For our first example, we'll create a rough first cut two element L-Match for use over the range of 950 to 1050 MHz. We would like it to match a 100 ohm fixed load to a 50 ohm source. We selected element values to give a newbie practice in creating a good match.


Although this network is topologically correct, (it's capable of making this narrow band match), its VSWR, (with the element values given), will be very poor. Its your job to make it better! Don't worry - we'll help.

Enter the SmithMatch Module by choosing "(1) SmithMatch" from the Main Menu. either by pressing "1" or by using the "F1" function key. As you may recall, the screen display will look as follows:

            SmithMatch Module

            System Z0 [<Enter>=Quit]  ? _

Enter "50" in response to the Z0 (characteristic impedance) question. and then press <Enter>. The next question will be:

            Filename: [<Enter>=Quit] ? _

Type in the file name TWOFREQ. Its the test file we created when we were studying the File Utility. You will see the following display:

VSWR:  1.5                                                                                                  03-19-2005 @ 09:50:35             System Z0:  50  ohms             Data File   :  TWOFREQ              Freq             RL            XL            VSWR              950.0           100.000    0.000        2.000              1050.0         100.000    0.000        2.000                      Command ? _              Ckt: \Load

Note that, after the chart loaded, we've added a VSWR = 1.5 circle onto the Smith Chart. The program will ask you, the first time, if you want one - all you need do is answer "Y" to the question. You can add a 2nd VSWR circle by typing "V," at the "Command ? _" prompt, at any time. You might want this to mark an outer bound on the quality of your match.

What you're now looking at is a Smith Chart plot of a fixed 100 ohm load. Its a little HARD to see on this page, but its a small circle about in the middle of the right half of the chart, right on the axis of reals. Do you see it?

If the load file contained complex impedances, instead of a purely real value, the locus of all points would be spread out, due to the effects of frequency upon the reactive component; a small circle would mark the low end of the frequency band.

Note that, at both frequency points, the VSWR = 2.0. This is exactly what 100 ohms should look like in a 50 ohm system.

At the very bottom left corner of the screen above, you'll see the statement:

             Ckt: \Load

What this means is that the screen circuit file is empty, and that the plot is just the contents of a load impedance file named "TWOFREQ." As you add circuit elements, one at a time, the on-screen circuit file will grow. It will show you both the code number, and the value of each element that you've entered and saved.

Note: You can visit Appendix A from here, but you must use the BACK button on your browser to return to this page.

Finally, you'll see the question:

           Draw VSWR circle (Y/N) ? _

Please answer "Y" and then press <Enter>. Type "1.5" to draw a VSWR=1.5 circle on-screen. Remember, at any time, you may draw a second VSWR circle, perhaps an outer bound. Simply type "V" from the "Command ?" prompt. For a list of several other on-screen commands, see Appendix B.

Note: You can visit Appendix B from here, but you must use the BACK button on your browser to return to this page.

Now let's create this two element L-Match network. The first element, the one closest to the load, is a shunt capacitor. You'll find it listed in Appendix A, you'll see that the element code number is "5," and that the units are pF. Let's make a guess at a value of 5 pF for this first element.

Type "5" at the "Command ?" prompt. You'll be asked the question:

                       Shunt C (pF) ? _

Type "5" and press <Enter>.

If you're an old hand at this, you'll remember that a shunt capacitor causes clockwise rotation along a circle of constant admittance. As you can see on your screen, (see the plot below), that's exactly what happened.

VSWR:  1.5                                                                                                  03-19-2005 @ 09:54:11             System Z0:  50  ohms             Data File   :  TWOFREQ              Freq             RI            XI            VSWR              950.0           10.094    -30.124        6.807              1050.0           8.417    -27.764        7.813                      Command ? _              Ckt: \5(5)\Load

We have a problem here because we went to far. It would have been better to add less capacity and stop our rotation at the 50 ohm resistance circle. If we had done that, we could then add a series inductor and rotate clockwise into chart center for a near perfect VSWR!

Note that the input impedance and VSWR listing on the left side of the screen have been up-dated to reflect the input impedance of the load impedance now shunted by a 5 pF capacitor.

Note that the on-screen question on the command line is now:

                     Save Element (Y/N) ? _

If you type "Y" the element value you added will be considered "permanent." If you type "N" you'll be able to go back one step and try a lower value of shunt capacitor. The first plot will stay on-screen, as a marker, and you can try different element values until you get it right.

However, for now, lets do the unforgivable, and accept the crummy 5 pF value. Don't worry, we have a good reason!

Type "Y" and press <Enter>.

The important thing to notice is that now the on-screen circuit file, at the bottom of the screen, has been up-dated. It now shows "Ckt:\5(5)\Load." The first number is the element code, and the second number is the capacitor value. In this case, they both are "5."

Now let's add the second element. The code number for a series inductor is given in Appendix A as "1" and the units are nH. Type "1" at the command prompt, press <Enter>, and then enter "10" to specify a 10 nH series inductor.

It is quite obvious that we are way out in left field with these two element values, but notice that the series inductor did cause clockwise rotation on a circle of constant resistance.

Next, we'll show you what you should see on your screen now.

VSWR:  1.5                                                                                                  03-19-2005 @ 09:58:46             System Z0:  50  ohms             Data File   :  TWOFREQ              Freq             RI            XI            VSWR              950.0           10.094     29.566        6.739              1050.0           8.417     38.210        9.473                      Command ? _              Ckt: \1(10)\5(5)\Load

When you type "Y" and press <Enter>, the on-screen circuit file will be up-dated and your screen will look like the plot we show above.

O.K., so now you know what LC values not to use? Go back and try to do it the right way! Here is how to "Restart." Type "R" at the command line. This will cause a restart. This is another on-screen command that is explained in Appendix B.

All your (our) mistakes will be removed, and you'll be back at the beginning. This time, try better LC values until you get it right.

Try a shunt capacitor less than half the original. Keep at it until the clockwise rotation stops at the 50 ohm circle. Then add a series inductor to rotate in to chart center for a nice VSWR. The series L should also have a lower value.

Here is the L-Match circuit with a proper set of values: