The six element network shown below appeared in Microwave Journal in 1983. See Appendix D, and then press the BACK button to return here. It is an excellent design based on equations presented in the article. It is almost optimum. We'll show you how to improve it!


The source impedance is in parallel form, while the load is in series form. They represent, respectively, the output impedance of the first stage, and the input impedance of the second stage.

By now, you should be able to create two .IMP load files for the RC values shown, but, don't bother; we've included both for you in the \mwdata4 sub-directory. We've named the source file "S1," and the load file "L1."

If you wanted to create "S1" yourself, you would need to calculate the impedance of the parallel RC network shown that has a 192 ohm resistor paralled with a 0.1 pF capacitor. This is easy to do with Sceptre, our frequency domain circuit analysis program. A second alternative is just to create a .IMP file with the 192 ohm resistor in it, and place the 0.1 pF shunt C in the match network as a fixed element.

To create the "L1" file, you would do the same as above, this time using the 9 ohm resistor that's in series with the 0.57 pF capacitor.

It would be a good idea for you to use the File Utility and list both the "S1" and "L1" files to see what is in them. Its very important that you know how to create them.

A question for you: If you were to analyze this network using SmithMatch, what would you use for the value of Z0, the system characteristic impedance ? Answer: 192 ohms.

The following plot was made using our SmithMatch program, using Z0 = 192 ohms. It shows the input VSWR, as seen by the source, i.e., the 1st stage, as it looks into the network terminated by the 2nd stage.We'll show you a new plot after we're done.

VSWR:  1.5                                                                                                  04-13-2005 @ 09:10:02             System Z0:  192  ohms             Data File   :  L1              Freq               RI                 XI            VSWR              16000.0      187.773          0.526       1.023              17000.0      177.419       -16.722       1.128              18000.0      159.046       -31.166       1.295              19000.0      141.908       -30.394       1.424              20000.0      137.852       -19.807       1.420              21000.0      153.378         -5.216        1.254              22000.0      198.339         -4.677        1.041              Command ? _              Ckt: \5(0.1)\1(0.48)\4(0.299)\1(0.34)\2(0.127\4(0.14)\1(0.032)\Load

Note: If you look close at the line just above, i.e., the SmithMatch Ckt: line, you'll notice there are 7 elements and not 6. The reason is that, to make the analysis simpler, we put the 0.1 pF shunt C, which is part of the source, into the network.

As we said, this match network is a pretty good one! About the only negative about it is the 1.4 VSWR bump in the middle of the band. Wait and see what happens when OptiMatch chews on this bone for a second or two.

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

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

This time, choose "C" for a complex match and press <Enter>. Then, when asked, enter the source and load filenames as "S1" and "L1."

Now, as you've done before, enter the six elements, one at a time, using the Element Library in Appendix A, if you have to. Be sure to start at the load.

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] ? _

This time choose to do a constrained optimization. Type "Y" and then press <Enter>.

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

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

Now, let's do it! OptiMatch will now begin its work.

OptiMatch online on 04-13-2005 @ 09:18:12     Source Filename  :  S1     Load Filename      :  L1     Circuit Optimization with 6 variables and Z0=192 ohms     Constrained Optimization     Initial Analysis           VSWR( 1 ) = 1.022742           VSWR( 2 ) = 1.127684           VSWR( 3 ) = 1.295578           VSWR( 4 ) = 1.423570           VSWR( 5 ) = 1.420702           VSWR( 6 ) = 1.254436           VSWR( 7 ) = 1.041507     I       VAR            GRAD     1    0.032000    +2.267819E+01     2    0.140000    +9.267260E+00     3    0.127000    -1.006779E+00     4    0.340000    -9.113691E+00     5    0.299000    +6.261857E+00     6    0.480000    -2.327729E+00     ITN = 0     ERR F= 3.68910     ITN = 1     ERR F= 2.65879     ITN = 2     ERR F= 2.29931     ITN = 3     ERR F= 2.06672     ITN = 4     ERR F= 1.95163     ITN = 5     ERR F= 1.79903        .   .   .        .   .   .        .   .   .     ITN = 14                                          ITN = 14     ERR F= 1.66857                           ERR F (Start)  :  3.68910                                                              ERR F (Now)  :  1.66857     FunctionTermination                 Change            :  -122 %     Final Analysis           VSWR( 1 ) = 1.114490           VSWR( 2 ) = 1.117977           VSWR( 3 ) = 1.105987           VSWR( 4 ) = 1.100796           VSWR( 5 ) = 1.122628           VSWR( 6 ) = 1.083289           VSWR( 7 ) = 1.145460     I       VAR            GRAD     1    0.026066   -9.457239E-02     2    0.122880   +0.141574E+00     3    0.126040   +1.245591E-02     4    0.333671   -1.340070E-02     5    0.246509   +4.987147E-02     6    0.457985   -2.434992E-03     Auto or Expert mode (A/E) [<Enter>=Quit] ? _

Note that we are into the numeric noise floor on most of the variables. Press <Enter> to Quit, and we'll look at the results.

Here is the complex interstage match network with the final optimized values:


Here is a plot of the input impedance of the optimized complex interstage match network made with our SmithMatch program: Note that the VSWR bump is now gone.
Please press <Enter> to Quit.