Demystifying Modeling and Simulation Using Applications
Modeling and simulation is a complex topic, usually left to experts of the EMC field as the amount of knowledge and understanding that goes into creating a model can be tremendous. At the same time, however, models tend to either fall short by not being able to accurately describe real-world parasitics or are application specific. This usually leaves the engineer working on design out of the upfront simulation, as the amount of effort and cost needed to understand and obtain these models are beyond their reach given the timing in most projects. This, however, is counter intuitive as the more effort put into understanding electromagnetic interactions upfront will greatly reduce design/hardware cost as development of a product goes on.
To address this, in this article we’ll discuss creating a set of models and simulations using a 3D solver and SPICE to examine resonant structures, the return path, and the result of parasitics in real-world components. To be able to create an inclusive set of simulations that introduces background information and application, the list of topics was limited to situations that people interact with in design, reviews and troubleshooting.
In addition, the tools shouldn’t include only a 3D solver or SPICE, but incorporate both techniques as each tool is formulated for solving individual problems. While I don’t plan on being exhaustive, I intend to show you that with these same tools, you can create examples that help solidify your understanding of these phenomena and act as a springboard for more complex simulations, even compelling you to try your own!
Resonant Structures
We first focus our attention on antennas and their radiating structures. There are few other topics in EMC that are as ubiquitous in product design with a need to be understood as resonant monopole and dipole antenna structures. We choose this topic to start because antennas, or any radiators, have a reciprocity characteristic that makes them especially problematic—from applications such as printed circuit board traces to wiring looms. For this reason, engineers must be trained to spot physical constructs that result in unintentional radiators or antennas.
To better understand radiators and what makes an efficient one, we start with some important resonant structure parameters. The first being the wavelength of the incident wave on the structure. We define the relationship between the frequency and wavelength below.
Another important factor in determining whether structure is resonant or not is the length of the structure in comparison to the wavelength of the signal being transmitted or of the frequencies being coupled to the conductor. Lastly, where the RF source is being fed to the antenna structure, either from the center or from the end, is also an important factor.
With these things, we can begin to form an easy-to-understand model of a dipole antenna, shown in Figure 1 (left), and similarly a monopole antenna shown in Figure 1 (right).
These figures abstract the complexity out of these simple resonant structures, and bring to light the following:
- There needs to be a return path, which is modeled as a parasitic capacitance, allowing the energy to return to the source.
- Regardless of where the source of energy is, to be able to return it needs a ground plane that is connected to the source.
To realize these structures, virtually, we’ll start by creating them in a simulation tool. These don’t have to be high-fidelity models, since we’re just focused on visualization. We can model the dipole as a center-loaded wire, and the monopole as an end-loaded wire with a back plane (these results are shown in Figure 3).
Now that we have a physical model of these structures, let’s examine the length and understand how efficient the radiating structure can be. To do this, we look to the length of the element in relation to the frequency (or harmonics) of interest. For a simple dipole and monopole resonant structure, we characterize them as being most efficient by the following:
In our conceptual model, we’ll do this by defining the length of the element as some function of lambda. However, this means very little to us without defining what is meant by making a radiator efficient. We define this by looking at the currents and voltages of the structure. At resonance, the currents are the largest at the feed point either at the center (dipole) or end (monopole); both are depicted in Figure 2, with the monopole being half the length of the figure.
It’s important to draw attention to the current and voltages distribution, as they appear fairly linearly across the element. By shortening, or lengthening, the structure or by changing the frequency, we change the resonance and by association the distribution of current and voltage along the structure. In our physical model of the structure, we can simply simulate the structure and we can show the results in Figure 2 for both the dipole and monopole structures in Figure 3.
If we change the length (or the frequency) of the length of the element, we can show that the distribution of the currents in the element change.
At resonance, for this reason, the dipole and monopole structures are usually depicted as a series resonant circuit, shown in Figure 5.
After understanding the basics of resonant structures, often the next question is, “Is this good, or bad?” And that answer, predictably, is that it depends. To showcase this dependency, we’ll take the resonant dipole and monopole, and create familiar structures out of them. First, we’ll take an example that improves upon the limited bandwidth of the dipole antenna. This antenna, the log periodic dipole (LPDA), is ubiquitous in EMC testing because of its ability to direct energy across a wide range of frequencies to a target.
However, at first the function of this antenna may seem confusing as there are multiple elements and each of those elements has different characteristics. After understanding that the LPDA is really nothing more than a series of dipole antennas linked together, we can use our understanding of the dipole antenna we created to analyze it. To create one of these antennas, we need to first define some basic design principals underscored below.
- The radius and length are interrelated based on a scale factor:
- The spacing factor is defined as the ratio of the distance between the elements to twice the length of that element:
- And the upper and lower frequencies of the antenna are limited by the length of the shortest and longest dipole element, with the upper frequency limit being the smaller dipole and the lower frequency limit being the larger dipole.
Following a similar analysis as the original dipole, to see how the LPDA functions, we look to the currents on the elements and relate them back to the series resonant single dipole. (Figure 6)
Using the solver, we’re able to graph the antenna current as a function of frequency. Starting at the lower design limit of the antenna. Working to the highest designed frequency, we’re able to verify the operation of a LPDA. It makes use of the resonance of each dipole element to increase the usable frequency of the structure over that of a single element antenna (shown in Figure 7).
Next, we expand our understanding of a monopole antenna to include a common situation where an electronic controller unit case is grounded to a large metal frame with a ground strap. Here, the large metal frame acts as the back plane while the strap acts as the monopole antenna. However, unlike the monopole discussed previously, we now have the addition of a metal structure connected to the other end of the monopole interacting with the currents on the structure. This situation is referred to as a top hat monopole (Figure 8).
To simulate this structure, understand its differences, and to avoid its creation in your product, we can easily modify the original monopole antenna simulation by adding a metal disk at the other end. We examine the currents and notice that the current in the element is no longer focused on one end, but is now drawn up to the metal top hat.
In production, this setup must be recognized so that whatever conductive material (ground strap, wire loom, etc.) doesn’t have a conductive chassis to work against as a reference plane resulting in a monopole, and an increase in the radiation efficiency of that monopole.
Characteristics of a PCB Trace and Return Path
In addition to radiating structures, another phenomenon that is often difficult to conceptualize but frequently encountered is fully understanding the various parameters that characterize the return path. Using a mix of SPICE and a 3D solver, we can create simulations that allow us to easily investigate the effects of capacitive crosstalk between traces, skin effect and mutual inductance between traces and in the return path.
We begin our investigation by creating a sample situation that allows us to parameterize the characteristics important to the skin effect and capacitive coupling shown in Figure 9.
This setup allows us to simulate a major tenant of PCB design. Do not route sensitive traces (an ADC and PWM, for example) in parallel to each other. This is to avoid any sort of mutual capacitance that may occur between these two parallel conductors, providing a pathway for energy to wirelessly couple between traces. A simple representation of the mathematical relationship is represented below:
However, not only does the shared capacitance affect the coupled signal, but so does the skin depth of the current in the trace itself, which contributes to resistive losses. This leads us to another characteristic of printed circuit board design, that current isn’t evenly distributed inside the conductor in which it is traveling. This situation is described in Figure 10.
As frequency increases, the skin depth decreases as the inverse relationship which results in the increase of the trace resistance; the mathematical relationship is defined below.
This effect, much like mutual capacitance, is difficult to demonstrate due to the complex nature of printed circuit board trace coupling. However, by taking the setup shown in Figure 9, we can use a 3D solver and create a variety of experiments such as the one shown in Figure 11.
In this experiment, we choose to fix the distance and vary the width of the conductor. We’ll be able to not only analyze the effect capacitive coupling has as a function of frequency but be able to analyze the skin depth’s effect on the resistive losses in the source and victim conductor as well.
By analyzing the results at the load of the source conductor, we can clearly see the effects of the skin depth on the resistive losses, as frequency increases the current in the trace decreases. Simultaneously, we can witness that at lower frequencies the larger the width of the trace, the greater the magnitude of current in the trace. Next, we turn our attention to the results at the load of the victim conductor, and we observe the opposite.
Here, we can see that as the frequency increases, the mutual capacitance between the two traces allows for more current to couple as a [mostly] linear function of frequency. This simulation of two tightly coupled traces allows the user to change the thickness of the trace, or the separation distance while keeping other factors constant allowing an ease of experimentation.
Another mechanism that is often overlooked because of its difficulty in visualization, but that can drastically affect how current returns to its source, is mutual inductance in the return path. Luckily, using SPICE and treating the mutual inductance as a transformer, we can easily show how it affects the current return path. To start, we’ll begin with another simplified situation found in Figure 14.
At DC, we can easily say that the current will take the path of least resistance, through the bottom resistor. However, as frequency increases, the mutual inductance between the two return paths begins to play a factor in the impedance. We can expand upon Figure 14 with Figure 15, by attributing these real-world parameters to the circuit.
As mentioned, we can model the mutual inductance between the secondary return path and the source path as a transformer. Using SPICE, we can model the above circuit, and even parameterize the coupling coefficient between the source and secondary inductances to characterize its effect shown in Figure 17.
After performing small signal analysis on the circuit in Figure 16, we can begin to see the effect the mutual coupling has on the return current by drawing the current up through the secondary path (L2 in Figure 16) as frequency increases instead of the more intuitive path (resistor R3).
Therefore, we’re able to demonstrate the effect mutual inductance has on the return path as a function of frequency. This showcases another often-overlooked tenant of PCB design that as the frequency increases, the return path currents trend closer to the source conductor due to the mutual inductance the two traces share.
SPICE Analysis of an Unshielded Near-Field Probe
We finish our discussion by demonstrating how to use the SPICE language to model real-world parasitics, in the form of an unshielded near-field magnetic pickup loop. This loop, pictured in the setup in Figure 18, functions by capturing the flux generated by the time-changing current in the circuit under test.
This flux, which is proportional to the current in the loop will then generate a voltage that is measurable on the oscilloscope. We call this linkage the mutual inductance that links the current in the loop to the voltage generated by the near-field probe, and it is represented by the following.
In practice, however, the probe is held at a probe angle of 0, allowing the full amount of flux to pierce the near-field loop, resulting in a signal that is proportional to the rate of change of the current in the loop; a physical representation is shown below in Figure 19.
However, looking back in Figure 18, it should be noticed that while this loop functions as a basic test device, it’s unshielded, which at higher harmonics and frequencies will result in unintended stray capacitive coupling between the current loop and the probe. As shown in Figure 20, this stray capacitance can cause ringing in the measurement.
To better understand this phenomenon and modify the parameters generating the ringing, we can model this circuit in SPICE, the results of which are shown in Figure 21.
Now that we have a basic model for the:
- Mutual inductance coupling between the probe and current loop
- The shared mutual capacitance between the probe and current loop
- The inner winding capacitance found between each winding of the probe loop
- Simulations such as the ones shown in Figure 21 can be run with either the STEP command or via the monte-carlo command to see what effect changing the mutual capacitance (C1) or the inner winding capacitance (C2) has on the probe loop.
This result underscores the presence for a grounded electric field shield on commercial probes in order to not negatively affect any current measurements; the result could easily be simulated, but be very boring, by grounding the mutual capacitance.
Conclusion
In printed circuit board, sensing, and electrical systems design, it’s important to recognize the small nuances that often make designing with those components difficult. The ability to become familiar with these nuances gives the designer a greater chance of positively affecting the design earlier in the process, where less-expensive fixes have a greater impact on the design of the system. For this reason, it’s important to create a framework that allows you, the designer, to become familiar with concepts such as:
- Situations and scenarios that make up resonating structure, so as to not design those into your product.
- Real-world factors that affect the return path of the current in PCB design.
- Modeling real-world parasitics of non-ideal devices in SPICE.
The next time you sit down to a design review, or to layout your next product, you’ll be able to approach your problem with the knowledge gained from playing with these simple representations of complex problems.
