Let’s consider an example: One important use of the Smith chart is to calculate the impedance of the load when the only measurement available is at the end of a transmission line connected to the load. A complete circle equals 1/2 wavelength, or 180 electrical degrees.
TRANSMISSION LINE SMITH CHART GENERATOR
Moving clockwise is equivalent to moving toward the generator while moving counterclockwise is equivalent to moving toward the load. A SWR of 1.0 is simply a point at the center of the chart, while an SWR of infinity is a circle coinciding with the outside edge of the chart. A line of constant standing wave ratio (SWR) is a circle centered at 50 ohms. Reactance above the horizontal axis is positive (inductive) while reactance below the horizontal axis is negative (capacitive). Lines of constant reactance are arcs with one end on the outside circle and the other end at infinity. (Most Smith Charts are normalized to a system impedance of 1 ohm, but the same principles apply.) The system impedance of 50 ohms is at the center of the chart. Zero resistance appears at the far left side of the horizontal axis and infinite resistance appears at the far right side. Resistance is shown on the horizontal axis and lines of constant resistance are represented by circles that cross the horizontal axis and are aligned with the far right side of the chart. (See Equation 1.) Solving this equation is messy when done manually, but even when a computer is available, the Smith chart is the preferred solution because it aids understanding.Ī simplified Smith chart is shown in Figure 2. The Smith chart is used to solve the transmission line impedance equation, where Z 0 is the characteristic impedance of the transmission line (usually 50 ohms), Z L is the load impedance, b is the propagation constant of the line, and l is the distance on the line measured from the load. Similarly, lines of constant reactance also become arcs, but with their ends at the chart edge. It helps to think of the problem in the following way: If we start with a rectangular-coordinate system like the one in Figure 1, and distort the reactance axis (y axis) into a number of circles with incrementally larger radii, we now represent constant resistance by a circle rather than a vertical line. This behavior is much better represented on a polar-coordinate system. Impedance can be plotted in a rectangular-coordinate system, but the repeating cycle is very messy to represent. Starting at the load and working backward, the load impedance appears again at a distance of 1/2 wavelength and the cycle repeats. The ratio of voltage to current - which is the definition of impedance - also changes with position on the line. When an antenna or other load is connected to a transmission line and a RF signal is generated at the opposite end, the interaction between energy in the line and the load will create reflections on the line.
A positive reactance indicates an inductive circuit while a negative reactance indicates a capacitive circuit. In general, impedance is written as Z=R+jX, where R is the resistance and X is the reactance. Before we jump into the structure of the Smith Chart, let’s recall that impedance is a complex number that consists of a real part (resistance) and an imaginary part (reactance).
Perhaps most importantly, thinking in terms of the Smith chart develops intuition about transmission-line and impedance-matching problems.
TRANSMISSION LINE SMITH CHART SOFTWARE
In fact, it is an integral part of computer-aided design (CAD) software and the radio-frequency network analyzer. In this day of personal computers, spreadsheets and smartphones, a graphical solution may seem quaint but the Smith chart is still an essential tool for radio-design engineers. The Smith chart is a graphical aid for solving transmission line problems.