W8WWV - SMC - Series Matching Calculator Software

Greg Ordy

## What is SMC?

SMC computes the lengths of two different types (impedances) of transmission lines. When these two lines are connected in series (in the right order!), they perform an impedance match between a 50 Ohm transmission line, and a complex impedance, usually the impedance at an antenna. The goal is to reduce the SWR to 1.0.

In the typical scenario, the antenna impedance is close to, but not exactly, 50 Ohms of resistance (50 + j 0 Ohms). The SWR will, therefore, be greater than 1.0. It is desired to lower the SWR as much as possible. Available resources include 50 Ohm transmission line, and transmission line of another impedance. Often this is 75 Ohm line, such as RG-11. It could be a parallel combination of 50 Ohm line, creating a 25 Ohm line. It can be any line or parallel combination of lines that has an impedance other than 50 Ohms. An antenna analyzer or other measurement device is used to determine the impedance at the antenna.  The frequency, antenna impedance, and the important characteristics (impedance and velocity factor) of the two lines are supplied to SMC. It then computes two lengths, a length of 50 Ohm line, and a length of the other line. The 50 Ohm line is connected directly to the load, usually the antenna. The other impedance line is connected to the opposite end of the 50 Ohm line. Their combination results in the transformation of the load impedance into 50 Ohms at the input of the second line section. From that point, standard 50 Ohm transmission line runs the remainder of the distance back to the radio, with an SWR of 1.0.

This technique will not work on all load impedances. There is a finite range of impedance values which can be matched by this technique. The range is related to the impedance values of the two transmission lines. The range is increased when the impedance between the two different transmission line impedances increases. In practice, the typical impedance values of verticals, dipoles, and even loops, can be matched back to 50 Ohms by using nothing more than 50 and 75 Ohm line. If you are running low power, this could be, for example, RG-8X and RG-59. If you are running high power, this could be RG-8 and RG-11. Certainly use transmission line which can handle your power level.

This approach works because any transmission line which is not terminated in its characteristic impedance will act as an impedance transformer. The impedance at the input will be a function of the impedance values (line and load) and the length of the line. By cleverly picking specific lengths of line, and lines of different impedance, it may be possible to arrive at a desired value, such as 50 + j 0 Ohms, a match to the rest of the feedline and radio.

The history and math behind this technique can be found on a page by L.B. Cebik, W4RNL. The technique is also described in recent editions of the ARRL Antenna Book. My program uses the equations in the ARRL Antenna Book, 18th edition, page 26-4.

## Using SMC

In order to use SMC you must supply several values. You need:

1. Target Frequency: The computed solution is a function of frequency. You must specify the frequency.

2. Load Impedance: The complex load impedance, expressed as an unsigned resistance value and signed reactance value.

3. Transmission Line #1: This is the series section that connects to the load. Its impedance is also the final matched impedance. The transmission line can be specified either from a drop-down list of popular choices, or, as explicit impedance and velocity factor values. The important data are the impedance and velocity factor. The list of transmission line choices does nothing more then set values in the impedance and velocity factor data fields. Transmission line #1 is typically the 50 or 52 Ohms coaxial cable. Even if you find the line you want on the list, verify the impedance and velocity factor, since they are the important parameters.

4. Transmission Line #2: The second transmission line. The impedance must be different than the impedance of line #1 in order to achieve useful matches.

Here is a screen capture of SMC showing the results of an example computation. SMC Example Screen Capture

The frequency (7.050) has been entered into the frequency field. Units are MHz. The transmission line labeled Z0 is the matched line going back to the radio. As the screen indicates, this is the same as the Z1 transmission line. I have selected RG-213 cable from the drop-down list. The impedance (50 Ohms) and velocity factor (66%) have been automatically filled in, but they can be edited if desired. Feel free to specify a transmission line with an impedance of 32 Ohms and a velocity factor of 27%.

The transmission line labeled Z2 is the different transmission line, type RG-11 in this example. Its impedance is 75 Ohms.

The load impedance is 32 - j 4 Ohms. This might represent a short vertical antenna with a small amount of capacitive reactance.

When all of the fields are filled in, click the Compute button. The solution will appear in the L1 and L2 fields. If a solution is not possible, a message box will indicate that result. If a solution is not possible, you must try an alternate transmission line for Z2. One simple choice is two parallel 50 Ohm cables, creating a 25 Ohm cable. Another choice is to parallel two 75 Ohm cables creating a 37.5 Ohm cable.

For this example, we find that L1 is 31.934 feet, and L2 is 8.594 feet. The lengths are also shown in meters, degrees, and wavelengths.

This means that if you want to match a 32 - j 4 Ohm load to a 50 Ohm transmission line, you should cut a 31.934 foot length of the Z1 transmission line, and connect it to the load. Cut a 8.594 foot length of the Z2 transmission line and connect it to the free end of the Z1 cable. The free end of the Z2 cable is now matched to the Z0 impedance. Although there will be standing waves on the Z1 and Z2 cables, the Z0 line will be flat and matched, all the way back to the radio.

I have used this program several times to match real antennas, and it does indeed do the job. I put male coax connectors on the ends of the cables and use female barrel connectors between all of the sections.

## System Requirements

SMC is a Windows program in the form of a dialog box. It should run on all versions of Windows. SMC does not touch the registry. It does not read files. You can save the results in a text file. You can also directly print the results. SMC is a simple calculator with a fill in the blank user interface.

SMC is a contained in a single file (smc.exe). There is no companion installation or removal program. After you download the program you can execute it. If you don't need it, delete it. If you want a shortcut, you have to create it manually.

A second file, smc.hlp contains the context help messages. To be honest, there is little extra value in these messages. If you want to download the file, be sure to place it in the same folder that holds the smc.exe file, so that the program can find the companion help text.