In solving transmission-line problems, prime center is usually assigned a value equal to the characteristic impedance of the transmission line to be used. 1B represents an impedance of 0.5 × 200 = 100 ohm resistance, and 1.0 × 200 = 200 ohm negative (capacitive) reactance (Z = 100 - j200). 1B).įor example, if a value of 200 is assigned to prime center, then point C in Fig. If a value of 50 ohm had been assigned to prime center, the same impedance would be plotted at the intersection of the 50/50 = 1.0 resistance circle and the 100/50 = 2.0 reactance circle (point B in Fig. If we assign a value of 100 ohm to prime center (Z 0 = 100), the z point will be plotted at the intersection of the 50/100 = 0.5 resistance circle and the 100/100 = 1.0 positive reactance circle (point A in Fig. Suppose we have an impedance consisting of 50 ohm resistance and 100 ohm inductive reactance (Z = 50 + j100). The plotting of complex impedances can best be explained by one or two examples. Values to the right of the resistance axis are positive (inductive), and those to the left of the resistance axis are negative (capacitive). All points along any reactance circle have the same reactive value as the point where the reactance circle touches the reactance axis (outer circle). The reactance axis is also calibrated in percentages of a selected value - usually the value assigned to prime center. These are reactance circles, the large outer circle being the reactance axis. Superimposed on the resistance-circle pattern are segments of other circles tangent to the resistance axis at R = ∞. All points along any resistance circle have the same resistive value as the point where the circle crosses the resistance axis. 1A) are centered on the resistance axis, are tangent to the outer circle at the R = ∞ point, and pass through the calibrated points on the resistance axis. It is common practice to indicate actual impedance values in capital letters (Z 1, Z A, Z L, etc.) and corresponding normalized values in small letters (z 1, z A, z L, etc.). This process permits the use of the numbers printed on the Smith Charts for values irrespective of their magnitudes. This is called "normalizing." Similarly, points on the Chart are converted back to actual resistance values by multiplying by the value assigned prime center. It is seen that in each case the point on the Chart for any resistance value is determined by dividing the value by the number assigned to prime center. If a value of 50 ohm is assigned to prime center, corresponding values will be 25, 10 and 100 ohm. If prime center is assigned a value of 100 ohm, then 0.5 represents 50 ohm, 0.2 represents 20 ohm, 2.0 represents 200 ohm, etc. The calibration of this line runs from 0 at the top to infinity (∞) at the bottom. The numbers along this line indicate percentages of the value assigned to the center point - the 100 per cent point indicated by the numeral 1.0 - usually referred to as prime center. The only straight line on the Chart - the vertical one in Fig. 1, the Smith Chart (1) consists basically of a circle upon which are placed various circular scales. But a brief description of its construction and some of its simpler applications will show that it is far less complicated than its aspect.
In All probability, the chief reason that more use of the Smith Chart is not made by amateurs in solving some of their antenna-feeding problems is its formidable appearance at first glance. In this article, K6CRT discusses the use of the Chart in some of its simpler applications.
This device eliminates the need for mathematical gymnastics and greatly reduces the laborious task of solving most transmission-line problems. One of the most useful tools at the disposal of the radio engineer is a transmission-line calculator known as the Smith Chart.
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