How to Draw Constant Vswr Circle on Smith Chart
The Smith Chart
Dorsum: Antenna Theory (Home)
In this tutorial, we will introduce and explain Smith Charts, and then given an introduction to impedance matching. We will and then utilise the Smith Chart to perform impedance matching with transmission lines and lumped components (capacitors and inductors).
Introduction to Smith Charts
Up: Smith Chart and Impedance Matching Table of Contents
The Smith Chart is a fantastic tool for visualizing the impedance of a transmission line and antenna organization equally a function of frequency. Smith Charts tin can exist used to increase understanding of transmission lines and how they behave from an impedance viewpoint. Smith Charts are also extremely helpful for impedance matching, as we will run into. The Smith Chart is used to display an bodily (physical) antenna'south impedance when measured on a Vector Network Analyzer (VNA).
Smith Charts were originally developed around 1940 by Phillip Smith as a useful tool for making the equations involved in transmission lines easier to dispense. Run across, for case, the input impedance equation for a load attached to a transmission line of length L and characteristic impedance Z0. With modernistic computers, the Smith Chart is no longer used to the simplify the calculation of manual line equatons; yet, their value in visualizing the impedance of an antenna or a transmission line has non decreased.
The Smith Chart is shown in Figure 1. A larger version is shown hither.
Effigy 1. The basic Smith Chart.
Figure 1 should expect a little intimidating, as it appears to exist lines going everywhere. There is nothing to fear though. We will build up the Smith Chart from scratch, so that you tin sympathize exactly what all of the lines hateful. In fact, we are going to learn an fifty-fifty more complicated version of the Smith Chart known as the immitance Smith Chart, which is twice as complicated, simply also twice every bit useful. Simply for at present, just admire the Smith Chart and its curvy elegance.
This section of the antenna theory site volition nowadays an introduction to Smith Nautical chart nuts.
Smith Nautical chart Tutorial
We'll now begin to explicate the fundamentals of the Smith Chart. The Smith Chart displays the complex reflection coefficient [Equation 1, below], in polar class, for an capricious impedance (nosotros'll call the impedance ZL or the load impedance). The reflection coefficient is completely adamant past the impedance ZL and the "reference" impedance Z0. Note that Z0 can be viewed as the impedance of the transmitter, or what is trying to deliver power to the antenna. Hence, the Smith Chart is a graphical method of displaying the impedance of an antenna, which can be a single point or a range of points to display the impedance every bit a function of frequency. For a primer on complex math, click hither.
Recall that the complex reflection coefficient (
For this Smith Chart tutorial, we will assume Z0 is 50 Ohms, which is often, just not ever the example. Note that the Smith Nautical chart can be used with any value of Z0.
The complex reflection coefficient, or
Effigy 2. The Complex Reflection Coefficient must lie somewhere inside the unit circle.
In Figure ii, we are plotting the set of all values for the circuitous reflection coefficient, forth the real and imaginary centrality. The middle of the Smith Chart is the point where the reflection coefficient is zero. That is, this is the simply point on the Smith Nautical chart where no power is reflected past the load impedance.
The outter ring of the Smith Chart is where the magnitude of
Let's await at a few examples.
Smith Nautical chart Case 1. Suppose 
From equation [1], nosotros can solve for ZL to exist:
.Figure 3. plotted on the Smith Chart.
Since
Smith Chart Example 2. Suppose 
Figure four. plotted on the Smith Chart.
From Equation [2] and using Z0=50, we notation that
ZL = twenty.27 + i*21.62 [Ohms].
Smith Chart Example 3. 
Figure 5. =-i plotted on the Smith Nautical chart.
From Equation [ii] and with Z0=50,
VSWR on the Smith Chart
Since VSWR is but a part of the absolute value of
Smith Nautical chart Lecture
Here nosotros present an introduction video to Smith Charts. This video can be skipped if you like; the material is covered in the remaining sections. However, if you similar videos, hither is another medium of presenting the Smith Chart that may be beneficial. Particularly, the Immittance Smith Chart is discussed in terms of the reflection coefficient. An example antenna impedance is plotted on the Smith Nautical chart and explained. The goal of this movie is to present the information using a different method (video instead of webpage), which will hopefully increase your understanding of Smith Charts.
To sum up this page so far, the Smith Nautical chart is a plot of the reflection coefficient. Since the reflection coefficient corresponds directly to an impedance, we are actually plotting the impedance of a device on the Smith Nautical chart. In the next section, we'll start filling in some of the crazy lines on the Smith Chart visible in Figure 1.
Side by side: Constant Resistance Circles
Smith Chart Table of Contents
Topics Related To Antenna Theory
Antenna Tutorial (Home)
Intro to Smith Charts
Smith Charts Video
Abiding Resistance Circles
Abiding Reactance Curves
Impedance Transformations
Impedance Matching: Series 50 and C
Impedance Matching: Tx Lines
The Comprisal Smith Chart
Impedance Matching: Parallel L and C
Impedance Matching: Parallel Tx Lines
Immittance Charts
Impedance Matching on Immittance Charts
Dual-Ring Impedance Matching
Source: https://www.antenna-theory.com/m/tutorial/smith/chart.php
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