At any specified point along a waveguide
the angle of the current reflection coefficient always lags that
of the voltage reflection coefficient by 180°.
Angle of Transmission Coefficient, Degrees
At a specified point along a waveguide, the phase angle of the
transmitted wave relative to that of the corresponding incident
wave. The. "transmitted" wave is the complex ratio of the resultant
of the incident and reflected wave to the incident wave. The angle
of the transmission coefficient has a fixed relationship to a specific
combination of waveguide impedances or admittances and, accordingly,
to a specific locus on the impedance or admittance coordinates of
a Smith Chart, this locus being a straight line stemming from the
origin of the coordinates.
Note: The angles of both the voltage and the current transmission
coefficients are represented on Smith Charts by a single linear
angle scale at the periphery, referenced to the origin of the impedance
or admittance coordinates, and ranging between 0 and ±90°. The
angle of the voltage transmission coefficient is directly obtainable
for any point on the impedance coordinates by projecting the point
along a straight line stemming from the origin of the impedance
coordinates to the intersection of the peripheral scale labeled
"Angle of Transmission Coefficient, Degrees." Similarly, the angle
of the current transmission coefficient is directly obtainable for
any point on the admittance coordinates.
Attenuation (1 dB Maj. Div.)
The losses due to dissipation of power within a waveguide and/or
the radiation of power therefrom when the waveguide is match-terminated.
On Smith Charts attenuation is expressed as a ratio, in dB, of the
relative powers in the forward-traveling waves at two separated
reference points along the waveguide.
Note: On a Smith Chart, "attenuation' is a radially scaled parameter.
The attenuation scale is divided into dB (or fraction of dB) divisions
which are not designated with specific values, with an arbitrarily
assignable (floating) zero point. The number of attenuation scale
units (dB) radially separating any two impedance or admittance points
on the impedance or admittance coordinates of a Smith Chart is a
measure of the attenuation in the length of waveguide which separates
the two reference points.
Coordinate Components
The normalized rectangular components of the equivalent series
or parallel input impedance or admittance of a waveguide or circuit.
which are represented on Smith Charts by two captioned families
of mutually orthogonal circular curves comprising the coordinates
of the chart.
Note 1: Coordinate components on the three Smith Charts printed
in red on translucent sheets in the back cover envelope are:
Chart A
1. the equivalent series circuit impedance coordinates: resistance
component R/Z0 and inductive (or capacitive) reactance
component ± j X/Z0.
2. the equivalent parallel circuit admittance coordinates: conductance
component G/Y0 and inductive (or capacitive) susceptance
component -/+ jB/Y0.
Chart B
1. the equivalent parallel circuit impedance coordinates: parallel
resistance component R/Z0 and parallel inductive (or
capacitive) reactance component ± jX/Z0.
2. the equivalent series circuit admittance coordinates: series
conductance components G/Y0 and series inductive (or
capacitive) component -/+ jB/Y0.
Chart C
1. the equivalent series circuit impedance or shunt circuit admittance
coordinates with negative real parts: negative resistance component
-R/Z0 and negative conductance component -G/Y0.
Note 2: The inductive reactance and inductive susceptance
coordinate components represent equivalent primary circuit elements
which are capable of storing magnetic field energy only. The resistance
component and the conductance component of the coordinates represent
equivalent primary circuit elements which are capable of dissipating
electromagnetic field energy. The negative resistance component
and the negative conductance component of the coordinates represent
equivalent circuit elements which are capable of releasing electromagnetic
field energy, as would be represented by the equivalent circuit
of a generator.
Impedance or Admittance Coordinates
The families of orthogonal circular curves representing the real
and imaginary components of the waveguide or circuit impedance
and/or admittance, and comprising the main body of a Smith Chart.
The designated values of the curves are normalized with respect
to the characteristic impedance and/or the characteristic admittance
of the waveguide, and the entire range of possible values lies within
a circle. Enlarged portions of Smith Chart coordinates are sometimes
used to represent or display a portion of the total area of the
coordinate system, thereby providing improved accuracy or readability.
Note: Most commonly, Smith Chart impedance or admittance coordinates
express components of the equivalent series circuit impedance or
parallel circuit admittance. However, a modified form of Smith Chart
expresses components of the equivalent parallel circuit impedance
or series circuit admittance. A coordinate characteristic which
is common to all Smith Charts is that a complex impedance point
on the impedance coordinates and a complex admittance point on the
admittance coordinates which is diametrically opposite, and at equal
chart radius, always represent equivalent circuits.
Negative Real Parts
On the Smith Chart form in Fig. 12.5, a designation of the sign
of the normalized resistance component of the impedance, or the
normalized conductance component of the admittance coordinates.
Note 1: See "Coordinate Components (Chart C)."
Note 2: A Smith Chart whose impedance or admittance coordinates
are designated with negative real parts is useful in portraying
conditions along a waveguide only when the returned power is greater
than the incident power.
Normalized Current EQUATIONS HERE
The rms current which would exist at a specified point along
a hypothetical waveguide having a characteristic impedance of one
ohm (or a characteristic admittance of one mho) and transmitting
one watt of power to a load. This current is the vector sum of the
incident and reflected currents at the point.
Note 1: The actual current at any specified power level in a
waveguide is obtainable from the normalized current by multiplying
it by the square root of the ratio of the power and characteristic
impedance (or by the square root of the product of the power and
characteristic admittance).
Note 2: A plot of normalized current and/or normalized voltage
is provided as an overlay for Smith Chart impedance or admittance
coordinates in Fig. 4.2.
Normalized Voltage EQUATONS HERE
The rms voltage which would exist at a specified point along
a hypothetical waveguide having a characteristic impedance of one
ohm (or a characteristic admittance of one mho) and transmitting
one watt of power to a load. This voltage is the vector sum of the
incident and reflected voltages at the point.
Note 1: The actual voltage at any specified power level in a
waveguide is obtainable from the normalized voltage by multiplying
it by the square root of the product of the power and characteristic
impedance (or by the square root of the ratio of the power and characteristic
admittance).
Note 2: See Note 2 in definition for normalized current.
Percent Off Midband Frequency n ·Δƒ
Captions for peripheral scales near the pole regions on expanded
Smith Charts, which relate specific values of the frequency deviation,
from the resonant or antiresonant frequency, to the impedance or
admittance characteristics of open- and short-circuited stub transmission
lines n quarter wavelengths long. Δƒ is the deviation
from the midband frequency in percent.
Peripheral Scales
The four scales encircling the impedance or admittance coordinates
of the Smith Chart, individual graduations on each of which are
applicable to a straight line locus of points on the impedance or
admittance coordinates.
Note: Each graduation on each of the three outermost of these
scales is applicable to all points on the impedance or admittance
coordinates which are radially aligned therewith; each graduation
on the innermost of these is applicable to all points on the coordinates
which are in line with the graduations and the point of origin of
the impedance or admittance coordinates.
Radially Scaled Parameters
A set of guided wave parameters represented by a corresponding
number of scales whose overall lengths equal the radius of a Smith
Chart, and which are used to measure the radial distance between
the center and the perimeter of the impedance or admittance coordinates,
at which point a specific value of the parameter exists.
Note 1: Radially scaled parameter values are mutually related
to each other as well as to a circular locus of normalized impedances
or admittances centered on these coordinates (see Chap. 14, Par.
14.8).
Note 2: The use of radial scales to represent radially scaled
parameter values avoids the need to superimpose families of concentric
circles on the impedance or admittance coordinates which (if all
parameters were thus represented) would completely obscure the coordinates.
Reflection Coefficients E or I
At a specified point in a waveguide, the ratio of the amplitudes
of the reflected and incident voltage or current waves. If the waveguide
is lossless the magnitude of the "Reflection Coefficients E or I"
is independent of the reference position. If it is lossy the magnitude
will diminish as the reference position is moved toward the generator.
Note 1: At any specified reference position along any uniform
waveguide the magnitude of the voltage reflection coefficient is
equal to that of the current reflection coefficient.
Note 2: On a Smith Chart the "Reflection Coefficients E or I"
is a radially scaled parameter.
Reflection Coefficient P
At a specified point in a waveguide the ratio of reflected to
incident power.
Note 1: In a uniform lossless waveguide the "Reflection Coefficient
P" is independent of the reference position.
Note 2: When expressed in dB the "Power Reflection Coefficient
P" is equivalent to the "Return Loss, dB."
Note 3: On a Smith Chart the "Reflection Coefficient, P" is a
radially scaled parameter.
Reflection Coefficient, X or Y Component
In a waveguide, the in-phase or quadrature-phase rectangular
component, respectively, of the "Reflection Coefficients E or Il"
represented on a Smith Chart as a rectangular-coordinate overlay.
(See Chap. 8.)
Reflection Loss, dB
A nondissipative loss introduced at a discontinuity along a uniform
waveguide, such as at a mismatched termination. "Reflection Loss,
dB" can be expressed as a ratio, in dB, of the reflected to the
absorbed power at the discontinuity and/or at all other points along
a uniform waveguide toward the generator therefrom.
Note 1: If the input impedance of a lossless waveguide is matched
to the internal impedance of the generator, a compensating gain
will occur at the generator end of the waveguide. Any difference
between the "Reflection Loss, dB" at each end of a waveguide corresponds
to the increase in attenuation in a waveguide due to reflected power
from the load.
Note 2: On a Smith Chart "Reflection Loss, dB" is a radially
scaled parameter.
Return Gain, dB
In a waveguide terminated in an impedance or admittance with
a negative real part, the ratio in dB of the power in the reflected
and incident waves.
Note 1: On a Smith Chart whose impedance or admittance coordinates
are designated with negative real parts this is a radially scaled
parameter.
Return Loss, dB
In a waveguide, the ratio in dB of the power in the incident
and reflected waves. The term "Return Loss, dB" is synonymous with
"Power Reflection Coefficient" when the latter is expressed in dB.
Note: On a Smith Chart this is a radially scaled parameter.
Smith Chart
A circular reflection chart composed of two families of mutually
orthogonal circular coordinate curves representing rectangular components
of impedance or admittance, normalized with respect to the characteristic
impedance and/or characteristic admittance of a waveguide. Peripheral
scales completely surrounding the coordinates include a set of linear
waveguide position and phase angle reference scales. The Smith Chart
also includes a set of radial scales representing mutually related
radially scaled parameters.
Note: The Smith Chart is commonly used for the graphical representation
and analysis of the electrical properties of waveguides or circuits
[25].
Standing Wave Loss Coefficient (Factor)
The ratio of combined dissipation and radiation losses in a waveguide
when mismatch-terminated and when match-terminated.
Note 1: A specific value of this coefficient applies to the transmission
losses integrated over plus or minus one-half wavelengths from the
point of observation, as compared to the attenuation in the same
length of waveguide. Thus, spatially repetitive variations in transmission
loss within each standing half wavelength are smoothed.
Note 2: On a Smith Chart this is a radially scaled parameter.
Standing Wave Peak, Const. P
The ratio of the maximum amplitude of the standing voltage or
current wave along a mismatch-terminated waveguide to the amplitude
of the corresponding wave along a match-terminated waveguide when
conducting the same power to the load.
Note: On a Smith Chart this is a radially scaled parameter.
Standing Wave Ratio (dBS)
In a waveguide, twenty times the logarithm to the base 10 of
the standing wave ratio (S).
Note: On a Smith Chart this is a radially scaled parameter.
Standing Wave Ratio (SWR)
The ratio of the maximum to the minimum amplitudes of the voltage
(or current) along a waveguide.
Note 1: For a given termination, and in a given region along
a waveguide the SWR is identical for voltage or current. If the
waveguide is lossy the SWR will diminish as the point of observation
is moved toward the generator.
Note 2: On a Smith Chart the SWR is a radially scaled parameter.
Transmission Coefficient E or I
At a specified point along a waveguide the ratio of the amplitude
of the transmitted voltage (or current) wave to the amplitude of
the corresponding incident wave.
Note 1: The "transmitted voltage (or current) wave" is the complex
resultant of the incident and reflected voltage (or current wave
at the point.
Note 2: On the Smith Chart the "Transmission Coefficient
E or I" is a linear scale equal in length to the diameter of the
impedance or admittance coordinates and pivoted from their origin.
As so plotted, this scale applies to voltage in relation to impedance
coordinates or to current in relation to admittance coordinates.
Transmission Coefficient P
In a waveguide, the ratio of the transmitted to the incident
power. The "Transmission Coefficient P" is equal to unity minus
the "Reflection Coefficient P."
Note: On a Smith Chart the "transmission Coefficient P" is a
radially scaled parameter.
Transmission Coefficient, X and Y Components
In a waveguide, the in-phase and quadrature-phase components
of the "Transmission Coefficient E or I" represented on a Smith
Chart as a rectangular coordinate overlay. (See Chap. 8.)
Transmission Loss Coefficient
In a waveguide, the "Standing Wave Loss Coefficient (Factor)."
Note: On Smith Chart this is a radially scaled parameter.
Transmission Loss, 1-dB Steps
A term used on Smith Charts to indicate the total losses due
to dissipation of power within a waveguide and/or the radiation
of power therefrom when the waveguide is match-terminated. "Transmission
Loss" is expressed as a ratio in dB of the relative powers in the
forward-traveling waves at two separated reference points along
the waveguide.
Note: As above defined and used on earlier Smith Charts,
the term is synonymous with the term "Attenuation (1 dB Maj. Div.)"
which is used on more recent Smith Charts. The change in designation
was made to avoid possible misunderstanding of the foregoing Smith
Chart usage of the term which in other usage frequently means the
total losses when the waveguide is mismatch-terminated. (See "Standing
Wave Loss Coefficient (Factor).")
Wavelengths Toward Generator (or Toward Load)
In a waveguide, the relative distances and directions between
any two reference points, represented on Smith Charts by the two
outermost peripheral scales expressing electrical lengths in wavelengths
from an arbitrarily selected radial reference locus on the impedance
or admittance coordinates.
Note: On Smith Charts with fixed scales, the zero points of these
scales are arbitrarily referenced to the position of a voltage standing
wave minimum on the impedance coordinates and/or a current standing
wave minimum or admittance coordinates. On a Smith Chart instrument,
in which these scales are rotatable with respect to the impedance
or admittance coordinates, the zero point may be aligned with any
other reference position on the coordinates.
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