In this example, we'll optimize a three-element distributed line network for minimum VSWR over the 2000 to 3000 MHz range. It will match a 10 ohm fixed load to a 50 ohm source.

The first cut network, shown below, was created using our SmithMatch program. It's a "quickie," and is a good way to introduce another convention.


The following plot was made using our SmithMatch program. It shows the first cut input VSWR of the 2-3 GHz Broadband TRL Match network as it is right now. We'll show you a new plot after we're done.

VSWR:  1.5                                                                                             04-12-2005 @ 12:42:11             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

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 third question following the two above will be:

            Filename ? _

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

You'll next be asked:

            # of Elements [Max=15] ? _

Type "3" and press <Enter>. Again, note the cautionary comment that 15 elements is the maximum allowed.

You'll next be asked to specify the element code of each component in the match network. This number is an integer in the range 1 to 18, and corresponds to the lumped and distributed circuit elements listed in the Element Library. Please see Appendix A, (use the BACK button to return here), and determine the element code for a TRL, a transmission line element.You should find it listed as "16." Note that there are two degrees of freedom in a distributed line: Z0, the characteristic impedance, and theta, the electrical line length.

Another convention in OptiMatch, as well as in SmithMatch, is that when you enter theta, the electrical length of a distributed line, like element codes 16, 17, or 18, in the Element Library, you must specify the length in degrees at the low end of the band.

In this instance, since the band is 2 to 3 GHz, all line lengths must be specified at 2 GHz. The computation is simple, as shown on the circuit schematic above, we want the line lengths to be 90 degrees at 3 GHz, or 3000 MHz, so, to find the lengths at 2 GHz, or 2000 MHz, just multiply the desired length in degrees, (90), by the fraction 2/3. The "2" is the low band edge, and "3" is the reference frequency for the 90 degree lines.

To make sure we're clear on this, let's try one more example. Suppose 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.

Let's enter the three TRL lines now:

            # 1  Element Code ? _

Plase enter "16" in answer to the question above, and then press <Enter>.

            TRL Z0,Theta = ? _

Plase enter "-20,60" in answer to the question above. Note that the two data entries are each separated by a comma, there are no spaces, and that Z0, the parameter we want to vary, is prefaced by a minus sign. Now press <Enter>.

In like fashion, enter the two remaining TRL's. Element #2 is -30,60 and element #3 is -40,60. Press <Enter> after each entry.

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, what you'll see on-screen really depends on the speed of the PC you're using.

Here is what you will, or will not see!

OptiMatch online on 04-12-2005 at 13:03:28     Load Filename  :  TRL3     Circuit Optimization with 3 variables and Z0=50 ohms     Initial Analysis           VSWR( 1 ) = 1.780308           VSWR( 2 ) = 1.776622           VSWR( 3 ) = 1.667839           VSWR( 4 ) = 1.422222     I       VAR            GRAD     1  20.000000    +8.209932E+00     2  30.000000    -1.861780E+00     3  40.000000    -1.142717E+00     ITN = 0     ERR F= 6.79793     ITN = 1     ERR F= 3.03664     ITN = 2     ERR F= 0.87967     ITN = 3     ERR F= 0.89878     ITN = 4     ERR F= 0.89029     ITN = 5     ERR F= 0.81792     ITN = 6     ERR F= 0.39951     ITN = 7     ERR F= 0.40890     ITN = 8     ERR F= 0.39183                                  ITN = 9     ITN = 9                                                    ERR F (Start)  :  6.79793     ERR F= 0.39183                                   ERR F (Now)  :  0.39183                                                                      Change            :  -1635 %     Function Termination     Final Analysis           VSWR( 1 ) = 1.071065           VSWR( 2 ) = 1.054606           VSWR( 3 ) = 1.062028           VSWR( 4 ) = 1.000632     I       VAR            GRAD     1  12.889194   +1.428978E-02     2  22.407070   +1.122429E-02     3  38.884953   +4.986007E-03     Auto or Expert mode (A/E) [<Enter>=Quit] ? _

You'll note that this particular optimization ended with a Function Termination. This indicates a well behaved error function.

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


Once again there was quite a change, wasn't there? Take a moment to study the relative size of the gradients that were computed at the beginning and end. In particular, look at the change in the gradient for element 1, the 20 ohm TRL. The initial indication was that this line was most sensitive, and should change the most - and it did.

Please press <Enter> to Quit.