Electromagnetic Interference is nothing but electromagnetic pollution. It is neither seen nor sensed nor is it audible and hence it is a silent threat.
The main aim of this chapter is to provide the basics of advanced topics related to field theory. They include:
An elementary treatment of some advanced topics required at the undergraduate level of Engineering is provided in this chapter. Some biological effects of electromagnetic radiation are also presented.
In the first and second Maxwell’s equations, namely
|
∇ × H = Ḋ + J |
and |
∇ × E = − Ḃ, |
Ḋ is displacement electric current density, J is conduction current density and Ḃ is the magnetic displacement current density. These relations are good enough to solve most of the problems that were considered till now.
However, there are many cases where the knowledge of fictitious magnetic currents and charges is extremely useful. Although the fields are generated by electric current and charge distributions, it is possible to compute the fields from the equivalent distributions of fictitious magnetic currents and charges.
For example, an electric current loop is considered to be equivalent to a magnetic dipole. The EM field generated by a small horizontal electric current loop is identical to that of a vertical magnetic dipole. Similarly, the fields produced by magnetic current loop and electric dipole are the same.
Keeping these facts in mind, the first and second Maxwell’s equations are written as:
|
∇ × H = Ḋ + J |
(9.1) |
and |
∇ × E = −Ḃ − M |
(9.2) |
where M is the magnetic conduction current density (V/m2). Analogy of surface electric current density, Js is the surface magnetic current density, Ms. It is evident from Equations (9.1) and (9.2) that there exists full symmetry and duality in Maxwell’s equations. These current densities are defined as
|
Js ≡ an × H |
and |
Ms ≡ E × an |
Maxwell’s equations for magnetic currents in the absence of electric currents are given by
In the absence of magnetic currents, they are expressed as
The superscripts e and m refer to fields due to electric and magnetic currents respectively.
It is interesting to introduce Vector electric potential, bringing analogy from magnetic fields.
Vector electric potential, F is defined as
or,
If the currents Jx, Mx produce fields Ex, Hx and if the currents Jy, My produce fields Ey, Hy in a linear and isotropic medium, then the Maxwell’s equations are:
where a = σ + jω∈, b = jωμ.
Using the properties of isotropic media, from Equation (9.3), we can write
If all the sources are contained within a finite volume, the far-fields constitute spherical waves and the surface integral of Equation (9.4) becomes zero. Hence
Equations (9.5) is written as
|
|
|
〈x, y〉 represents reaction of field y on the source x. Similarly, 〈y, x〉 represents reaction of x on y.
The principle of reciprocity is an inter-relationship between any two source-field pairs. Equations (9.5) and (9.6) are the expressions of such pairs. It is possible to state that if
then the reciprocity exists.
If x and y represent two sets of source currents and fields, then according to the principle of reciprocity, we can write the above as
Here 〈x, y〉 is known as ‘reaction’ of field x on source, y and 〈y, x〉 is known as ‘reaction’ of field y on source x.
〈x , x〉 represents the reaction of field x on its own source x and it is known as self-reaction.
Self reaction is defined as
Let the region 1 represented by μ1, σ1, ∈1 contain a system of sources, S1 and let region 2 represented by μ2, σ2, ∈2 contain no sources (Fig. 9.1).
S1 indicates the presence of sources and Sf indicates source free region.
In region 1, the actual fields are (Ei + Er, Hi + Hr) and in region 2 the fields are E2 and H2.
Fig. 9.1 Regions containing sources and source free regions
Induction theorem states that the induced or scattered fields are produced by electric and magnetic current sheets and the current densities are represented by
|
Js = an × Hi |
|
Ms = −an × Ei |
where |
Hi = (Ht2−Htr) |
|
Ei = (Et2−Etr) |
|
Et2 = tangential component of E2 |
|
Etr = tangential component of Er |
|
Ht2 = tangential component of H2 |
|
Htr = tangential component of Hr |
|
Ei = induced electric field |
|
Hi = induced magnetic field |
|
an = unit normal vector to the sheet |
Equivalence theorem states that current distributions and induced fields are related by
|
Js = an × Hi |
|
Ms = −an × Ei |
where |
Hi = Ht2 [Htr = 0] |
|
Ei = Et2 [Etr = 0] |
It is clear from this theorem that the Equivalence Theorem is a particular case of Induction Theorem, that is, when region 1 and region 2 have the same constants, there are no reflected waves. Under these conditions both the theorems are identical.
EMI/EMC Engineering is a unique and specialised subject. It came into prominence with the tremendous advances in technology and proliferation of a variety of electronic instruments and devices which produce electromagnetic emissions. In fact, the world is highly saturated with such emissions from a variety of sources. The effect of such sources is spread throughout the electronic spectrum.
EMI is defined as the undesirable signal which causes unsatisfactory operation of a circuit or device.
EMC is defined as the ability of electronic and communication equipment to be able to operate satisfactorily in the presence of interference and not be a source of interference to the nearby equipment.
Electromagnetic susceptibility (EMS) is the capability of a device to respond to EMI.
Basic types of EMI These are of two types. They are:
These are divided mainly into two types:
I. Natural EMI sources are of the following types:
Terrestrial and Extra-terrestrial
II. Man-made EMI sources are many.
The devices which are susceptible to EMI are listed below.
EMI is coupled in two ways:
EMI is considered to be a silent and unknown threat. On many occasions, intermittent malfunctions or random failures of equipment are experienced by several users. They are attributed to be due to the presence of EMI. In view of this, the threat due to EMI is silent and has proved to be hazardous.
Common effects of EMI
The effective methods to eliminate EMI are:
The first four methods are popular for different applications. A few basics are presented below.
Shielding
The main object of shielding is to restrict radiations to a specified region to prevent it from entering susceptible devices. The quality of shielding is expressed in the form of shielding effectiveness of the material. Shielding of materials can be solids, screens and braids. They can be in the form of boxes, partitions, cables and connector shields.
Shielding effectiveness (Se) It is defined as the ratio of incident power to transmitted power.
For electric fields, we have
For magnetic fields,
The shielding effectiveness for electric fields in dB can be written as the sum of three terms, that is,
Se(dB) | = | RdB + AdB + MdB | |
where | RdB | = | reflected loss |
AdB | = | absorption loss | |
MdB | = | multiple re-reflections and transmission losses |
Shielding is done by good conducting materials. Some examples of shielding materials are silver, copper, aluminium, gold, brass and bronze.
Reflection loss is very high at low frequencies and for high conductivity materials.
It is expressed as
The absorption loss for the materials (μr σr >> 1) is given by
|
AdB |
= |
8.6859 t / δ |
where |
t |
= |
thickness of the shield |
|
δ |
= |
depth of penetration |
The multiple reflection loss is given by
MdB is negligible for shields made of good conductors (ƞ << ƞ0). If t >> δ and .
The effective magnetic shielding materials are the ones with high permeability. Examples: Mumetal, Steel.
Grounding
Grounding provides a conducting path between electronic devices and the ground. Ground is nothing but some reference point. It is a circuit concept.
The ideal ground is characterised by zero potential and impedance.
The types of grounding techniques are:
The ground plane is in the form of a wire or a conductive rod.
Bonding
It provides a low-impedance path between two conducting surfaces. It is a part of grounding and represents its physical implementation.
It creates a homogeneous structure for current flow and suppresses the creation of potentials between two metallic parts.
Bonding is useful to protect against the effects of shocks and to protect circuits from current return paths. They reduce potential difference between the devices and carry large faulty currents.
Bonding is of two types:
Direct bonding is made by metal-to-metal between the connected elements. Indirect bonding is made by contact using conductive jumpers.
Bonding quality is represented by its DC and AC resistances and also bonding effectiveness.
where |
l |
= |
length of the bond, (m) |
|
σ |
= |
conductivity, (mho/m) |
|
s |
= |
cross-sectional area, (m2) |
|
δ |
= |
depth of penetration, (m) |
|
w |
= |
width of the bond, (m) |
Bonding effectiveness (Be) It is defined as the difference between induced voltage in the case of an equipment with a bond trap and the induced voltage in the case of an equipment without a bond trap. It is expressed in dB.
Filtering
These are used to filter out conducted EMI. The filtering effectiveness is expressed by Insertion loss (IL). It is defined as
where |
V01 |
= |
output voltage with filter |
|
V02 |
= |
output voltage without filter |
For low pass inductive filters,
Insertion loss
For low pass capacitive filter,
Insertion loss
where ω = angular frequency = 2π f
EMC standards are required for trouble free co-existence and to ensure satisfactory operation. They are also required to provide compatibility between electrical, electronic, computer, control and other systems. Standards are required as manufacturer-user interaction and user’s knowledge on EMI are limited.
They are also required for establishing harmonised standards to reduce international trade barriers and to improve product reliability and life of the product.
These are of two types:
Military Standards
These include emission and susceptibility standards. Emission standards specify emission limits in voltage or current, power or field strengths in specified frequency ranges. Susceptibility standards specify conducted spike or radiated field parameters.
Military EMC standards are made in order to ensure system-to-system compatibility in a real time military environment. Equipments are classified based on their deployment environment. In these standards, test procedures are well defined. Military standards are more stringent than civilian standards. Most of the military standards are broadly based on MIL-STD 461 and 462.
Civilian Standards
Civilian EMC standards are applicable for equipments used for commercial, industrial and domestic applications. The emission standards are specified to protect broadcast services from interference. These also take into account the physiological interference effects experienced by human beings.
The advantages are:
EM waves, light, heat, X-rays and gamma rays are all different forms of electromagnetic radiation. However, they differ in their wavelength. These radiations have hazardous effects on man and material. The effects can be divided into two categories:
Table 9.1 Effects of EM Radiation
Frequency (GHz) |
Effect |
---|---|
0.1 |
Warming of exposed areas. |
0.15−1.2 |
Overheating occurs and causes damage to internal organs. |
1.0−3.3 |
Lens of the eye and kidneys are susceptible to damage when tissues are heated up. |
3.3−10 |
Noticeable skin heating occurs. |
10−100 |
Skin acts as either a reflector or an absorber and hence heating takes place. |
The damaging levels depend on frequency, ambient temperature, body resistance and weight of individuals.
Exposure over an energy density of 10 mw/cm2 at any frequency is considered to be not safe.
Radiation limits in the frequency range of 0.1 to 100 GHz when personnel are exposed to EM radiations are:
ESD results from the separation of static charge.
Effects of ESD:
Methods of Separation of Charge
Rubbing of two types of insulating material causes charge to be separated from one material to the other. The charge separation creates high fields and hence causes a voltage difference between the two materials. This leads to a breakdown of the air and intensive arcs are produced. A direct conduction path will result if one material comes in contact with a conductor. This phenomenon is a familiar one when we walk across a carpet on a dry day and touch a metallic doorknob. When the resulting arc current enters sensitive devices, they are damaged.
If two neutral insulators are brought in contact, charge is transferred from one to another. When they are separated, they become charged. At this time, one material is positively charged and the other one is negatively charged. The degree of charge transfer depends on many factors. For example, if Nylon is rubbed against Teflon, electrons will be transferred from Nylon to Teflon. Hence Nylon acquires (+)ve charge and Teflon acquires (–)ve charge.
In fact, touching an insulator with a conductor creates charge separation but the degree is less than that of two insulators.
Grounding a conductor will bleed off the charge but grounding an insulator will not.
ESD wrist straps can be worn to prevent building up of charge.
If a high resistance of the order of 1 MΩ is connected from the installer’s wrist to earth ground, any static charge stored on the body’s skin is discharged to the ground.
It is interesting to know some facts about the frictionally generated charges.
ESD causes component destruction by:
The techniques to prevent the ESD effects are:
Whenever a nuclear detonation takes place, energy is released and this appears as electromagnetic pulse. These pulses affect the operation of electrical and electronic equipment even at great distances. The far-field characteristics of the radiated EMP produced by a single high altitude detonation is found to have significant variation in amplitude, wave shape and propagation characteristics. These depend on weapon yield, location of the observer, the height and location of the burst and orientation of earth’s magnetic field.
The EMP amplitude spectrum covers a broad frequency range which extends from low to microwave frequencies.
A typical EMP waveform can be represented by
where |
t |
= |
time in seconds |
|
a |
= |
normalisation factor = |
|
t1 |
= |
time to peak value |
|
Em |
= |
E(t1) |
The Fourier transform of the equation is
A typical EMP wave form is shown in Fig. 9.2.
Fig. 9.2 A typical EMP wave form
Most of the engineering problems/models are in the form of differential equations. Systems with one independent variable can be modeled by ordinary differential equations. But systems with two or more independent variables require the use of partial differential equations. It is possible to obtain the solution for some of these equations in closed form. But majority of the large sets of simultaneous differential equations and non-linear ones do not have analytical solutions and hence the application of numerical techniques is required.
The most useful numerical techniques are:
In all these methods, discretisation of a continuous region into a finite number of sections is made. Moreover, they require the solution of a set of algebraic equations only. The solution of differential or integral equations is not required. These methods are extremely useful for the design as well as analysis of an electromagnetic system. Problems involving the determination of current distribution in a current element or a dipole and the field distribution in a slot are easily solved by these methods.
For modeling static field systems, Laplace’s and Poisson’s equations can be used. These require the solution of differential equations. It is possible to obtain analytical solutions when the regions have regular geometrical shapes like triangular, circular, elliptical, rectangular and so on. But for arbitrarily shaped regions, the field solutions are obtained using FDM, FEM and MOM techniques.
It is a numerical technique in which the domain is divided into a number of discrete points. It consists of a set of difference equations. FDM is useful to solve the spatial distribution of electromagnetic fields in different media.
Solution by this method is approximate and error can be reduced by taking more number of discrete points in a specified region. For example, Poisson’s equation can be solved for V (x, y, z) in any arbitrary region using the boundary conditions. However, the analysis for fields in an arbitrarily shaped region is complex by this method.
FEM is a technique useful to solve the problems containing differential equations numerically. This method is easily applicable to solve the problems involving arbitrarily shaped regions. The method basically consists of:
Solution can be obtained either by Iterative method or by Band matrix method.
FEM is a better method than FDM and MOM as it is easy to apply to complex regions and it is possible to write universal general purpose programmes to solve different types of problems. At the same time, it is constrained by a few drawbacks. For instance, the preparation of data is complex and involved. The programming part is also involved compared to FDM and MOM.
It is basically an incremental numerical technique. It is useful to find the integrand from the integral equation. An equation is known as an integral equation if the integrand is an unknown.
This method makes use of equations of unknown potentials or fields in integral form to find out the potential or field distribution in a medium.
An example of integral equation is
where ρν (r′) is an unknown.
r′ = (x′, y′, z′), r = (x, y, z)
ρυ (r′) = ρυ (x′, y′, z′)
V(r) = V(x, y, z)
ρʋ is the source of the potential function. r is the distance between the source and potential. ρʋ is an unknown function and V is a known function. The method of moments consists of the following steps:
where F is an integral operator and y is a known function.
X is an unknown output function.
where aN is an unknown constant and XN (x) is a known function and is called a basis or expansion function.
This consists of one equation with N unknowns. It is not possible to solve it as such. It is required to have N independent linear equations. Hence, applying boundary conditions at N points, we have N equations.
For the sake of analogy, we can have
Problem 9.1 For a copper shield, find the reflection loss in dB at (a) 1 kHz and (b)10 MHz.
Solution
Problem 9.2 Determine reflection loss for a steel shielding at (a) 10 kHz and (b) 10 MHz. For steel, μr = 1,000, σr = 0.1.
Solution
Problem 9.3 For nickel shield, find the absorption loss when t / δ = 1, t/ δ= 2, t / δ = 4.
Solution If t / δ= 1
If t / δ = 2
If t / δ =4
Problem 9.4 Find multiple reflection loss due to a shielding material for which ƞ<<ƞ0 and t / δ = 0.1.
Solution We have
1. Electric power lines are sources of EMI. |
(Yes/No) |
2. Computers are susceptible to EMI. |
(Yes/No) |
3. Walkie Talkies radiate and they are susceptible to EMI. |
(Yes/No) |
4. Automobiles are sources of EMI. |
(Yes/No) |
5. Aircraft is not susceptible to EMI. |
(Yes/No) |
6. Submarines are not susceptible to EMI. |
(Yes/No) |
7. Radar is a man-made source of EMI. |
(Yes/No) |
8. Human beings are susceptible to EMR. |
(Yes/No) |
9. Animals are susceptible to EMR. |
(Yes/No) |
10. Medical equipment is susceptible to EMI. |
(Yes/No) |
11. Kitchen mixie is a source of EMI. |
(Yes/No) |
12. Hair drier is a source of EMI. |
(Yes/No) |
13. Television is susceptible to EMI. |
(Yes/No) |
14. Fluorescent lamp is a source of EMI. |
(Yes/No) |
15. Isolation is a method of EMI control. |
(Yes/No) |
16. Grounding is a method of EMC design. |
(Yes/No) |
17. Proper cable design reduces EMI. |
(Yes/No) |
18. Washing machines are sources of EMI. |
(Yes/No) |
19. Light dimmers in automobiles are sources of EMI. |
(Yes/No) |
20. Cell phones are sources of EMI. |
(Yes/No) |
21. FEM is more useful than FDM. |
(Yes/No) |
22. FEM is a numerical technique using a set of algebraic equations. |
(Yes/No) |
23. Numerical evaluation of integrals is more accurate than the numerical evaluation of differential equations. |
(Yes/No) |
(Yes/No) |
|
25. If 〈x, y〉 = 〈y, x〉 reciprocity is said to exist. |
(Yes/No) |
26. It is easy to shield electric fields than to shield magnetic fields. |
(Yes/No) |
27. Reflection loss is very large for electric fields and plane waves. |
(Yes/No) |
28. Reflection loss is usually small for low frequency magnetic fields. |
(Yes/No) |
29. Shielding is said to be excellent, if the attenuation is > 90 dB. |
(Yes/No) |
30. The unit of magnetic conduction density is _____. |
|
31. The unit of surface magnetic current density is _____. |
|
32. Surface magnetic current density is defined as _____. |
|
33. Vector electric potential, F is defined by _____. |
|
34. The unit of vector electric potential is _____. |
|
35. The unit of reaction is _____. |
|
36. Self-reaction is represented by _____. |
|
37. Reciprocity in field theory is said to exist if _____. |
|
38. EMI means _____. |
|
39. EMC represents _____. |
|
40. EMS means _____. |
|
41. EMI is mainly from _____. |
|
42. EMI enters the system by _____. |
|
43. EMI can be controlled by _____. |
|
44. EMI from antennas can be controlled by _____. |
|
45. Filtering is a technique suitable to control _____. |
|
46. Two types of EMC standards are _____. |
|
47. FCC means _____. |
|
48. CISPR represents _____. |
|
49. The main advantage of EMC standards is that _____. |
|
51. The main effects of EMI/EMR are _____. |
|
52. High EMR susceptible organs of human beings are _____. |
|
53. ESD means _____. |
|
54. ESD originates due to _____. |
|
55. The safe EMR exposure limit is _____. |
|
56. The effect of ESD is that _____. |
|
57. ESD causes _____. |
|
58. EMP means _____. |
|
59. The damaging levels due to EMR in human beings depend on _____ |
|
60. Two major sources of EMI are _____. |
|
61. FDM means _____. |
|
62. FEM represents _____. |
|
63. MOM means _____. |
|
64. The unit of self-reaction is _____. |
1. Yes |
2. Yes |
3. Yes |
4. Yes |
5. No |
6. No |
7. Yes |
8. Yes |
9. Yes |
10. Yes |
11. Yes |
12. Yes |
13. Yes |
14. Yes |
15. Yes |
16. Yes |
17. Yes |
18. Yes |
19. Yes |
20. Yes |
21. Yes |
22. Yes |
23. Yes |
24. Yes |
25. Yes |
26. Yes |
27. Yes |
28. Yes |
29. Yes |
30. V/m2 |
|
|
31. V/m |
32. Ms= E × a n |
33. ∇ × F ≡ −∈Em |
34. Farad-Volt/m |
35. Watts |
36. 〈x, x〉 |
37. 〈x, y〉 = 〈 y, x〉 |
38. Electromagnetic interference |
39. Electromagnetic compatibility
40. Electromagnetic susceptibility
41. Man-made and natural sources
42. Conduction and radiation
43. Shielding
44. Polarisation control
45. Conducted EMI
46. Military and civilian
47. Federal Communications Council
48. Committee International Special Perturbations Radioelectriques
49. Product life is increased
50. German EMC standard
51. Thermal and non-thermal
52. Eyes and kidneys
53. Electrostatic discharge
54. Separation of static charges
55. 10 mW/cm2 for exposures greater than 30 seconds
56. Intense arc discharge current takes place
57. Component destruction
58. Electromagnetic pulse
59. Frequency and ambient temperature
60. Nuclear detonations and lightning
61. Finite difference method
62. Finite element method
63. Method of moment
64. Watt
1. (b) |
2. (b) |
3. (b) |
4. (a) |
5. (b) |
6. (a) |
7. (a) |
8. (b) |
9. (a) |
10. (a) |
11. (a) |
12. (b) |
13. (a) |
14. (a) |
15. (c) |
16. (d) |
17. (b) |
18. (c) |
19. (b) |
20. (d) |
μr = 1, σr = 1.05 for silver.
For aluminium, μr = 1, σr = 0.61.