# Noise Suppression Products/EMI Suppression Filters

Noise Suppression Basic Course Section 1
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 4

## Spatial conduction and its countermeasures

### 4-3. Noise antenna

Antenna works as a mediator between the conductor conduction and spatial conduction of noise. If you understand the nature of antenna, you can design electronic devices that cause less noise with smaller costs and you can use shields and EMI suppression filters appropriately.
Basic antennas are dipole antenna and loop antenna.
In terms of noise suppression, each of the various structures of electronic devices is understood as a variation of basic antenna or a combination of those as shown in Fig. 4-3-1 and Fig. 4-3-2. Through this modeling, frequencies and directions of high noise emission or sensitivity can be identified.
This chapter will describe the nature of basic antennas.

Fig. 4-3-1 Example of modeling in which a digital signal wiring is understood as an antenna

Fig. 4-3-2 Example of modeling in which an interface cable is understood as an antenna

#### Two types of basic antennas

Fig. 4-3-3 shows models of the basic antennas that are considered in this section.

##### (1) Dipole antenna

Fig. 4-3-3(a) shows a dipole antenna. In general, when a voltage is applied between two wires, an electric field occurs in the surrounding space. Conversely, if two wires are placed in an electric field, a voltage is induced. The dipole antenna utilizes this function and is basically sensitive to electric fields.

##### (2) Monopole antenna

The monopole antenna in Fig. 4-3-3(b) is an antenna that uses one of the wires of dipole antenna as a ground surface. Since its function as an antenna is similar to dipole antenna, it is handled as a type of dipole antenna in this section.

##### (3) Loop antenna

Fig. 4-3-3(c) shows a loop antenna. When you apply a current through the loop-shaped wire like this, a magnetic field occurs in a way to penetrate the loop. Conversely, if the magnetic field that penetrates the loop changes, an induced electromotive force occurs to the wire. The loop antenna utilizes this function and is basically sensitive to magnetic fields.

##### (4) Emission of radio wave

If a voltage or current is applied to an antenna as above, an electric field or magnetic field occurs around it. This electromagnetic field creates radio waves, which is then emitted. However, not all of the electromagnetic field around the antenna is converted into radio waves. In many cases, most of the energy of the electric field and magnetic field goes back to the antenna. In this section, the component that is converted into radio waves without going back to the antenna is called emission.

Fig. 4-3-3 Basic antenna

#### 4-3-2. Basic nature of antenna

When a circuit emits radio waves, an antenna works as a doorway to receive the radio waves. In this section, some terms that express the functions of antenna will be introduced.

##### (1) An antenna that can easily emit radio waves

An antenna that emits stronger radio waves (when a voltage or current is applied) is considered to be an efficient antenna. In general, as the shape becomes larger, it is more likely to emit radio waves. This nature will be described in the following sections.
The strength of the emission is in proportion to the power that the antenna receives. This power increases as the voltage or current applied to the antenna increases. However, it is also affected by the level of the impedance matching between the antenna and signal source as shown in Fig. 4-3-4.
In addition, an antenna that can easily emit radio waves tends to be efficient in receiving radio waves as well. This section focuses on noise emission for explanation on the premise of such a nature of antenna. The impedance matching for receiving radio waves makes use of the the impedance of the load that is connected to the antenna.
Please note that an efficient antenna that we are calling here is different from an antenna with a large gain that is considered in the antenna theory. Also note that the explanation is on the premise that the antenna itself does not cause any loss.

Fig. 4-3-4 Radio wave emission and impedance matching

##### (2) Polarization and antenna direction

The orientation of the electric field and magnetic field of the radio waves transmitted in the air is called polarization. Antennas have a highly sensitive direction for this polarization. Fig. 4-3-5 shows the direction of a basic antenna.
Dipole antenna is highly sensitive to an electric field in the direction of stretching out the antenna elements (hereinafter "antenna axis") and does not receive electric fields that are perpendicular to the elements. Since this is the same for emitting radio waves, it will not generate an electric field that is perpendicular to the axis.
In case of loop antenna, there is an axis in the direction perpendicular to the loop plane, and the antenna is highly sensitive to magnetic fields in the direction of the axis. There is no sensitivity to magnetic fields that are perpendicular to the axis (parallel to the loop plane).

Fig. 4-3-5 Polarization of radio wave and antenna direction

##### (3) Emission pattern

The emission of antenna does not necessarily go evenly to all directions. The strength varies depending on the direction. This is called emission pattern. Although an antenna that intensively emits in one direction is considered to have a good directivity, an antenna with a good directivity is not desirable in the case of noise suppression.
Fig. 4-3-6 shows the emission patterns of basic antennas. As shown in the figure, both dipole antenna and loop antenna have the same shape in the emission pattern even though the orientation is different. However, these are patterns for the case that the size of antenna is very small for the wavelength. If the frequency increases, the size of antenna will not be negligible for the wavelength resulting in changes in the pattern. Please also note that these only represent the component that is emitted as radio waves and are different from the distribution of the electromagnetic field near the antenna.

Fig. 4-3-6 Emission pattern of basic antenna (for low frequencies)

The following sections will describe the nature of these basic antennas and the relationship with noise emission. First of all, dipole antennas will be explained and then based on the explanation, loop antennas will be explained.

#### 4-3-3. Dipole antenna

##### (1) Dipole antenna

An antenna that applies a voltage between two open lines to emit radio waves is called dipole antenna. If the line length is very short for the wavelength as shown in Fig. 4-3-7(a), the noise emission is weak. However, if the total length is getting closer to approx. 1/2 wavelength (that means 1/4 wavelength on one side) as shown in Fig. 4-3-7(b), it is easier for the current to flow (called resonance) and is more likely to emit strong radio waves. As shown in Fig. 4-3-7(c), a monopole antenna formed by grounding one side of the dipole antenna is also considered to be a variation of dipole antenna. In this case, strong radio waves occur at the frequency that makes the antenna length form 1/4 wavelength.

Fig. 4-3-7 Dipole antenna

##### (2) How much strength is needed to cause radio emission?

How much strength is needed for a dipole antenna to cause radio emission? Fig. 4-3-8 shows an example of calculation for the strength of radio waves by an electromagnetic simulator.
This test applies 1V sine wave to the base of the antenna placed in the vertical position and measures the electric field strength from a point 10m away in the horizontal direction. The reflection from the floor and the center of the antenna height are considered for the purpose of the noise measurement. The thickness of the antenna is set to 1mm, and the output impedance of the signal source is set to 10 ohms, and then the calculation is based on the frequency of 10MHz multiplied by an odd number on the premise that the noise is caused by the harmonics of digital signal.
Fig. 4-3-8(a) shows a case that the length of the antenna is as short as 40mm. The radio waves are relatively limited.
Fig. 4-3-8(b) shows a case that the length of the antenna is 200mm. The radio waves significantly increase and show a peak at 690MHz.
Fig 4-3-8(c) shows a case that the length of the antenna is extended to 1m. The increase of radio waves has reached a ceiling, and there are peaks at 150MHz, 430MHz and 730MHz.
As above, the longer the antenna length, the stronger the radio wave becomes as a general trend. Then when it reaches a certain length, peak frequencies start to appear. However, even if it is extended over a certain length, the maximum strength would not go any higher.

Fig. 4-3-8 Frequency characteristics of dipole antenna (calculated values)

According to the noise regulations for digital devices, the limit has been set to 30 to 40dB µ V/m at the distance of 10m. Since the range displayed in the graph of Fig. 4-3-8 is far stronger than this limit, you can see that a direct input of 1V signal will cause emission of radio waves that substantially exceeds the limit of the noise regulations.

##### (3) Connecting a digital signal to a dipole antenna

When a digital signal is connected as a noise source, how much emission would it cause? Fig. 4-3-9 shows calculation results of emission strength when the harmonics explained in Section 2-4 is connected to the 20cm antenna of Fig. 4-3-8(b).
Fig. 4-3-9(a) is the same data as Fig. 4-3-8(b), wherein 1V sine wave is connected as a signal source.
Fig. 4-3-9(b) shows a calculation result for the case of connecting an ideal 10MHz digital pulse. The displayed range of the vertical axis has been shifted by 40dB in the graph. Even though the noise source is digital signal harmonics, you can see that it emits radio waves that exceed the limit for CISPR class 2 by 30dB.
Fig 4-3-9(c) shows a calculation result for the case of using a trapezoidal wave with a transition time of 20ns for the pulse wave as described in Section 2-4-4. In this case, the result can stay within the limit.
As above, dipole antennas are capable of emitting very strong radio waves. Therefore, you need to design carefully so that the shape of the wire and/or structure used in the electronic device does not have a shape of dipole antenna. If you cannot avoid the shape of dipole antenna, it is effective to use an EMI suppression filter etc. in a preventive manner so that the harmonics are reduced by delaying the rise time of the signal.

Fig. 4-3-9 Emission when connected to 10MHz digital signal (calculated values)

##### (4) Relationship between antenna length and wavelength

In Fig. 4-3-8, there is a relationship between the peak frequency and the size of antenna. Fig. 4-3-10 shows a diagram that compares the antenna length with the wavelength of each frequency.
As shown in the diagram, the lengths of 200mm and 1m form 1/2 wavelength respectively at 750MHz and 150MHz. These frequencies almost correspond to the peaks in Fig. 4-3-8. As above, dipole antennas tend to easily emit radio waves at a frequency that makes its length form 1/2 wavelength.
Fig. 4-3-8(c) also shows peaks of radio waves in a cycle other than approx. 150MHz (1/2 wavelength). These are odd multiples of the frequency that makes the antenna length form 1/2 wavelength (in this case 150MHz) at which radio waves tend to be easily emitted. At these frequencies, the antenna causes standing wave and resonance as described in Section 3-3-6 making it more likely to cause current flow.
In terms of noise suppression, it is important to keep the wiring length (that possibly works as an antenna) shorter than the wavelength so as to reduce noise emission. As a guideline, Fig 4-3-9 indicates the range that forms 1/20 wavelength. If your design can manage to keep the length of wiring or cable within this range, noise problems can be reduced.

Fig. 4-3-10 Relationship between antenna length and wavelength

The following Sections 4-3-4 to 4-3-15 describe the factors that determine the efficiency of antenna in converting noise into radio waves. The contents will be slightly technical. If you are not so interested, please skip to Section 4-3-16.

#### 4-3-4. Input impedance

Why do dipole antennas cause strong radio wave emission at the frequency of 1/2 wavelength? One of the reasons is input impedance.
Fig. 4-3-11 shows a graph that calculates the input impedance of the antenna used in Fig. 4-2-8. If the antenna is very short in comparison with the wavelength, you can see that the input impedance is 1000 ohms or more, resulting in almost no current flow. In contrast, the frequencies that make the length form an odd multiple of 1/2 wavelength cause the input impedance to be a local minimum point of about 100 ohms (the lowest point is approx. 73 ohms), making it more likely to cause current flow. (In Fig. 4-3-8, the frequency seems to be slightly shifted due to 20MHz increment)
As above, since the input impedance of antenna is reduced and thus causes current flow at the frequencies that make the length form an odd multiple of 1/2 wavelength, it is (simply) understood that strong radio waves are emitted.
This local minimum point is slightly on the lower frequency side of the frequency that makes the length form 1/2 wavelength (depending on the antenna thickness). At this point, the impedance becomes a pure resistance without any reactance, which means the antenna is resonating. Since it has reactance at other frequencies, it can be called inductive (reactance is in the positive status just like an inductor) or capacitive (reactance is in the negative status just like a capacitor) depending on the polarity of reactance.

Fig. 4-3-11 Input impedance of dipole antenna (calculated values)

The resistance component of the antenna input impedance represents radiation resistance. This radiation resistance represents the function of antenna to convert electric current into radio waves, wherein a higher radiation resistance causes emission of stronger radio waves with the same current flow. Although the resistance component of input impedance is not always the same as the radiation resistance, this resistance component can be a guideline for the radiation resistance.
Fig. 4-3-12 shows an example of the resistance component of dipole antenna (1m length calculated in Fig. 4-3-8). It tends to be approx. 73 ohms at the resonance frequency for 1/2 wavelength.
In the frequency range that the antenna becomes shorter than 1/2 wavelength, the input impedance is high and it is hard for the current to flow, while the resistance component is also getting smaller. In this frequency range, even if some current flows, it is less likely to cause emission.
In contrast, in the frequency range of exceeding 1/2 length, the ratio of resistance component becomes higher. In this frequency range, the conditions allow emission even with a very small current flow. For this reason, high level emission is observed in the frequency range outside the resonance frequency in the high frequency range of Fig. 4-3-8(c).

Fig. 4-3-12 Resistance component of input impedance

As it is understood from Fig. 4-3-12, the dipole antenna resonates not only at odd multiples of 1/2 wavelength but also at the frequencies of even multiples. However, those impedances reach local maximum not allowing current flow, thus causing relatively weak emission. However, if the signal source impedance is high, these frequencies of even multiples can cause even better impedance matching, which may result in strong emission.

#### 4-3-6. Impedance matching

##### (1) Impedance matching

To express the phenomenon of strong radio wave emission more accurately, the concept of impedance matching explained in Section 3-3-6 is used. When the output impedance of the signal source is the same as the load impedance, the maximum energy is transmitted due to impedance matching.
Under the conditions of Fig. 4-3-8, as the input impedance of antenna becomes closer to 10 ohms, more energy is transferred and thus causes stronger radio wave emission. Inversely, it is understood that as the impedance goes away from 10 ohms, more energy is reflected to the noise source side, thus causing weaker radio waves.

##### (2) Conjugate matching

To even more accurately express impedance matching, the concept of conjugate matching is used.
The conjugate matching means a status of cancelling out the imaginary parts (reactance components) in addition to adding up the real parts (resistance components) of the impedance as shown in Fig. 4-3-13. This way allows the maximum energy transmission to a circuit with reactance such as an antenna. Since conjugate matching cancels out reactance, it is considered as a type of resonance status.
So far the output impedance of the signal source has been set to a resistance of 10 ohms in the calculation, there are cases that the signal source has some reactance. In such cases, it is understood that conjugate matching is approximately achieved at a frequency that the antenna has the reactance to be cancelled out and thus it is more likely to emit radio waves. Therefore, if the signal source has some reactance, the resonance frequency of the antenna is shifted and it is more likely to emit radio waves at a frequency other than 1/2 wavelength.

Fig. 4-3-13 Conjugate matching

#### 4-3-7. Matching circuit

##### (1) Example of frequency change due to conjugate matching

As an example of antenna resonance frequency being shifted by conjugate matching, Fig. 4-3-14 shows an example of calculation for the emission when small inductance (50nH) is added to the signal source under the conditions of Fig. 4-3-8(b). It is understood that adding inductance causes the resonance frequency to be shifted towards the low frequency side.
This level of inductance (50nH) can be easily caused by changing the wiring length by several centimeters. In case of noise suppression for electronic devices, the noise strength may significantly vary by changing the wiring length between circuits (without changing circuit operations) as explained above. It is understood that one of the factors is a change in the resonance of the antenna that emits noise.

Fig. 4-3-14 Example of change in resonance of dipole antenna

##### (2) Matching circuit

Since using this method can cause resonance in the low frequency range with a relatively short antenna, it is useful when making a compact wireless. The circuit for adjusting the conjugate matching such as 50nH inductance added in this example is called matching circuit. In general, matching circuits adjust both reactance and resistance components.
In case of noise suppression, an inductor or capacitor that has been added to eliminate noise can unintentionally form a matching circuit and thus increase noise emission. In order to reduce this risk, you should choose to use a noise suppression component with a largest loss possible.

#### 4-3-8. Emission pattern

What direction are radio waves emitted from a dipole antenna?
Fig. 4-3-15 shows a result of calculation over ± 5m range of the electric field surrounding the 1m length dipole antenna shown in Fig. 4-3-8(c). In the figure, the antenna is located at the center in the upright position. The reflection from the floor has not been considered. The output impedance of the signal source is 0 ohm. As the color changes from blue to red, the electric field becomes stronger.
Fig. 4-3-15(a) is a case of 30MHz in frequency. In the relatively low frequency range, the electric field is concentrated around the antenna and looks like spreading towards the top and bottom sides. The reason why the shape is different from the basic pattern shown in Fig. 4-3-6 is that the near field has primarily been observed (described later).
Fig. 4-3-15(b) is a case of 1/2 wavelength resonance. As the frequency increases, the electric field starts to spread crosswise and then extensively spreads at the resonance frequency. This frequency range becomes relatively closer to the basic pattern shown in Fig. 4-3-6.
Fig. 4-3-15(c) is a case of 3/2 wavelength resonance. You can see that the emission is split up into 6 directions. As the frequency increases, the emission tends to be split up into directions.

Fig. 4-3-15 Calculation result of the electric field surrounding a dipole antenna

Fig. 4-3-16 Calculation result of the magnetic field surrounding a dipole antenna

Likewise, Fig. 4-3-16 shows a calculation result of the magnetic field. (The color scale has been adjusted so that the electric field and magnetic field have the same color in the far field.)
The shapes of the electric field and magnetic field are significantly different in the low frequency range shown in (a). In addition, the strengths of the electric field and magnetic field become identical as they move away from the antenna in the high frequency range shown in (b) and (c). The difference in the distribution between the electric field and magnetic field is related to the wave impedance, which will be described later.

#### 4-3-9. Theoretical properties of dipole antenna

Although you can use an electromagnetic simulator to observe how the radio waves are emitted from a dipole antenna as shown in Figs. 4-3-15 and 16, it can also be calculated based on the electromagnetic theory if it is a simple model. In this section, only the simplest result will be presented. So, please refer to technical books [Reference 3] for details.
If you are only considering the far filed, the radio waves emitted from a very short antenna can be expressed by the following formulas. The basic emission pattern shown in Fig. 4-3-6 is a shape based on these formulas.

Fig. 4-3-17 Electric field emitted by a very small dipole antenna

Here, l , I and ω respectively represent the antenna length (m), current (A) and angular frequency (Hz). The wavelength λ is inversely proportional to the frequency. From the formulas, it is understood that the radio waves emitted from a relatively small dipole antenna has the following properties.

1. (i) The strength of radio waves is proportional to the antenna length, current and frequency, while it is inversely proportional to the distance.
2. (ii) The radio waves have been polarized. An antenna in its vertical position as shown in the figure does not generate any electric field ( E Φ ) in the horizontal direction.
3. (iii) The direction of the maximum emission is the crosswise direction ( θ =90 ° ) in the figure.

It is understood that when the length of the wiring that forms an antenna is shortened, the emission of radio waves can be reduced even with the same current.

#### 4-3-10. Loop antenna

Another basic antenna is loop antenna.
Loop antenna is an antennal that emits radio waves by flowing currents through the loop wiring as shown in Fig. 4-3-3(c). Just like a dipole antenna, the emission is only weak when the wiring is short, but as the loop wiring becomes longer to form a large area, the emission tends to be stronger.
Fig. 4-3-18 shows a calculation result of the emission from a square-shaped loop antenna. The calculation conditions are the same as those for dipole antenna in Fig. 4-3-8. The loop is in the flat position.
(a) shows a case that each side is as small as 20mm. The emission has relatively been kept in small.
(b) shows a case that each side is 100mm. A peak starts to appear at 810MHz as the emission increases.
(c) shows a case that each side is 0.5m. Emission peaks appear at the lowest of 170MHz and also at frequencies of its approximate integral multiples. The strength of the emission is almost constant at 170MHz and above.
As above, loop antennas also show similar frequency characteristics as a dipole antenna. However, the difference is that the emission peaks appear at around frequencies that the loop length (4 times one side) forms the integral multiples of the wavelength.

Fig. 4-3-18 Loop antenna

#### 4-3-11. Resonance frequency of loop antenna

##### (1) Input impedance

Fig. 4-3-19 shows a calculation result of input impedance under the conditions for the calculation in Fig. 4-3-18.
Fig. 4-3-19(a) shows the input impedance. Just like the case of dipole antenna, it is understood that the impedance reaches a local minimum at the frequencies with strong emission. Just like a dipole antenna, a standing wave appears and resonates over the wiring at these frequencies.

##### (2) Resistance component

Fig. 4-3-19(b) shows the resistance component for the case of 100mm on each side. Just like the case of dipole antenna, the impedance and resistance match with each other at both local maximum and minimum points of the impedance at which it is understood that the antenna is resonating. In addition, the local maximum point does not make a peak of emission due to being unable to achieve impedance matching with the signal source just like the case of dipole antenna.

Fig. 4-3-19 Input impedance of loop antenna (calculated values)

##### (3) Antenna length and resonance frequency

The local minimum point of a loop antenna occurs when the loop length forms an integral multiple of the wavelength. Therefore, the frequencies with strong emission will be integral multiples of the first frequency. (Since dipole antennas involve odd multiples, the intervals between resonance frequencies seem narrower for loop antennas)
The resonance frequencies for a loop antenna occur on the frequency side slightly higher the normal frequency, which is determined by the physical length. For example, the local minimum point in Fig. 4-3-19(b) indicates 810MHz even though it is supposed to be 750MHz based on one wavelength. (It is shifted towards the lower frequency side in the case of dipole antenna)

#### 4-3-12. Electromagnetic field surrounding loop antenna

Just like the case of the dipole antenna above, Fig. 4-3-20 shows calculation results of the electric field and magnetic field around a loop antenna. As shown in Fig. 4-3-18(c), a square-shaped loop antenna with 0.5m on each side is placed in the direction that the axis is pointing the top and bottom of the page (therefore, the area of the loop is perpendicular to the page) for calculation.
Fig. 4-3-20(a) shows the electromagnetic field at a relatively low frequency of 30MHz. It is understood that the area of strong electromagnetic field is limited to the vicinity of the antenna. Furthermore, the shape of the magnetic field is different from the basic pattern shown in Fig. 4-3-6.
Fig. 4-3-20(b) shows the electromagnetic field at 170MHz, which causes one-wavelength resonance. It is understood that the arrangement of the figure causes emission towards the top and bottom sides. This case is also different from the basic pattern in Fig. 4-3-6.
Fig. 4-3-20(c) shows the electromagnetic field at 310MHz, which causes two-wavelength resonance. In this case, the antenna emits to the crosswise direction and its shape is close to the basic pattern in Fig.4-3-6.
Therefore, you need to be aware that the electromagnetic field in the vicinity of loop antenna could be different from the basic pattern shown in Fig. 4-3-6. The basic pattern in Fig. 4-3-6 indicates a shape that is measured from a distance sufficiently far from the antenna that is sufficiently small for the wavelength.

Fig. 4-3-20 Calculation result of the electromagnetic field surrounding a loop antenna

#### 4-3-13. Theoretical properties of loop antenna

Just like we did for dipole antenna, the basic emission characteristics of loop antenna can also be calculated as shown in Fig. 4-3-21 based on the electromagnetic theory [Reference 3] . The basic pattern in Fig. 4-3-6 is based on these formulas.

Fig. 4-3-21 Electric field emitted by a very small loop

Here, S , I and ω respectively represent the loop area (m 2 ), current (A) and angular frequency (Hz). The wavelength λ is inversely proportional to the frequency. From the formulas, it is understood that the radio waves emitted from a relatively small loop antenna has the following properties.

1. (i)The strength of radio waves is proportional to the loop area, current and the square of frequency, while it is inversely proportional to distance.
2. (ii) The radio waves have been polarized. An antenna in its horizontal position as shown in the figure does not generate any electric field (Eθ) in the vertical direction.
3. (iii) The directions of the maximum emission are the crosswise direction (θ=90°) in the figure.

The strength of radio waves is determined by the area of loop antenna S without direct regard to the length of the wiring. If the wiring is designed in a way to keep S small, the emission of radio waves can be reduced.
The calculation results shown in Fig. 4-3-18 do not seem to indicate that the emission is proportional to the square of frequency. The reasons for the effects include that the current is not constant due to the significantly varying input impedance of antenna and the antenna cannot be considered as a very small loop in the high frequency range.

#### 4-3-14. Near field and far field

Generally, the electric field and magnetic field around an antenna become weaker as they move away from the antenna. Then, how weak are they?
In order to simplify the phenomenon, let's consider that a current of 100MHz flows evenly in a short antenna. Fig 4-3-22 shows the calculation results of the electric field and magnetic field based on the electromagnetic theory. In the figure, we can see that:

1. (i) The electric field is strong in the close vicinity of dipole antenna
In this zone, the electric field is attenuated in proportion to the cubic of distance, while the magnetic field is attenuated in proportion to the square of distance
2. (ii) The magnetic field is strong in the close vicinity of loop antenna
In this zone, the magnetic field is attenuated in proportion to the cubic of distance, while the electric field is attenuated in proportion to the square of distance
3. (iii) For both type of antennas, both electric field and magnetic field are attenuated in proportion to the distance in the relatively far field.
In this case, the ratio of the electric field to the magnetic field is 377 ohms.
4. (iv) The transition to the zone (iii) is around 0.5m

That means these zones (i) and (ii) correspond to the near field described in Section 4-2-6, while the zone (iii) corresponds to the far field. The far field of (iii) is considered to be emitting radio waves as waves.
The transition distance of (iv) varies in accordance with the frequency and it has been known to be λ /2 π (approx. 0.5m at 100MHz).
The graph in Fig. 4-3-22 represents the specific status at the fixed frequency of 100 MHz so as to facilitate understanding. The graph can be applied to frequencies other than 100MHz by normalizing the horizontal axis to the distance for the wavelength. Please refer to technical books [Reference 3] for details.
The electric field and magnetic field are sharply reduced by the distance in the near field. In terms of noise suppression, it is effective to keep a distance. However, if the distance need to be short, shieling is required due to extremely strong electromagnetic emission.

Fig. 4-3-22 Distance characteristics of the electric field and magnetic field surrounding a dipole antenna

#### 4-3-15. Wave impedance

When using an electromagnetic shield near an antenna, the effectiveness of the shield varies depending on the wave impedance. Wave impedance is a ratio of the electric field to the magnetic field at a certain location. As shown in Fig. 4-3-22, the wave impedance is high near a dipole antenna due to its strong electric field, while the wave impedance is low near a loop antenna due to its strong magnetic field.
Fig. 4-3-23 shows wave impedances calculated from the calculation results of Fig. 4-3-22. A dipole antenna may cause a high impedance of 10 kilo ohms or more in its immediate vicinity (1cm or less), while a loop antenna may cause a low impedance of 10 ohms or less in its immediate vicinity. However, for both antennas, the distance over λ /2 π (0.48m at 100MHz) turns into far field and the wave impedance settles to 377 ohms. This value is determined by the dielectric constant and magnetic permeability of the space where the radio waves transmit.

Fig. 4-3-23 Calculation results of wave impedance

#### 4-3-16. To design electronic devices that are less likely to emit noise

##### (1) Reduce the wiring length and loop area

As described above, the emission of radio waves depends on the length and loop area of antenna. This is the reason why electronic devices are less likely to emit radio waves when their wiring lengths are reduced.
Even if you cannot reduce the wire length, if you reduce the gap formed by the wire, the loop area is reduced and thus the emission is reduced. Fig. 4-3-24 shows the change in emission when the gap area made by a 40cm wire is reduced. It is understood that more emission can be reduced as the shape changes from (a), (b) to (c). In addition, the emission peak at approx. 750MHz tends to stay relatively high. At this frequency the round-trip wire forms a transmission line, which forms a 1/2 wavelength resonant circuit, thus causing a large current.

##### (2) Noise is likely to remain at the resonating frequency

Also in the case of dipole antenna, if you reduced the gap between the folded wires as shown in Fig. 4-3-25, the emission is reduced. This is due to the effect of reducing the radiation resistance even though the resonance frequency and current value are unchanged. Just like a loop antenna, the noise is likely to remain at the resonance frequency. In order to eliminate this type of resonance, it is advantageous to use noise suppression components with a large loss described in the following section.

Fig. 4-3-24 Change in emission by reducing the loop area (calculated values)
Fig. 4-3-25 Change in emission by the angle of the lines (calculated values)

##### (3) Reduce noise by low-pass filter

When strong noise emission occurs at the resonance frequency due to the strong resonance as shown in Fig. 4-3-24(c) and Fig. 4-3-25(c), using a low-pass filter that uses LC may shift the resonance frequency, resulting in making strong noise at another frequency. Fig. 4-3-26 shows an example that uses an inductor as a low-pass filter.
Fig. 4-3-26(a) is the same as the calculation result shown in Fig. 4-3-25(c). Strong resonance is seen at about 750MHz.
Fig. 4-3-26(b) shows the case of attaching a 50nH inductor as an EMI suppression filter for suppressing this noise. Although details are described in Chapter 6, an inductor or bypass capacitor works as a low-pass filter, which prevents noise from being transmitted to the antenna. Fig. 4-3-26(b) also shows that the noise at 750MHz has been dropped by the effect of the low-pass filter. However, you can also see that the noise increases at 430MHz. Therefore, you need to be aware that carelessly attaching a noise suppression component to a resonant circuit may change the resonance status and increase the noise.

##### (4) Use EMI suppression filters with a large loss

In order to prevent such a failure, you should choose to use an EMI suppression filter with a large loss. Fig. 4-3-26(c) shows an example of adding a 100 ohms resistor in series with the inductor. You can see that the resonance has disappeared and the noise emission has been reduced in the entire frequency range. Ferrite bead is one of the components that have the characteristics of both inductor and resistor in this manner. Ferrite beads are described in detail in Chapter 6.

Fig. 4-3-26 Effect of loss by a noise suppression component (calculated value)

##### (5) Any wire protruding from the shielding case works as a monopole antenna

Shielding is effective for suppressing the spatial conduction of noise. If you can thoroughly enclose the entire electronic device, the shield will effectively work. However, many of electronic devices have a wire going through the shield, working as a doorway for noise and thus impairing the shielding effect.
In this case of antenna model, the wire that goes through can be considered as a monopole antenna over the shield that works as a ground surface. Fig. 4-3-27(a) shows the model diagram of this case. In this model, the shorter the length of the protruding wire, the less noise it emits. This tendency is also qualitatively obtained in the noise suppression for actual electronic devices.

##### (6) Shielding case works as a dipole antenna

In this model, when the wire is very short (in this case 1cm) as shown in Fig. 4-3-27(a), there is almost no emission. However, in actual noise suppression, noise may be emitted at a strong level that is not negligible even with a wire of 1cm.
This is because the shield itself works as the other part of the dipole antenna as shown in Fig. 4-.3-27(b). In this case, the main part of the antenna that emits radio waves is not the protruding wire but the shielding case itself. In this situation, you may say that the noise has been induced to the shielding case since the shield has been broken.
The function of the antenna in this situation changes depending on the size and shape of the shielding case. The resonance frequency can be considered based on the resonance frequency of the dipole antenna including the size of the shield. Fig. 4-3-7(c) shows the calculation result in the case of modeling this as a dipole antenna. Although the peak frequency is the same as Fig. 4-3-27(b), stronger emission has been observed.

##### (7) Insert a filter for a protruding wire even if it is only short

If a wire that contains noise comes out from the shield, you have to be careful even if it is only short. It is recommended to use an EMI suppression filter at the point where such a wire goes through the shield.

Fig. 4-3-27 Examples of shielding case that works as an antenna (calculated values)

### “4-3. Noise antenna” - Key points

• Antenna works as a mediator between the conductor conduction and spatial conduction
• Basic antennas are dipole antenna (monopole antenna) and loop antenna
• A dipole antenna creates and receives electric fields
• A loop antenna creates and receives magnetic fields
• When impedance-match occurs between the noise source and antenna, strong emission occurs due to resonance
• To reduce noise, make the antenna small and suppress resonance