Smith chart which shows how the complex impedance of a transmission line varies along its length

This article is about the graphical devices called nomograms. For a description of the Japanese puzzle see nonogram. Additionally, there are monograms, small motifs of combined letters.

A nomogram or nomograph is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function. Like a slide rule, it is a graphical analog computation device; and, like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Most nomograms are used in applications where an approximate answer is appropriate and useful. Otherwise, the nomogram may be used to check an answer obtained from an exact calculation method. Image File history File links Size of this preview: 513 × 600 pixelsFull resolution (1146 × 1340 pixel, file size: 356 KB, MIME type: image/png) La bildo estas kopiita de wikipedia:en. ... Image File history File links Size of this preview: 513 × 600 pixelsFull resolution (1146 × 1340 pixel, file size: 356 KB, MIME type: image/png) La bildo estas kopiita de wikipedia:en. ... An impedance Smith chart (with no data plotted) The Smith Chart, invented by Phillip H. Smith (1905-1987),[1][2] is a graphical aid or nomogram designed for electrical and electronics engineers specialising in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits. ... Electrical impedance or simply impedance is a measure of opposition to a sinusoidal electric current. ... A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission. ... An example of a Paint by Numbers puzzle. ... The Chi-Rho, a monogram of the first two letters in the Greek word for Christ E and L embroider for clothes and bedding, for a wife by the initials E L or L E A monogram is a motif made by overlapping or combining two or more letters or... A typical 10 inch student slide rule (Pickett N902-T simplex trig). ...

The slide rule is intended to be a general-purpose device. Nomograms are usually designed to perform a specific calculation, with tables of values effectively built in to the construction of the scales.

A nomogram typically has three scales: two scales represent known values and one scale is the scale where the result is read off. The known scales are placed on the outside; i.e. the result scale is in the center. Each known value of the calculation is marked on the outer scales and a line is drawn between each mark. Where the line and the inside scale intersects is the result. The scale marks include 'tick marks' to indicate exact number locations, and labeled reference values. These scales may be linear, logarithmic or have some more complex relationship. Straight scales are useful for relatively simple calculations, but for more complex calculations, simple or elaborate curved scales may need to be used. The word linear comes from the Latin word linearis, which means created by lines. ... A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ...

Usage is simple — a taut string or other straight edge is placed so as to contact the two known values on their lines. The required answer is read off another line. This allows calculation of one variable when the other two are known. Additional lines are sometimes added that are simple conversions of one of the other variables.

One common nomogram that defies the above definition is a temperature graph. On this graph, degrees Fahrenheit and degrees Celsius are both indicated. While it is drawn as a single line with two scales, the two different scale markings indicate that there are actually two lines overlapping each other. Fig. ... Fahrenheit is a temperature scale named after the German physicist Daniel Gabriel Fahrenheit (1686–1736), who proposed it in 1724. ... Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ...

Examples of nomograms:

• Spiral-shaped nomogram -- the Cornu spiral
• The Smith chart (see figure, right), used in electronics and systems analysis
• nonlinearly ruled graph paper - probability rule, semi-log rule or log-log rule, all intended to represent various non-linear functions as straight lines on a graph.

In mathematics and optics, the two Fresnel integrals, S(x) and C(x) arise in the description of near field Fresnel diffraction phenomena, and are the integrals defined as follows: . Some may use π t2/2 instead of t2, in which case the S(x) and C(x) above should... An impedance Smith chart (with no data plotted) The Smith Chart, invented by Phillip H. Smith (1905-1987),[1][2] is a graphical aid or nomogram designed for electrical and electronics engineers specialising in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits. ... Electronics is the study of the flow of charge through various materials and devices such as, semiconductors, resistors, inductors, capacitors, nano-structures, and vacuum tubes. ... This article does not cite its references or sources. ... Graph paper or quad-ruled paper is writing paper that is printed with fine lines making up a regular grid. ...

More examples

Parallel electrical resistance nomogram.

Image File history File links Download high resolution version (706x719, 23 KB)Nomogram for calculating resistances in parallel This particular graphic version of a well-known kind of nomogram is copyright ©2003 by Daniel P. B. Smith and licensed under the terms of the Wikipedia copyright. ... Image File history File links Download high resolution version (706x719, 23 KB)Nomogram for calculating resistances in parallel This particular graphic version of a well-known kind of nomogram is copyright ©2003 by Daniel P. B. Smith and licensed under the terms of the Wikipedia copyright. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

Parallel-resistance/thin-lens nomogram

The nomogram below performs the computation

This nomogram is interesting because it performs a useful nonlinear calculation using only straight-line, equally-graduated scales.

A and B are entered on the horizontal and vertical scales, and the result is read from the diagonal scale. Being proportional to the harmonic mean of A and B, this formula has several applications. For example, it is the parallel-resistance formula in electronics, and the thin-lens equation in optics. In mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. ... Electronics is the study of the flow of charge through various materials and devices such as, semiconductors, resistors, inductors, capacitors, nano-structures, and vacuum tubes. ... Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ...

In the example below, the green line demonstrates that parallel resistors of 56 and 33 ohms have a combined resistance of about 21 ohms. It also demonstrates that an object at a distance of 56 cm from a lens whose focal length is 21 cm forms a real image at a distance of about 33 cm. A multimeter can be used to measure resistance in ohms. ... Look up lens in Wiktionary, the free dictionary. ... The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror. ...

Chi-squared test computation nomogram

Chi-square distribution nomogram.

The nomogram below can be used to perform an approximate computation of some values needed when performing a familiar statistical test, Pearson's chi-square test. This nomogram demonstrates the use of curved scales with unevenly-spaced graduations. Image File history File links Download high resolution version (451x661, 75 KB)Nomogram for a calculation required for the chi-squared test Nomogram invented and designed by Daniel P. B. Smith. ... Image File history File links Download high resolution version (451x661, 75 KB)Nomogram for a calculation required for the chi-squared test Nomogram invented and designed by Daniel P. B. Smith. ... In probability theory and statistics, the chi-square distribution (also chi-squared or χ2  distribution) is one of the theoretical probability distributions most widely used in inferential statistics, i. ... Pearsons chi-square test (χ2) is one of a variety of chi-square tests – statistical procedures whose results are evaluated by reference to the chi-square distribution. ...

The relevant expression is

The blue line demonstrates the computation of

(9 − 5)²/ 5 = 3.2

The red line demonstrates the computation of

(81 − 70)² / 70 = 1.7

In performing the test, Yates' correction for continuity is often applied, and simply involves subtracting 0.5 from the observed values. A nomogram for performing the test with Yates' correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart. Yates correction for continuity, or Yates chi-square test, adjusts the formula for Pearsons chi-square test by subtracting 0. ...

External links

Look up nomogram in
Wiktionary, the free dictionary.

• Charts, graphs and nomographs that provide new insights.
• Nomogram from Wolfram Research