Sometimes it is necessary to have S-parameters of two port devices, such as 
GaAs FETs for example, given as three ports.  

FETS are almost always measured as two port devices, with the source 
leads grounded.   Published S-parameter data for GaAs FETs is almost always  
presented this way.  While two port s-parameters measured this way 
are satisfactor for a variety of circuit simulations, there are many 
instances where three port s-parameters for the FET are needed.   When the FET 
is used in either a common-gate or common-drain configuration, or if the 
source is used as part of a feed-back ciruit, or whenever the FET's source 
isn't directly grounded are just a few examples of when it would be helpful to 
have the FET's three port s-parameters.

In other words, you have a three-terminal device, and you want to use it as a 
three port device, but you only have two port S-parameters.  How do you derive 
the three-port S-parameters from the two-port S-parameters?

The computer program described in this article provides a means for converting 
two port s-parameters into three port s-parameters.  It is completely 
general, so of course it will work on any set of two port s-parameters and 
convert them into three port s-parameters.  

Most top of the line microwave CAD programs, such as TouchStone and Super 
Compact, do this for you automatically.  You just enter in the three 
circuit nodes the device connects to and the program does the rest.  
The algorithim this article is based upon duplicates what is already available 
in these other programs.

This article, therefore, is primarily targeted at those who have less 
sophisticated programs and need to enter in three port data, or for those who 
may have the more expensive programs and just want to know how to do the 
derivation.  


Step 1: Convert the S-paramters of the two port into Z parameters

Step 2: Add the Z-parameters of a 50 ohm resistor to the Z-parameters 
calculated above.  This has the effect of putting a 50 ohm resistor in the 
common lead.  

Step 3: Converting the  Z-parameters of step 2 back into S-parameters 
gives some of the sought after three-port S-parameters, in a two-port 
format, specifically; S11, S12, S21, and S22 of the three port. 

Step 4: Convert the Z-parameters from step 1 into ABCD parameters.

Step 5: Re-calculate these ABCD parameters by first connecting a resistor of 
charactistic impedance with the output port, and then interchanging the ouput 
port with the common.  

Step 6: Converting the ABCD parameters from Step 5 back into S-parameters 
gives additional elements of the the three-port S matrix as follows:   S12 
calculated this way is really the S13 for our three-port, similarly, S22 is 
S33, and S21 is S31.

Step 7: Going back to the ABCD parameters produced in step 4, 
re-calculate the ABCD parameters by interchanging the common port with 
the input port after first putting a resistor of characteristic impedance in 
the input port.

Step 7: Repeat step 6.  Now S12 is S32, S21 is S23.  Also, S11 will be 
S33 and S22 will be S22, but these will be redundant, as they're already 
been calculated in previous steps.

At this point all the three-port S-parameters have been calculated.

Step 8:  Convert these S-parameters back into polar form and print them out. 



As an example of the us of this program sample output is shown for converting 
the published two port S-parameters for a GaAs FET into three port 
S-parameters.  The results agreed exactly with the output from TouchStone.  





This program was written in compiled Microsoft (TM) FORTRAN for an IBM XT.  It 
could be re-written in other languages or for use other compilers.  The 
advantage of writing circuit analysis programs in FORTRAN over other 
languages such as BASIC, for example, is that most FORTRAN compilers readily 
handle complex numbers.  If this algorithim were written in BASIC, extra 
subroutines would have been necessary to handle the multiplication, addition, 
subtraction and division of complex numbers.