Changes

== Computing Port Characteristics From Time-Domain Data Exciting Multiport Structures in EM.Cube ==

For the computation of the SIn many electromagnetic modeling problems, your physical structure can be treated as a one-parameters in [[EMport, two-port or multiport circuit.Tempo]], the Each port may contain a voltage or current source associated with each port is excited separately with all the other ports turned off. Due to the existence of an internal source resistances, tuning the other sources off is indeed equivalent to terminating the other ports resistance or may have been terminated in their characteristics impedances (matched ports)a resistive or complex impedance. When the jth port is excitedTo characterize such circuits, all the S_ij a number of parameters are calculated together based on the following definition: :<math> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math> where V_i is the voltage across Port i, I_i is the current flowing into Port i and Z_i is the characteristic impedance of Port itypically defined. The sweep loop then moves to the next most widely used port until all ports have been excited. Besides the characteristics are scattering (S) parameters, the admittance (Y) and impedance (Z) parameters are also calculated based on the following relationships: :<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot and admittance ([U]+[S]Y) \cdot ([U]parameters. One-[S])^{-1} \cdot [\sqrt{Z_0}] }</math> :<math> \mathbf{ [Y] = [Z]^{-1} } </math> where <math>\mathbf{[U]}</math> is the identity matrix of order N, and <math>\mathbf{\sqrt{Z_0}}</math> is port circuits are typically excited using a diagonal matrix whose diagonal elements are the square roots of port characteristic impedancesvoltage source in series with an internal resistance. The voltage standing wave ratio (VSWR) of the structure at the first port is also computed based source might be lumped and confined to a single point or to an infinitesimal region, or it can be distributed on the following definition: :<math> \text{VSWR} = \frac{|V_{max}|}{|V_{min}|} = \frac{1+|S_{11}|}{1-|S_{11}|} </math> == Admittance/Impedance Characteristics of Gap Sources in the MoM Solvers == a specified surface. The [[EM.Cube]]'s MoM-based computational modulesthat offer voltage sources are [[EM.Tempo]], [[EM.Picasso]] and [[EM.Libera]]. In other words, provide a number of gap source types for which there three modules are the only ones that allow you can to compute the port characteristics, <i>i.e.</i> S/Z/Y parametersof a physical structure. These Each modules offers a number of special source types are:for this purpose.

| Metal Rectangular metal (PEC or conductive sheet) traces

| Slot Rectangular slot traces

| PEC lines and thin wireswire lines and polylines

Once one set Each of the above source types is used to compute a certain type of port characteristics, i.e. either S parameters, or Y parameters or Z parameters. Once one set of parameters are computed, the other parameters are calculated based on the well-known matrix relationships given in the previous section.

If your physical structure has two or more sources, but you have not defined any ports, all the lumped sources excite the structure simultaneously. However, when you assign N ports to the sources, then you have a multiport structure that is characterized by an N×N scattering matrix, an N×N impedance matrix, and an N×N admittance matrix. To calculate these matrices, [[EM.Cube]] uses a binary excitation scheme in conjunction with the principle of linear superposition. In this binary scheme, the structure is analyzed N times. Each time one of the N port-assigned sources is excited, and all the other port-assigned sources are turned off. The N solution vectors that are generated through the N binary excitation analyses are finally superposed to produce the actual solution to the problem. However, in this process, [[EM.Cube]] also calculates all the port characteristics.  For example, [[EM.Tempo]] primarily computes the S-parameters. For the computation of the S-parameters in [[EM.Tempo]], the source associated with each port is excited separately with all the other ports turned off. Due to the existence of internal source resistances, tuning the other sources off is indeed equivalent to terminating the other ports in their characteristics impedances (matched ports). When the jth port is excited, all the S_ij parameters are calculated together based on the following definition: :<math> S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i} </math> where V_i is the voltage across Port i, I_i is the current flowing into Port i and Z_i is the characteristic impedance of Port i. The sweep loop then moves to the next port until all ports have been excited. The other parameters are then calculated as: :<math>\mathbf{ [Z] = [\sqrt{Z_0}] \cdot ([U]+[S]) \cdot ([U]-[S])^{-1} \cdot [\sqrt{Z_0}] }</math> :<math> \mathbf{ [Y] = [Z]^{-1} } </math> where <math>\mathbf{[U]}</math> is the identity matrix of order N, and [<math>\mathbf{\sqrt{Z_0}}</math>] is a diagonal matrix whose diagonal elements are the square roots of port characteristic impedances. In [[EM.Picasso]] and [[EM.Libera]], the Y-parameters are computed directly from the gap voltage sources. A gap source on a metal strip or a metal wire behaves like a series voltage source with a prescribed strength (of 1V and zero phase by default) that creates a localized discontinuity on the path of electric current flow (<b>J</b>_s). At the end of the MoM simulation, the electric current passing through the voltage source (V_s) is computed and integrated to find the total input current (I_in). From this one can calculate the input admittance as

Once In the case of gap sources on metal traces and probe sources on PEC vias, turning a source off means shorting a series voltage source. The electric currents passing through these sources are then found at each port location, and the admittance or impedance parameters are determinedfound as follows: :<math> I_m = \sum_{n=1}^N Y_{mn} V_n, one can find their complementary parameter set\quad \quad Y_{mn} = \frac{I_m}{V_n} \bigg|_{V_k=0, k \ne n}</math> The other parameters are then calculated as:  :<math>\mathbf{ [S] = [Y_0] \cdot ([Z]-[Z_0]) \cdot ([Z]+[Z_0])^{-1} \cdot [Z_0] }</math>

:where ['''Z<mathsub> \mathbf{ [Y0</sub>'''] = is a diagonal matrix whose diagonal elements are the port characteristic impedances, and [Z]^{-1} } '''Y<sub>0</mathsub>'''] is a diagonal matrix whose diagonal elements are the port characteristic admittances.

The scattering parameters can then be On the other hand, a gap source on a slot trace behaves like a shunt current source with a prescribed strength (of 1A and zero phase by default) that creates a localized discontinuity on the path of magnetic current flow (<b>M</b>_s). At the end of a planar MoM simulation, the magnetic current passing through the current source (I_s) is computed from and integrated to find the impedance parameters using total input voltage across the following relationship:current filament (V_in). From this one can calculate the input impedance as

:<math>Z_{in} = \mathbffrac{ [S] V_{in}}{I_s} = [Y_0] \cdot ([Z]-[Z_0]) frac{\cdot ([Z]+[Z_0])^int_W \hat{-1y} \cdot [Z_0] \mathbf{M_s} \,dy} {V_s} = \frac{\int_W E_y \, dy}{V_s}</math>

where ['''Z₀'''] is The same principle applies to the gap sources on slot traces. The figure below shows how to place two gap sources with opposite polarities a diagonal matrix whose diagonal elements are quarter guide wavelength away from their shorted ends to calculate the port characteristic impedancescorrect input impedance of the CPW line looking to the left of the gap sources. Note that in this case, you deal with shunt filament current sources across the two slot lines and ['''Ythat the slot line carry magnetic currents. The end of the slot lines look open to the magnetic currents, but in reality they short the electric field. The quarter-wave CPW line acts as an open circuit to the current sources. In the case of gap sources on slot traces, turning a source off means opening a shunt filament current source. The magnetic currents passing through the source locations, and thus the voltages across them, are then found at all ports, and the impedance parameters are found as follows: :<submath>V_m = \sum_{n=1}^N Z_{mn} I_n, \quad \quad Z_{mn} = \frac{V_m}{I_n} \bigg|_{I_k=0, k \ne n}</submath>'''] is  <table><tr><td> [[Image:PMOM61(1).png|thumb|left|480px|Placing two oppositely polarized gap sources a diagonal matrix whose diagonal elements are quarter guide wavelength away from the port characteristic admittancesshort end of a CPW line to effectively create an open circuit beyond the gap location.]] </td></tr></table>