In this example, we'll show you how to handle a situation where you want to analyze (or design) an interstage match between a complex source and load.

Below is a six-element network that appeared in Microwave Journal in 1983. It is an excellent design based on equations presented in the article. Its almost optimum!


 
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, of a microwave amplifier.

By now, you should be able to create a .IMP load file for the RC load values shown. But, don't bother, we've included the load .IMP file for you. We named it "L1."

To model the source, set the reference impedance, Z0, equal to 192 ohms. That way, all VSWR calculations done by SmithMatch will reflect what the source actually sees. Make sense? We'll include the reactive part of the source, i.e., the shunt 0.1 pF capacitor, as the last element in the match network. In other words, we'll employ parasitic absorption, and just include it as part of the match network! Slick, huh?

If you need to calculate the series impedance of a parallel RC network like the one shown above, it's easy to do it with Sceptre, our frequency domain circuit analysis program.

To try this example, choose "(1) SmithMatch" from the Main Menu, as before, by either pressing "1" or by using the "F1" function key.

            SmithMatch Module

            System Z0 [<Enter>=Quit]  ? _

Enter "192" as the System Z0 reference impedance and press <Enter>.

            Filename ? _

Enter "L1" as the name of the .IMP load impedance file and then press <Enter>.

The RC load file, which represents the impedance of a series connected 9 ohm resistor, and a 0.57 pF capacitor, will appear on your screen. As before, a small circle will mark the low end of the band.

Here is a Smith Chart plot of the load file as it should appear on your screen with a VSWR = 1.5 circle:

VSWR:  1.5                                                                                                  03-19-2005 @ 11:02:19             System Z0:  192  ohms             Data File   :  L1              Freq               RL             XL          VSWR              16000.0       9.000      -17.450       21.510              17000.0       9.000      -16.420       21.490              18000.0       9.000      -15.510       21.473              19000.0       9.000     -14.690       21.458              20000.0      9.000     -13.960       21.446              21000.0       9.000      -13.290       21.436              22000.0       9.000     -12.690       21.427                      Command ? _              Ckt: \Load

As you can see above, the VSWR looking into the second stage of this amplifier is quite high, and this, given the bandwidth involved, explains why the match network has six elements in it. In the normal "scheme of things," you'll likely never design a network with more than nine elements in it.

This match network will not actually be built using lumped elements, that would be impossible. They're just being used as a design artifice here. Using them simplifies the design. Once the lumped design is completed, the network will be converted to distributed form, and then realized in microstrip.

Enter the six elements, one at a time, starting at the load end. When you reach the input of the network, be sure to add the 0.1 pF shunt C which is part of the source impedance.

Here is what the screen should look like when you're done. If it doesn't, press "R" to restart and repeat the analysis to find where your mistake is.

VSWR:  1.5                                                                                                  03-19-2005 @ 11:10:51             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     -19.007       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

Wow, that's a great match, isn't it? But, look close, there is a VSWR bump in the 19-20 GHz region. Can you fix that? We can!

Look below. We've re-done the sketch of this complex interstage match network with a better set of values. Guess where they came from? A "no brainer," huh? We used OptiMatch to smooth out the bump by tweaking the element values in it.



You really should try these values to see what the match looks like in optimized form.

Type "Q" to Quit and then press <Enter> to return to the SmithMatch Module entry point.