You couple two or more sources using the '''Port Definition Dialog'''. To do so, you need to change the default port assignments. First, delete all the ports that are to be coupled from the Port List of the dialog. Then, define a new port by clicking the '''Add''' button of the dialog. This opens up the Add Port dialog, which consists of two tables: '''Available''' sources on the left and '''Associated''' sources on the right. A right arrow ('''-->''') button and a left arrow ('''<--''') button let you move the sources freely between these two tables. You will see in the "Available" table a list of all the sources that you deleted earlier. You may even see more available sources. Select all the sources that you want to couple and move them to the "Associated" table on the right. You can make multiple selections using the keyboard's '''Shift''' and '''Ctrl''' keys. Closing the Add Port dialog returns you to the Port Definition dialog, where you will now see the names of all the coupled sources next to the name of the newly added port.
{{Note|It is your responsibility to set up coupled ports and coupled [[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|transmission lines]]]]]]]]]]]]]]]]]]]] properly. For example, to excite the desirable odd mode of a coplanar waveguide (CPW), you need to create two rectangular slots parallel to and aligned with each other and place two gap sources on them with the same offsets and opposite polarities. To excite the even mode of the CPW, you use the same polarity for the two collocated gap sources. Whether you define a coupled port for the CPW or not, the right definition of sources will excite the proper mode. The couple ports are needed only for correct calculation of the port characteristics.}}
[[File:PMOM51(2).png|800px]]
[[File:PMOM82.png]]
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=== Running a Frequency Sweep ===
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In a frequency sweep, the operating frequency of a planar structure is varied during each sweep run. [[EM.Cube]]'s [[Planar Module]] offers two types of frequency sweep: Uniform and Adaptive. In a uniform frequency sweep, the frequency range and the number of frequency samples are specified. The samples are equally spaced over the frequency range. At the end of each individual frequency run, the output data are collected and stored. At the end of the frequency sweep, the 3D data can be visualized and/or animated, and the 2D data can be graphed in EM.Grid.
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To run a uniform frequency sweep, open the '''Simulation Run Dialog''', and select the '''Frequency Sweep''' option from the dropdown list labeled '''Simulation Mode'''. When you choose the frequency sweep option, the '''Settings''' button next to the simulation mode dropdown list becomes enabled. Clicking this button opens the '''Frequency Settings''' dialog. The '''Frequency Range'''is initially set equal to your project's center frequency minus and plus half bandwidth. But you can change the values of '''Start Frequency'''and '''End Frequency''' as well as the '''Number of Samples'''. The dialog offers two options for '''Frequency Sweep Type''': '''Uniform''' or '''Adaptive'''. Select the former type. It is very important to note that in a MoM simulation, changing the frequency results in a change of the mesh of the structure, too. This is because the mesh density is defined in terms of the number of cells per effective wavelength. By default, during a frequency sweep, [[EM.Cube]] fixes the mesh density at the highest frequency, i.e., at the "End Frequency". This usually results in a smoother frequency response. You have the option to fix the mesh at the center frequency of the project or let [[EM.Cube]] "remesh" the planar structure at each frequency sample during a frequency sweep. You can make one of these three choices using the radio button in the '''Mesh Settings''' section of the dialog. Closing the Frequency Settings dialog returns you to the Simulation Run dialog, where you can start the planar MoM frequency sweep simulation by clicking the '''Run''' button.
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[[File:PMOM126.png]]
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Figure 1: [[Planar Module]]'s Frequency Settings dialog.
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=== Adaptive Frequency Sweep ===
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Frequency sweeps are often performed to study the frequency response of a planar structure. In particular, the variation of scattering [[parameters]] like S<sub>11</sub> (return loss) and S<sub>21</sub> (insertion loss) with frequency are of utmost interest. When analyzing resonant structures like patch antennas or planar filters over large frequency ranges, you may have to sweep a large number of frequency samples to capture their behavior with adequate details. The resonant peaks or notches are often missed due to the lack of enough resolution. [[EM.Cube]]'s [[Planar Module]] offers a powerful adaptive frequency sweep option for this purpose. It is based on the fact that the frequency response of a physical, causal, multiport network can be represented mathematically using a rational function approximation. In other words, the S [[parameters]] of a circuit exhibit a finite number of poles and zeros over a given frequency range. [[EM.Cube]] first starts with very few frequency samples and tries to fit rational functions of low orders to the scattering [[parameters]]. Then, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, all the possible rational functions of higher orders are tried out. The process continues until adding new intermediate frequency samples does not improve the resolution of the "S<sub>ij</sub>" curves over the given frequency range. In that case, the curves are considered as having converged.
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You must have defined one or more ports for your planar structure run an adaptive frequency sweep. Open the Frequency Settings dialog from the Simulation Run dialog and select the '''Adaptive''' option of '''Frequency Sweep Type'''. You have to set values for '''Minimum Number of Samples''' and '''Maximum Number of Samples'''. Their default values are 3 and 9, respectively. You also set a value for the '''Convergence Criterion''', which has a default value of 0.1. At each iteration cycle, all the S [[parameters]] are calculated at the newly inserted frequency samples, and their average deviation from the curves of the last cycle is measured as an error. When this error falls below the specified convergence criterion, the iteration is ended. If [[EM.Cube]] reaches the specified maximum number of iterations and the convergence criterion has not yet been met, the program will ask you whether to continue the process or exit it and stop.
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{{Note|For large frequency ranges, you may have to increase both the minimum and maximum number of samples. Moreover, remeshing the planar structure at each frequency may prove more practical than fixing the mesh at the highest frequency.}}
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[[File:PMOM127.png]]
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Figure 1: Settings adaptive frequency sweep [[parameters]] in [[Planar Module]]'s Frequency Settings Dialog.
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=== Examining Port Characteristics ===
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If your planar structure is excited by gap sources or probe sources or de-embedded sources, and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y) [[parameters]] of the designated ports. The scattering [[parameters]] are defined based on the port impedances specified in the project's Port Definition dialog. If more than one port has been defined in the project, the S/Z/Y matrices of the multiport network are calculated. Note that the S/Z/Y matrices of an N-port structure are related to each other through the following equations:
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:<math>\mathbf{ [S] = [Y_0] \cdot ([Z]-[Z_0]) \cdot ([Z]+[Z_0])^{-1} \cdot [Z_0] }</math>
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:<math>\mathbf{ [Y] = [Z]^{-1} } </math>
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:<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot ([U]+[S]) \cdot ([U]-[S])^{-1} \cdot [\sqrt{Z_0}] }</math>
<!--[[File:PMOM121.png]]-->
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where <math>\mathbf{[U]}</math> is the identity matrix of order N, <math>\mathbf{[Z_0]}</math> and <math>\mathbf{[Y_0]}</math> are diagonal matrices whose diagonal elements are the port characteristic impedances and admittances, respectively, and <math>\mathbf{[\sqrt{Z_0}]}</math> is a diagonal matrix whose diagonal elements are the square roots of port characteristic impedances. The voltage standing wave ratio (VSWR) of the structure at the first port is also computed:
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:<math>\text{VSWR} = \frac{|V_{max}|}{|V_{min}|} = \frac{1+|S_{11}|}{1-|S_{11}|}</math>
<!--[[File:PMOM122.png]]-->
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At the end of a planar MoM simulation, the values of S/Z/Y [[parameters]] and VSWR data are calculated and reported in the output message window. The S, Z and Y [[parameters]] are written into output ASCII data files of complex type with a "'''.CPX'''" extension. Every file begins with a header consisting of a few comment lines that start with the "#" symbol. The complex values are arranged into two columns for the real and imaginary parts. In the case of multiport structures, every single element of the S/Z/Y matrices is written into a separate complex data file. For example, you will have data files like S11.CPX, S21.CPX, ..., Z11.CPX, Z21.CPX, etc. The VSWR data are saved to an ASCII data file of real type with a "'''.DAT'''" extension called, VSWR.DAT.
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If you run an analysis, the port characteristics have single complex values, which you can view using [[EM.Cube]]'s data manager. However, there are no curves to graph. You can plot the S/Z/Y [[parameters]] and VSWR data when you have data sets, which are generated at the end of any type of sweep including a frequency sweep. In that case, the ".CPX" files have multiple rows corresponding to each value of the sweep parameter (e.g. frequency). [[EM.Cube]]'s 2D graph data are plotted in EM.Grid, a versatile graphing utility. You can plot the port characteristics directly from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]].
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[[File:PMOM128.png]]
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Figure 1: Selecting port characteristics data to plot from the Navigation Tree.
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You can also see a list of all the port characteristics data files in [[EM.Cube]]'s Data Manager. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Simulate Toolbar''' or select '''Simulate > Data Manager''' from the menu bar, or right click on the '''Data Manager''' item of the Navigation Tree and select '''Open Data Manager'''... from the contextual menu. You can also use the keyboard shortcut '''Ctrl+D''' at any time. Select any data file by clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You can change the format of complex data plots. In general complex data can be plotted in three forms:
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# Magnitude and Phase
# Real and Imaginary Parts
# Smith Chart
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[[File:PMOM129.png]]
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Figure 2: [[EM.Cube]]'s Data Manager showing a list of the port characteristics data files.
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In particular, it may be useful to plot the S<sub>ii</sub> [[parameters]] on a Smith chart. To change the format of a data plot, select it in the Data Manager and click its '''Edit''' button. In the Edit File Dialog, choose one of the options provided in the dropdown list labeled '''Graph Type'''.
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[[File:PMOM130.png]]
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Figure 3: Changing the graph type by editing a data file's properties.
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[[File:PMOM134.png|800px]]
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Figure 4: The S<sub>11</sub> parameter plotted on a Smith Chart graph in EM.Grid.
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=== Rational Interpolation Of Scattering Parameters ===
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The adaptive frequency sweep described earlier is an iterative process, whereby the Planar MoM simulation engine is run at a certain number of frequency samples at each iteration cycle. The frequency samples are progressively built up, and rational fits for these data are found at each iteration cycle. A decision is then made whether to continue more iterations. At the end of the whole process, a total number of scattering parameter data samples have been generated, and new smooth data corresponding to the best rational fits are written into new data files for graphing. [[EM.Cube]]'s [[planar Module]] also allows you to generate a rational fit for all or any existing scattering parameter data as a post-processing operation without a need to run additional simulation engine runs.
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You can interpolate all the scattering [[parameters]] together or select individual [[parameters]]. You do this post-processing operation from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select Smart Fit. At the top of the Smart Fit Dialog, there is a dropdown list labeled '''Interpolate''', which gives a list of all the available S parameter data for rational interpolation. The default option is "All Available [[Parameters]]". Then you see a box labeled '''Number of Available Samples''', whose value is read from the data content of the selected complex .CPX data file. Based on the number of available data samples, the dialog reports the '''Maximum Interpolant Order'''. You can choose any integer number for '''Interpolant Order''', from 1 to the maximum allowed.
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{{Note|Interpolant order more than 15 will suffer from numerical instabilities even if you have a very large number of data samples.}}
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You can use the '''Update''' button of the dialog to generate the interpolated data for a given order. The new data are written to a complex data file with the same name as the selected S parameter and a "'''_RationalFit'''" suffix. While this dialog is still open, you can plot the new data either directly from the Navigation Tree or from the Data Manager. If you are not satisfied with the results, you can return to the Smart Fit dialog and try a higher or lower interpolant order and compare the new data.
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[[File:PMOM131.png]]
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Figure 1: [[Planar Module]]'s Smart Fit dialog.
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[[File:PMOM133(2).png|400px]]
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Figure 2: The S<sub>11</sub> parameter plot of a two-port structure in magnitude-phase format.
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[[File:PMOM132(2).png|400px]]
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Figure 3: The smoothed version of the S<sub>11</sub> parameter plot of the two-port structure using [[EM.Cube]]'s Smart Fit.
== Working with Planar MoM Simulation Data ==
Figure 2: An example of the 3D mono-static radar cross section plot of a patch antenna.
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=== Running a Frequency Sweep ===
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In a frequency sweep, the operating frequency of a planar structure is varied during each sweep run. [[EM.Cube]]'s [[Planar Module]] offers two types of frequency sweep: Uniform and Adaptive. In a uniform frequency sweep, the frequency range and the number of frequency samples are specified. The samples are equally spaced over the frequency range. At the end of each individual frequency run, the output data are collected and stored. At the end of the frequency sweep, the 3D data can be visualized and/or animated, and the 2D data can be graphed in EM.Grid.
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To run a uniform frequency sweep, open the '''Simulation Run Dialog''', and select the '''Frequency Sweep''' option from the dropdown list labeled '''Simulation Mode'''. When you choose the frequency sweep option, the '''Settings''' button next to the simulation mode dropdown list becomes enabled. Clicking this button opens the '''Frequency Settings''' dialog. The '''Frequency Range'''is initially set equal to your project's center frequency minus and plus half bandwidth. But you can change the values of '''Start Frequency'''and '''End Frequency''' as well as the '''Number of Samples'''. The dialog offers two options for '''Frequency Sweep Type''': '''Uniform''' or '''Adaptive'''. Select the former type. It is very important to note that in a MoM simulation, changing the frequency results in a change of the mesh of the structure, too. This is because the mesh density is defined in terms of the number of cells per effective wavelength. By default, during a frequency sweep, [[EM.Cube]] fixes the mesh density at the highest frequency, i.e., at the "End Frequency". This usually results in a smoother frequency response. You have the option to fix the mesh at the center frequency of the project or let [[EM.Cube]] "remesh" the planar structure at each frequency sample during a frequency sweep. You can make one of these three choices using the radio button in the '''Mesh Settings''' section of the dialog. Closing the Frequency Settings dialog returns you to the Simulation Run dialog, where you can start the planar MoM frequency sweep simulation by clicking the '''Run''' button.
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[[File:PMOM126.png]]
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Figure 1: [[Planar Module]]'s Frequency Settings dialog.
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=== Adaptive Frequency Sweep ===
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Frequency sweeps are often performed to study the frequency response of a planar structure. In particular, the variation of scattering [[parameters]] like S<sub>11</sub> (return loss) and S<sub>21</sub> (insertion loss) with frequency are of utmost interest. When analyzing resonant structures like patch antennas or planar filters over large frequency ranges, you may have to sweep a large number of frequency samples to capture their behavior with adequate details. The resonant peaks or notches are often missed due to the lack of enough resolution. [[EM.Cube]]'s [[Planar Module]] offers a powerful adaptive frequency sweep option for this purpose. It is based on the fact that the frequency response of a physical, causal, multiport network can be represented mathematically using a rational function approximation. In other words, the S [[parameters]] of a circuit exhibit a finite number of poles and zeros over a given frequency range. [[EM.Cube]] first starts with very few frequency samples and tries to fit rational functions of low orders to the scattering [[parameters]]. Then, it increases the number of samples gradually by inserting intermediate frequency samples in a progressive manner. At each iteration cycle, all the possible rational functions of higher orders are tried out. The process continues until adding new intermediate frequency samples does not improve the resolution of the "S<sub>ij</sub>" curves over the given frequency range. In that case, the curves are considered as having converged.
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You must have defined one or more ports for your planar structure run an adaptive frequency sweep. Open the Frequency Settings dialog from the Simulation Run dialog and select the '''Adaptive''' option of '''Frequency Sweep Type'''. You have to set values for '''Minimum Number of Samples''' and '''Maximum Number of Samples'''. Their default values are 3 and 9, respectively. You also set a value for the '''Convergence Criterion''', which has a default value of 0.1. At each iteration cycle, all the S [[parameters]] are calculated at the newly inserted frequency samples, and their average deviation from the curves of the last cycle is measured as an error. When this error falls below the specified convergence criterion, the iteration is ended. If [[EM.Cube]] reaches the specified maximum number of iterations and the convergence criterion has not yet been met, the program will ask you whether to continue the process or exit it and stop.
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{{Note|For large frequency ranges, you may have to increase both the minimum and maximum number of samples. Moreover, remeshing the planar structure at each frequency may prove more practical than fixing the mesh at the highest frequency.}}
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[[File:PMOM127.png]]
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Figure 1: Settings adaptive frequency sweep [[parameters]] in [[Planar Module]]'s Frequency Settings Dialog.
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=== Examining Port Characteristics ===
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If your planar structure is excited by gap sources or probe sources or de-embedded sources, and one or more ports have been defined, the planar MoM engine calculates the scattering, impedance and admittance (S/Z/Y) [[parameters]] of the designated ports. The scattering [[parameters]] are defined based on the port impedances specified in the project's Port Definition dialog. If more than one port has been defined in the project, the S/Z/Y matrices of the multiport network are calculated. Note that the S/Z/Y matrices of an N-port structure are related to each other through the following equations:
Â
:<math>\mathbf{ [S] = [Y_0] \cdot ([Z]-[Z_0]) \cdot ([Z]+[Z_0])^{-1} \cdot [Z_0] }</math>
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:<math>\mathbf{ [Y] = [Z]^{-1} } </math>
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:<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot ([U]+[S]) \cdot ([U]-[S])^{-1} \cdot [\sqrt{Z_0}] }</math>
<!--[[File:PMOM121.png]]-->
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where <math>\mathbf{[U]}</math> is the identity matrix of order N, <math>\mathbf{[Z_0]}</math> and <math>\mathbf{[Y_0]}</math> are diagonal matrices whose diagonal elements are the port characteristic impedances and admittances, respectively, and <math>\mathbf{[\sqrt{Z_0}]}</math> is a diagonal matrix whose diagonal elements are the square roots of port characteristic impedances. The voltage standing wave ratio (VSWR) of the structure at the first port is also computed:
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:<math>\text{VSWR} = \frac{|V_{max}|}{|V_{min}|} = \frac{1+|S_{11}|}{1-|S_{11}|}</math>
<!--[[File:PMOM122.png]]-->
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At the end of a planar MoM simulation, the values of S/Z/Y [[parameters]] and VSWR data are calculated and reported in the output message window. The S, Z and Y [[parameters]] are written into output ASCII data files of complex type with a "'''.CPX'''" extension. Every file begins with a header consisting of a few comment lines that start with the "#" symbol. The complex values are arranged into two columns for the real and imaginary parts. In the case of multiport structures, every single element of the S/Z/Y matrices is written into a separate complex data file. For example, you will have data files like S11.CPX, S21.CPX, ..., Z11.CPX, Z21.CPX, etc. The VSWR data are saved to an ASCII data file of real type with a "'''.DAT'''" extension called, VSWR.DAT.
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If you run an analysis, the port characteristics have single complex values, which you can view using [[EM.Cube]]'s data manager. However, there are no curves to graph. You can plot the S/Z/Y [[parameters]] and VSWR data when you have data sets, which are generated at the end of any type of sweep including a frequency sweep. In that case, the ".CPX" files have multiple rows corresponding to each value of the sweep parameter (e.g. frequency). [[EM.Cube]]'s 2D graph data are plotted in EM.Grid, a versatile graphing utility. You can plot the port characteristics directly from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select one of the items: '''Plot S [[Parameters]]''', '''Plot Y [[Parameters]]''', '''Plot Z [[Parameters]]''', or '''Plot VSWR'''. In the first three cases, another sub-menu gives a list of individual port [[parameters]].
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[[File:PMOM128.png]]
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Figure 1: Selecting port characteristics data to plot from the Navigation Tree.
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You can also see a list of all the port characteristics data files in [[EM.Cube]]'s Data Manager. To open data manager, click the '''Data Manager''' [[File:data_manager_icon.png]] button of the '''Simulate Toolbar''' or select '''Simulate > Data Manager''' from the menu bar, or right click on the '''Data Manager''' item of the Navigation Tree and select '''Open Data Manager'''... from the contextual menu. You can also use the keyboard shortcut '''Ctrl+D''' at any time. Select any data file by clicking and highlighting its row in the table and then click the '''Plot''' button to plot the graph. By default, the S [[parameters]] are plotted as double magnitude-phase graphs, while the Y and Z [[parameters]] are plotted as double real-imaginary part graphs. The VSWR data are plotted on a Cartesian graph. You can change the format of complex data plots. In general complex data can be plotted in three forms:
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# Magnitude and Phase
# Real and Imaginary Parts
# Smith Chart
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[[File:PMOM129.png]]
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Figure 2: [[EM.Cube]]'s Data Manager showing a list of the port characteristics data files.
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In particular, it may be useful to plot the S<sub>ii</sub> [[parameters]] on a Smith chart. To change the format of a data plot, select it in the Data Manager and click its '''Edit''' button. In the Edit File Dialog, choose one of the options provided in the dropdown list labeled '''Graph Type'''.
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[[File:PMOM130.png]]
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Figure 3: Changing the graph type by editing a data file's properties.
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[[File:PMOM134.png|800px]]
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Figure 4: The S<sub>11</sub> parameter plotted on a Smith Chart graph in EM.Grid.
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=== Rational Interpolation Of Scattering Parameters ===
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The adaptive frequency sweep described earlier is an iterative process, whereby the Planar MoM simulation engine is run at a certain number of frequency samples at each iteration cycle. The frequency samples are progressively built up, and rational fits for these data are found at each iteration cycle. A decision is then made whether to continue more iterations. At the end of the whole process, a total number of scattering parameter data samples have been generated, and new smooth data corresponding to the best rational fits are written into new data files for graphing. [[EM.Cube]]'s [[planar Module]] also allows you to generate a rational fit for all or any existing scattering parameter data as a post-processing operation without a need to run additional simulation engine runs.
Â
You can interpolate all the scattering [[parameters]] together or select individual [[parameters]]. You do this post-processing operation from the Navigation Tree. Right click on the '''Port Definition''' item in the '''Observables''' section of the Navigation Tree and select Smart Fit. At the top of the Smart Fit Dialog, there is a dropdown list labeled '''Interpolate''', which gives a list of all the available S parameter data for rational interpolation. The default option is "All Available [[Parameters]]". Then you see a box labeled '''Number of Available Samples''', whose value is read from the data content of the selected complex .CPX data file. Based on the number of available data samples, the dialog reports the '''Maximum Interpolant Order'''. You can choose any integer number for '''Interpolant Order''', from 1 to the maximum allowed.
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{{Note|Interpolant order more than 15 will suffer from numerical instabilities even if you have a very large number of data samples.}}
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You can use the '''Update''' button of the dialog to generate the interpolated data for a given order. The new data are written to a complex data file with the same name as the selected S parameter and a "'''_RationalFit'''" suffix. While this dialog is still open, you can plot the new data either directly from the Navigation Tree or from the Data Manager. If you are not satisfied with the results, you can return to the Smart Fit dialog and try a higher or lower interpolant order and compare the new data.
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[[File:PMOM131.png]]
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Figure 1: [[Planar Module]]'s Smart Fit dialog.
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[[File:PMOM133(2).png|400px]]
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Figure 2: The S<sub>11</sub> parameter plot of a two-port structure in magnitude-phase format.
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[[File:PMOM132(2).png|400px]]
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Figure 3: The smoothed version of the S<sub>11</sub> parameter plot of the two-port structure using [[EM.Cube]]'s Smart Fit.
=== Planar Module's Output Simulation Data ===