In this example, we'll analyze a three element distributed line network for use over the range of 2000 to 3000 MHz. We want to match a 10 ohm fixed load to a 50 ohm source.

The first cut network, shown below, is one way to make this match, and it will introduce an important convention.


 
The load impedance file for this example is named "TRL3." It contains a 10 ohm fixed resistor at four frequencies in the 2000 MHz to 3000 Mhz range.

To try this example, call the SmithMatch Module by choosing "(1) SmithMatch" from the Main Menu. as before, you may either by press "1" or use the "F1" function key.

            SmithMatch Module

            System Z0 [<Enter>=Quit]  ? _

Enter "50" as the system Z0 characteristic impedance,. and then press <Enter>.

            Filename ? _

Enter "TRL3" as the name of the .IMP load impedance file and then press <Enter>.

The 10 ohm load file will appear on your screen. As before, a small circle will mark the low end of the band. Do you see it below, over on the left half of the Smith Chart on the axis of reals?

VSWR:  1.5                                                                                                  03-19-2005 @ 10:10:22             System Z0:  50  ohms             Data File   :  TRL3              Freq             RL            XL            VSWR              2000.0         10.000    0.000        5.000              2333.0         10.000    0.000        5.000              2667.0         10.000    0.000        5.000              3000.0         10.000    0.000        5.000                      Command ? _              Ckt: \Load

Note that we have added a VSWR = 1.5 circle to the plot above.

When this is done, the "Command ?" prompt will appear. We're now going to add three TRL's, (transmission line circuit elements), one at a time, and analyze this first cut match.

As you would see, in Appendix A, the element code for a "TRL" is 16. Note that a distributed line has two degrees of freedom, its Z0 (characteristic impedance), in ohms, and its electrical line length, theta, in degrees.

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

An important convention in SmithMatch, (and OptiMatch), is that when you enter theta, the electrical length of a distributed element, like a 16, 17, or 18 in the Element Library, you specify the length in degrees at the low end of the band.

In this instance, since the band is 2 to 3 GHz, the line lengths must be specified at a frequency of 2 GHz. The computation is simple, just multiply the given length in degrees by the fraction 2/3. The "2" is the low band edge, and the "3" is the reference frequency for the 90 degree length lines.

When you type "16" at the "Command ?" prompt, to enter the Z0 = 20 ohm line closest to the load, you'll be asked to enter values for the two TRL parameters.

            TRL Z0,Theta  ? _

Note that there is a comma separating the two line parameters above. So type "20,60" and press <Enter>. For distributed elements, always type the two values separated by a comma.

VSWR:  1.5                                                                                                  03-19-2005 @ 10:14:32             System Z0:  50  ohms             Data File   :  TRL3              Freq             RI            XI            VSWR              2000.0         22.857    14.846        2.425              2333.0         29.602    14.277        1.890              2667.0         36.688      9.402        1.460              3000.0         40.000    - 0.000        1.250                      Command ? _              Ckt: \16(20,60\Load

Here is the screen display after adding the first TRL. Note how the impedance plot has spread out, and is moving in towards the center of the chart.

Type "Y" in response to the question:

            Save Element (Y/N)  ? _

Note that the on-screen circuit file has once again been up-dated. Now lets enter the second line, Z0 = 30 ohm TRL, and see what happens. When you see the screen below, save it as before.

VSWR:  1.5                                                                                                  03-19-2005 @ 10:19:51             System Z0:  50  ohms             Data File   :  TRL3              Freq             RI            XI            VSWR              2000.0         51.892    -11.703        1.261              2333.0         34.000    -14.775        1.686              2667.0         24.978      -8.088         2.871              3000.0         22.500       0.000         2.222                      Command ? _              Ckt: \16(30,60)\16(20,60\Load

Note that the second quarter-wave TRL caused the trace to flip, end for end, and that we're now closer to chart center at the low end of the band.

The Smith Chart is getting a bit cluttered. Let's clean it, O.K.? Type "C" for clean at the "Command ?" prompt. What you'll be left with is just the last trace drawn.

Finally, add the last TRL and look at the final results. Type "40,60" when asked, then, after cleaning the screen once again, you should see the following plot:

VSWR:  1.5                                                                                                  03-19-2005 @ 10:24:16             System Z0:  50  ohms             Data File   :  TRL3              Freq               RI            XI           VSWR              2000.0         28.359      -4.877       1.780              2333.0         30.549     11.797       1.776              2667.0         48.310     22.224       1.568              3000.0         71.111      -0.000       1.422                      Command ? _              Ckt: \16(40,60)\16(30,60)\16(20,60\Load

Note that the last quarter-wave section again flipped the trace end for end. Save this last element so that your on-screen circuit file will be up-dated and look like the plot we show above.

This is a pretty good first cut match. Its not all that great at the low end of the band, but its good enough for tweaking, either by hand, or better yet, by our OptiMatch program.

Here is the 2-3 GHz Broadband TRL Match circuit with the final optimized values shown below:


 
If you would like to try something interesting, repeat this analysis, but now use the Z0 values we obtained using OptiMatch that are given above.

When you're done, type "Q" at the command line and then press <Enter> to Quit.