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Scattering Parameters

The computation of scattering parameters occurs in two steps.

gd1 is used to perform a time-domain computation with an excited port mode.
Then gd1.pp is used to compute the scattering parameters from data that were recorded by gd1.

As a simple example, we use a very strange geometry where we want to compute the scattering parameters of. The input for gd1 is

 # /usr/local/gd1/examples-from-the-manual/spar-example-1.gdf

 define(LargeNumber, 1000)

 define( a, 1e-2 )
 define( b, 5e-3 )
 define( c, 5e-3 )
 define( d, 1e-2 )

 define(FREQ, 20e9)

 -general
    outfile= /tmp/UserName/spar-example
    scratch= /tmp/UserName/spar-example-scratch

    text()= A strange geometry, just an example

 -mesh
define(STPSZE, 3*a/60 )
    spacing= STPSZE
    graded= yes, qfgraded= 1.2, dmaxgraded= @clight / FREQ / 20
    perfectmesh= no

    pxlow= 0, pxhigh= c+b
    pylow= -STPSZE, pyhigh= d
    pzlow= 0, pzhigh= 3*a

    cxlow= ele, cxhigh= ele
    cylow= ele, cyhigh= ele
    czlow= ele, czhigh= ele

 -brick
    #
    # fill the universe with metal
    #
    material= 1
       volume= (-LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber)
    doit

    #
    # carve out the waveguide
    #
    mat 0
       xlow= 0, xhigh= c
       ylow= 0, yhigh= LargeNumber
       zlow= -LargeNumber, zhigh= LargeNumber
    doit

    #
    # Carve out resonator box
    #
    mat 0
       xlow= 0, xhigh= c+b
       ylow= 0, yhigh= LargeNumber
       zlow= a, zhigh= 2*a
    doit

 -volumeplot
   eyepos= ( 1.0, 2.30, 0.5 )
   showlines= yes
   scale= 3
   doit

 -fdtd
    -ports
       name= Input, plane= zlow, modes= 1, doit
       name= Output, plane= zhigh, modes= 1, doit

    -pexcitation
       port= Input
       mode= 1
       amplitude= 1
       frequency= FREQ
       bandwidth= 0.7*FREQ

    -time
       #
       # tminimum: the minumum time to be simulated
       # tmaximum: the maximum time to be simulated
       #   If the amplitudes have died down sufficiently
       #   at a time between tmin and tmax,
       #   the computation will stop.
       #
       tmin=   10/FREQ
       tmax= 1000/FREQ
       amptresh= 1e-3

 -fdtd
     doit

**Figure 5.4:** This volumeplot shows the discretised geometry.
$\begin{figure}\centerline{ \psfig{figure=/tmp/bruw1931/ps-Files/spar-example00.ps,width=18cm,bbllx=0pt,bblly=158pt,bburx=599pt,bbury=799pt,clip=} }\end{figure}$

We start gd1 with the command:

   gd1 <  spar-example-1.gdf | tee out

The next step is to tell the postprocessor that we wish the scattering parameters to be computed and plotted. In addition to the default values, we want to see the timedata that were recorded during the time-domain computation, and we want to see the scattering parameters in a smith-chart. The commands for the postprocessor gd1.pp are:

 -general, infile= @last
 -sparameter
    ports= all, modes= 1
    timedata= yes
    smithplot= yes, markerat 19e9, markerat 20e9, markerat 21e9
    doit

We get in total 9 plots.

$\begin{figure}\centerline{ \psfig{figure=spar-example00-excitation.0001.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

**Figure 5.5:** The data of the excitation. Above: The time history of the amplitude that was excited in the port with name 'Input'. Below: The spectrum of this excitation.
$\begin{figure}\centerline{ \psfig{figure=spar-example00-excitation.0002.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

$\begin{figure}\centerline{ \psfig{figure=spar-example00-Input-e_amp_of_mode-eq-0... ....ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

$\begin{figure}\centerline{ \psfig{figure=spar-example00-Input_out_1-freq-abs.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

**Figure 5.6:** The data of the scattered mode '1' in the port with name 'Input'. Above: The time history of its amplitude. This was computed by **gd1**. Below: The scattering parameter as amplitude plot, and in a smith-chart. These data are computed by **gd1.pp** by fouriertransforming the time history of this mode, and dividing by the spectrum of the excitation.
$\begin{figure}\centerline{ \psfig{figure=spar-example00-Input_out_1-freq-smith.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

$\begin{figure}\centerline{ \psfig{figure=spar-example00-Output-e_amp_of_mode-eq-... ....ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

$\begin{figure}\centerline{ \psfig{figure=spar-example00-Output_out_1-freq-abs.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

**Figure 5.7:** The data of the scattered mode '1' in the port with name 'Output'. Above: The time history of its amplitude. This was computed by **gd1**. Below: The scattering parameter as amplitude plot, and in a smith-chart. These data are computed by **gd1.pp** by fouriertransforming the time history of this mode, and dividing by the spectrum of the excitation.
$\begin{figure}\centerline{ \psfig{figure=spar-example00-Output_out_1-freq-smith.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

**Figure 5.8:** The sum of the squared processed scattering parameters. Since the structure is loss free, this sum should ideally be identical to '1' above the cut-off frequency. The sum of the computed parameters is only very near the cut-off frequency of the modes unequal '1'.
$\begin{figure}\centerline{ \psfig{figure=spar-example00-sum-power-freq.ps,width=14cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}$

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