## Reduce EMI with Good Signal Integrity Habits

Recently the ‘Signal Integrity Journal’ posted their ‘Top 10 Articles’ of 2019. All of the articles included were incredible, however, one stood out to me from the rest – ‘Seven Habits of Successful 2-Layer Board Designers’ by Dr. Eric Bogatin (https://www.signalintegrityjournal.com/blogs/12-fundamentals/post/1207-seven-habits-of-successful-2-layer-board-designers). In this work, Dr. Bogatin and his students were developing a 2-Layer printed circuit board (PCB), while trying to minimize signal and power Integrity issues as much as possible. As a result, they developed a board and described seven ‘golden habits’ for this board development. These are fantastic habits that I’m confident we can all agree with. In particular, there was one habit at which I wanted to take a deeper look:

“…Habit 4: When you need to route a cross-under on the bottom layer, make it short. When you can’t make it short, add a return strap over it..”

Generally speaking, this habit suggests to be very careful with the routing of signal traces over the gap on the ground plane. From the signal integrity point of view, Dr. Bogatin explained it perfectly – “..The signal traces routed above this gap will see a gap in the return path and generate cross talk to other signals also crossing the gap..”. On one hand, crosstalk won’t be a problem if there are no other nets around, so the layout might work just fine in that case. However, crosstalk is not the only risk. Fundamentally, crosstalk is an EMI problem. So, I wanted to explore what happens when this habit is ignored and there are no nearby nets to worry about.

To investigate, I created a simple 2-Layer board with the signal trace, connected to 5V voltage source, going over an air gap. Then I observed the near field and far field results using ANSYS SIwave solution. Here is what I found.

## Near and Far Field Analysis

Typically, near and far fields are characterized by solved E and H fields around the model. This feature in ANSYS SIwave gives the engineer the ability to simulate both E and H fields for near field analysis, and E field for Far Field analysis.

First and foremost, we can see, as expected, that both near and far Field have resonances at the same frequencies. Additionally, we can observe from Figure 1 that both E and H fields for near field have the largest radiation spikes at 786.3 MHz and 2.349GHz resonant frequencies.

Figure 1. Plotted E and H fields for both Near and Far Field solutions

If we plot E and H fields for Near Field, we can see at which physical locations we have the maximum radiation.

Figure 2. Plotted E and H fields for Near field simulations

As expected, we see the maximum radiation occurring over the air gap, where there is no return path for the current. Since we know that current is directly related to electromagnetic fields, we can also compute AC current to better understand the flow of the current over the air gap.

## Compute AC Currents (PSI)

This feature has a very simple setup interface. The user only needs to make sure that the excitation sources are read correctly and that the frequency range is properly indicated. A few minutes after setting up the simulation, we get frequency dependent results for current. We can review the current flow at any simulated frequency point or view the current flow dynamically by animating the plot.

Figure 3. Computed AC currents

As seen in Figure 3, we observe the current being transferred from the energy source, along the transmission line to the open end of the trace. On the ground layer, we see the return current directed back to the source. However at the location of the air gap there is no metal for the return current to flow, therefore, we can see the unwanted concentration of energy along the plane edges. This energy may cause electromagnetic radiation and potential problems with emission.

If we have a very complicated multi-layer board design, it won’t be easy to simulate current flow on near and far fields for the whole board. It is possible, but the engineer will have to have either extra computing time or extra computing power. To address this issue, SIwave has a feature called EMI Scanner, which helps identify problematic areas on the board without running full simulations.

## EMI Scanner

ANSYS EMI Scanner, which is based on geometric rule checks, identifies design issues that might result in electromagnetic interference problems during operation. So, I ran the EMI Scanner to quickly identify areas on the board which may create unwanted EMI effects. It is recommended for engineers, after finding all potentially problematic areas on the board using EMI Scanner, to run more detailed analyses on those areas using other SIwave features or HFSS.

Currently the EMI Scanner contains 17 rules, which are categorized as ‘Signal Reference’, ‘Wiring/Crosstalk’, ‘Decoupling’ and ‘Placement’. For this project, I focused on the ‘Signal Reference’ rules group, to find violations for ‘Net Crossing Split’ and ‘Net Near Edge of Reference’. I will discuss other EMI Scanner rules in more detail in a future blog (so be sure to check back for updates).

Figure 4. Selected rules in EMI Scanner (left) and predicted violations in the project (right)

As expected, the EMI Scanner properly identified 3 violations as highlighted in Figure 4. You can either review or export the report, or we can analyze violations with iQ-Harmony. With this feature, besides generating a user-friendly report with graphical explanations, we are also able to run ‘What-if’ scenarios to see possible results of the geometrical optimization.

Figure 5. Generated report in iQ-Harmony with ‘What-If’ scenario

Based on these results of quick EMI Scanner, the engineer would need to either redesign the board right away or to run more analysis using a more accurate approach.

## Conclusion

In this blog, we were able to successfully run simulations using ANSYS SIwave solution to understand the effect of not following Dr.Bogatin’s advice on routing the signal trace over the gap on a 2-Layer board. We also were able to use 4 different features in SIwave, each of which delivered the correct, expected results.

Overall, it is not easy to think about all possible SI/PI/EMI issues while developing a complex board. In these modern times, engineers don’t need to manufacture a physical board to evaluate EMI problems. A lot of developmental steps can now be performed during simulations, and ANSYS SIwave tool in conjunction with HFSS Solver can help to deliver the right design on the first try.

## Defining Antenna Array Excitations with Nested-If Statements in HFSS

HFSS offers various methods to define array excitations. For a large array, you may take advantage of an option “Load from File” to load the magnitude and phase of each port. However, in many situations you may have specific cases of array excitation. For example, changing amplitude tapering or the phase variations that happens due to frequency change. In this blog we will look at using the “Edit Sources” method to change the magnitude and phase of each excitation. There are cases that might not be easily automated using a parametric sweep. If the array is relatively small and there are not many individual cases to examine you may set up the cases using “array parameters” and “nested-if”.

In the following example, I used nested-if statements to parameterize the excitations of the pre-built example “planar_flare_dipole_array”, which can be found by choosing File->Open Examples->HFSS->Antennas (Fig. 1) so you can follow along. The file was then saved as “planar_flare_dipole_array_if”. Then one project was copied to create two examples (Phase Variations, Amplitude Variations).

Fig. 1. Planar_flare_dipole_array with 5 antenna elements (HFSS pre-built example).

# Phase Variation for Selected Frequencies

In this example, I assumed there were three different frequencies that each had a set of coefficients for the phase shift. Therefore, three array parameters were created. Each array parameter has 5 elements, because the array has 5 excitations:

A1: [0, 0, 0, 0, 0]

A2: [0, 1, 2, 3, 4]

A3: [0, 2, 4, 6, 8]

Then 5 coefficients were created using a nested_if statement. “Freq” is one of built-in HFSS variables that refers to frequency. The simulation was setup for a discrete sweep of 3 frequencies (1.8, 1.9 and 2.0 GHz) (Fig. 2). The coefficients were defined as (Fig. 3):

E1: if(Freq==1.8GHz,A1[0],if(Freq==1.9GHz,A2[0],if(Freq==2.0GHz,A3[0],0)))

E2: if(Freq==1.8GHz,A1[1],if(Freq==1.9GHz,A2[1],if(Freq==2.0GHz,A3[1],0)))

E3: if(Freq==1.8GHz,A1[2],if(Freq==1.9GHz,A2[2],if(Freq==2.0GHz,A3[2],0)))

E4: if(Freq==1.8GHz,A1[3],if(Freq==1.9GHz,A2[3],if(Freq==2.0GHz,A3[3],0)))

E5: if(Freq==1.8GHz,A1[4],if(Freq==1.9GHz,A2[4],if(Freq==2.0GHz,A3[4],0)))

Please note that the last case is the default, so if frequency is none of the three frequencies that were given in the nested-if, the default phase coefficient is chosen (“0” in this case).

Fig. 2. Analysis Setup.

Fig. 3. Parameters definition for phase varaitioin case.

By selecting the menu item HFSS ->Fields->Edit Sources, I defined E1-E5 as coefficients for the phase shift. Note that phase_shift is a variable defined to control the phase, and E1-E5 are meant to be coefficients (Fig. 4):

Fig. 4. Edit sources using the defined variables.

The radiation pattern can now be plotted at each frequency for the phase shifts that were defined (A1 for 1.8 GHz, A2 for 1.9 GHz and A3 for 2.0 GHz) (Figs 5-6):

Fig. 5. Settings for radiation pattern plots.

Fig. 6. Radiation patten for phi=90 degrees and different frequencies, the variation of phase shifts shows how the main beam has shifted for each frequency.

# Amplitude Variation for Selected Cases

In the second example I created three cases that were controlled using the variable “CN”. CN is simply the case number with no units.

The variable definition was similar to the first case. I defined 3 array parameters and 5 coefficients. This time the coefficients were used for the Magnitude. The variable in the nested-if was CN. That means 3 cases and a default case were created. The default coefficient here was chosen as “1” (Figs. 7-8).

A1: [1, 1.5, 2, 1.5, 1]

A2: [1, 1, 1, 1, 1]

A3: [2, 1, 0, 1, 2]

E1: if(CN==1,A1[0],if(CN==2,A2[0],if(CN==3,A3[0],1)))*1W

E2: if(CN==1,A1[1],if(CN==2,A2[1],if(CN==3,A3[1],1)))*1W

E3: if(CN==1,A1[2],if(CN==2,A2[2],if(CN==3,A3[2],1)))*1W

E4: if(CN==1,A1[3],if(CN==2,A2[3],if(CN==3,A3[3],1)))*1W

E5: if(CN==1,A1[4],if(CN==2,A2[4],if(CN==3,A3[4],1)))*1W

Fig. 7. Parameters definition for amplitude varaitioin case.

Fig. 8. Exciation setting for amplitude variation case.

Notice that CN in the parametric definition has the value of “1”. To create the solution for all three cases I used a parametric sweep definition by selecting the menu item Optimetrics->Add->Parametric. In the Add/Edit Sweep I chose the variable “CN”, Start: 1, Stop:3, Step:1. Also, in the Options tab I chose to “Save Fields and Mesh” and “Copy geometrically equivalent meshes”, and “Solve with copied meshes only”. This selection helps not to redo the adaptive meshing as the geometry is not changed (Fig. 9). In plotting the patterns I could now choose the parameter CN and the results of plotting for CN=1, 2, and 3 is shown in Fig. 10. You can see how the tapering of amplitude has affected the side lobe level.

Fig. 9. Parameters definition for amplitude varaitioin case.

Fig. 10. Radiation patten for phi=90 degrees and different cases of amplitude tapering, the variation of amplitude tapering has caused chagne in the beamwidth and side lobe levels.

# Drawback

The drawback of this method is that array parameters are not post-processing variables. This means changing them will create the need to re-run the simulations. Therefore, it is needed that all the possible cases to be defined before running the simulation.

## Frequency Dependent Material Definition in ANSYS HFSS

Electromagnetic models, especially those covering a frequency bandwidth, require a frequency dependent definition of dielectric materials. Material definitions in ANSYS Electronics Desktop can include frequency dependent curves for use in tools such as HFSS and Q3D. However, there are 5 different models to choose from, so you may be asking: What’s the difference?

In this blog, I will cover each of the options in detail. At the end, I will also show how to activate the automatic setting for applying a frequency dependent model that satisfies the Kramers-Kronig conditions for causality and requires a single frequency definition.

# Background

Recalling that the dielectric properties of material are coming from the material’s polarization

where D is the electric flux density, E is the electric field intensity, and P is the polarization vector. The material polarization can be written as the convolution of a general dielectric response (pGDR) and the electric field intensity.

The dielectric polarization spectrum is characterized by three dispersion relaxation regions α, β, and γ for low (Hz), medium (KHz to MHz) and high frequencies (GHz and above). For example, in the case of human tissue, tissue permittivity increases and effective conductivity decreases with the increase in frequency [1].

Each of these regions can be modeled with a relaxation time constant

where τ is the relaxation time.

The well-known Debye expression can be found by use of spectral representation of complex permittivity (ε(ω)) and it is given as:

where ε is the permittivity at frequencies where ωτ>>1, εs is the permittivity at ωτ>>1, and j2=-1. The magnitude of the dispersion is ∆ε = εs.

The multiple pole Debye dispersion equation has also been used to characterize dispersive dielectric properties [2]

In particular, the complexity of the structure and composition of biological materials may cause that each dispersion region be broadened by multiple combinations. In that case a distribution parameter is introduced and the Debye model is modified to what is known as Cole-Cole model

where αn, the distribution parameter, is a measure of broadening of the dispersion.

Gabriel et. al [3] measured a number of human tissues in the range of 10 Hz – 100 GHz at the body temperature (37℃). This data is freely available to the public by IFAC [4].

# Frequency Dependent Material Definition in HFSS and Q3D

In HFSS you can assign conductivity either directly as bulk conductivity, or as a loss tangent. This provides flexibility, but you should only provide the loss once. The solver uses the loss values just as they are entered.

To define a user-defined material choose Tools->Edit Libraries->Materials (Fig. 2). In Edit Libraries window either find your material from the library or choose “Add Material”.

To add frequency dependence information, choose “Set Frequency Dependency” from the “View/Edit Material” window, this will open “Frequency Dependent Material Setup Option” that provides five different ways of defining materials properties (Fig. 3).

Before choosing a method of defining the material please note [5]:

• The Piecewise Linear and Frequency Dependent Data Points models apply to both the electric and magnetic properties of the material. However, they do not guarantee that the material satisfies causality conditions, and so they should only be used for frequency-domain applications.
• The Debye, Multipole Debye and Djordjevic-Sarkar models apply only to the electrical properties of dielectric materials. These models satisfy the Kramers-Kronig conditions for causality, and so are preferred for applications (such as TDR or Full-Wave SPICE) where time-domain results are needed. They also include an automatic Djordjevic-Sarkar model to ensure causal solutions when solving frequency sweeps for simple constant material properties.
• HFSS and Q3D can interpolate the property’s values at the desired frequencies during solution generation.

Piecewise Linear

This option is the simplest way to define frequency dependence. It divides the frequency band into three regions. Therefore, two frequencies are needed as input. Lower Frequency and Upper Frequency, and for each frequency Relative Permittivity, Relative Permeability, Dielectric Loss Tangent, and Magnetic Loss Tangent are entered as the input. Between these corner frequencies, both HFSS and Q3D linearly interpolate the material properties; above and below the corner frequencies, HFSS and Q3D extrapolate the property values as constants (Fig. 4).

Once these values are entered, 4 different data sets are created (\$ds_epsr1, \$ds_mur1, \$ds_tande1, \$ds_tandm1). These data sets now can be edited. To do so choose Project ->Data sets, and choose the data set you like to edit and click Edit (Fig. 5). This data set can be modified with additional points if desired (Fig. 6).

Frequency Dependent

Frequency Dependent material definition is similar to Piecewise Linear method, with one difference. After selecting this option, Enter Frequency Dependent Data Point opens that gives the user the option to use which material property is defined as a dataset, and for each one of them a dataset should be defined. The datasets can be defined ahead of time or on-the-fly. Any number of data points may be entered. There is also the option of importing or editing frequency dependent data sets for each material property (Fig. 7).

Djordjevic-Sarkar

This model was developed initially for FR-4, commonly used in printed circuit boards and packages [6]. In fact, it uses an infinite distribution of poles to model the frequency response, and in particular the nearly constant loss tangent, of these materials.

where ε is the permittivity at very high frequency,  is the conductivity at low (DC) frequency,  j2=-1, ωA is the lower angular frequency (below this frequency permittivity approaches its DC value), ωB is the upper angular frequency (above this frequency permittivity quickly approaches its high-frequency permittivity). The magnitude of the dispersion is ∆ε = εs-ε∞.

Both HFSS and Q3D allow the user to enter the relative permittivity and loss tangent at a single measurement frequency. The relative permittivity and conductivity at DC may optionally be entered. Writing permittivity in the form of complex permittivity [7]

Therefore, at the measurement frequency one can separate real and imaginary parts

where

Therefore, the parameters of Djordjevic-Sarkar can be extracted, if the DC conductivity is known

If DC conductivity is not known, then a heuristic approximation is De = 10 εtan δ1.

The window shown in Fig. 8 is to enter the measurement values.

Debye Model

As explained in the background section single pole Debye model is a good approximation of lossy dispersive dielectric materials within a limited range of frequency. In some materials, up to about a 10 GHz limit, ion and dipole polarization dominate and a single pole Debye model is adequate.

The Debye parameters can be calculated from the two measurements [7]

Both HFSS and Q3D allow you to specify upper and lower measurement frequencies, and the loss tangent and relative permittivity values at these frequencies. You may optionally enter the permittivity at high frequency, the DC conductivity, and a constant relative permeability (Fig. 9).

Multipole Debye Model

For Multipole Debye Model multiple frequency measurements are required. The input window provides entry points for the data of relative permittivity and loss tangent versus frequency. Based on this data the software dynamically generates frequency dependent expressions for relative permittivity and loss tangent through the Multipole Debye Model. The input dialog plots these expressions together with your input data through the linear interpolations (Fig. 10).

## Cole Cole Material Model

The Cole Cole Model is not an option in the material definition, however, it is possible to generate the frequency dependent datasets and use Frequency Dependent option to upload these values. In fact ANSYS Human Body Models are built based on the data from IFAC database and Frequency Dependent option.

## Visualization

Frequency-dependent properties can be plotted in a few different ways. In View/Edit Material dialog right-click and choose View Property vs. Frequency. In addition, the dialogs for each of the frequency dependent material setup options contain plots displaying frequency dependence of the properties.

You can also double-click the material property name to view the plot.

## Automatically use causal materials

As mentioned at the beginning, there is a simple automatic method for applying a frequency dependent model in HFSS. Select the menu item HFSS->Design Setting, and check the box next to Automatically use casual materials under Lossy Dielectrics tab.

This option will automatically apply the Djordjevic-Sarkar model described above to objects with constant material permittivity greater than 1 and dielectric loss tangent greater than 0. Keep in mind, not only is this feature simple to use, but the Djordjevic-Sarkar model satisfies the Kramers-Kronig conditions for causality which is particularly preferred for wideband applications and where time-domain results will also be needed. Please note that if the assigned material is already frequency dependent, automatic creation of frequency dependent lossy materials is ignored.

# References

• D.T. Price, MEMS and electrical impedance spectroscopy (EIS) for non-invasive measurement of cells, in MEMS for Biomedical Applications, 2012, https://www.sciencedirect.com/topics/materials-science/electrical-impedance
• W. D. Hurt, “Multiterm Debye dispersion relations for permittivity of muscle,” IEEE Trans. Biomed. Eng, vol. 32, pp. 60-64, 1985.
• S. Gabriel, R. W. Lau, and C. Gabriel. “The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues.” Physics in Medicine & Biology, vol. 41, no. 11, pp. 2271, 1996.
• Dielectric Properties of Body Tissues in the Frequency Range 10 Hz – 100 GHz, http://niremf.ifac.cnr.it/tissprop/.
• A. R. Djordjevic, R. D. Biljic, V. D. Likar-Smiljani, and T. K. Sarkar, “Wideband frequency-domain characterization of FR-4 and time-domain causality,” IEEE Trans. on Electromagnetic Compatibility, vol. 43, no. 4, p. 662-667, Nov. 2001.