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Explore the World of Soft…e: Engineering & Science
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Explore_the_World_of_Software_Engineering_and_Science_HRS_Software_1998.iso
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sport.txt
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1997-09-18
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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.