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# Discontinuity_Modeling_EM_vs_Closed_Form

### Design Notes

Discontinuity Interaction- Modeling and Effects in Simulation Accuracy

This project demonstrates some important concepts in distributed element modeling in circuits.   Many times designers use discontinuity models freely without considering what is connected to them.  This practice can lead to modeling inaccuracies due to the assumptions made in discontinuity modeling.  This will be demonstrated by comparing linear distributed model results with EM simulation results.  This project will demonstrate the need to consider what is connected to discontinuity models when designing RF and Microwave circuits.

Overview

A discontinuity (bend, step, tee, etc) is modeled in the circuit simulator by the addition of parasitic reactive elements. In electromagnetics, the energy stored in these parasitic elements can be described as excitation of higher order evanescent (or cut-off) modes of the transmission line structure. These modes are the mechanism by which the energy of the parasitic elements is stored. These modes are not propagating, rather, the magnitude decays exponentially as they move away from the discontinuity.  While these effects are modeled via the parasitic elements in the circuit models, they assume that stored energy is not altered by adjacent circuit elements. In other words, it is assumed that the evanescent modes have completely decayed before another discontinuity is encountered in the circuit. If two discontinuities are hooked directly together, or the line between two discontinuities is short, then the discontinuities “talk” to one another and will cause modeling inaccuracies.  Electromagnetic (EM) simulators can properly model evanescent modes.   This project will compare simulation results from EM and circuit simulations to show the modeling errors in circuit simulations when discontinuities are too close.

Circuit Schematics

The six circuit schematics in this project have two bend discontinuity models with a line of varying length between them.  The line width is 16 um and the length varies from 0 um to 192 um.  The substrate is 50 um GaAs. The metal thickness is set to 0 to simulate a perfect conductor.

EM simulations

The six EM structures in this project have the same variations as the circuit schematics.  Each enclosure is adjusted for the different line lengths such that the spacing to the edge of the enclosure is identical for each simulation.    The Advanced Frequency Sweep (AFS) feature is used for each EM simulation to speed up the simulation time.

Graphs

Six of the graphs show the phase of s21 of each structure comparing EM versus circuit simulation.  Each simulation is simulated out to 20 GHz.   The length_vs_phase shows a plot of the length of line on the x-axis and the phase difference between the circuit and EM simulation at 20 GHz on the y-axis.

Results

The individual graphs show how the difference between the s21 phase decreases as the line length gets longer.  The graph length_vs_phase summarizes these results in one graph.   So from these graphs it is obvious that as the spacing between the discontinuities increases, the circuit results closer match the EM results.  This result is only showing a maximum phase difference of 2 degrees at 20 GHz.  However, if you had many discontinuities in your design, this error could add up quickly.

Visualization

You can animate the currents of the EM conductors in the 3D view, however they are not saved with this project.  Also, the AFS option can not be selected if currents are to be displayed. Two EM structures have been copied (single_freq_16um_spacing and single_freq_192_um spacing) and modified to run at a single frequency without the AFS option.

In order to view the currents, you will have to:

1- Right click on the proper EM structure and select Add Annotation

2- Choose "EM_Current" measurement and chose the desired EM structure from the Top Level Schematic drop down menu.

3- Resimulate the EM structure by right clicking on the structure and select Force ReSimulation

4- Once this simulation is complete, view the 3D representation of the EM structure and push the blue VCR style play button on the tool bar to turn on the currents.

The evanescent modes can be visualized with the EM structure simulation results.  You can view the currents on the conductors from an EM simulation result by pressing the Play button.

From the Project tab, double click on the EM_Current annotation that you created to bring up the Edit Annotation dialog where you can chose which frequency to display the currents.

To visualize the effects of the evanescent modes, look at the direction of the current arrows on the length of line and the colors for each grid, which represent current density.  First, look at the single_freq_16um_spacing structure.  The area to notice is the straight piece of line between the bend models.  You will notice that the arrows in this structure are pointing up and to the right.  Also, the current density colors are not symmetric about middle of the line.  Next, look at the single_freq_192_spacing structure.  You will notice that the arrows are pointing directly to the right and the colors are symmetric about the middle of the line after some length of the straight line.

The evanescent modes have decayed completely when the arrows and current density colors are symmetric about the center of the line.  In the single_freq_192_spacing EM structure, the evanescent modes have decayed after approximately 65 microns.  This is why the EM results and the circuit results are identical.  In all the other structures, the arrows are never completely parallel to the edge of the line and the current density is not symmetric about the middle of the line.  In all of these cases there is some modeling error in the circuit simulation.

EM Analysis Benefits

This example should demonstrate the importance of considering what is connected to your discontinuities in your designs.  You can perform this type of analysis to determine a rule of thumb for the spacing between discontinuities as a trade off between circuit error and circuit size.  The graph length_vs_phase has good information for making this trade-off.  If you design calls for close discontinuities, use the EM simulator to mode this section to get the most accurate results.