# Construction of a Circle Diagram

Author: Edmund A. Laport

For field-engineering purposes it is desirable to have a master chart from which blueprints can be made in any quantity for field use. The following information will enable one to reconstruct a chart like that of Fig. 4.58, the field of which embraces the range of values encountered in all except extreme cases.

1. Use a sheet of graph paper approximately 10 by 15 inches ruled in centimeters with 0.1-centimeter subdivisions or in 1/2 inches with 10 subdivisions. Locate 0, the origin of coordinates, at the middle of the left-hand long side of the sheet, when the long side is vertical. Then

a. Starting at 0, progressing upward on the left-hand scale, mark each major division in order 0.2, 0.4, 0.6, etc., to the top of the sheet. This will be the ratio scale for positive reactances.

b. Starting at 0, progressing downward along this same scale, mark the major divisions -0.2, -0.4, -0.6, -0.8, etc., to the bottom of the sheet. This will be the ratio scale for negative reactances.

c. Starting at 0, mark the horizontal scale so that successive major divisions are 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, etc., to the right-hand margin. This will be the ratio scale for resistances, or resistance axis.

2. Locate the point where resistance is 1.0 and reactance zero. This will be the focal point for the circle diagram.

3. With centers on the resistance axis, draw the following confocal circles:

 Location of center on resistance axis Circle radius in terms of resistance-scale units Mark the circle in terms of the following standing-wave ratio Q 1.02 0.18 1.2 1.06 0.34 1.4 1.11 0.49 1.6 1.18 0.62 1.8 1.25 0.75 2.0 1.45 1.05 2.5 1.67 1.33 3.0 1.89 1.61 3.5 2.13 1.88 4.0 2.36 2.14 4.5 2.60 2.40 5.0

4. Draw the following semicircles from centers on the reactance axis, using a radius that causes the semicircle to pass through the focal point 1.0 - j0.

 Location of center on reactance axis Mark the negative and positive ends of the semicircles Negative end (degrees) Positive end (degrees) -2.74 10 100 -1.74 15 105 -1.20 20 110 -0.84 25 115 -0.58 30 120 -0.36 35 125 -0.17 40 130 0 45 135 0.17 50 140 0.36 55 145 0.58 60 150 0.84 65 155 1.20 70 160 1.74 75 165 2.74 80 170

This gives a set of semicircles which all pass through the focal point and are orthogonal with respect to the Q circles and whose ends are marked in progression clockwise from 10 to 170 degrees in 5-degree steps.

This completes the circle diagram for a transmission line in terms of the ratios of resistance and reactance to that of its characteristic impedance at any distance from a resistive termination in degrees and for any standing-wave ratio from 1.00 to 5.0, the same as shown in Fig. 4.58. If drawn with care and skill, the accuracy of this chart will equal or surpass the usual accuracy of measurements.

Last Update: 2011-03-19