#Smith chart impedance and admittance how to#

The reason once around is only half a wavelength is due to the addition of two waves - the forward and reflective waves on the transmission line. One revolution around the VSWR circle is a one-half wavelength. VSWR can be depicted as a circle centered around the chart center (at “1.0”). All impedances are scaled relative to whatever characteristic impedance value you are working with. For the common 50 Ohm system, the center of the chart would be “normalized” to 1.0 units.

The center of the chart (r = 1.0 and x = 0) is always a “perfect match,” at least for a desired 50 Ohm, but can be any impedance you want. Once you plot the impedance point, other parameters - like Voltage Standing Wave Ratio (VSWR) or return loss - can be read off the Smith Chart. On the Smith Chart, the phase is actually the distance in wavelengths along the transmission line - the outer-most circle. Polar means there is a real part - the magnitude of the impedance point (or Γ L ) and the phase of the impedance. The reactance curves on the top half of the chart are inductance curves most notable are the 0.9 and 1.0 curves at the top that curve down to the right hand center. There are resistance circles from 0 to “∞” Ohms. The reflection coefficient Γ L is related to the load impedance Z L and the system impedance Z o as:

We know the reflection coefficient Γ L is defined as the ratio between the reflected voltage wave and the incident voltage wave, as shown in Figure 1. Sometimes, instead of considering the load impedance directly, you express its reflection coefficient, Γ L. A Smith Chart is utilized by examining the load and where the impedance must be matched. The Smith Chart is a polar plot of the complex reflection coefficient, Γ, for a normalized complex load impedance Zn = R + jX, where R is the resistance and X the reactance.

#Smith chart impedance and admittance how to#

There is some algebra involved in understanding the basic transmission line equations, but - once you understand how to move on the graph - you can forget the math and just read the chart. What Is a Smith Chart?Īlthough there are many computer programs 2, 3 and network analyzers that can solve impedance matching problems for you, a complete understanding of the Smith Chart is highly beneficial in understanding the nature of transmission lines. This chart closely resembles the chart we see today. According to his biography, his impedance coordinates were not orthogonal - which means perpendicular - and there were no true circles, but the standing wave ratio was linear.

The first graphical chart was limited by the range of data so he came up with a polar plot that was a scaled version of the first plot. He used a thermocouple bridge and voltmeter to make the measurements. Smith developed the first graphical solution in the form of a rectangular plot from his measurements of the maxima and minima voltages along the transmission line. Phillip Smith - Inventor of the Smith Chart. He relished the problem of matching the transmission line to the antenna a component he considered matched the line to space. Although Smith did a great deal of work with antennas, his expertise and passion focused on transmission lines. In 1928, he joined Bell Labs, where he became involved in the design of antennas for commercial AM broadcasting. Smith attended Tufts College and was an active amateur radio operator with the callsign 1ANB. The Smith Chart was invented by Phillip Smith, who was born in Lexington, MA on April 29, 1905. After reading this, you will have a better understanding of impedance matching and VSWR - common parameters in a radio station. The purpose of this article is to introduce you to the basics of the Smith Chart. The Smith Chart is one of the most useful tools in radio communications, but it is often misunderstood.