This example investigates how to calculate the cross talk between two closely spaced parallel microstrip transmission lines (TL). It is shown how a 2D simulation in MODE can be used to quickly calculate the cross talk along the length of a pair of microstrip TLs. The crosstalk from MODE is compared against fully 3D FDTD simulations of a realistic test bench setup using edge mounted SMA coaxial connectors to excite the microstrip line and measure the scattering parameters. At the conclusion of the study, a guard via fence is introduced between the microstrips to reduce the crosstalk. FDTD is required to simulate this structure due to the nonuniformity of the via fence along the length of the microstrip line.
Background
As digital circuits become more miniaturized on printed circuit boards (PCBs) and their clock frequency increases, the coupling (cross talk) between closely spaced transmission lines can significantly perturb the circuit’s signal integrity, limiting the performance in examples such as high-speed interconnects. In such instances, it is useful to characterize the crosstalk through both theoretical and numerical means.
The simplified test bench setup shown in the above figure is used to measure the cross talk between two microstrip lines on a grounded substrate. Each Port is matched to the characteristic impedance Z0 of the single, isolated microstrip transmission line. In this measurement, a voltage source is used to excite Port 1 and the received signal at Ports 2,3, and 4 is measured. The line of the left carrying the main signal is termed the “aggressor” which ideally should carry all the power to Port 2. However, the closely spaced transmission lines (s0) are loosely coupled and power is gradually leaked into the line on the right, termed the “victim”, which causes a measured signal on Port 3, termed near-end crosstalk (NEXT) and Port 4, termed far-end crosstalk (FEXT).
The analysis of crosstalk in microstrip lines follows the same approach used in many other types of transmission-line couplers, in which even and odd mode analysis and multiconductor transmission-line theory are used to find the four-port system’s scattering parameters. More details can be found in Collin [1]. In Hill [2], the scattering parameters of the parallel microstrip lines are shown to be related to the effective index and characteristic impedance of its even (nev,Zev) and odd (nodd, Zodd) modes and those of a single isolated transmission line (nms). These parameters can be approximated using quasi-static formulas [1] or be numerically evaluated with a high degree of accuracy such as in MODE (see the Coupled Microstrip example for details) or in the built-in characteristic impedance calculator in FDTD (see the Ports page for details ).
Parallel microstrip lines with a via fence placed between them.
Whereas crosstalk examples with simple geometries can be found theoretically, in many instances only a numerical approach is feasible. For instance, a guard trace and/or via fence is often used to alleviate the problem of crosstalk in high-speed and high-frequency electronic circuits. It consists of a guard microstrip trace of width gw grounded by a row of N platted vias of diameter vr that is placed between the signal-carrying traces. The above figure shows a representative via fence. The periodic nature of the via fence does not allow for a simple closed-form expression to calculate the cross talk.
This example shows how transmission-line theory in conjunction with simulated values for characteristic impedance can be used to quickly evaluate the crosstalk between two microstrip lines. The near-end and far-end crosstalk obtained from the built-in characteristic impedance calculator and theory is verified through 3D FDTD simulations using an experimental test bench presented in Hill [2] in which impedance-matched coaxial cables and connectors are used to excite and measure the scattering parameters. In lieu of experimental results, a comparison of the theoretical and simulated crosstalk will be presented. It is shown how FDTD can be used to simulate a more complex crosstalk example with a via fences placed between the two microstrip lines to reduce the crosstalk.
Simulation Setup
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| Without Vias | With Vias |
The file cross_talk.fsp contains the FDTD simulation for the crosstalk test bench in which the setup without a via fence is shown in the above figure on the left. The coaxial cables are (constructed from an inner PEC Circle and dielectric Ring with n=2 which is surrounded by an outer PEC Ring). These are attached to a standard SMA female end launch connector (constructed from PEC rectangles) which feeds the two ends of two parallel microstrip transmission lines (constructed from 2D PEC Sheets) that are placed on top of a substrate (constructed from a dielectric Rectangle structure with n=1.483). The substrate is conductor backed by a PEC metallic rectangle. The above figure on the right shows the test bench with a via fence (constructed with PEC rectangles and PEC circles).
The simulation regions is surrounded by PML boundaries on all sides except the y min boundary which is assigned as a metal. It is expected that the crosstalk will be at least two to four orders of magnitude lower in intensity than the driving signal. Therefore, in order to accurately measure this extremely small crosstalk, we reduce any noise introduced by PML reflections by increasing the PML layers in the direction of propagation (z).
At the coax-to-microstrip transition, the coaxial pin extends out over the microstrip a distance ph and is connected smoothly to the microstrip by a flush PEC Rectangle. This simple model of the transition (shown in the above figure) provides a first order approximation of the solder that would be used in practice to smoothly connect the two transmission-lines. In combination with the SMA model, we can accurately account for the parasitic effects of the device feed that would be observed in actual measurements.The TLs, coax, substrate, and SMA connectors are placed inside their own structure groups labeled ::Structure.
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Note : SMA Connectors These SMA connectors can be copied to other project files; however, the user must be sure to properly set the mesh order so that the coaxial cable’s dielectric core and pin passes through it. |
To obtain all scattering parameters of the device requires us to run only one simulation (here we are exploiting symmetry and reciprocity). In this arrangement, Port 1 injects the coaxial waveguide’s TEM mode over a frequency range of 0.5 - 4 GHz, and the transmission is measured at Ports 2, 3, and 4. Whereas the exact z position of the Ports on the coax doesn’t alter the absolute magnitude of the measured scattering parameters, the phase will change as the distance between the monitors varies. However, any additional phase incurred along the coax can be calibrated out in post processing.
A number of mesh override regions are placed throughout the simulation in regions the fields are highly confined including over the traces, coaxial waveguide, and at the transition. It is important to note that the mesh across the waveguide’s cross section will set the characteristic impedance and effective index of the transmission line in simulation.
The ::model analysis group is used to adjust the physical dimensions of the test bench, the position of the monitors, mesh override regions, and turning the guard trace on (guard=1) or off (guard=0). The above figure contains the list of variables that can be edited and their specific values for the upcoming comparison of simulation and theory.
Results and Analysis
Characteristic Impedance
Before the FDTD crosstalk simulation is run, the cross_talk_z0.lsf script file is used to calculate (Zev,nev) (Zodd, nodd) of the coupled microstrip lines, nms of the isolated microstrip line, and Zcoax of the coaxial waveguide. Before running this script, the cross_talk.fsp simulation file should be open.
The script first creates a fictitious port labeled z0_port that covers one of the microstrip lines. This port is used to calculate the isolated microstrip line's quasi-TEM mode's effective index, which is read from the port's results. Afterward, the port's dimensions is altered to span both microstrip lines. Following the techniques detailed in the coupled microstrip example that relate the even and odd mode to the common and differential mode of the coupled lines, the even and odd mode's characteristic impedance is found using the port's built-in characteristic impedance tool. Furthermore, their effective index is read from the port mode's results. At the end of the script, the coaxial line's impedance is read from Port 1 and the fictitious port is deleted.
Using the script, the following parameters were found: (Zev=44.9,nev=1.40) , (Zodd=41.7, nodd=1.36), nms=1.37, Zcoax=45. A finer mesh was used than the one found in the simulation file. These values are then used in the theoretical NEXT and FEXT calculation in the upcoming comparison to simulations.
Crosstalk
The simulation file cross_talk.fsp is first run with the guard trace turned off (guard=0). The simulation takes roughly 5 minutes to run on a good workstation. The script cross_talk.lsf is used to generate the scattering parameters and compare the simulated and theoretical NEXT and FEXT as shown in the above figure. It is clear that theory and simulation are well-matched. The simulated crosstalk being slightly higher than theory has also been observed in a comparable experimental measurement of the test bench and has been attributed to additional coupling at the coax-to-microstrip transition (Hill [2]).
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Note : Meshing and Simulation Time It should be noted that these crosstalk results and reported impedance and effective index were found with a finer mesh then the one specified in the simulation file, which is relatively coarse. This allows us to accurately capture the effective parameters and the parasitic effects of the SMA connectors. Furthermore, in the case of the guard via fence additional meshing regions will be required. Increasing the mesh density should be the last stage in these electrically large (wavelength-sized) simulations, as the simulation time will be increased (to get these results the simulation took roughly 30 minutes to complete). |
The via fence is now turned on (guard=1) in the simulation file cross_talk.fsp. Although not shown, the parameter sweep in the FDTD file’s Optimization and Sweeps tool was used to find an optimal guard width and via diameter of gw=vr=3mm. A comparison of the crosstalk between the case with and without the via fence is shown in the above figures. It is clear that the introduction of the via fence reduces the NEXT and FEXT by up to 8dB.
Related references
[1] Robert E. Collin, Foundations for Microwave Engineering, Second Edition. Wiley-Interscience (2001).
[2] Hill, David A., Kenneth Hale Cavcey, and Robert T. Johnk. "Crosstalk between microstrip transmission lines." IEEE Transactions on Electromagnetic Compatibility vol. 36, no. 4, pp. 314-321, 1994.