A transmission line that is terminated with a load impedance equal to the characteristic impedance Z_o of the line will not reflect an incident wave at that point, and the transmission line is said to be impedance matched. However, a transmission line that is terminated with a load impedance different than Z_o will reflect part of an incident wave back toward the generator. Reflections are often undesirable and should be eliminated. If the load impedance has a nonzero real part (i.e., it has a resistive component), it is possible to eliminate the reflection by placing a proper length of transmission line (the stub) at the right place. A properly located stub of the proper length will combine with the load impedance to give an equivalent impedance equal to Z_o, and thus impedance match the transmission line at the point where the stub joins the main transmission line. This procedure, known as single stub tuning or stub matching, is described in many intermediate level textbooks on electromagnetism. The stub is often terminated with a short for practical reasons, although other terminations can be used. Stub tuning can give impedance matching only at a single frequency, and cannot be used to eliminate reflections of broadband signals such as pulses.

The problem usually encountered is one of finding the length and position of a stub that will give zero reflection for a given load impedance, frequency and transmission line characteristics. This Java applet calculates all combinations of stub lengths less than half-wave long and stub positions that does this, calculates the reflection spectrum as a function of stub length and position, and shows the procedure on a Smith chart. The applet is divided into three panels:

1. The upper panel is a graph of the power reflection coefficient (measured at the left end of the transmission line in the middle panel) as a function of frequency. The yellow (----) curve is the reflection coefficient with the stub while the red (----) curve is the reflection coefficient without the stub. Either an open or a shorted stub can be selected. The frequency resolution of the graph can be changed to fine, medium or coarse to accommodate different processor speeds - use the finest frequency resolution that gives an acceptably fast response. By selecting the linear or dB buttons at top, the graph can display either a linear or logarithmic scale for the reflection coefficient. Finally, there is a blue (----) frequency cursor that can be moved with the LEFT and RIGHT arrow keys (SHIFT for larger step size) or dragged with the mouse. It is necessary to click on this panel before using the arrow keys.

   The Smith Chart button opens a Smith admittance chart. The white grid lines are g = 1 (circle) and b = 0 (line).

   The stub load can be either a short or open circuit. The yellow arc (----) shows the transformation of the stub load (filled square) to the admittance at the end of the stub (open circle). If the arc goes around the Smith chart more than once, only the fractional revolution is yellow. The filled red (----) square represents the load admittance, and the red arc shows the transformation of this load admittance to the point where the stub joins the main transmission line. If the arc goes around the chart more than once, only the fractional revolution is red. The blue (----) line represents the change in the transformed load admittance when the stub admittance is added to it. The net admittance is the open blue circle at the end of this line; this point should be at the center of the Smith chart for impedance matching.

2. The middle panel is a drawing of a transmission line with a load at the right end and with a yellow (----) tuning stub whose position and length can be varied either by dragging it with the mouse or by using the LEFT, RIGHT, UP and DOWN arrow keys (SHIFT for larger step size). It is necessary to click in this panel before using the arrow keys. As the stub changes position and length, the reflection coefficient in the upper panel is re-plotted using the new values of the stub parameters. The dark blue (----) dashed stubs show the location and length of stubs that will impedance match the transmission line at the cursor frequency in the upper panel. These will change as the frequency cursor is moved. The stub can be moved to one of these impedance matching positions by clicking slightly above the transmission line with the mouse. The stub location (measured from the load) and its length are displayed above and to the right of the stub, respectively.

3. The lower panel is used to change the transmission line and stub characteristic impedance and index of refraction, and to change the load at the right end of the transmission line. There are five choices for the load.
   • Constant admittance is a load that is independent of frequency, but for which the real part (conductance) and the imaginary part (susceptance) can be independently varied.

   • Constant impedance is another load that is independent of frequency, but for which the real part (resistance) and the imaginary part (reactance) can be independently varied.

   • Inductance is a load consisting of an inductor with a series resistance, The inductive reactance is proportional to frequency, but the series resistance is independent of frequency. The inductance and series resistance can be independently varied.

   • Capacitance is a load consisting of a capacitor with a parallel or shunt resistance. The capacitive reactance is inversely proportional to frequency, but the parallel resistance is independent of frequency. The capacitance and parallel resistance can be independently varied.

   • Smith chart uses the Smith chart to specify the load admittance. Drag the red square on the Smith chart to the point corresponding to the desired admittance. The real and imaginary parts of the admittance value are displayed in the bottom text fields.