In this example, we'll analyze a four element lumped / distributed line network. It will match a FET whose small signal 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 pretty good "as is," but it can be made better. Can you do it with your present tools?

The scheme used by the designer is to, alternately, series resonate, parallel resonate, and then series resonate once again to make a first-cut match
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The 0.3 nH series L is resonant with the  0.5 pF load reactive part at 13 GHz (band center). Then, we have two stubs, one open and one shorted, they provide -j50 and +j50 and parallel resonate. Finally, with the input impedance at about 15.5 ohms, at band center, we again series resonate, this time with a quarter-wave long TRL, at 13 GHz, whose Z0 is the geometric mean of 15.5 and 50 ohms This gives a near perfect match at 13 GHz. Neat, huh?

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 the References in Appendix E for further information.

Note: The author mentioned above provides three Smith Chart plots in his book, but, the last one, is NOT a "follow-on" to the second. The last plot purports to show what you see looking in to the left side of the network below, but, in reality, the plot he shows is not that, but actually an optimized plot.


 

            SmithMatch Module

            System Z0 [<Enter>=Quit]  ? _

Enter "50" as the System Z0 reference characteristic impedance and press <Enter>.

            Filename ? _

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

The RC load file will appear on-screen. As usual, a small circle will mark the low end of the band.

VSWR:  2                                                                                                  03-19-2005 @ 10:35:14             System Z0:  VENDELIN              Freq               RL             XL            VSWR                8000.0       15.000      -39.789       5.565              10000.0       15.000      -31.831       4.775              12000.0       15.000      -26.526       4.341              13000.0       15.000      -24.485       4.194              14000.0       15.000      -22.736       4.077              16000.0       15.000      -19.894       3.905              18000.0       15.000      -17.684       3.786                      Command ? _              Ckt: \Load

This time, when asked for a VSWR, type "2" and press <Enter>.

You'll now need to specify the element code for each component, one at a time, in the match network. If you haven't done so yet, its probably a good idea to print it out. By now, the Element Library in Appendix A should be familiar. Look up the codes for a series L, an OST, an SST, and a TRL. The codes are, respectively, 1, 17, 18, and 16.

Note: You can visit Appendix A from here, but you must use the BACK button on your browser to return to this page.
By now you should be able to enter all four elements on your own. Remember, to start at the load and enter the series L first.

When you enter the three transmission line elements, remember the convention in SmithMatch, (as well as in OptiMatch), that the electrical line lengths of distributed elements are always specified at the low end of the band.

In this instance, since the band is 8 to 18 GHz, the line lengths must be specified at 8 GHz. As before, to compute the low end line length, just multiply the given length in degrees by the fraction 8/13. The "8" is the low band edge, and the "13" is the reference frequency for the lines.

The correct command line data entries for the OST and SST elements are "50,27.692." Are these the values you were going to use?

Here is what the Smith Chart plot should look like:

VSWR:  2                                                                                                  03-19-2005 @ 10:45:37             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

This is not an "easy match" to make, and we weren't able to get it any better, (by hand), than George did. Can you?

Here is the 8-18 GHz Broadband FET Match circuit in optimized form, courtesy of our OptiMatch program!



It would be a good idea for you to re-run this analysis using the optimized element values so you can see the difference that a good optimizer like OptiMatch can make!
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When you're done, just press "R" for restart, and then <Enter>. There is no need to have to re-enter the .IMP file name, etc. If you would rather Quit, type "Q" and then press <Enter>.