In this example, we'll optimize a four-element lumped / distributed line network. It will match a FET whose input impedance was modelled over the range of 8000 to 18000 MHz as a series RC network. The FET input model consists of a 15 ohm resistor in series with a 0.5 pF capacitor.

The first cut network is shown below. For an empirical design, its really pretty good "as is," but, optimization will make it even better!


The step-by-step creation of this network is detailed by George Vendelin in his book "Design of Amplifiers and Oscillators by the S-Parameter Method." See Appendix D for more information. Be sure to press the BACK button on your browser to return here.

The following plot was made using our SmithMatch program. It shows the first cut input VSWR of the 8-18 GHz Broadband FET Match network as it is right now. We'll show you a new plot after we're done.

VSWR:  2.0                                                                                             04-12-2005 @ 13:25:03             System Z0:  50  ohms             Data File   :  VENDELIN              Freq               RI             XI            VSWR                8000.0       17.351      -11.339       3.849              10000.0       21.661       10.190       2.425              12000.0       44.186       14.361       1.388              13000.0       52.267        -0.069       1.045              14000.0       44.772      -13.896       1.367              16000.0       25.468      -12.086       2.114              18000.0       22.469          1.442       2.228              Command ? _              Ckt: \16(28,55.385)\18(50,27.692\17(50,27.592)\1(0.3)\Load

To try this example, enter the OptiMatch Module by choosing "(1) OptiMatch" from the Main Menu, either by pressing "1" or by using the "F1" function key. The screen display will look as follows:

            OptiMatch Module

Units:       Normal

Defaults:  Normal

            System Z0 [<Enter>=Quit]  ? _


Enter "50" as the System Z0 reference impedance and then press <Enter>. The next question will be:

            Real or Complex Match (R/C): [<Enter>=Real] ? _

Press <Enter> to tell OptiMatch that this is a real match.

The question following the two above will be:

            Filename ? _

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

You'll next be asked:

            # of Elements [Max=15] ? _

Type "4" and press <Enter>. As always, 15 elements is the maximum allowed.

You'll next be asked to specify the element code of each component in the match network. By now, the Element Library in Appendix A should be quite familiar to you. Look up the codes for a series L, an OST, SST, and TRL. The correct codes are, respectively, "1," "17," "18," and "16."

Remember the convention in OptiMatch, as well as in SmithMatch, that the electrical line length of distributed elements are always specified, in degrees, at the low end of the band.

In this instance, we have a band of frequencies extending from 8 to 18 GHz, and we know a line is 45 degrees long at mid-band, i.e., 13 GHz. What is the electrical length of such a line at 8 GHz, the low end of the band? You would calculate this as 8/13 X 45 = 27.692 degrees. Using the same fraction on the 90 degree TRL, we get 55.385 degrees for it.

Enter the element values as requested. Make the series L and the distributed line Z0's variables by using a minus sign. Hold the electrical line lengths fixed. Be sure to enter each value separated by a comma with no spaces.

Note: At this point, you'll be asked "Print Logfile (Y/N) [<Enter>=No] ? _" Please press <Enter>.

If you choose the option to 'Print Logfile,' the data will be directed to 'Logfile.txt' within the \mwdata4 sub-directory, and not to the screen. Right-click on 'Logfile.txt' to print it, and then DELETE the file; it will re-create when next needed.

            Constrained Optimization (Y/N) [<Enter>=No] ? _

Press <Enter> in response to the above question. This will specify an unconstrained optimization.

            Auto or Expert mode (A/E) [<Enter>=Quit] ? _

Type "A" in answer to the question above, and press <Enter> to choose Auto mode.

OptiMatch will now begin its work. Again, here is what you will, or will not see, depending on the speed of your PC!

OptiMatch online on 04-12-2005 @ 13:36:13     Load Filename  :  VENDELIN     Circuit Optimization with 4 variables and Z0=50 ohms     Initial Analysis           VSWR( 1 ) = 3.048956           VSWR( 2 ) = 2.424977           VSWR( 3 ) = 1.388393           VSWR( 4 ) = 1.045353           VSWR( 5 ) = 1.366853           VSWR( 6 ) = 2.114406           VSWR( 7 ) = 2.227641     I       VAR            GRAD     1    0.300000    -1.857661E-02     2  50.000000    +0.427345E+00     4  50.000000    +1.928835E+00     6  28.000000    -1.072323E+01     ITN = 0     ERR F= 22.43306     ITN = 1     ERR F= 15.88501     ITN = 2     ERR F= 15.73923     ITN = 3     ERR F= 14.49981     ITN = 4     ERR F= 13.02885     ITN = 5     ERR F= 11.54350        .   .   .        .   .   .        .   .   .     ITN = 13     ERR F= 8.46624     ITN = 14     ERR F= 8.45868     ITN = 15     ERR F= 8.45834                                 ITN = 17     ITN = 16                                                ERR F (Start)  :  22.43306     ERR F= 8.45974                                 ERR F (Now)  :   8.45974                                                                     Change            :  -166 %     Search Limit Termination     Final Analysis           VSWR( 1 ) = 1.811548           VSWR( 2 ) = 1.608137           VSWR( 3 ) = 1.375021           VSWR( 4 ) = 1.317823           VSWR( 5 ) = 1.396289           VSWR( 6 ) = 1.455514           VSWR( 7 ) = 1.375297     I       VAR            GRAD     1    0.318806   +3.719322E-04     2  26.000076   -7.450210E-04     4  27.604441   -1.079570E-04     6  31.423861   -9.483536E-04     Auto or Expert mode (A/E) [<Enter>=Quit] ? _

You'll note that the on-screen display of this particular optimization ended with a Search Limit Termination. This means that, internally, the optimization algorithm tried 100 times, (the default limit), to find a way to further reduce the error function, and then gave up. When this happens, you can be pretty certain that you're either there, or you're trapped in a local minima.

Here is the broadband FET match circuit with the final optimized values shown:


Here is a plot of the input impedance of this optimized match network made with our SmithMatch program:
Please press <Enter> to Quit.