# Recognizing the Signs of Structural Resonances

Has it happened to you? When troubleshooting an electromagnetic interference (EMI) issue, you’ve tried various combinations of components and saw the signal of interest reduced. But another frequency signal unexpectedly raised above the limit line. Or, you introduced a chassis plane on your printed circuit board (PCB), only to find the radiated emissions became much worse instead of getting better. These are typical cases of “tuning the resonances of a circuit.”

Most EMI emissions are related to structural resonances. Structural resonances are also one of the main reasons that electromagnetic compatibility (EMC) can be mystifying. Unknowingly, engineers often spend days and months tuning the resonances of a circuit by adding passive elements such as inductors and capacitors. Sometimes, they are lucky enough to finally arrive at a combination that would give them a pass. But most of the time, solutions are hard to find.

A tremendous amount of work has been done on the subject of structural resonances and an overview of these works can be found in Reference 1. Two practical case studies are also presented in Reference 1 to demonstrate methods to identify, locate, and fix EMI issues that are associated with structural resonances.

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EMC engineering often requires problems to be resolved (but not studied) within a limited time. Therefore, techniques that are effective but also save time are encouraged. There are indicators that signal the presence of structural resonances, and engineers can learn to use these indicators to locate the resonant structure and fix the EMI issues. This article also explores some practical techniques in troubleshooting EMI issues that are caused by structural resonances. Case studies are presented to illustrate these techniques.

## Root Causes

The following conditions need to be met in order for a structure to resonate:

1. There needs to be a resonant structure. In electrical terms, this means an undamped/lightly damped L-C circuit. Physically, this could mean anything in an electrical system. Two typical cases are shown in Figure 1. As shown, two PCBs that have a cable connection represent an L-C circuit where the inductive component L depends on the length of the cable and the capacitance component C depends on the structure of the PCBs (areas and the distance between the PCBs). For larger system installations such as the one shown in Figure 1(b), L depends on the length of the ground leads of each cabinet and C depends on the area of the side wall of the cabinet and the distance between the two cabinets.
2. There needs to be an excitation source. Translated into EMC terms related to emissions, the excitation source could be any switching source on a PCB or in a system. For immunity, the excitation source could be an external RF field, an ESD event, or a lightning strike, as shown in Figure 1.
3. An antenna-like structure can also be treated as a structural resonance depending on the physical size of the conductor. Since an antenna is excited most effectively when the size of the antenna (often a wire) is either one-half or one-quarter the wavelength of the exciting frequency, the physical length of the antenna determines the resonance frequencies.

## Locating the Structural Resonances

Generally speaking, there are three methods to locate structural resonances which include the analytical, frequency domain and time domain techniques.

An analytical approach generally requires experience and technical know-how to model/simulate the system. For small systems with known issues, such as the case study presented in Reference 1, simple mathematical calculations are often good enough to give an estimation of the resonant frequency of the device under test (DUT). Often, an analytical approach is achieved either by 3D full-wave simulation or some specialized EMC software.

The benefit of the analytical approach is that it can make a prediction before a prototype is built, making this approach popular in the design and development of automotive, aerospace, and space applications. Often, such companies have simulation models that have been validated in the past and that can be easily modified for a new study. But for companies that don’t have existing models, building a simulation can be a costly and lengthy journey.

In the frequency domain, there are two main techniques. Measuring the reflected power by a magnetic field loop is discussed in Reference 2 and the same method was demonstrated in Reference 1. This method requires a small magnetic field loop to “sniff” suspicious structures, often on the PC board level. Williams introduced a far-field measurement using a spectrum analyzer with a tracking generator (see Reference 3). A reference signal is injected into the DUT by the tracking generator output and an antenna is used for measuring the response signal. This method is particularly useful in applications where the PCB ground resonates with the enclosure (chassis). Both methods are practical and only require a small amount of test set-up. The drawback of these methods are they are often limited to PCB board-level investigation and are not useful in large systems.

In the time domain, measuring the resonant current with an RF current monitoring probe when a pulse is injected into the system is often used (see Reference 4). This serves as an effective technique when it comes to troubleshooting large systems or where multiple PCBs are interconnected.

Table 1 summarizes the techniques and pros and cons of each method.

 Method Equipment Pros Cons Analytical assessment Simulation software such as full wave simulator or specialized EM simulation software This method allows engineers to “see” the resonance even before the prototype is built. The learning curve of this software is often long. It takes a long time to accurately build a model. Licence to run the software can be costly. Measuring reflected power with a small magnetic field loop Magnetic field loops, a network analyzer or a spectrum analyzer with a tracking generator, a directional coupler A low-cost measurement and it can be very efficient. As demonstrated in References 1 and 3. This method has its limitations when it comes to large systems as the magnetic field loops reach their physical limit. Using a far-field antenna An antenna, a spectrum analyzer with a tracking generator Test set-up is relatively easy, the result is straight-forward. One needs to know where in the system to inject the reference signal. Measuring resonance using an RF current monitoring probe RF current probes, an oscilloscope, a pulse generator (such as an ESD simulator or EFT generator) This is a time domain measurement, suitable for large system installations High-energy pulse generator is often expensive to buy/rent.

#### Table 1: Methods of locating structural resonances

These techniques are introduced and demonstrated in Reference 1. This article further explores more practical approaches based on the characteristics of structural resonances.

## Resonances Increase the Amount of Emissions

One of the typical characteristics of structural resonances is that resonances can increase the amount of emissions because the final radiator is more efficient than the original radiator (see Reference 5). The following case study demonstrates the point.

During the radiated emission tests of a large-size electric vehicle, it was found that a narrowband spike at 222MHz exceeded the limit (Figure 2a). It was found that the noise came from a camera that was fitted in the cabin of the vehicle. Multiple ferrites were used on the power leads of the camera, but the improvement was not significant enough to suppress the noise (this is another sign of structural resonances). The test also showed an “inconsistency,” as the same noise was measured a lot lower on some occasions (as shown in Figure 2b). We accidentally discovered that the difference in the emission results was caused by the door of the vehicle. When the door was open, the noise emission was significantly less than when the door was closed.

By themselves, the vehicle cameras and their associated circuitry including the 20 cm long power leads were not an efficient radiator at the frequencies (and the harmonics) contained in the circuits. As shown in Figure 3, when the door was closed, it was positioned near the camera area. The door was mainly glass, but the frame, together with the mechanical structure linking the door, was part of the metal enclosure and should be considered an EMC concern. Even though the door was not in physical contact with the camera, the parasitic capacitance and inductance coupled the RF energy of the camera onto it, and the noise at 222 MHz was radiated very efficiently. At 222 MHz, a halfwave length wire is about half a meter. The structure shown in Figure 3 can easily act as an efficient antenna.

Identifying and locating the structural resonance is often the most difficult part of the job when it comes to EMI troubleshooting. In this case, it makes sense that the ferrites on the camera power leads were not effective as the final radiator was not suppressed. A more sensible approach is to segregate the noise source by shielding the camera power lead with aluminum foil and locating it away from the door. This also serves as a cost-effective way of fixing the issue. The noise was significantly reduced when the door was closed as shown in Figure 4.

## Resonances Absorb More Energy in Immunity Tests

In this case study, a device failed the immunity tests (both radiated immunity and bulk current injection (BCI) tests) in the frequency range of 200 and 400 MHz, and the range of 800 and 900 MHz. In other frequency ranges, the device worked as normal without error.

The PCB of the DUT has a size of roughly 50 mm × 50 mm, forming a 200 mm-long loop. The assumption was that traces and tracks on the PCB might have formed an efficient loop antenna within the 200-350 MHz frequency range. Electromagnetic wave travels in an FR4 material at a speed of 1.5×108 m/s, based on equation v=λf, where v is the speed of light in FR4 and f is the frequency. For a 200 MHz wave, a full wavelength is then calculated to be 750 mm. A quarter of wavelength (where the radiation is the strongest) is 187.5 mm. The PCB itself can resonate at a frequency range of 200 MHz. It would probably absorb more RF energy at 200 MHz (and its harmonics) which is injected from the noise source in the immunity tests.

Using an RF current monitoring probe, we measured the RF in front of and behind the PCB in the immunity test, as shown in Figure 5. A frequency sweep was performed from 100 MHz to 1GHz. The RF amplifier injected the same level of RF noise into the main connector cable via a BCI probe from a frequency range of 100 MHz and 1 GHz. The results are shown in Figure 6.

The yellow trace showed results in location 2 and the pink trace showed the results in location 1. The blue trace is the difference between the two measurements. Basically, the positive profile shown in the blue trace (as shown from frequency point markers 1 and 2 and from frequency point markers 3 and 4) means the PCB amplifies the input signal, whereas with the rest of the frequency range, the PCB attenuates the RF noise (shown as negative profile). We now know why we had an immunity issue between 200 MHz and 400 MHz and between 840-920 MHz.

The solution to this immunity problem requires a common mode choke (CMC) that works most effectively in the frequency range of interest, together with decoupling capacitors. The capacitance values are 470pF as they work effectively in this frequency range.

## Ferrites Often Don’t Work

Another sign of structural resonances is that ferrites often don’t work as effectively as they should. For instance, in the first case study, ferrites on the power lead of the camera didn’t suppress the noise as one would hope. Using a ferrite as a filter element to reduce cable resonance is usually effective as ferrites are resistive (lossy) and should act as a damping element. But if the main structural resonance is not the cable, adding ferrite sometimes adds reflections. As a result, the noise level stays the same or shifts with frequency.

Figure 7 shows the conducted emission of a newly developed PCB design which created a resonance issue between 50 and 100 MHz. As it can be seen, the new design improved the low-frequency performance of the PCB but failed significantly at high frequency. What the engineers found was that even with multiple ferrites on the power cable, the conducted emission could not be reduced. In the frequency between 50 and 100 MHz, the noise profile stayed high.

It was found during the layout review that the engineers had neglected to connect the chassis and the ground plane of the PCB. As a result, the ground plane of the PCB started resonating with the chassis when the DUT was in operation. A high dV/dt was developed on the ground plane with reference to the chassis, driving the emissions up. A quick copper tape connection between the ground and chassis points on the PCB (shown in Figure 8a) reduced the noise by more than 20dB in the frequency range of interest (Figure 8b).

## Conclusion

When troubleshooting EMI issues, there are a few signs that indicate structural resonances. Structural resonances increase emissions in the resonant frequency range (and its harmonics) and they also cause the system under test to be more sensitive to external interference at the resonant frequency. Sometimes, adding ferrites cannot fix the problems caused by structural resonances, and adding capacitors shifts the resonant frequency. The first step in fixing these issues is to identify and locate the resonant structure. Once this is done, solving the problems often involves isolation, damping, and improving the ground connections.

## References

1. M. Zhang, “Structure Resonances: Ways To Identify, Locate, and Fix EMI Issues,” Signal Integrity Journal.
2. D. Smith, “Measuring Structural Resonances,” https://emcesd.com.
3. T. Williams, “Controlling Resonances in PCB-Chassis Structures.”
4. D. Smith, “Measuring Structural Resonances in the Time Domain,” https://emcesd.com.
5. B.R. Archambeault, PCB Design for Real-World EMI Control, Kluwer Academic Publishers, Norwell, Massachusetts, 2002.

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