For our first example, we'll optimize a 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.

This is a very simple example, but will take more time than those to follow. Here is where you'll learn 90% of what you need to know to use OptiMatch properly.

This simple network could be designed directly from a set of equations, or tables, or a good first cut could have been created using our SmithMatch program.

However, so as to demonstrate what OptiMatch can do, let's assume we don't know this, and that we have chosen the element values shown below. Although the network is topologically correct, because of the poor element values chosen, it has a terrible VSWR!

To give you a visual before and after view of what OptiMatch can do for you, the following plot was made using our SmithMatch program. It shows the poor input VSWR of the L-Match network as it is right now. We'll show you a new plot after we're done.

VSWR:  2.0                                                                                       04-12-2005 @ 12:14:35             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

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] ? _

Since our source is purely resistive, and equal to 50 ohms, just press <Enter>. If our source was complex, as it usually is in an interstage match situation, you could do one of two things: First, you could choose "Complex," but then OptiMatch would want you to tell it the name of a "Source File," or, you could enter "Real" and manually enter the reactive component into the overall match network as a fixed element next to the source resistance.

You may create a Source File using the File Utility in exactly the same manner as you create a .IMP load impedance file. You'll see an example of a complex source later on.

The third question following the two above will be:

            Filename ? _

Enter "TWOFREQ" as the name of the .IMP load impedance file and then press <Enter>. We used this file as an example in the File Utility section of this User Manual.

You'll next be asked:

            # of Elements [Max=15] ? _

Since our network shown up near the beginning has two elements in it, enter "2" and press <Enter>. Please 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 shunt C and the series L used in this L-Match network. You should find them listed as "5" and "1," respectively.

The convention in OptiMatch, as well as in SmithMatch, is that components are entered in order starting at the load. In this example, the shunt C is closest to the load, so enter a "5" and press <Enter>.

You'll now be asked to enter the value of the shunt C. Enter "-5" for its 5 pF value. Let's stop a moment and mention another convention. If you want an element to be a variable, as we do here, preface its value with a minus "-" sign. If you want an element to be held fixed in value, don't.

Now that you know the convention regarding variables, complete the match network by entering a series L. Any problem? You should have used a "1" as the element code, and then specified its value as "-10" since its value is 10 nH and we want it to be a variable. Be sure to press <Enter> where appropriate.

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.

Now, to continue, the next question needs some explanation:

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

If you answer "Y" to the above question, the optimizer will not let any of the element values go negative. OptiMatch does this by working with the square and the square root of an element value rather than with the actual value. At times this is a useful option to have. For now, answer "N" by just pressing <Enter>.

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

The final question is whether to choose Auto or Expert mode. Auto mode is best in most cases. It uses what we've found to be a good set of general purpose algorithm variables. Expert mode lets you vary certain algorithm variables "on the fly," ones we call the primary defaults. Changing the default variable set was discussed earlier. For now, type "A" in answer to the question above, and press <Enter>.

OptiMatch will now begin its work. You'll see that OptiMatch first performs an initial analysis of input VSWR at each frequency in the operating band. After displaying its calculations, the algorithm will then list the start values for each variable, and compute each variables gradient. The gradient is, put simply, the relative sensitivity of each element, i.e., its relative influence on input VSWR. The smaller the gradient calculated, the less effect the element has on input VSWR.You'll quickly see the final calculations of optimized input VSWR, along with the final element values, and gradients.

Here is what you will or will not, see, depending on the speed of your computer!

OptiMatch online on 04-12-2005 at 12:25:22     Load Filename  :  TWOFREQ     Circuit Optimization with 2 variables and Z0=50 ohms     Initial Analysis           VSWR( 1 ) = 6.739229           VSWR( 2 ) = 9.472666     I       VAR            GRAD     1  5.000000    +1.785512E+02     2  10.00000    +1.205604E+02     ITN = 0     ERR F= 133.47504     ITN = 1     ERR F= 15.14208     ITN = 2     ERR F= 2.37841     ITN = 3     ERR F= 1.19406     ITN = 4     ERR F= 0.39341     ITN = 5     ERR F= 0.29953     ITN = 6     ERR F= 0.29948     ITN = 7     ERR F= 0.30012     ITN = 8     ERR F= 0.30014     ITN = 9     ERR F= 0.30022                                ITN = 11     ITN = 10                                               ERR F (Start)  :  133.47504     ERR F= 0.30024                                ERR F (Now)  :   0.30024                                                                   Change            :  -44356 %     Search Limit Termination     Final Analysis           VSWR( 1 ) = 1.079858           VSWR( 2 ) = 1.064825     I       VAR            GRAD     1  1.581643    -1.361278E-04     2  7.908394    -1.331655E-05     Auto or Expert mode (A/E) [<Enter>=Quit] ? _

Let's talk about the sequence of events you may, or may not, have seen, and what it all means.

First, OptiMatch computed the input VSWR of our L-Match network using the initial element values of 5 pF and 10 nH. As expected, the VSWR was very poor, being in the range of 6 to 9. Next, using differential calculus, OptiMatch computed and output, on-screen, the individual variable gradients. If you're familiar with calculus, you'll recognize them as being quite large indicating the initial element values are far from optimum.

Then, after computing an initial value for the error function, OptiMatch went into an iterative loop and reduced the error function from (about) 133 to 0.3 in 10 iterations. If you did see what was happening on-screen, you'll remember that the initial and current error function values were displayed in a box on the upper right corner of the screen. Also shown was a number corresponding to the cumulative percentage change in the error function.

Here is the L-Match circuit with the final optimized values shown:


Do you see the small circle right next to the center of the Smith chart? That's a pretty good match!

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.

In addition to listing the final variable element values, OptiMatch also displays the final input VSWR, and the variable gradients. Compare the final value of these two gradients to the initial values. This extreme change ties in with the error function decrease of 44,356% over 10 full iterations.

At this point, you can quit by pressing the <Enter> key, or, you could restart the optimizer by typing "A," (for Auto), and then <Enter>. You might try a restart and see what happens. The optimizer will pivot, about its current point on the surface of the error function, and try a new search direction, but, as you'll see, to no avail. Note that, in the fifth decimal place, that the error function actually went up! You're in what we call the numeric noise floor. You've reached the practical limit of calculation. The gradients are now very small.

There are times when a restart will produce a slightly lower error function, so its good practice to give it a kick from time to time. You want to make sure you are at a global minimum, and not a local minimum. For now, its over. Press <Enter> to quit.

Things will move faster now, because we've now presented most of the basics.