Technical Article

# An Overview of Radiated Emissions

June 22, 2021 by Luca Pellegrini

## Part 1 of this series on radiated emissions demystifies the generation and propagation of radiated electromagnetic interferences, providing an essential and intuitive overview.

Conducted emissions and radiated emissions are often a nightmare for design engineers. They have to identify and understand the sources of EMI in their projects, find effective countermeasures, and finally, pass the planned emissions test at an accredited laboratory. The whole process can be complicated, costly, and time-consuming.

The article that presented an overview of conducted emissions showed that conducted emissions are considered a culprit at low frequency, while radiated emissions affect systems at high frequency. The breakpoint between conducted and radiated emissions is conventionally set at 30MHz, as summarized in the following table:

##### Table 1. Typical emissions propagation methods for different frequencies.
 Frequency f Wavelength  λ Critical length L Typical dimension Emissions 100 KHz 3 km 500 m Public distribution network cables Conducted (low frequencies) 300 KHz 1 km 150m 1 MHz 300 m 50 m Building cables 3 MHz 100 m 15 m 10 MHz 30 m 5 m 30 MHz 10 m 1.5 m Device connection cables 30 MHz 10 m 1.5 m Device connection cables Radiated (high frequencies) 100 MHz 3 m 50 cm 300 MHz 1 m 15 cm Copper planes and traces of printed circuit boards 1 GHz 30 cm 5 cm

The critical length, as explained in the article about conducted emissions, is the minimum approximate size of structures that can easily be the source of emissions. In the case of radiated emissions, the table shows that the device cables with a minimum length of some ten of centimeters can radiate EMI starting from the lowest frequency of 30MHz, while PCB traces and copper planes, with a typical size of some centimeters, can start to radiate EMI above 100MHz.

It is essential to understand the basic principles of the generation of radiated emissions and how they propagate. Often, an intuitive understanding is enough to identify the EMI sources in practical applications.

## Generation of Radiated Emissions

Basically, talking about electromagnetic fields, we consider two kinds of field generators:

• Elementary E-field generator: any voltage applied across elementary conductors produces an electric field between them. The field (E-field) is measured in V/m; it is proportional to the applied voltage and divided by the distance between conductors;
• Elementary H-field generator: any current flowing into an elementary conductor produces a magnetic field around the conductor. The field (H-field) is measured in A/m; it is proportional to the current and divided by the distance from the conductor.
##### Figure 1. Elementary E-field and H-field generators.

Real-world circuits are built from conductors and components, where alternating voltages generate alternating currents in the conductors, so generally speaking, everywhere there is the possibility to generate E-fields and H-fields that, combined, in turn, can cause complex unintentional electromagnetic fields, or EMI radiation.
In this messed-up situation, how to come out of trouble? Here is where engineering plays its role.

The goal is to focus on the system parts that can be the main radiated EMI generators. Remember, we don’t want to absolutely eliminate all kinds of radiation; it would not be possible. We just want to minimize the radiated EMI and keep it below the limits provided by EMC regulations.

Some simple basic principles can be assumed to identify the potential high-frequency field generators:

• A circuit node driven with high dv/dt voltage is mainly an E-field generator
• A conductor carrying a high di/dt current is mainly an H-field generator

With the above statements, we can assume that, in a region of the space close to nodes and conductors, E-fields and H-fields are generated separately, and they are not related to each other.  In this region of the space, called the near-field region, the exact distribution of fields depends on the spectrum and magnitude of generating signals and on the particular geometry of structures radiating the fields.

The following picture and equations can express this concept:

##### Figure 2.  Generation of E/H fields from circuit signals.

$$\vec{E_{p21}}(f)=\vec{M_{21}}(f)\bullet \vec{V_{p1}}(f)$$

$$\vec{H_{p43}}(f)=\vec{N_{43}}(f)Ip_{p3}(f)$$

In the circuit of Figure 2, the voltage of the circuit node at point p1 generates an E-field vector in the space at point p2. For each frequency, the magnitude and direction of such an E-field come from the amplitude of the generating voltage at point p1 and a factor M, which depends on the distance between points p1-p2 and the physical layout and geometry of the system in the region close to p1 and p2.
Similarly, the current in the conductor at point p3 generates an H-field vector in the space at point p4. For each frequency, the magnitude and direction of such an H-field come from the amplitude of the generating current flowing at point p3 and a factor N, which depends on the distance between points p3-p4 and the physical layout and geometry of the system in the region close to p3 and p4.

In conclusion, for each point of the space in the near-field region, it can be assumed that:

• The resulting E-field is the sum of all the E-fields generated by all circuit nodes
• The resulting H-field is the sum of all the H-fields generated by all circuit conductors

Considering the complexity of real systems and physical layouts, the resulting three-dimensional distribution of the E-field and H-field moving around a typical electronic product can be complex and almost impossible to predict or easily simulate, with good precision.

## The Propagation of Radiated Emissions

The theory of electromagnetic fields dominated by Maxwell’s laws states that moving away from the source, the complex three-dimensional distribution of the fields transforms progressively in a simpler and well-defined distribution. The region of the space where this transformation of fields occurs is called the transition region, and, at the end, in the far-field region, the E and H fields become orthogonal to each other, as shown in the following picture:

##### Figure 3.  Representation of E/H field planes in the far-field region.

To better understand how the propagation of fields happens in the different space regions, the following picture shows a generic source of E and H fields and an example of the resulting field lines in the near-field and far-field regions:

##### Figure 4. An example of E/H field lines in different space regions.

Figure 4 shows that, in the near-field region, field lines can assume very complex patterns depending on signals, geometry, and layout of the device. Increasing the distance from the generic field source, the field lines change during propagation to progressively approximate the final configuration of the far-field, where the field lines are aligned with planes orthogonal to the direction of propagation.

An interesting parameter that changes in different propagation regions is the wave impedance, defined as the ratio of the E-field to H-field magnitudes for each point of the space:

$$Z_{W}=\frac{\left| E \right|}{\left| H\right|}= \left [ \frac{\frac{V}{m}}{\frac{A}{m}}= \frac{V}{A}= \Omega \right ]$$

The following graph shows the wave impedance of the electromagnetic field radiated by elementary sources (elementary dipole and elementary loop) as a function of the distance from the source:

##### Figure 5. Wave impedance in different space regions.

In the near field region, the elementary dipole (E-field generator) radiates mainly electric field, so the wave impedance has a high value. On the contrary, the elementary loop (H-field generator) radiates the magnetic field primarily, so the wave impedance in the near-field region has a low value.

Increasing the distance from the field source, the wave impedance changes progressively going through the transition region and, at the end, is stabilized to a constant value in the far-field region. Such constant value, in the free space, is calculated as:

$$Z_{0}=\sqrt{\frac{\mu_{0}}{\epsilon_{0}}}= 120\cdot \pi\cong 377\Omega$$

In the far-field region, the propagation of electromagnetic waves has very interesting properties:

• E and H are both orthogonal to the direction of propagation – called plane waves
• The wave impedance is constant for all points of the space
• E and H don’t depend on the geometry and layout of the source

Since in this region the distribution of fields is well defined, as explained above, and it almost doesn’t change with position, the far-field region is preferable for the measurement of radiated emissions during compliance tests since it provides more stable and repeatable measurements.

Considering that, at the minimum frequency of 30MHz, the wavelength is 10m (see Table 1), the limit between the near-field region and far-field region can be calculated as:

$$d_{LIMIT}= \frac{\lambda }{2\pi }\cong \frac{10m}{6}\cong 1.5m$$

The distance of 1.5m from the field source can be considered the absolute minimum distance for far-field measurements. In fact, standard distances used to measure radiated emissions are 3m and 10m, where the electromagnetic field has the form of plane waves for all measured frequencies.

## Putting Theory Into Practice for Radiated Emissions Compliance

This article introduced the basic principles that are useful to understand the generation and propagation of radiated emissions.

Putting such principles together, Part 2 of this series will analyze the standard PCB and cable radiation modes, also suggesting remedies, fixes, and troubleshooting techniques. The article will also cover an overview of common regulatory standards related to radiated emissions and explain the testing procedure for product compliance.

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