Electromagnetic Wave Propagation, Radiation and Scattering Applications

#### **Chapter 6**

## Electromagnetism of Microwave Heating

*Rafael Zamorano Ulloa*

#### **Abstract**

Detailed electrodynamic descriptions of the fundamental workings of microwave heating devices are presented. We stress that all results come from Maxwell equations and the boundary conditions (BC). We analyze one by one the principal components of a microwave heater; the cooking chamber, the waveguide, and the microwave sources, either klystron or magnetron. The boundary conditions at the walls of the resonant cavity and at the interface air/surface of the food are given and show how relevant the BC are to understand how the microwaves penetrate the nonconducting, electric polarizable specimen. We mention the application of microwaving waste plastics to obtain a good H2 quantity that could be used as a clean energy source for other machines. We obtained trapped stationary microwaves in the resonant cavity and traveling waves in the waveguides. We show 3D plots of the mathematical solutions and agree quite well with experimental measurements of hot/cold patterns. Simulations for cylindrical cavities are shown. The radiation processes in klystrons and magnetrons are described with some detail in terms of the accelerated electrons and their trajectories. These fields are sent to the waveguides and feed the cooking chamber. Whence, we understand how a meal or waste plastic, or an industrial sample is microwave heated.

**Keywords:** microwave heating, resonant cavity, cooking chamber, waveguide, klystron, magnetron, boundary conditions, food-air interface, Lienard-Wiechert potentials, Jefimenko fields

#### **1. Introduction**

Microwaves are everywhere and permeate the universe. They reach earth constantly and we produce them in many medical, industrial, chemical, domestic, and research on magnetic and dielectric materials and in devices and equipment [1–13]. The modern communications technology uses them intensely, Wi-Fi, all around the world, every second, every day [14]. Many medical applications are concentrated in cancer treatments by giving hyperthermia to the cancerous cells while avoiding to damage healthy cells. Microwave ablation is widely used in many types of cancers, bone, cardiac arrhythmic tissue, thyroid glands, skin cancer, and many other damaged tissues [2, 3, 15, 16]. The apparatus is constituted basically by a microwave source, a waveguide that ends in an antenna that, as a needle, penetrates the tissue [2, 3, 15, 16]. Industrial applications go from thermally treating/curing polymers, rubber, and plastics to quickly heat cement and minerals, and to assist vulcanization [4, 5, 17, 18]. Chemical applications are mainly directed to organic and/or inorganic synthesis and accelerating reactions, and to search for novel synthesis routes and

novel products. Chemical microwave heating has been used for decades [6, 7]. Research in magnetics and in dielectrics includes heat transfer and/or electromagnetic excitation of matter [10–13]. Domestic technology uses them to heat up quickly and easily food, coffee, and water in microwave ovens (MWO) built for such function, see **Figure 1(D)** [8, 9]. By far, the two most commonly used microwave configurations include a source of microwaves, typically a klystron or a magnetron, a waveguide for these microwaves, and a resonant chamber where the microwaves are used to treat, to modify, to cure, to excite, or to heat up a sample put in the microwave chamber. There are two most common geometries of microwave chambers, cylindrical and rectangular [4–13]. **Figure 1(A)** shows an electric field pattern simulated inside a typical cylindrical cavity (3.4 cm of radius and 4.22 cm of height) used in a research equipment, in which magnetic samples are resonantly excited [19]. The magnetic field (not shown) is vertical (and orthogonal to E) and mostly concentrated along the *z*-axis at *r* = 0 and to its close vicinity. **Figure 1(B)** shows an electron paramagnetic resonance spectrometer that uses a cylindrical microwave chamber feed by a rectangular waveguide that collects the 9.4-GHz low-power microwaves produced by a klystron inside the box-labeled microwave bridge. **Figure 1(C)** is a calculated stationary electric field pattern from the solutions to Maxwell equations found in this work for a rectangular cavity. **Figure 1(D)** shows a typical domestic microwave oven of dimensions 26 cm 30 cm 34 cm.

A universal advantage of microwave heating in industrial, medical, chemical, and domestic processes is that it does it quickly and efficiently. Yet, several investigations are pursued to find even faster and better microwave heating schemes and profiles [15–17].

The three main parts of these heating devices constitute a source, a waveguide, and a heating chamber. **Figure 2(A)** shows the essential parts of a microwave oven commonly used to heat food. In addition to the already large number of industrial microwave heating applications, very recently, microwaving plastic waste decomposition has been proposed as a central step in order to generate clean hydrogen, H2, out of heating a one-to-one mixture of triturated waste plastics with the catalyst FeAlOx [20]. Edwards et al. [21] have used microwaves to transform waste plastic bags, milk empty bottles, and other supermarket waste plastics, **Figure 2(B)**, in a clean hydrogen energy source. A 1:1 mixture of the catalyst FeAlOx and waste plastics heated up with microwaves in a cylindrical cavity

#### **Figure 1.**

*Microwaves in cylindrical and rectangular geometries. (A) Simulation of the electric field, circular, pattern formed inside a cylindrical microwave cavity. (B) The microwave bridge, the rectangular waveguide, and a cylindrical cavity of a commercial electron paramagnetic resonance spectrometer used to excite magnetic samples. Here, heating is not desired, and the microwave power used is 1 mW or less. (C) A stationary electric field pattern calculated in this work from the solutions to Maxwell equations. The pattern is calculated for the planes* x *and* y *with the coordinate* z *maintained fixed at an arbitrary height. (D) A typical domestic microwave oven (MWO), open and showing its internal chamber height* h *= 38 cm, and width* a *= 32 cm and* b *= depth, 30 cm.*

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

#### **Figure 2.**

*Microwave heating. (A) A typical 1000 Watts, 2.45-GHz domestic microwave oven (MWO) cooking a chicken. (B) Plastic pollution derived from tons and tons of waste plastic bottles and supermarket bags. (C) Clean production of H2 by microwaving waste plastic bags and bottles mixed 1:1 with the catalyst FeAlOx within a cylindrical cavity, the input power is 1000 Watts, and H2 gas is liberated and carried toward a separate container. The cylindrical cavity operates in the TM010 mode.*

(as shown in **Figure 2(C)**) for 10, 30, and 60 s extracts 85–90% of molecular hydrogen that is sent through a column to be stored in a separate chamber for its eventual utilization as a clean energy source. The principle of operation is the same for the domestic microwave oven with a rectangular heating chamber and for this microwave heater that is used to transform waste plastics within a cylindrical heating chamber. This transformation process is clean and fast and could help to reduce drastically the world's wide plastic contamination problem. Plastics invade mountains [22], forests, lakes, oceans, and cities [20–22]. As the hydrogen density content in plastic bags is around 14% per weight, its transformation into H2 and multifaceted fullerenes might offer an opportunity of clean energy production for the countries interested in producing clean H2 as a viable energy source for industrial and domestic usage and contribute to slowing down the global climate change [23]. Using tons and tons of garbage plastics, H2 can be produced in high quantities and then used as a clean industry and house energy supply, this way contributing to combat the global warming. We consider this kind of potential application relevant for the plastic industry and pollution problems and much more relevant for its contribution to a cleaner, greener planet. Microwave heating is used globally, also, to cook or just heat up meals, water, coffee, and pizza. These microwave ovens operate at a power of 1000 Watts; the meals are put into a rectangular resonant cavity that is the cooking chamber that gives them their familiar "box" appearance. In this box, microwaves are delivered unevenly (see uneven electric field pattern calculated here and shown in **Figure 1(C)**), to the meals, and they readily penetrate the matter, making electric dipoles (mainly from water and fatty molecules) to oscillate frenetically; then, this excitation energy is passed to the rest of the specimen as heat.

In a few seconds or minutes, the specimen is hotter than at the start of the microwaving [5–13]. The utility of microwaves is multiple and of large range. In spite of the generalized use of microwave ovens, an informal survey has indicated to us that more than 90% of our STEM students do not really know how MWOs operate. The basic physics required to understand their workings is completed by the end of the undergraduate class work. This is telling us the degree of sophistication and depth that this technology carries, just as many other modern technologies do, as the Wi-Fi itself. A primal objective of this chapter is to describe its electromagnetic physics and to give the fundamentals. All comes from Maxwell equations. We emphasize the fact that most of the microwave heating devices (as the two devices shown in **Figure 2**) are composed of three essential electromagnetic parts: the production of the microwaves, their wave-guided structure that brings the

microwaves from their origins toward the resonant cavity, being the third essential component, that is, the cooking chamber. Aforesaid, some devices use rectangular resonant cavities and others use cylindrical resonant cavities. We focus on rectangular cavities and just mention some results for cylindrical cavities.

We want to emphasize that the study of the electromagnetic functioning of a domestic, an industrial, or a laboratory MWO is an ideal technological case to see how the whole of the theory is applied. These microwave "boxes" contain all of the fundamental physics required to produce (in klystrons or magnetrons) microwaves, then input them into a loss-less waveguide, and finally get them to bath a rectangular heating chamber, or a cylindrical chamber, without appreciable microwave radiation being absorbed at the metallic walls. Their absorption is mainly carried out, precisely, by the specimen we want to heat up.

Our discussion has five parts: First, in Section 2, we deal qualitatively, in detail, with the fundamental constituents of a microwave heating system and the physical processes involved. Then, in Section 3, we analyze the boundary conditions, and in Section 4, we treat mathematically the resonant cavity. A description of the physics of this resonant cavity that keeps confined the microwaves all the time necessary for the food to warm up, or even be cooked, is given. We show that standing wave patterns are the solutions to Maxwell equations. Section 5 treats the rectangular waveguide and the general form of the traveling waves in them is obtained. The process of wave guiding the microwaves is the one that carries the microwaves from its source to the heating chamber. Then, in Section 7, we treat the production of microwaves in klystrons and/or magnetrons by radiating, accelerated, electrons moving in straight lines, or curved trajectories.

#### **2. Fundamental constituents of a microwave heater**

In formal terms, a domestic microwave oven [8, 9], or an industrial system [4, 5] or a laboratory prototype for clean extraction of H2 from microwaving waste plastics [20, 21], is constituted by three fundamental parts shown in **Figure 2(A)** and **(C)** and in **Figure 3**.

(A) The resonant cavity: Once the microwaves are inside the rectangular cooking chamber, **Figure 2(A)**, or inside a cylindrical resonant cavity, **Figure 2(C)**, these microwaves display themselves stationary wave patterns since they are confined within good conducting walls, see **Figure 1(A)** and **(C)**. These waves rebound incessantly from these metallic walls without, practically, any energy loss. These wave patterns are specific for each geometry and each set of dimensions and the boundary conditions at the walls, as we show below.

In MWOs, the sixth wall is the see-through door that allows access to the interior of the chamber. The see-through window is covered by a metallic mesh with many

#### **Figure 3.**

*Food being cooked in a microwave oven. (A) The meal is already hot and steam is actually getting out of the meat, and the green wavy arrow is pointing to the possibility that some microwaves get out of the oven. (B) The microwaves rebound from all six metallic surfaces of the "box" (yellow) and are reflected and transmitted from the surface of the specimen been heated (blue and red).*

#### *Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

small holes of *r* ≈ 1 mm radius that does not allow microwaves to escape; the condition *λ* > > *r* holds and, hence, it functions as a continuous metallic, highly reflecting, surface. The receptacle we see when we introduce the meal to be microwaved is the resonant cavity as shown in **Figure 3**. Electromagnetically, a rectangular resonant cavity, beneath the plastic covers, conforms to a metallic box of about 30 � <sup>32</sup> � 38 cm3 dimensions. A 3D standing wave pattern is selfestablished due to the boundary conditions that have to be fulfilled at the walls, see **Figure 1(C)**.

Hence, maxima and minima and zeroes of the electric field *E* ! and magnetic

field *B* ! appear at different locations, *x*, *y*, *z*, inside the cooking chamber. These microwaves bouncing continuously from the six walls bath constantly and heat our meal.

Can the microwaves, green wavy arrows in **Figure 3**, escape from the cooking chamber? Not in principle, unless some malalignment, or broken piece is there. Within the resonant cavity, the microwaves bounce back and forth from the metallic walls (yellow in **Figure 3(B)**) without any loss of electromagnetic energy.

Then, the microwaves hit the chicken at multiple points (blue-green wavy arrows), at the interface between food and air, reflection and refraction take place, and Snell's law and Fresnel equations have to be fulfilled [24–29]. Some microwaves are reflected (blue-green lines), and others are transmitted inside the chicken body (red wavy arrows). These red microwaves are responsible for heating, and they are the ones that transmit, quite efficiently, vertiginous motions vibrations, at 2.45 GHz, to the electric dipoles that are part of the meal (mostly water, but also some fatty molecules). These red microwaves penetrate several centimeters through the specimen. The electromagnetic energy carried out by the Poynting vector of these red microwaves, *S* ! ð Þ¼ *r*, *t E* ! ð Þ� *r*, *t H* ! ð Þ *r*, *t* , is converted into frenetic Jiggling of these polar molecules and then converted into heat by their interactions with surrounding, neighboring molecules. Heat can be so high that some steam (water vapor) can be seen through the window in just a few seconds, see **Figure 3 (A)**. This process is the moment of energy conversion: from electromagnetic energy with 1000 Watts of power to motion, vibrations, mechanical energy. But that excited motion starts, rapidly, to pass to neighboring nonpolar atoms and molecules and locally, all the surrounding matter, starts jiggling more and more, which is heat. *Microwave energy has been transformed into heat inside our meal being microwaved*. In **Figure 3**, the wavy red lines represent the microwaves that get into the specimen and excite the electric dipoles within it. We show that at multiple points of incidence-reflection-transmission on the food-air interface, this bathing is by no means uniform since the microwaves distribute inhomogeneously inside the resonant cavity, see **Figure 1(C)**. This is the reason why the specimen is placed on a rotating plate, so some homogeneous heating is achieved.

Normally, it is expected that the ceramic (or the plastic), from which the cup for coffee or water is made, does not get heated while the liquid inside it. In order to get such result, it is necessary to minimize the composition of electric dipoles in the structure of the ceramics, glass, or plastic that makes the cup or the dish, effectively rendering this object transparent to the microwaves.

(B) The metallic waveguide: The microwave radiation from the source is immediately channeled through a horn-like metallic collector toward a rectangular waveguide through multiple reflections on its conducting metallic walls, and the radiation is guided almost without attenuation to the resonant cavity of the MWO. A rectangular waveguide is shown in **Figures 1(B)** and **4(C)**. The good conductor quality of the waveguide is the responsible for no-attenuation microwaves at the

#### *Electromagnetic Wave Propagation for Industry and Biomedical Applications*

#### **Figure 4.**

*Constituent parts of a microwave oven, or a laboratory microwave heater. (A) A magnetron typically used to generate microwaves in a domestic MWO. (B) A microwave generator, klystron, that is frequently used in microwave laboratory equipment where low power is required. (C) A hollow rectangular waveguide of a, b cross section and coupled to another waveguide, of the same dimensions, from aforesaid (taken from Feynman Phys. Lectures, vol. II. [24]) both microwave trains join and interfere at the union of the metallic structures. (D) An example of microwaving solids and trapping gasses that are detached, from the specimen, in the process. Microwaving plastic waste mixed 1:1 with FeAlOx inside the transformation chamber, which is an aluminum TM010 resonant cavity (it is the analog of the microwave oven chamber). Principle of operation was modified from [21], not the actual experimental setup.*

waveguide walls even after multiple reflections. More detail on waveguides can be found in Refs. [24-29]. The waveguide terminates in a "mouth" that connects with the cooking chamber. This way both parts are coupled.

(C) The source of microwaves: For low-power applications, 1 mW or less, a klystron is used as the source of microwaves. For higher-power applications of microwave heating, around 1000 Watts, a magnetron is used. In both cases, it is a tube in which electrons are ejected from a hot cathode to a space where they get immediately accelerated and precisely, this acceleration produces electric and magnetic radiation fields, orthogonal to each other and to the propagation direction. Its power is proportional to the acceleration squared, Prad *α a*<sup>2</sup> , and is schematically depicted in **Figure 4(A)** and **(B)**. Those accelerated electrons emit radiation at the same frequency of the acceleration that in this case is in the 2–3 GHz range.

Now let us be more quantitative. We start with the electromagnetic boundary conditions.

#### **3. Microwave heating of food or of an industrial sample**

When microwave radiation hits the surface of a specimen, what we have is incidence of electromagnetic fields on the interface between meal and air, two nonmagnetic, nonconducting media, and the laws of Snell and Fresnel of reflection and refraction have to be fulfilled. But, they will be obeyed once the boundary conditions for *E* ! and *D* ! and for *H* ! and *B* ! are fulfilled. Let us see what they are as follows:

#### **3.1 Continuity of the normal component of the displacement field,** *D*

Let us suppose we have the interface between any two media such as water-air, plastic-metal, raw meat-hot air, a catalyst-plastic, ceramic-coffee, and so on as shown in **Figure 5**, that is, the boundary. The boundary condition on *D* ! is obtained from applying Gauss law to a very small cylinder (purple) of differential area and differential high that crosses the boundary as shown in **Figure 5(A)**. Then, the Gauss integral ∮ *E* ! � *<sup>n</sup>* !*da* on the closed surface is decomposed into three integrals, one on *S*<sup>1</sup> within medium 1, another one on surface *S*<sup>2</sup> within medium 2, and a third integral on the lateral surface, which goes to zero because the high of the cylinder is as small as we wish; then after integrating the only two integrals we are left with

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

#### **Figure 5.**

*Boundary conditions on D*! *. (A) Gaussian, very small, cylinder on the interface between two different media 1 and 2. The difference* Dn*<sup>1</sup>* � Dn*<sup>2</sup> between the normal components of D*! *is equal to the surface charge density* σƒ*. When surface charge is zero, then* Dn*<sup>1</sup> =* Dn*2, the normal components of the displacement field are continuous. (B) The same condition applies on the surface of meat when field D*! *hits its surface inside a microwave oven, in this case* σ<sup>ƒ</sup> *= 0 and* Dn*<sup>1</sup> =* Dn*2. In (B) the boundary interface is the skin of a chicken being microwaved.*

produce (*Dn*<sup>1</sup> � *Dn*2)*S* = *σƒS* [25–29]. When the interface carries no electric charge, as is usually the case with microwave heating, then *σ<sup>ƒ</sup>* = 0. Hence, (*Dn*<sup>1</sup> = *Dn*2). And so, the normal component of the displacement vector is continuous through the interface of air-chicken!, or air-plastic, or air-ceramic, and so on.

Only in the case of the boundary between a conductor and a dielectric *Dn* = *σƒ*, being *σ<sup>ƒ</sup>* the free charge density on the interface as represented with the "+" signs in **Figure 5(A)**. For the cases we are interested here, all the metallic walls in the cooking chamber (resonant cavity) and the waveguide are not charged, then *σ<sup>ƒ</sup>* = 0 and so *Dn*<sup>1</sup> = *Dn*2.

On the other hand, when the *D* ! , field of the microwaves in the cooking chamber enters the surface, *Dn*2, of the piece of food (sample, specimen, system), as shown in **Figure 5(B)**, it travels much more distance inside (several centimeters.) the sample and in its way excites electric dipoles (mostly water molecules and fat dipolar and other organic dipolar moieties) and gradually, but fast, transfers most of its energy to them. After a relaxation time period, ≈ 10�<sup>6</sup> sec, the dipoles transfer all that juggling energy to vibrations of the bulk and appear as heat (measured as *kBT*).

#### **3.2 Continuity of the tangential component of the electric field intensity**

Consider the blue, rectangular, path shown in **Figure 6(A)** and **(B)** with two sides parallel to the boundary and arbitrarily close to it. The two vertical sides are infinitesimal. Stokes theorem states that ∮ ∇ � *E* ! � *da*! <sup>¼</sup> <sup>∮</sup> *<sup>E</sup>* ! � *d l* ! . If the vertical paths are as short as we wish, *Et* does not vary significantly over them and their integrals are zero. And the line integral of *E* ! � *d l* ! is *Et*1*L*–*Et*2*L*. By Stokes's Theorem, this line integral is equal to the integral of ∇ � *E* ! over the surface enclosed by the path C [25–29].

By definition, the enclosed area is zero. So, *Et*1*L*–*Et*2*L* = 0, hence *Et*<sup>1</sup> = *Et*2. The tangential component of *E* ! is therefore continuous across the boundary. Applying this reasoning to the interface of a piece of food and the air in a microwave oven, as shown in **Figure 6(B)**, everything follows and the tangential component of *E* ! in the cooking chamber just above the surface of that matter is continuous with the tangential component of *E* ! just inside "the chicken."

#### **Figure 6.**

*Boundary condition on E*! *. (A) Closed path of integration crossing the interface between two different media 1 and 2. Whatever be the surface charge density* <sup>σ</sup>f*, the tangential components of E*! *on both sides of the interface are equal:* Et*<sup>1</sup> <sup>=</sup>* Et*2. The tangential components of E*! *field are continuous no matter what medium 1 is and what medium 2 is. (B) The same analysis for a piece of chicken, or a cup of coffee, or melting cheese in a microwave oven follows: The tangential components of E*! *are continuous. Et*<sup>2</sup> *contributes, at most, to some heating on the surface of the meal.*

For the case of the metallic walls of the heating chamber and the walls of the waveguide, we have the case of a boundary between a dielectric (hot air) and a conductor, then *E* ! ¼ 0 in the conductor and *Et* = 0 in both media. The magnetic part of the microwaves also obeys corresponding boundary conditions, namely: *B*1*<sup>n</sup>* = *B*2*<sup>n</sup>* and *H*1*<sup>t</sup>* = *H*2*t*, and *B*2*<sup>n</sup>* is quite capable of exciting magnetic dipoles inside the specimen, but food, beverages, water, and coffee do not possess magnetic moments, which are not magnetic. So, we do not treat here magnetic heating, even though it is a very active field of research [10, 11]. We concentrate on heating through electric dipoles inside the cooking chamber, as shown in **Figures 3, 5**, and **6**. Next, we describe more quantitatively the electromagnetics in the cooking chamber.

#### **4. Microwave cooking chamber as a resonant cavity**

Aforesaid, the empty cooking chamber in a microwave oven (MWO) is a closed rectangular space where, once microwaves are input, they bounce back and forth from metallic walls on the six sides and confine the electromagnetic waves in such space. This is an electromagnetic resonant cavity (ERC) in which electromagnetic waves (EMW) move in space and time periodically and, very importantly, forming standing wave patterns with nodes and anti-nodes. The cooking chamber is then electromagnetically a resonant cavity that imposes on the microwaves boundary conditions at the six walls. The *E* ! field, just outside and parallel to each wall, *Et*, must be zero and the normal component of *B* ! must be continuous [25–29]. When food, water, coffee, cheese, or any other food are introduced in it, a dielectric medium with ε 6¼ ε<sup>0</sup> and air with ≈ *ε*<sup>0</sup> are now the composite dielectric that fills the resonant cavity, as shown in **Figure 3**. Dielectrics do not perturb considerably the standing wave patterns that form the microwaves inside the MWO.

Let us be more quantitative, and take a standard microwave oven of dimensions *a* = 30 cm, *b* = 32 cm, and *c* = 38 cm as shown in **Figure 1(D)**. We will take the walls as perfect conductors as first approximation, boundary conditions on the six walls have to be fulfilled, and there will be multiple reflections at the metallic boundary surfaces. **Figure 7** shows how a sinusoidal electromagnetic field wave bounces back from a perfect conducting surface [25–29].

#### **Figure 7.**

*The standing wave pattern resulting from the reflection of a microwave at the surface of a good conductor wall of the cooking chamber. The curvy lines show the standing waves of E*! *and H*! *at some particular time. The nodes E* ! *and of H*! *are not coincident but are spaced* λ*/4 apart as shown. Modified from [25].*

An arbitrary standing wave pattern in the resonant cavity can then be obtained as an appropriate superposition of these standing waves. Let us consider the closed region (cooking chamber) with walls of sides *a*, *b*, and *c*, and with the origin at one corner as shown in **Figure 3**. The cavity is filled with a linear dielectric, food (material described by *μ*<sup>0</sup> and *ε*). Both fields, *E* ! and *H* ! , inside should obey Maxwell equations and each field component satisfies the wave equation; the solutions are stationary, confined, trapped microwaves. Applying separation of variables first to the time variable, it results in a solution of the form *e* �*iωt* . Therefore, we have now, let us say, for

$$\propto \left( \vec{r}, t \right) = \psi\_0 = E\_{0\_x} X(\varkappa) Y(\jmath) Z(z) e^{-i\alpha t} \tag{1}$$

which, when substituted into the wave equation, leads to the Helmholtz equation ∇<sup>2</sup> *<sup>ψ</sup>*<sup>0</sup> <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> <sup>0</sup>*ψ*<sup>0</sup> <sup>¼</sup> 0 where *<sup>k</sup>*<sup>2</sup> <sup>0</sup> <sup>¼</sup> ð Þ *<sup>ω</sup>=<sup>υ</sup>* <sup>2</sup> . This result is actually valid for any kind of coordinate system. Helmholtz equation is readily solved in rectangular coordinates by separation of variables. If we write, *ψ*<sup>0</sup> ¼ *X x*ð Þ*Y y*ð Þ*Z z*ð Þ and proceed with the standard separations, we obtain [28, 29].

$$\begin{aligned} \Psi\_0 \left( \overrightarrow{r} \right) &= \left( \mathbf{C}\_1 \sin \mathbf{k}\_1 \mathbf{x} + \mathbf{C}\_2 \cos \mathbf{k}\_1 \mathbf{x} \right) \left( \mathbf{C}\_3 \sin \mathbf{k}\_2 \mathbf{y} + \mathbf{C}\_4 \cos \mathbf{k}\_2 \mathbf{y} \right) \\ &\times \left( \mathbf{C}\_5 \sin \mathbf{k}\_3 \mathbf{z} + \mathbf{C}\_6 \cos \mathbf{k}\_3 \mathbf{z} \right) \end{aligned} \tag{2}$$

where *k*1, *k*2, and *k*<sup>3</sup> are the wave numbers in the *x*, *y*, *z* dimensions and are related to the frequency *ω* of the microwave field by the dispersion relation *k*<sup>2</sup> <sup>1</sup> þ *k*2 <sup>2</sup> <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> <sup>3</sup> <sup>¼</sup> *<sup>k</sup>*<sup>2</sup> <sup>0</sup> <sup>¼</sup> ð Þ *<sup>ω</sup>=<sup>υ</sup>* <sup>2</sup> . Combining this *ψ*<sup>0</sup> *r* ! with the temporal solution *<sup>T</sup>*(*t*), we get any one of the components of the *E* ! and *H* ! field as

$$\begin{aligned} \mathbf{E\_x} &= (\mathbf{C\_1}\sin\mathbf{k\_1x} + \mathbf{C\_2}\cos\mathbf{k\_1x})(\mathbf{C\_3}\sin\mathbf{k\_2y} + \mathbf{C\_4}\cos\mathbf{k\_2y})\\ &\times (\mathbf{C\_5}\sin\mathbf{k\_3z} + \mathbf{C\_6}\cos\mathbf{k\_3z})\mathbf{e^{-i\alpha t}}\end{aligned} \tag{3}$$

The boundary conditions that obey each *E* ! and *H* ! field component are going to make the difference of the fields through the fact that the constants, *C*1, *C*2, … , *C*6, of each component will take different values, including zero. The boundary condition *E*1*<sup>t</sup>* = *E*2*<sup>t</sup>* at any metallic wall (*Emetal* = 0) makes for tangential components to be zero. Hence, *Ex* will be a tangential component and must therefore vanish at the faces *y* = 0 and *b* and *z* = 0 and *c*. We see that this requires that *C*<sup>4</sup> = *C*<sup>6</sup> = 0 and that *k*<sup>2</sup> ¼ *nπ=b* and *k*<sup>3</sup> ¼ *pπ=c* for sin ð Þ¼ *k*2*b* 0 and sin ð Þ¼ *k*3*c* 0, and where *n* and *p* are integers.

Then we have for *Ex*:

$$E\_{\mathbf{x}} = \left(C\_1' \sin k\_1 \mathbf{x} + C\_2' \cos k\_1 \mathbf{x}\right) \sin k\_2 y \sin k\_3 yz^{-i\alpha t} \tag{4}$$

where *C*<sup>0</sup> <sup>1</sup> ¼ *C*1*C*3*C*<sup>5</sup> and *C*<sup>0</sup> <sup>2</sup> ¼ *C*2*C*3*C*5. Repeating this whole procedure for *Ey* and its boundary conditions and for *Ez* and its boundary conditions we get

$$E\_{\mathcal{Y}} = \sin k\_1 \mathcal{x} \left( C\_3' \sin k\_2 \mathcal{y} + C\_4' \cos k\_2 \mathcal{y} \right) \sin k\_3 \mathcal{z} e^{-i\alpha t} \tag{5}$$

$$E\_x = \sin k\_1 x \sin k\_2 y \left( C\_5' \sin k\_3 x + C\_6' \cos k\_3 z \right) e^{-iat} \tag{6}$$

and *k*<sup>1</sup> ¼ *mπ=a*. Substituting the expressions of *k*1, *k*2, *k*<sup>3</sup> into the dispersion relation, we obtain all the possible frequencies of oscillation in this cooking chamber of *a*, *b*, *c* dimensions

$$
\pi \left( \frac{a}{\nu} \right)^2 = \left( k\_1^2 + k\_2^2 + k\_3^2 \right) = \pi^2 \left[ \left( \frac{m}{a} \right)^2 + \left( \frac{m}{b} \right)^2 + \left( \frac{p}{c} \right)^2 \right] \tag{7}
$$

Notice that *k*<sup>1</sup> = *km*, *k*<sup>2</sup> = *kn*, and *k*<sup>3</sup> = *kp*. Each set of integers (*n*, *m*, *p*) define a mode of *E* ! field. From this relation aforesaid, we see that frequency ω takes only particular values determined by *m*/*a*, *n*/*b*, and *p*/*c*. There are many combinations of (*n*, *m*, *p*) called modes and then corresponding *k* values and "mode" frequencies *ωnmp*. Each *ωnmp* is a mode of vibration of the electric field and of the *H* ! field (that we obtain below).

It is important to note that if any two of the integers *m*, *n*, *p* are zero, then the other corresponding two *k*1, *k*2, *k*<sup>3</sup> are zero, and from the expressions for *Ex*, *Ey*, *Ez* we see then that all three components of *E* ! are zero. Hence, as a consequence all components of *H* ! become zero since *H* ! ¼ *ξk* ! �*E* ! and no standing wave pattern is sustained in the cooking chamber. We define the vector wave number *k* ! with components *k*<sup>1</sup> = *kn*, *k*<sup>2</sup> = *km*, and *k*<sup>3</sup> = *kp*. The vector electric field must satisfy Maxwell's equations and, in particular, the first Maxwell equation (Gauss Law in differential form) with *ρ<sup>ƒ</sup>* = 0. We must have *ε*∇ � *E* ! ¼ 0. To apply divergence we construct *∂Ex*/*∂x*, *∂Ey*/*∂y*, *∂Ez*/*∂z* with the field components above, we obtain

$$\begin{aligned} &-\left(k\_1 C\_2' + k\_2 C\_4' + k\_3 C\_6'\right) \sin k\_1 \mathbf{x} \sin k\_2 y \sin k\_3 x \\ &+\left[\left(k\_1 C\_1' \cos k\_1 \mathbf{x} \sin k\_2 y \sin k\_3 x\right) + \left(k\_2 C\_3' \sin k\_1 \mathbf{x} \cos k\_2 y \sin k\_3 x\right)\right] \\ &+\left(k\_3 C\_3' \sin k\_1 \mathbf{x} \sin k\_2 y \cos k\_3 x\right)\right] = 0 \end{aligned} \tag{8}$$

The three terms on the left must sum up to zero. One way to have this zero is to ask for each term individually be zero, then we set *k*1C'<sup>2</sup> þ *k*2C'<sup>4</sup> þ *k*3C'<sup>6</sup> ¼ 0 *and also* C'<sup>1</sup> ¼ C'<sup>3</sup> ¼ C'<sup>5</sup> ¼ 0. The only surviving constants are *C*<sup>0</sup> 2, *C*<sup>0</sup> 4, and *C*<sup>0</sup> <sup>6</sup> and the resulting field components are now

$$E\_{\mathbf{x}} = \left(\mathbf{C}'\_2 \cos k\_1 \mathbf{x}\right) \sin k\_2 y \sin k\_3 z e^{-i\alpha t} \tag{9}$$

$$E\_{\mathcal{Y}} = \sin k\_1 \mathcal{x} (\mathbf{C}'\_4 \cos k\_2 y) \sin k\_3 z e^{-i\alpha t} \tag{10}$$

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

$$E\_z = \sin k\_1 x \sin k\_2 y \left( C\_6' \cos k\_3 z \right) e^{-i\alpha t} \tag{11}$$

The amplitude of each of these waves is *C*<sup>0</sup> 2, *C*<sup>0</sup> 4, and *C*<sup>0</sup> 6. So, let us rename them as *C*0 <sup>2</sup> ¼ *E*1, *C*<sup>0</sup> <sup>4</sup> ¼ *E*2, and *C*<sup>0</sup> <sup>6</sup> ¼ *E*3, we find that the last conditions can be written as [28, 29].

$$k\_1 E\_1 + k\_2 E\_2 + k\_3 E\_3 = \overrightarrow{k} \cdot \overrightarrow{E} = \mathbf{0} \tag{12}$$

The expressions for the field components finally become

$$E\_{\mathbf{x}}(\mathbf{x}, \mathbf{y}, \mathbf{z}; t) = E\_1 \cos k\_1 \mathbf{x} \sin k\_2 \mathbf{y} \sin k\_3 \mathbf{z} e^{-i\alpha t} \tag{13}$$

$$E\_{\mathcal{V}}(\mathbf{x}, y, z; t) = E\_2 \sin k\_1 \mathbf{x} \cos k\_2 y \sin k\_3 z e^{-i\alpha t} \tag{14}$$

$$E\_x(\mathbf{x}, y, z; t) = E\_3 \sin k\_1 \mathbf{x} \sin k\_2 y \cos k\_3 z e^{-i\alpha t} \tag{15}$$

So that *E*1, *E*2, and *E*<sup>3</sup> are the amplitudes of the respective components.

We now show, in **Figure 8**, a 3D plot of the *Ey* component for the mode *n* = 2, *m* = 4, *p* = 3, and a 3D plot of the *Ez* component for the mode *n* = 3, *m* = 5, *p* = 2. It is immediately apparent that the number of maxima, minima, and nodes increases as the mode number (*n*, *m*, *p*) increases. Both plots show in the horizontal plane the projections of these maxima and minima. When thinking in the rectangular microwave cavity, this 2D plot represents the heating power at different spots at a *z* = constant plane (height in the microwave oven). This is just a very simplified picture of what the hot and cold spots are inside the 3D microwave chamber. The whole hot/cold distribution spots are the superpositions of many (*n*, *m*, *p*) electromagnetic standing wave patterns.

The color code used in **Figure 8(A)** and **(B)** represents maxima (red) and minima (blue) of the electric field of the microwaves. Since the energy delivered to

#### **Figure 8.**

*Calculated and experimental electric field stationary wave patterns inside a rectangular cavity. (A) 3D plot of the* Ey *stationary pattern for the mode* n *= 2,* m *= 1,* p *= 3, evaluated from Eq. (14) at an arbitrary* z *fixed value. (B) 3D plot of the* Ez *stationary pattern for the mode* n *= 2,* m *= 1,* p *= 3, evaluated from Eq. (15) at an arbitrary* z *fixed value. In both cases, the projection in the* x*–*y *plane of the maxima, minima, and nodes is shown. (C) The experimental determination of the hot/cold spots in a rectangular chamber,* a *= 36 cm,* b *= 24 cm, and* c *= 26.5 cm. Note the alternating pattern of hot/cold spots in the stationary pattern (adapted from [30]).*

the sample goes as the square of the electric field, then red and blue extrema become hot spots and the nodes become cold spots and are located between the red and blue spots. In the 2D projection, the regions between the blue and red zones are the cold spots. Experimental measurements on the standing wave patterns in microwave ovens have been reported and nicely agree with the theoretical calculations [30, 31]. In **Figure 8(C)**, we show one of those measurements carried out on three perpendicular planes, *x*–*z*, *y*–*z*, and *x*–*y*. The agreement between our calculations, planar 2D plots, and the experimental hot/cold spots in **Figure 8** is very satisfactory. The general pattern calculated and measured in the three planes consists of alternating maxima, minima, and nodes for each mode (*n*, *m*, *p*) as given by formulas (12)–(15).

The results in Eqs. (12)–(15) are very much like that one found for a plane wave [25–29]. Thus, for a given mode, a particular set (*n*, *m*, *p*), *E* ! <sup>0</sup> must be perpendicular to the vector *k* ! ¼ ð Þ *mπ=a x*^ þ ð Þ *nπ=b* ^*y* þ ð Þ *pπ=c* ^*z*.

For cylindrical cavities, stationary electromagnetic wave patterns are also obtained. Cylindrical cavities are very frequently used in research and in industrial applications as we showed above in **Figure 2(C)** for decomposition of waste plastics into *H*<sup>2</sup> and a set of fullerene solid compounds. Here, without any calculations, we show in **Figure 9** the electric field stationary wave pattern that we simulated from the cylindrical solutions for the TM010 mode. It is shown as a manner of contrast with the stationary pattern that results in rectangular geometry.

Calculating the magnetic field, we start from our knowledge of *E* ! and of the vector wave number *k* ! . From the third Maxwell equation, we have ∇ � *E* ! ¼

�*<sup>μ</sup> <sup>∂</sup><sup>H</sup>* ! *∂t* <sup>¼</sup> *<sup>i</sup>ωμ<sup>H</sup>* ! . For example, using the expressions for *Ex*, *Ey*, *Ez* just found above, we have

$$
tau\_x = \frac{\partial E\_x}{\partial y} - \frac{\partial E\_y}{\partial z} = (k\_2 E\_3 - k\_3 E\_2) \sin k\_1 \mathbf{x} \cos k\_2 y \cos k\_3 \mathbf{z} e^{-i\omega t}.\tag{16}$$

Since *k*2*E*3–*k*3*E*<sup>2</sup> is the *x* component of *k* ! � *E*<sup>0</sup> !, it is desirable to define a vector *H*<sup>0</sup> ! by *H*<sup>0</sup> ! <sup>¼</sup> <sup>1</sup> *ωμ k* ! � *E*<sup>0</sup> ! for, if we let its rectangular components be *<sup>H</sup>*1, *<sup>H</sup>*2, and *<sup>H</sup>*3, then we can write *Hx* as

#### **Figure 9.**

*Simulation of the stationary pattern of the electric field inside a cylindrical resonant cavity,TM010 mode. (A)*

*The electric field is concentric with minima close to* r *= 0, and E*! *= 0 exactly at* r *= 0. The field is tangent to the metallic wall and very small at* R *=* r*. (B) A top view of the same electric field stationary pattern [19]. This stationary field configuration is established in cylindrical cavities,TM010 mode, used for research at low microwave powers to excite magnetic specimens.*

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

$$H\_x = -iH\_1 \sin\left(k\_1 \mathbf{x}\right) \cos\left(k\_2 y\right) \cos\left(k\_3 x\right) e^{-i\alpha t} \tag{17}$$

Similarly, we find the other two components of *H* ! to be

$$H\_{\mathcal{Y}} = -iH\_2 \cos \left(k\_1 \mathbf{x} \right) \sin \left(k\_2 \mathbf{y} \right) \cos \left(k\_3 \mathbf{z} \right) e^{-i\alpha t} \tag{18}$$

and

$$H\_x = -iH\_3 \cos\left(k\_1 \mathbf{x}\right) \cos\left(k\_2 y\right) \sin\left(k\_3 x\right) e^{-i\alpha t} \tag{19}$$

We see that *Hx* = 0 at *x* = 0 and *x* = *a*, that is, at the walls for which it is a normal component; similarly, *Hy* and *Hz* vanish at *y* = 0 and *b* and *z* = 0 and *c*, respectively. Thus, the boundary conditions on *H* ! have been automatically satisfied once *E* ! was made to satisfy its own boundary conditions. Furthermore, it is easily verified that the two remaining Maxwell equations that we have not yet used are satisfied, that is, ∇ � *H* ! ¼ 0 and ∇ � *E* ! ¼ � *<sup>∂</sup><sup>B</sup>* ! *=∂t* One needs to use *<sup>k</sup>* ! � *<sup>H</sup>*<sup>0</sup> ! <sup>¼</sup> 0, as well as *<sup>H</sup>xEz* and the relation dispersion in its form *k* ! � *k* ! <sup>¼</sup> *<sup>k</sup>*<sup>2</sup> <sup>0</sup> <sup>¼</sup> *<sup>ω</sup>*<sup>2</sup> *<sup>ν</sup>*<sup>2</sup> <sup>¼</sup> *<sup>ω</sup>*<sup>2</sup>*με:* Each component of *<sup>E</sup>* ! varies as *e* �*iωt* , while the components of *H* ! are proportional to �*ie*�*iω<sup>t</sup>* <sup>¼</sup> *<sup>e</sup>* �*<sup>i</sup> <sup>ω</sup>t*<sup>þ</sup> <sup>1</sup> ð Þ<sup>2</sup> ½ � *<sup>π</sup> :* Thus, the electric and magnetic fields are not in phase in these standing waves but instead *H* ! leads *E* ! by 90° as shown in **Figure 7**. A given *k* ! corresponds to a given mode, that is, a given set of integers *m*, *n*, *p* in k aforesaid. Now *k* ! � *E* ! tell us that the vector *E*<sup>0</sup> must be chosen to be perpendicular to *k* !. However, there are two independent mutually perpendicular directions along which *E*<sup>0</sup> ! can be chosen and still be perpendicular to a *k* !.

Thus, for each possible value of *k* !, there are two possible independent directions of polarization of *E*<sup>0</sup> !, so that there are two distinct modes for each allowed frequency given by *ωnmp*. This property is known as degeneracy and is a fundamental and important feature of electromagnetic standing waves. If *a*, *b*, *c* are all different, then the various frequencies given by *ωnmp* will generally be different. However, if there are simple relations among the dimensions, it is possible that different choices of the integers will give the same frequency so that we will also have degeneracy, but arising in a different manner. As an extreme example, consider a cube for which *a* = *b* = *c*, so that *ωnmp* reduces to *ω υ* <sup>2</sup> <sup>¼</sup> *<sup>π</sup> a* <sup>2</sup> *<sup>m</sup>*<sup>2</sup> <sup>þ</sup> *<sup>n</sup>*<sup>2</sup> <sup>þ</sup> *<sup>p</sup>*<sup>2</sup> ð Þ. Thus, all combinations of integers that have the same value of *<sup>m</sup>*<sup>2</sup> <sup>þ</sup> *<sup>n</sup>*<sup>2</sup> <sup>þ</sup> *<sup>p</sup>*<sup>2</sup> will have the same frequency and the modes will be degenerate.

#### **5. The Poynting vector of the microwave fields inside the cooking chamber**

Remembering that *S* ! ð Þ¼ *r*, *t E* ! ð Þ� *r*, *t H* ! ð Þ *r*, *t* , taking the expressions of *E* ! and *H* ! Inside the cooking chamber, then we obtain *S* !ð Þ¼ *<sup>r</sup>*, *<sup>t</sup>* <sup>∣</sup>*E*k*H*<sup>∣</sup> ^ *<sup>k</sup>* <sup>¼</sup> *<sup>ξ</sup>* � *<sup>υ</sup>* � ð Þ *<sup>ε</sup>=*<sup>2</sup> *<sup>E</sup>*<sup>2</sup>^ *k* ¼ *<sup>ξ</sup>* � *<sup>υ</sup>u*^ *k* [25–29]. This result is the general one obtained in any electrodynamic circumstance, of course, and microwave ovens fulfill it. And the average Poynting vector is *Sav* ¼ *Power=Area* ¼ *Energy=Area* � *time*. What these expressions tell us is that microwave energy and microwave power inside the cooking chamber are

traveling-moving, yes energy, and power, between the six walls in stationary wave patterns and in accord with the propagation vector *k* ! and carrying perpendicular to it the *E* ! and *H* ! fields. The microwave power deposited on a surface area of 1 mm<sup>2</sup> is then *Pav* = *Sav.A*. Since *E* ! and *H* ! inside the microwave oven have nodes and anti-nodes, then *S* !ð Þ *<sup>r</sup>*, *<sup>t</sup>* and consequently microwave power, *P r*ð Þ , *<sup>t</sup>* have nodes and anti-nodes at some positions along *x*, *y*, and *z*, and the heating is not uniform due to this standing wave feature of the microwave fields inside the cavity. Experimental results on the standing wave patterns have been reported and nicely agree with the theoretical calculations [30, 31]. Theoretically and experimentally standing microwave patterns are obtained. The reason of the rotating plate is to move in circular fashion the food to be heated and reach a more uniform microwave bathing on the food. Most of the time it is accomplished, but not always, as pizza fans report.

Now that we have a detailed treatment of the electromagnetic fields inside the cooking chamber, we want to develop some expressions for the *E* ! and *H* ! fields traveling on the waveguide from the magnetron toward the resonant cavity.

#### **6. The waveguide in microwave heating systems, TE and TM modes**

In research and technologically bound situations, the resonant cavities we saw above are feed with microwaves by means of waveguides connecting the source to the microwave cavity, see **Figures 2** and **4**. We can think of a waveguide as constructed from a cavity by taking the � *z* walls to infinity; then, the trapped stationary waves in the cavity can now travel indefinitely toward � infinity as plane waves. As soon as we start taking the �*z* walls to infinity, we start liberating boundary conditions and in that dimension we are allowing free traveling waves. The remaining walls at *x* = 0, *a*, and *y* = 0, *b* continue limiting our bouncing waves along these dimensions. We will continue taking the bounding surfaces as perfect conductors. A question to ask at this point is; Is it possible to transfer electromagnetic energy along a *waveguide*, that is, a tube with open ends? From everyday experience, we already know that this is possible from the simple fact that we can see through long straight pipes. So, the answer is yes, but: How is this carried out? Solutions to the wave equations have the answer, but first we review quickly boundary conditions on perfect conductors.

#### **7. Boundary conditions at the surface of a perfect conductor**

We recall that a *perfect conductor* is one for which *σ* ! ∞, more precisely, one for which the ratio *Q* = *εω*/*σ* ! 0. *Q* ≤ð Þ 1*=*50 ≪ 1 for common metals even at very high frequencies so that *Q* = 0 should be a good first approximation for metallic boundaries. Plane waves traveling freely along the *z* direction take the form *E x*ð Þ , *y* exp ½ � *i*ð Þ *ωt* � *kz* , where the *E x*ð Þ , *y* part has to be found but we already know that fulfills boundary conditions at the metallic walls. We remember that *δ* = (2/ *μσω*) 1/2 for a good conductor so that *<sup>δ</sup>* ! 0 as *<sup>σ</sup>* ! <sup>∞</sup>. Therefore, the electric field is zero at any point in a perfect conductor since the skin depth is zero. Since the tangential components of *E* ! are always continuous, we see that *E* ! *tang* ¼ 0 just outside of the surface. In other words, *E* ! has no tangential component at the surface of a perfect conductor so that *E* ! must be normal to the surface [25–29]. *B* ! inside the conductor is *B* ! ¼ ð Þ *k=ω k* ! � *E<sup>τ</sup>* ! so that *B* ! will also be transverse. Consequently, the transverse component of *B* ! inside will also vanish as *σ* ! ∞. Since *B* ! has no normal component, the boundary condition *B*1*<sup>n</sup>* = *B*2*<sup>n</sup>* implies that *B* ! *norm* ¼ 0 just outside the conductor. Thus, at the surface of a perfect conductor and outside of it, *B* ! has no normal component; that is, it must be tangential to the surface. We see that *all* of the field vectors will be zero inside a perfect conductor. This simplifies greatly the general boundary conditions. To repeat: At the surface of a perfect conductor, *E* ! is normal to the surface and *B* ! is tangential to the surface. To put it another way, *E* ! has no tangential component while *B* ! has no normal component.

#### **8. Propagation characteristics of waveguides**

**Figure 10** shows a waveguide that extends indefinitely in the *z* direction and of arbitrary and constant cross section in the *xy* plane. We take the boundary walls as perfect conductors and the interior of the cavity is filled with a linear nonconducting medium described by *μ*<sup>0</sup> and *ɛ*. If *ψ* is any component of *E* ! or *B* ! , we

know that it satisfies the scalar wave equation ∇<sup>2</sup> *<sup>ψ</sup>* � <sup>1</sup> *υ*2 *∂*2*ψ <sup>∂</sup>t*<sup>2</sup> ¼ 0 where *υ*² = l/*μɛ* and *υ* would be the speed of a plane wave in the medium. Again, by separation of variables we easily find *ψ*ð Þ¼ *x*, *y*, *z*, *t ψ*0ð Þ *x*, *y e i k*ð Þ *gz*�*ω<sup>t</sup>* .

We note that this is *not* a plane wave since the amplitude *ψ*<sup>0</sup> is not a constant but depends on *x* and *y*, the cross section [28, 29]. The quantity *kg* is the *guide propagation constant, or simply the kz constant of separation of the Z(z) component* of the whole solution and can be written as *kg* = 2*π*/*λ<sup>g</sup>* here *λ<sup>g</sup>* is the guide wavelength, that is, the spatial period along the guide, the *z* axis.

#### **Figure 10.**

*A waveguide made of a perfect conductor with arbitrary and constant cross section. A set of propagation vectors* k*1,* k*2,* k*3, etc., are shown to impinge on different points on the metallic walls and reflect back following Snell law. Transmission is not depicted since perfect conducting walls are considered, and hence, the skin depth tends to zero, which implies zero transmission.*

Continuing with the separation of variables now for the *x* and *y* variables, we obtain again a Helmholtz equation in 2D *<sup>∂</sup>*2*ψ*<sup>0</sup> *<sup>∂</sup>x*<sup>2</sup> <sup>þ</sup> *<sup>∂</sup>*2*ψ*<sup>0</sup> *<sup>∂</sup>y*<sup>2</sup> <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> *<sup>c</sup>ψ*<sup>0</sup> <sup>¼</sup> 0, where *<sup>k</sup>*<sup>2</sup> *<sup>c</sup>* <sup>¼</sup> *<sup>k</sup>*<sup>2</sup> <sup>0</sup> � *<sup>k</sup>*<sup>2</sup> *g* and *<sup>k</sup>*<sup>0</sup> <sup>¼</sup> *<sup>ω</sup> <sup>υ</sup>* <sup>¼</sup> <sup>2</sup>*<sup>π</sup> λ*0 . Writing *kc* <sup>¼</sup> <sup>2</sup>*<sup>π</sup> <sup>λ</sup><sup>c</sup>* we obtain a wavelength relation <sup>1</sup> *λ*2 *c* <sup>¼</sup> <sup>1</sup> *λ*2 0 � <sup>1</sup> *λ*2 *g* . Therefore, we have found for a waveguide that we will get wave propagation *only* if *k*<sup>0</sup> > *kc*, or *λ*<sup>0</sup> < *λc*. For this reason, *λ<sup>c</sup>* is called the *cutoff wavelength*. It is very common to state this result in terms of a cutoff frequency *<sup>ω</sup><sup>c</sup>* defined by *kc* <sup>¼</sup> *<sup>ω</sup><sup>c</sup> <sup>υ</sup>* so that kg<sup>2</sup> can also be written as *k*<sup>2</sup> *<sup>g</sup>* <sup>¼</sup> <sup>1</sup> *<sup>υ</sup>*<sup>2</sup> *<sup>ω</sup>*<sup>2</sup> � *<sup>ω</sup>*<sup>2</sup> *c :* Then, wave propagation is possible only if *ω* > *ω*<sup>2</sup> , that is, if the applied frequency is greater than the cutoff frequency.

#### **9. Rectangular guide**

This guide has a rectangular cross section of sides *a* and *b*, which we take to be located in the *xy* plane. It is relevant to mention that for either type of mode, TE or TM, we have to solve an Helmholtz equation and apply boundary conditions as aforesaid. We continue using separation of variables and write *ψ*0(*x*, *у*) = *X*(*x*)*Y*(*y*); then, the same arguments as used in resonant cavity section above lead us to the separated equations

$$\frac{1}{X}\frac{\partial^2 X}{\partial x^2} = -\frac{1}{Y}\frac{\partial^2 Y}{\partial y^2} - k\_c^2 = \text{const.} = -k\_1^2 \tag{20}$$

so that, (*d*<sup>2</sup> *X*/*d x*<sup>2</sup> ) + *k*<sup>2</sup> <sup>1</sup>*<sup>X</sup>* = 0 and (*d*<sup>2</sup> *Y*/*d y*<sup>2</sup> ) + *k*<sup>2</sup> <sup>2</sup>*Y* = 0 the separation constants have been selected with minus sign since the solutions should be periodic. Hence, *k*2 <sup>1</sup> <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> <sup>2</sup> <sup>¼</sup> *<sup>k</sup>*<sup>2</sup> *<sup>c</sup>* is the dispersion relation in terms of the constants of separation for this 2D differential equation. Solving these in terms of sine and cosine functions, we find that *ψ*0ð Þ¼ *x*, *y* ð Þ *C*<sup>1</sup> sin *k*1*x* þ *C*<sup>2</sup> cos *k*1*x* ð Þ *C*<sup>3</sup> sin *k*2*y* þ *C*<sup>4</sup> cos *k*2*y* , where the C's are constants of integration. This expression for *ψ*<sup>0</sup> contains a total of four constants.

Let us calculate for ТЕ *modes*. Here, we set E*<sup>z</sup>* ¼ 0 and write

$$\mathcal{H}\_{\mathbf{z}} = (C\_1 \sin k\_1 \mathbf{x} + C\_2 \cos k\_1 \mathbf{x})(C\_3 \sin k\_2 \mathbf{y} + C\_4 \cos k\_2 \mathbf{y})\tag{21}$$

With E*<sup>z</sup>* ¼ 0, and with ∇ � *E* ! ¼ �*∂<sup>B</sup>* ! *=*∂t, we find that when we substitute H*<sup>z</sup>* into *Ex* and *Ey* coming from ∇ � *E* ! and after some algebra [28].

$$\mathcal{E}\_{\mathbf{x}} = \frac{i\alpha\mu k\_{2}}{k\_{\varepsilon}^{2}} (\mathbf{C}\_{1}\sin k\_{1}\mathbf{x} + \mathbf{C}\_{2}\cos k\_{1}\mathbf{x})(\mathbf{C}\_{3}\sin k\_{2}\mathbf{y} - \mathbf{C}\_{4}\cos k\_{2}\mathbf{y})\tag{22}$$

$$\mathcal{E}\_{\mathcal{V}} = \frac{i\alpha\mu k\_1}{k\_\varepsilon^2} (\mathcal{C}\_1 \cos k\_1 \mathcal{x} - \mathcal{C}\_2 \sin k\_1 \mathcal{x}) (\mathcal{C}\_3 \sin k\_2 \mathcal{y} + \mathcal{C}\_4 \cos k\_2 \mathcal{y}) \tag{23}$$

From the boundary conditions E*x*ð Þ¼ *у* ¼ 0 0 and E*x*ð Þ¼ *у* ¼ *b 0* and similarly, from the boundary conditions that E*y*ð Þ¼ x 0 must satisfy at *x* = 0 and *x* = *a*, then evaluating first for the zero values of *x* and *у*, we get

$$\mathcal{E}\_{\mathbf{x}}(\mathbf{x}, \mathbf{0}) = \mathbf{0} = \frac{i\alpha\mu k\_2 C\_3}{k\_c^2} (\mathbf{C}\_1 \sin k\_1 \mathbf{x} + \mathbf{C}\_2 \cos k\_1 \mathbf{x}) \tag{24}$$

$$\mathcal{E}\_{\mathcal{Y}}(0,\mathcal{y}) = \mathbf{0} = -\frac{i\alpha\mu k\_1 \mathbf{C}\_1}{k\_c^2} (\mathbf{C}\_3 \sin k\_2 \mathbf{y} + \mathbf{C}\_4 \cos k\_2 \mathbf{y}) \tag{25}$$

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

Notice that we have here established a 2D homogeneous Sturm-Liuville problem and we expect to obtain as solutions eigenvalues and eigenfunctions. From the aforesaid boundary conditions, we must have *C*<sup>1</sup> = 0 and *C*<sup>3</sup> = 0. Therefore, at this stage, Ex, Ey, H*<sup>z</sup>* have simplified to

$$\mathcal{H}\_{\mathbf{z}} = \mathbf{C}\_2 \mathbf{C}\_4 \cos k\_1 \mathbf{x} \cos k\_2 \mathbf{y} \tag{26}$$

$$\mathcal{E}\_{\mathbf{x}} = -\frac{i\alpha\mu k\_2 C\_3}{k\_c^2} C\_2 C\_4 \cos k\_1 \mathbf{x} \sin k\_2 \mathbf{y} \tag{27}$$

$$\mathcal{E}\_{\mathcal{Y}} = \frac{i\alpha\mu k\_1 C\_1}{k\_c^2} C\_2 C\_4 \sin k\_1 \propto \cos k\_2 \text{y} \tag{28}$$

We still have boundary conditions to satisfy at the two remaining faces. We see that the requirement E*x*ð Þ¼ *x*, *b* 0 leads to sin *k*2*b* = 0 so that *k*2*b* = *nπ* where *n* is an integer. Similarly, E*y*ð Þ¼ a, *y* 0 gives the condition that *k*1*a* = *mπ* with *m* an integer. Thus, we have found the eigenvalues *<sup>k</sup>*<sup>1</sup> <sup>¼</sup> *<sup>m</sup><sup>π</sup> <sup>a</sup>* and *<sup>k</sup>*<sup>2</sup> <sup>¼</sup> *<sup>n</sup><sup>π</sup> <sup>b</sup>* , these are the eigenvalues of the solution. So that *k*<sup>2</sup> <sup>1</sup> <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> <sup>2</sup> <sup>¼</sup> *<sup>k</sup>*<sup>2</sup> *<sup>c</sup>* shows that the allowed values of *kc* <sup>2</sup> are *k*<sup>2</sup> *<sup>c</sup>* ¼ *k*2 *c mnπ*<sup>2</sup> *<sup>m</sup> a* � �<sup>2</sup> <sup>þ</sup> *<sup>n</sup> b* � �<sup>2</sup> h i. The cutoff wavelengths and frequencies can now be found by using *kc* <sup>2</sup> above into our *λ<sup>c</sup>* <sup>2</sup> and *ω<sup>c</sup>* <sup>2</sup> equations. The corresponding guide propagation constants are

$$k\_{\rm g}^2 = \left(\frac{2\pi}{\lambda\_{\rm g}}\right)^2 = k\_0^2 - \pi^2 \left[ \left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2 \right] \tag{29}$$

The only quantity left undetermined is the arbitrary amplitude *C*2*C*<sup>4</sup> of H*z*. If we set *C*2*C*<sup>4</sup> = *H*0, then we find that the amplitudes of a general ТЕ mode in a rectangular guide are as follows:


where *kc* and *kg* are as above. Multiplying each of these amplitude factors by the wave propagation term we get, for example, for the *Ex* field

$$E\_{\mathbf{x}} = -\frac{i\alpha\mu}{k\_c^2} \left(\frac{n\pi}{b}\right) H\_0 \cos\left(\frac{m\pi\chi}{a}\right) \sin\left(\frac{n\pi\chi}{b}\right) e^{i\left(k\_\pi x - at\right)}\tag{30}$$

Since �*<sup>i</sup>* <sup>¼</sup> *<sup>e</sup>*�*i*ð Þ <sup>1</sup>*=*<sup>2</sup> *<sup>π</sup>*, the exponential factor can be written exp *i kgz* � *<sup>ω</sup><sup>t</sup>* <sup>þ</sup> <sup>1</sup> <sup>2</sup> *<sup>π</sup>* � � � � , which shows that *Ex* leads *Hz* in time by 90°. Similarly, *Hx* and *Hy* lead *Hz* by 90° while *Ey* lag *Hz* by this same amount.

We now particularize to the simplest case which is also the most used. The *TE*<sup>10</sup> *mode*, we set m = 1 and *n* = 0 and we particularize the above equations for these particular values of *m* and *n*, we show now without calculations that:

$$k\_{\mathfrak{g}} = \left[ \left( \frac{a}{\nu} \right)^2 - \left( \frac{\pi}{a} \right)^2 \right]^{1/2}.$$

The field amplitudes are

$$\mathcal{E}\_{\mathcal{Y}} = ia\mu \left(\frac{a}{\mathfrak{x}}\right) H\_0 \sin\left(\frac{\pi\infty}{a}\right) \tag{31}$$

$$\mathcal{H}\_{\mathfrak{x}} = -ik\_{\mathfrak{g}} \left( \frac{a}{\mathfrak{x}} \right) H\_0 \sin \left( \frac{\pi \mathfrak{x}}{a} \right) \tag{32}$$

$$\mathcal{H}\_{\mathfrak{z}} = H\_0 \cos \left( \frac{\pi \infty}{a} \right) \tag{33}$$

While E*<sup>x</sup>* ¼ E*<sup>z</sup>* ¼ 0 and H*<sup>y</sup>* ¼ 0. Inserting these amplitudes into the complete *E* ! and *H* ! field expressions above and taking the real parts of the resulting expressions, we find the only nonzero field components to be

$$E\_{\mathcal{V}} = -H\_0 a \mu \left(\frac{a}{\pi}\right) \sin\left(\frac{\pi \chi}{a}\right) \sin\left(k\_{\mathcal{S}} z - a\epsilon\right) \tag{34}$$

$$H\_{\mathbf{x}} = H\_0 k\_{\mathbf{g}} \left( \frac{a}{\pi} \right) \sin \left( \frac{\pi \infty}{a} \right) \sin \left( k\_{\mathbf{g}} z - a t \right) \tag{35}$$

$$H\_x = H\_0 \cos\left(\frac{\pi x}{a}\right) \cos\left(k\_\mathcal{g} z - at\right) \tag{36}$$

We see that the values of the *Ey* are independent of *y*; hence, the electric field lines are straight lines with constant magnitude at a given value of *x* but with a magnitude that does vary with *x* and is a maximum at the center where *x* = (*a*/2). The lines of *Hx* are straight with their maximum value at the center as well. The value of *Hz*, on the other hand, is zero in the center as has opposite signs on the two sides of the center.

TM *modes*. In this case, we set H*<sup>z</sup>* ¼ 0 and set E*<sup>z</sup>* equal to the expression for *ψ*<sup>0</sup> given above; hence, ∇ � *E* ! ¼ �*∂<sup>B</sup>* ! *=∂t* is again applicable. This case is actually simpler because E*<sup>z</sup>* can be a tangential component and must vanish for *x* ¼ 0 and *a* and *y* ¼ and *b*. We have again an homogeneous Sturm-Liouville problem and expect eigenvalues and eigenfunctions. Proceeding in the same manner as before, we see that we must now have *C*<sup>2</sup> = *C*<sup>4</sup> = 0, while *k*1, *k*2, and *kc* are given, again as above. Thus, the TE and TM modes of a rectangular waveguide have the same set of cutoff wavelengths, the same eigenfrequencies, and cutoff frequencies; the field configurations can be expected to be different however. Setting *C*1*C*<sup>3</sup> = *E*0, we find that (21) gives the starting point for the TM calculation to be <sup>E</sup>*<sup>z</sup>* <sup>¼</sup> *<sup>E</sup>*<sup>0</sup> sin *<sup>m</sup>π<sup>x</sup> a* sin *<sup>n</sup>π<sup>y</sup> b* . We now use this E*<sup>z</sup>* to calculate the rest of the field amplitudes following the above procedure. We note that *m* = *n* = 0 makes E*<sup>z</sup>* and then all the other field components, zero; thus, there is no TM00 mode. Furthermore, if *m* = 0 or *n* = 0, E*<sup>z</sup>* ¼ 0 and all of the fields are zero. Thus, it is not possible to have a TM*m*<sup>0</sup> or TM0*<sup>n</sup>* mode, in contrast to the TE case.

We have now calculated in detail the electric and magnetic fields that propagate in rectangular waveguides as the ones shown in **Figures 1(B), 2(A)**, and **3(C)**. The field patterns are stationary wave patterns in the *x*–*y* direction and traveling waves along the *z* direction as given by Eqs. (30)–(36).

Let us proceed now to the last of the physical components of a microwave heater, the very source of 1000 Watts microwaves.

#### **10. Radiation of accelerated point charges in klystrons and magnetrons**

Klystrons and magnetrons produce microwaves that carry power; typically, klystrons are used when little power is needed, from 1 watt to milliwatts and even

#### *Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

microwatts. Magnetrons are used in higher-power applications, 1000 Watts, or more. Clearly, magnetrons are better suited for microwave heating. Both rely on electrons being accelerated (these electrons are labeled *em*) and made move in periodic trajectories inside cylindrical chambers. Both devices are shown in **Figure 11**. Notice the motion of electrons in them. Straight trajectories in klystrons, *w*(*t*), **Figure 11(A)**, and curved trajectories, *Ç*(*t*), in magnetrons, see **Figure 11(B)**. To expose relevant physics of accelerated electrons, em, produced in klystrons and Magnetrons is to describe the *E* ! *rad* and *B* ! *rad* microwave radiation fields produced inside their structures and from these, the Poynting vector, *S* ! *r* !, *t* <sup>¼</sup> *<sup>E</sup>* ! *rad* � *H* ! *rad* that describes flux of such energy through space.

A microwave power, *Prad* ¼ *S* ! � *Area*, comes with this traveling energy. For klystrons, the accelerated electrons travel along straight lines, inside vacuum tubes, back and forth, due to voltage differences, Δ*V*<sup>12</sup> ≥ 860 Volts, applied at the ends of the cylindrical tube (chamber), see **Figure 11(A)**. So acceleration is linear and is *a* !ð Þ¼ *<sup>z</sup>*, *<sup>t</sup> d v*!ð Þ*<sup>z</sup>=dt* <sup>¼</sup> *<sup>d</sup>*<sup>2</sup> *w* !ð Þ *<sup>z</sup>*, *<sup>t</sup> dt*<sup>2</sup> ¼ *w*€ !ð Þ *<sup>z</sup>*, *<sup>t</sup>* , in which *<sup>a</sup>* ! <sup>¼</sup> *<sup>w</sup>*€ ! is parallel to *v* ! and parallel to the tube axis, *z* !, see **Figure 11(A)**, and the acting force producing such acceleration is *F* ! ¼ *eE* ! ¼ *e*ð Þ �∇*V*<sup>12</sup> *:* For magnetrons, the trajectories of the accelerated electrons are wavy circular with average radius *a* ≤ *r* ≤ *b*, as shown in **Figure 11(B)** and **(C)**. The wavy *ç* ! *r* !, *t* trajectories of the accelerated electrons in magnetrons are the effect of a combined magnetic force *F* ! *mag* <sup>¼</sup> *<sup>q</sup>* \_ *ç* ! ð Þ*<sup>t</sup> xB*^*ez* and the total electric force between these electrons and the charges located in pairs along the *b* radius, *σ* � and � *Q* at the cathode. What we have now is, charged particles, *em*, moving along trajectories, *w* !ð Þ *<sup>z</sup>*, *<sup>t</sup>* , in klystrons, and *<sup>ç</sup>* !ð Þ *z*, *t* , in magnetrons, both have velocities \_ *w* ! ð Þ *<sup>z</sup>*, *<sup>t</sup>* , \_ *ç* ! ð Þ *<sup>z</sup>*, *<sup>t</sup>* , and accelerations, *<sup>w</sup>*€ !ð Þ *<sup>z</sup>*, *<sup>t</sup>* , € *ç* ! ð Þ *<sup>z</sup>*, *<sup>t</sup>* . Charged particles in motion produce electric potentials and electromagnetic fields just as static charges do,

#### **Figure 11.**

*Microwave sources, reflex klystron, and magnetron. (A) The basics of a klystron that produces accelerated electrons through an alternating electric potential difference Δ*V*12(*ωt*), these* em *travel the distance* d*; then, the acceleration is reversed,* em *travel to the left now, and this repeats thousands of times at a GHz frequency. (B) In a magnetron hot electrons ejected from a central cathode, travel in circular-wavy trajectories inside a cylinder due to the Lorentz force F*! <sup>¼</sup> *e E*! þ *υ* !ð Þ*t xB*^*ez , where <sup>υ</sup>* !ðÞ¼ *<sup>t</sup> <sup>∂</sup> <sup>ç</sup>* ! *r* !, *t <sup>=</sup>∂<sup>t</sup>* <sup>¼</sup> \_ *ç* ! *r* !, *t is the velocity of the* em *electrons, E*! *is the total electric field due to the perimetral charges (+,* �*), (+,* �*), (+,* �*), and the central* �Q *charge. B*! *is a constant magnetic field (from a magnet) applied along the* ^*ez axis. These two forces combined produce the curved-wave trajectory ç* ! *r* !, *t . (C) A complete diagram of the magnetron structure with the constant magnetic field B*^*ez, the charge distribution (proper of magnetrons) that produces a total E*! *field and the curved electron trajectories ç* ! *r* !, *t .*

#### *Electromagnetic Wave Propagation for Industry and Biomedical Applications*

#### **Figure 12.**

*A moving charged particle following a trajectory* w*(*tr*).* ∣*r* !‐*w* !ð Þ <sup>t</sup>*<sup>r</sup>* <sup>∣</sup> *is the distance the "radiated field" from the moving electron must travel, and (*<sup>t</sup> � tr*) is the time it takes to make the trip, we shall call w*!ð Þ <sup>t</sup>*<sup>r</sup> the retarded position of the charge,* s ! *is the vector distance from the retarded position to the point the radiated electromagnetic wave arrived "to us" (now, at our time* t*2), which is at r*!*, clearly* s ! <sup>¼</sup> *<sup>r</sup>* !‐*w* ! ð Þ <sup>t</sup>*<sup>r</sup> .*

except that here we have to calculate retarded potentials and retarded fields. For single charged particles, the resulting potentials are the well-known Lienard-Wiechert potentials [26–29, 32]. We present them here now. We take an accelerated electron moving in a general trajectory given by *ç* ! *r* !, *t* � �, or *<sup>w</sup>*(*r*,*t*) � position of *<sup>q</sup>* at time *t*. Now, *V r*!, *t* � � <sup>¼</sup> <sup>1</sup> 4*πϵ*<sup>0</sup> Ð *<sup>ρ</sup> <sup>r</sup>* !0 , *tr* � � ? *dτ*<sup>0</sup> gives the electric potential at *r* at time *t* (**Figure 12**) [2, 26–29]. The retarded integration is not trivial, and the retardation in the *q=*? term in the potential aforesaid throws in a factor *<sup>q</sup>* 1�s !�<sup>v</sup> !*=c* , where v! is the velocity of the charge at the retarded time, and s ! is the vector from the retarded position to the point *r* ! where we are standing and measuring [24, 26–29, 32]. Then, Ð *ρ r* !0 , *tr* � �*dτ*<sup>0</sup> <sup>¼</sup> *<sup>q</sup>* 1�s !�<sup>v</sup> !*=c* . It follows, then, that *V r*!, *t* � � <sup>¼</sup> <sup>1</sup> 4*πϵ*<sup>0</sup> *qc* s*c*�s !� *<sup>v</sup>* ! ð Þ. Meanwhile, since the current density of a rigid object is *J* ! ¼ *ρ υ* !, we also have *A* ! *r* !, *t* � � <sup>¼</sup> *<sup>μ</sup>*<sup>0</sup> 4*π* Ð *<sup>ρ</sup> <sup>r</sup>* !0 , *tr* � �<sup>v</sup> !ð Þ *tr* <sup>s</sup> *<sup>d</sup>τ*<sup>0</sup> <sup>¼</sup> *<sup>μ</sup>*<sup>0</sup> 4*π* v ! ? Ð *ρ r* !0 , *tr* � �*dτ*<sup>0</sup> . Or *A* ! *r* !, *t* � � <sup>¼</sup> *<sup>μ</sup>*<sup>0</sup> 4*π qc*v ! ?*c*�? !� *<sup>v</sup>* ! <sup>¼</sup> <sup>v</sup> ! *<sup>c</sup>*<sup>2</sup> *V r*!, *t* � �. These are the famous Lienard-Wiechert potentials for a moving point charge. By using *E* ! ¼ �∇<sup>V</sup> � *<sup>∂</sup><sup>A</sup>* ! *=∂t* and *B* ! ¼ ∇ � *A* ! , the corresponding fields are evaluated. It seems to us that only two authors, Jefimenko and Griffiths, give detailed derivation of these fields. The differential operations should be carried out with great care as these authors do, and we refer to those calculations and just take their results here:

$$\overrightarrow{E}\left(\overrightarrow{r},t\right) = \frac{q}{4\pi\epsilon\_0} \frac{\overrightarrow{r}}{\left(\overrightarrow{r}\cdot\overrightarrow{u}\right)^3} \left[\left(c^2 - \nu^3\right)\overrightarrow{u} + \overrightarrow{r}\times\left(\overrightarrow{u}\times\overrightarrow{a}\right)\right] = \overrightarrow{\mathbf{E}}\_{\text{vel}} + \overrightarrow{\mathbf{E}}\_{\text{accl}}\tag{37}$$

where *u* ! <sup>¼</sup> *<sup>c</sup>* ^ s ! � *<sup>v</sup>* !, and, very importantly, E! vel *<sup>α</sup>* <sup>1</sup>*=*?<sup>2</sup> and E! accel *α* ?. And the magnetic field is

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

!

$$
\overrightarrow{B}\left(\overrightarrow{r},t\right) = \frac{1}{c}\overrightarrow{\sigma} \times \overrightarrow{E}\left(\overrightarrow{r},t\right) \tag{38}
$$

!

*B* follows the same time dependence as *E :* The first term in *E* ( *r* !, *t*) is called the **velocity field**, and the triple cross-product is called the **acceleration field**. With these potentials and Jefimenko fields, we are now in the position to describe more quantitatively the radiation produced in klystrons and magnetrons. Hence, the accelerated electrons, *em*, inside these devices produce *V* and *A* ! potentials and *E* ! and *B* ! fields. In klystrons, the radiation fields are, as they are, captured by the mouth of a waveguide and send to a resonant cavity in which they produce standing patterns of stationary microwaves for their use.

!

Finally, in magnetrons, the perimetral charges, *σ* � experience Lorentz forces due to these Jefimenko fields, *F* ! <sup>¼</sup> *<sup>q</sup>*<sup>∓</sup> *<sup>E</sup>* ! *<sup>J</sup>* <sup>þ</sup> \_ *ç* !ð Þ*t xB* ! *J* ; hence, these charges move inside the conducting core behind radius b and around the cylindrical cavities, see **Figure 9(C)**, and cut from the solid metal (usually copper). These moving charges, in turn, produce their own retarded potentials, *Vσ*(*wt*), *A* ! *<sup>σ</sup>*ð Þ *wt* and fields, *E* ! *<sup>σ</sup>*ð Þ *wt* and *B* ! *<sup>σ</sup>*ð Þ *wt* . We end up with total fields, *E* ! *<sup>t</sup>*ð Þ *wt* and *B* ! *<sup>t</sup>*ð Þ *wt* , inside the magnetron space, including the cylindrical cavities (eight of them most of the time) behind the radius *b*. These cylindrical cavities are there, precisely, to trap microwaves in them and due to their perfect conducting walls, *E* ! *tot*ð Þ *wt* and *B* ! *tot*ð Þ *wt* reflected from them with almost no losses, and so these cavities sustain stationary microwave patterns of cylindrical geometry. The same process takes place in the eight cylindrical cavities distributed along the perimeter of radius b. With a simple wire antenna, microwaves are taken out of these cavities and sent to the entrance of the waveguide; then, these microwaves travel the short distance inside the waveguide and end up in the cooking chamber of the microwave oven; hence, our coffee absorbs so much the energy of these microwaves; the electric dipoles in the water vibrate and jiggle; frenetically, at 2.45 GHz, in a few seconds our coffee is hot and ready to drink.

#### **11. Conclusions**

In this chapter, detailed electrodynamic descriptions of the fundamental workings of microwave heating devices were given. We analyzed one by one the principal components of a microwave heater; the cooking chamber, the waveguide, and the microwave sources, either klystron or magnetron. The boundary conditions at the walls of the resonant cavity and at the interface between air and the surface of the food were stressed. It was shown how relevant the boundary conditions are to understand how the microwaves penetrate the nonconducting, electric polarizable specimen. In addition to microwave food, we mentioned the important application of microwaving waste plastics to obtain a good *H*<sup>2</sup> quantity that could be used as a clean energy source for other machines and so contributing to a cleaner planet. We did use Maxwell equations to obtain trapped stationary microwaves in the resonant cavity and traveling waves in the waveguides. We showed 3D plots of a few lower *Ex*, *Ey*, *Ez* modes calculated directly from the solutions obtained here and compared the general trend with experimentally obtained microwave heated patters inside rectangular cavities. The agreement is very good. We did simulate a single electro-magnetic field mode inside a cylindrical cavity in order to contrast with the stationary patterns obtained in rectangular cavities. The radiation processes in klystrons and magnetrons were stated in terms of the accelerated electrons

produced. Then, using the Lienard-Wiechert potentials produced by these electrons, the Jefimenko fields were written. When all these are put together, we understand how a meal or a waste plastic, or an industrial sample, is microwave heated.

### **Author details**

Rafael Zamorano Ulloa Superior School of Physics and Mathematics, IPN, Mexico City, Mexico

\*Address all correspondence to: davozam@yahoo.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Electromagnetism of Microwave Heating DOI: http://dx.doi.org/10.5772/intechopen.97288*

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[30] Kamol S. Three-dimensional standing waves in a microwave oven. American Journal of Physics. 2010;**78**: 492-495. DOI: 10.1119/1.3329286

[31] Steyn-Ross A. Standing waves in a microwave oven. The Physics Teacher. 1990;**28**:474-476. DOI: 10.1119/ 1.2343114

[32] Jefimenko OD. Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields. 2nd ed. New York: Appleton-Century-Crofts; 1966. ISBN: 978-0-917406-08-9

#### **Chapter 7**

## High-Frequency Electromagnetic Interference Diagnostics

*Ling Zhang, Yuru Feng, Jun Fan and Er-Ping Li*

#### **Abstract**

Electromagnetic interference (EMI) is becoming more troublesome in modern electronic systems due to the continuous increase of communication data rates. This chapter reviews some new methodologies for high-frequency EMI diagnostics in recent researches. Optical modules, as a typical type of gigahertz radiator, are studied in this chapter. First, the dominant radiation modules and EMI coupling paths in an explicit optical module are analyzed using simulation and measurement techniques. Correspondingly, practical mitigation approaches are proposed to suppress the radiation in real product applications. Moreover, an emission source microscopy (ESM) method, which can rapidly localize far-field radiators, is applied to diagnose multiple optical modules and identify the dominant sources. Finally, when numerous optical modules work simultaneously in a large network router, a formula based on statistical analysis can estimate the maximum far-field emission and the probability of passing electromagnetic compatibility (EMC) regulations. This chapter reviews a systematic procedure for EMI diagnostics at high frequencies, including EMI coupling path analysis and mitigation, emission source localization, and radiation estimation using statistical analysis.

**Keywords:** Electromagnetic interference, Emission source microscopy, Optical modules, High frequency, Industrial products

#### **1. Introduction**

Electromagnetic interference (EMI) problems are drawing more and more attention in modern electronic devices and systems. Industrial products have to satisfy electromagnetic compatibility (EMC) requirements, such as US Federal Communications Commission (FCC) regulations. However, the increase in data rate and source complexity is making EMI diagnostics more troublesome. For a sophisticated product with various potential radiation modules, investigating the root cause of radiation, main coupling paths, and practical mitigation approaches is challenging. Moreover, in a complicated system with numerous potential highfrequency radiation sources, identifying the dominant trouble-makers and quantifying the total contribution from these sources is a tedious and time-consuming process. This chapter presents a systematic procedure for high-frequency EMI diagnostics in industrial products by reviewing some recently published methodologies. As a typical high-frequency radiation source, optical modules are studied in this chapter.

First, the interior EMI coupling paths and possible mitigation methods of optical modules are studied [1–6]. The internal mechanism can be analyzed to alleviate the radiation problem at the design stage or propose mitigation solutions. Building fullwave simulation models is a standard method to understand the behind physics. However, it is challenging to run reliable full-wave simulations for intricate structures. The adopted strategy in [1, 2] is to correlate the total radiated power (TRP) in simulation and measurement to ensure a reliable simulation model. Based on the simulation model, the EMI coupling paths are also investigated. Besides, a concept of energy parcels and their trajectories can provide a more intuitive visualization of the coupling paths. Eventually, according to the analysis result of the EMI coupling paths, mitigation solutions are proposed in both simulation and measurement to suppress the EMI coupling paths, which can effectively reduce the far-field radiation to meet EMC regulations.

For a large system with multiple radiators, identifying the dominant sources is a vital but tedious process. Near-field scanning is a standard method for EMI diagnostics [7, 8]. However, detecting near field also includes evanescent waves that do not contribute to far-field radiation. Under some circumstances, near-field probes cannot reach close enough to all locations and components due to mechanical limitations. Emission source microscopy (ESM) is a scanning technique to localize sources contributing to far-field radiation [9]. Sparse ESM [10] is an improved ESM method that identifies the dominant sources through sparse scanning samples. Therefore, sparse ESM is a more efficient method than near-field scanning to determine the main contributor for far-field radiation at high frequencies. In [10], the sparse ESM technique is used to localize the dominant sources among multiple optical modules rapidly. Also, in [11], an absorbing material is utilized to mitigate radiation from the identified sources.

Another problem with large amounts of radiators in a complex system is the required hardware and testing time for EMC regulation tests. Hence, the authors in [12, 13] derived a mathematical relation using statistical analysis to fast predict the maximum radiation from a large system with numerous similar sub-systems, with a level of certainty provided. Also, measurements were performed to validate the estimation.

This chapter provides an insightful review of EMI diagnostic approaches in different aspects at high frequencies, including source modeling, coupling path analysis and visualization, EMI mitigation, source localization, and emission level prediction. The remaining sections of this chapter are organized as follows. In Section 2, the EMI coupling path analysis and mitigation approaches for optical modules are elaborated. The emission source microscopy (ESM) algorithm is then introduced and applied to optical modules in Section 3. In Section 4, the method for estimating the emission level from multiple radiators is explained. Finally, a conclusion is provided.

#### **2. EMI coupling paths analysis and mitigation**

#### **2.1 Modeling optical sub-assembly (OSA) module**

The diagram of a typical optical link is shown in **Figure 1** [1]. The cage connector and the transceiver module are enclosed by the connector shield cage located on the line card PCB. The cage connector, through which the signal is transmitted, connects the line card PCB and the transceiver circuit board. The signal sent to the transceiver circuit board is further transmitted to the silicon photonic subassembly. The electrical-to-optical (and vice versa) interface assembly converts the electrical signal into an optical signal, which is subsequently transferred to other devices through an optical fiber cable. The cage connector, the optical transceiver module,

#### **Figure 1.**

*Structure diagram of the optical transceiver module [1].*

**Figure 2.**

*Optical sub-assembly test board. (a) Experimental test setup. (b) the corresponding simulation model [1].*

#### **Figure 3.**

*(a) The simulation model of the test board with the connector only. (b) TRP comparison between measurement and simulation for the test board with the connector only [2].*

and the optical cable ferrule were identified as the primary radiation contributors [3, 4]. The aluminum ferrule surrounding the optical fiber cable forms a radiating antenna that is causing the most EMI problems in meeting regulatory requirements for optical transceiver modules.

The optical sub-assembly (OSA) module was modeled in full-wave simulations [2]. The real structure and simulation model for the OSA module is shown in **Figure 2**. There are mainly three parts in the OSA module to be investigated: the connector, the flex cables, and the electrical-to-optical interface assembly. Firstly, the simulation model for the OSA module needs to correlate well with measurements. The adopted strategy [2] was to gradually increase the model complexity and verify the model accuracy step by step. TRP comparison was used for model validation. **Figures 3**–**5** show the TRP comparison between simulation and measurement for different models. In **Figure 3**, only the connector was kept. In **Figure 4**, the flex cables were included in the model. The entire OSA module was considered in **Figure 5**.

#### **Figure 4.**

*(a) The simulation model of the test board with the long flex PCB. (b) TRP comparison between measurement and simulation for the test board with the long flex PCB [2].*

**Figure 5.** *TRP comparison between measurement and simulation for the test board with OSA model as shown in Figure 2 [2].*

In **Figures 3**–**5**, the TRP results of simulation and measurement agree reasonably well, indicating the accuracy of the simulation model. Several experiments were designed to quantify the contributions from different parts of the model by utilizing an absorbing material [2], as shown in **Figure 6**. This systematic investigation concludes that the connector and the flex cables are two dominant radiation sources above 10 GHz. In comparison, the electrical-to-optical interface assembly has little contribution to the radiation.

In the OSA module, the connector and the flex cables were diagnosed as the primary radiation contributors above 10 GHz. The structure of the entire optical transceiver module is shown in **Figure 7**, including the OSA module and an enclosure. There are two individual modules in each optical transceiver module – a transmitter optical subassembly (TOSA) and a receiver optical sub-assembly (ROSA) module. Only the TOSA model will be used for analysis since the interior structure of the ROSA cannot be obtained due to confidentiality. A simulation model was built to place the OSA module within an enclosure to mimic the actual design and analyze the coupling paths from the OSA module to the external EMI radiation. This type of optical transceiver module has two working modes at 25.78 GHz and 27.95 GHz. The following EMI analysis will concentrate on 25.78 GHz. The mechanism at 27.95 GHz is similar to 25.78 GHz and hence is omitted.

#### **2.2 Coupling paths analysis by simulations**

**Figure 8(a)** shows a simulation model in which an OSA module is inserted into a shielding enclosure without the enclosure top. One signal trace was excited with a

*High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

#### **Figure 6.**

*Use absorbing material to cover different parts of the OSA module to determine their contribution to the radiation. (a) the entire OSA module. (b) the flex cables. (c) the connector. (d) the electrical-to-optical interface assembly [2].*

#### **Figure 7.**

*Structure diagram of the optical transceiver module [1].*

#### **Figure 8.**

*(a) OSA simulation model only without the enclosure top. (b) Surface current distribution at 25.78 GHz in top view [1].*

lumped port. The surface current under this circumstance is plotted in **Figure 8(b)**. The surface current is mainly distributed over the connector and the flex cables, as expected. There is little current on the electrical-to-optical interface assembly. It does not contribute to the radiation of the OSA module, which has been validated by applying absorbing materials.

Subsequently, an enclosure was added to the model in **Figure 8**, as shown in **Figure 9**. The right end of the module in **Figure 7** is inserted into a cage connector on a line card. The leakage near the cage connector is negligible compared to the leakage from the optical fiber cable in the front. Therefore, in the simulation model **Figure 9(a)**, the enclosure end that should be connected with a line card was shielded with PEC. In this manner, the coupling path and radiation from the optical output end can be focused on and studied.

As illustrated by **Figure 9(b)**, there is a gap between the cylindrical metal port and the enclosure. The optical fiber cable is connected to this port. Moreover, a mechanical handle insertion area has a small gap and can also potentially cause EMI leakage. Experimental work proved these gaps to be the primary leakage points, as will be introduced later.

After the enclosure top is added to the simulation model, the surface current distributions are plotted in **Figure 9(c)**–**(e)**. Compared to the current distribution in **Figure 8(b)**, more current appears in the other places, including the enclosure, the electrical-to-optical interface assembly, and the cylindrical metal port that egresses the shielding enclosure. In **Figure 9(e)**, an evident radiation leakage can be observed from the gap. The simulation comparison between **Figure 9** and **Figure 8** demonstrates that "the enclosure cavity provides an EMI coupling path for propagating modes that can illuminate slots and seams in the OSA enclosure" [1]. The aluminum ferrule of the optical fiber cable inserted into the TOSA port forms a monopole antenna that can be efficiently excited with the current leakage. Typically, a network equipment system has tens of or even hundreds of such monopole antennas, which can cause severe EMI issues in meeting compliance requirements.

#### **Figure 9.**

*(a) A simulation model for the optical transceiver module, enclosed in a complete enclosure. (b) the positions of the handle insertion area and the gap between the cylindrical metal part and the enclosure. (c) Surface current distribution on the OSA module and the enclosure bottom at 25.78 GHz, with the enclosure top being hidden. (d) Surface current distribution on the OSA module and the enclosure top at 25.78 GHz, with the enclosure bottom being hidden. (e) Surface current distribution on the enclosure surface in front view at 25.78 GHz [1].*

#### **2.3 EMI mitigation of optical transceiver modules**

The primary radiation sources and the dominant coupling paths have been determined by using simulation and measurement techniques. In this section, mitigation approaches will be proposed correspondingly to suppress the radiation leakage in both simulation and measurement. The effectiveness of the mitigation methods will, in turn, validate the analyzed coupling paths.

#### *2.3.1 EMI mitigation in simulation*

**Figure 10** shows simulation models with absorbing material being placed at different locations. **Table 1** compares the simulated TRP for the models in **Figure 10** at 25.78 GHz and 27.95 GHz. After adding absorbing material above the flex cables on the underside of the enclosure lid, a TRP reduction of 4–7 dB is achieved at the two frequencies. The TRP is further reduced by 2–3 dB by adding absorbing material to the cylindrical egress of the electrical-to-optical module and the handle insertion areas. Adding absorbing material on the metal surface of the electrical-to-optical module and the cylinder can significantly reduce the TRP by 8–9 dB.

#### *2.3.2 EMI mitigation in measurement*

One chassis with functioning optical transceiver modules did not meet the FCC Class A limit plus a required margin at 25.78 GHz and 27.95 GHz in an EMC test. For example, one measurement showed that one line card with four optical transceiver modules passed the FCC Class A limit by 0.4 dB with no margin typically required in EMC regulations. Based on the analysis result of the dominant coupling paths, some mitigation approaches were implemented in the measurement to suppress the EMI radiation and meet the FCC Class A limit with more margins.

#### **Figure 10.**

*(a) A simulation model with closed enclosure (enclosure top being hidden) and without absorber. (b) a simulation model with a sealed enclosure, an absorbing material of 26 mm 16 mm, and a thickness of 1 mm on the enclosure lid underside above the flex cables. (c) a simulation model with a closed enclosure, with absorbing material of 1 mm thickness on the enclosure top above the flex cables, and to the space between the cylindrical metal part of the electrical-to-optical module and the enclosure, as well as the leakage space on the two handle sides of the enclosure. (d) a simulation model with a closed enclosure and absorbing material with a thickness of 0.5 mm on the metal of the electrical-to-optical interface assembly and the metal cylinder inside the enclosure [1].*

#### *Electromagnetic Wave Propagation for Industry and Biomedical Applications*


#### **Table 1.**

*TRP simulation results of Figure 10 [1].*

#### **Figure 11.**

*EMI mitigation methods in the production hardware. (a) Adding absorbing material inside the enclosure above the flex cables and adding grounding O-rings around the cylindrical metal portion of the electrical-to-optical module. (b) Adding some silver-plated spring around the cylindrical metal and adding absorbing material on the handles on two sides [1].*


#### **Table 2.**

*Mitigation of radiated emissions [1].*

**Figure 11** shows some mitigation methods, such as adding absorbing material, O-rings, and silver-plated spring. **Table 2** shows the EMC test results after applying the mitigation solutions on two line cards with eight optical transceiver modules. Compared with the FCC Class A limit, the largest margin is increased to 15 dB after implementing the mitigations. This outcome corroborates the EMI coupling paths and the mitigation approaches discussed earlier.

A systematic approach has been elaborated to investigate the EMI coupling paths in an optical transceiver module. The procedure includes building simulation models, identifying the dominant radiation modules, analyzing EMI coupling paths through simulations, and finally validating the coupling paths by mitigation in measurements.

The EMI coupling paths in the optical transceiver module can be concluded as follows. The cage connector [4], the connector between the transceiver circuit board and the flex cables, and the flex cables are the dominant radiation sources [1]. *High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

The module enclosure provides a cavity-like structure for the propagating modes to radiate from the gap between the electrical-to-optical module and the enclosure. The aluminum ferrule surrounding the optical fiber can be excited with the leakage current and radiate efficiently like a monopole antenna. **Figure 12** illustrates the concluded coupling paths. For a large equipment rack, the EMI can violate regulatory limits with many tens or hundreds of such modules. Mitigation approaches such as absorbing material and elastomer O-rings can effectively suppress EMI radiation in the actual product applications.

#### **2.4 EMI coupling paths visualization**

#### *2.4.1 Definition of EM energy parcels*

The simulation method in [1] demonstrated the coupling paths, but it did not directly show the coupling paths. Li *et al.* [14, 15] proposed a concept to intuitively visualize coupling paths by utilizing the analogy between the flow of EM energy and fluid flow. The flow of EM energy can be imagined as a certain amount of energy parcels propagating in space. The EM energy flow is defined by the Poynting vector, meaning that the EM energy flow follows the law of conservation of energy. Eq. (1) defines the instantaneous velocity of EM energy parcels.

$$
\overrightarrow{\boldsymbol{\upsilon}}\,\boldsymbol{\upsilon}\prime\_{\boldsymbol{s}}\rangle = \frac{\overrightarrow{\boldsymbol{S}}\,\mathrm{(J/m^{2}s)}\,,\tag{1}
$$

where Vector *S* represents the instantaneous Poynting vector and is given by Eq. (2), and *u* means the total magnetic and electric energy density defined by Eq. (3).

$$
\overrightarrow{\mathcal{S}} = \overrightarrow{E} \times \overrightarrow{H}.\tag{2}
$$

$$
\mu = \mu \frac{\overrightarrow{H} \cdot \overrightarrow{H}}{2} + \varepsilon \frac{\overrightarrow{E} \cdot \overrightarrow{E}}{2}.\tag{3}
$$

The time-averaged velocity of the energy parcels is defined as Eq. (4), which is a constant value.

$$
\overrightarrow{v}\_{av} = \frac{\overrightarrow{S\_{av}}}{u} = \frac{\text{Re}\left[\overrightarrow{S}\right]}{u}.\tag{4}
$$

**Figure 12.** *Summary of the EMI coupling paths in the optical transceiver module [1].*

Therefore, the trajectory of the energy parcels can be acquired by calculating the streamline (tangential line) of the real part of the complex Poynting vector [14, 15]. The trajectories are tracked back from the receiver antenna to visualize the energy path from the transmitter to the receiver.

#### *2.4.2 Apply coupling path visualization to optical modules*

Some researchers applied the trajectory concept of energy parcels to visualize the EMI coupling paths on quad form-factor pluggable (QSFP) modules and propose corresponding mitigation approaches [5, 6]. In [5], an EMI issue related to a QSFP module possessing a heatsink was studied. The issue is that when an optical module is inserted, the heatsink on top of the optical module rises. Thus an air gap is created by the rising heatsink, and the shielding effectiveness (SE) of the QSFP shielding cage is degraded. **Figure 13** describes the measurement setup to quantify the SE of the QSFP shielding cage. There were two reverberation chambers (RC): one side is noisy, and the other side is quiet. A transmitter (Tx) antenna and a receiver (Rx) antenna were placed on the noisy and quiet sides, respectively.

The potential coupling paths related to the rising heatsink are depicted in **Figure 14**. The rising heatsink provides a guiding structure for the propagating waves. The EM waves can penetrate the cage from the path between the heatsink and the cage. This path around the cage guides the EM waves through the cage. Besides, there is a small gap between the cage and the line card PCB so that EM waves can go through the cage from the bottom.

The concept of energy parcels and their trajectories was applied to validate the above hypothesis about the coupling paths [5]. The result of the trajectories is shown in **Figure 15**. It can be observed that the rising heatsink behaves as a guided

**Figure 13.** *Measurement setup for the shielding effectiveness of the optical module [5].*

**Figure 14.** *Potential coupling paths when there is a heatsink [5].*

*High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

**Figure 15.**

*Reversed tracked energy parcels from the receiver antenna (Rx) to the transmitter antenna (Tx). (a) Top view. (b) Side view [5].*

**Figure 16.** *Comparison between the averaged SE of the cage with and without the gasket [5].*

structure for the propagating waves, and the area between the heatsink and the top of the cage contributes as a leakage path.

According to the analysis result using the coupling path visualization, a mitigation approach was applied by placing a window frame gasket between the cage and the heatsink [5]. The change of SE is plotted in **Figure 16**. The SE of the QSFP shielding cage is notably improved by a few decibels over the entire frequency range. This improvement corroborates the EMI coupling paths concluded from the trajectory visualization of energy parcels. Similarly, the same approach was adopted in [6] to investigate the coupling paths for flyover QSFP connectors. Also, corresponding mitigation methods using an absorbing material were demonstrated to work effectively.

#### **3. Emission source microscopy (ESM)**

The emission source microscopy (ESM) method [9] can identify far-field radiation sources by scanning the far field over a plane above a device under test (DUT) and back-propagating the field onto the DUT plane to localize the dominating sources. Both the field magnitude and phase are required for the back-propagation calculation. Therefore, phase measurement is needed. A typical way of measuring the field phase from an active DUT is shown in **Figure 17**. Antenna *B* is the reference antenna with a fixed location for phase measurement. Antenna *A* is the scanning antenna that moves with a scanning robot to acquire the field information at different locations. Antenna *A* and *B* are connected to the channel *A* and *B* of a vector network analyzer (VNA). The VNA operates at the tuned receiver mode and

**Figure 17.** *ESM system setup [10].*

**Figure 18.** *Diagram of ESM algorithm.*

receives signals at channels *A* and *B* simultaneously. The phase difference between *A* and *B* is used as the field phase, while the signal magnitude received by channel *A* is the field magnitude.

#### **3.1 Algorithm description**

**Figure 18** illustrates the ESM algorithm. There is a scanning plane and a source plane, which are parallel to the *x-y* plane. The distance between them is *h*. The far field, including magnitude and phase, is collected on the scanning plane. Suppose that *Et*ð Þ *x*, *y*, *h* is the tangential field on the scanning plane, and *Et*ð Þ *x*, *y*, 0 is the tangential field on the source plane. The mathematical calculation of the ESM algorithm [9] can be summarized by Eq. (5).

$$E\_t(\mathbf{x}, \mathbf{y}, \mathbf{0}) = F^{-1}\left\{ F[E\_t(\mathbf{x}, \mathbf{y}, h)] \cdot \mathbf{e}^{jk\_x h} \right\},\tag{5}$$

where *kz* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>k</sup>*<sup>2</sup> � *<sup>k</sup>*<sup>2</sup> *<sup>x</sup>* � *<sup>k</sup>*<sup>2</sup> *y* q is the *z* component of the propagation vector if *k*<sup>2</sup> *<sup>x</sup>* þ *k*2 *<sup>y</sup>* <sup>≤</sup>*k*<sup>2</sup> ; *kz* ¼ *j* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *k*2 *<sup>x</sup>* <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> *<sup>y</sup>* � *<sup>k</sup>*<sup>2</sup> <sup>q</sup> if *k*<sup>2</sup> *<sup>x</sup>* <sup>þ</sup> *<sup>k</sup>*<sup>2</sup> *<sup>y</sup>* <sup>&</sup>gt; *<sup>k</sup>*<sup>2</sup> ; *kx* and *ky* are the spatial frequencies of 2D Fourier transform; *F* and *F*�<sup>1</sup> are the forward and reverse 2D Fourier transform operators, respectively. The basic idea behind this ESM method is to decompose the scanning field into plane waves with different propagation vectors in *x*, *y*, and *z* directions.

In [11], an electronic system with multiple physical layer transceivers was diagnosed using the ESM method. The source location at a frequency of interest was precisely localized. Afterward, by applying an absorbing material to the identified source location, the radiated power at the corresponding frequency was effectively suppressed.

#### **3.2 Sparse ESM**

Using the original ESM method [9], dense and uniform scanning samples are needed, which is time-consuming and inefficient in fast EMI diagnostic applications. Therefore, a sparse ESM method [10] was proposed to improve the scanning speed using sparse samples. Even though background noise is introduced to the reconstructed images, the scanning time is significantly reduced. Mathematical derivations show that the signal-to-noise ratio (SNR) of the reconstructed images is proportional to the number of sparse samples. Thus, the dominant radiation sources can be identified using an appropriate number of scanning points.

The sparse ESM method can locate dominant sources, but the absolute field strength of the reconstructed images is not trustable. More sparse samples will increase the field magnitude of the reconstructed images due to the mathematical process of Fourier transform. To tackle this limitation, a nearest-neighbor interpolation method [10] was adopted to interpolate the scanning field and calculate the radiated power from the sources. **Figure 19** shows an example of the nearestneighbor interpolation method. According to the sparse samples, the scanning domain is segmented into multiple polygon areas, and each polygon represents the area closest to one scanning sample. Afterward, the radiated power through the scanning plane can be calculated according to Poynting's theorem expressed in Eq. (6) [10].

$$P\_{\text{tot}} = \iint\_{A} \frac{\left| \overrightarrow{E} \right|^2}{2\eta} \cdot d\mathbf{S} = \sum\_{i} \frac{\left| \overrightarrow{E}\_i \right|^2}{2\eta} \cdot A\_i,\tag{6}$$

where η is the free space wave impedance; *E* ! *<sup>i</sup>* is the field at sampling location *i*; *Ai* is the area of the corresponding nearest-neighbor region.

To validate if radiated power can be accurately calculated, an experiment was performed [10] using the setup in **Figure 20**. Two horn antennas were utilized as the transmitter and receiver, respectively. Antenna *B* was at a fixed position, and Antenna *A* was moved manually through a scanning robot to obtain the radiated field of Antenna *B*. Assume that the main beam of Antenna *B* is narrow, which is true in most cases. The scanning plane is sufficiently large compared with the main beam of Antenna *B*. Hence, the radiated power of Antenna *B* can all propagate through the scanning plane. Moreover, the polarization direction of Antenna *A* and *B* are aligned with each other. Thus, it is reasonable to expect that the radiated

**Figure 19.** *An example of the nearest-neighbor interpolation [10].*

**Figure 20.**

*Measurement setup for validating the nearest-neighbor interpolation method in calculating the radiated power [10].*

#### **Figure 21.**

*(a) Scanning samples when N* ¼ 100*. (b) Reconstructed image when N* ¼ 100*. (c) Scanning samples when N* ¼ 454*. (d) Reconstructed image when N* ¼ 454*. (e) E field magnitude on the scanning plane after using nearest-neighbor interpolation when N* ¼ 454*. (f) the convergence of calculated radiated power as a function of the number of samples [10].*

*High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

power of Antenna *B* can be all captured by Antenna *A* using the nearest-neighbor interpolation method.

A vector network analyzer (VNA) was utilized to measure the scanning field through *S*<sup>21</sup> as shown in **Figure 20**. The measured E field values of Antenna *A* can be obtained through the antenna factor of Antenna *A*. If the incident voltage of Antenna *B* is 1 V, the incident power of Antenna *B* will be calculated as 10 dBm in a 50-Ω transmission line system. In other words, the expected radiated power calculated using the nearest-neighbor interpolation method is 10 dBm.

**Figure 21** presents the measurement process using the measurement setup in **Figure 20**. With the increase of sampling number, the quality of the reconstructed image is also improved according to the conclusion in [10]. **Figure 21(e)** shows the scanning field after using the nearest-neighbor interpolation method. **Figure 21(f)** plots the convergence of the calculated radiated power for two different scans, which both converged to 10 dBm as expected. This experiment demonstrates that the sparse ESM method can locate dominant radiation sources and estimate radiated power by sparse scanning samples.

#### **3.3 Apply ESM to optical transceiver modules**

Optical transceiver modules are widely used in Gigabit Ethernet systems to transmit high-frequency data of several hundred gigabits per second (Gbps). Serious EMI problems can be caused at high frequencies by a large number of these modules. EMI diagnostics of multiple potential radiation modules is troublesome. The sparse ESM method introduced earlier is a valuable tool to locate radiation sources efficiently and quantify radiated power. In this section, the sparse ESM method is applied to diagnose multiple optical transceiver modules. **Figure 22** shows a real-world DUT with 16 optical transceiver modules, which generate 15 distinct radiation peaks around 10.3125 GHz. The frequency peak # 11 was selected in this measurement. The sparse ESM was adopted to identify the optical transceiver module that caused frequency # 11 among the 16 modules.

A zero span of a VNA was used, as explained in [9], to focus on frequency # 11. The field magnitude and phase on a scanning plane were measured using the VNA tuned-receiver mode, as illustrated in **Figure 17***.* **Figure 23** shows the measured field, reconstructed image, and calculated radiated power. The total number of scanning samples was 352.

In **Figure 23(b)**, the reconstructed source image has a clear hotspot corresponding to the location of one pair of optical transceiver modules. Interestingly, as shown in **Figure 23(c)**, the reconstructed field phase shows a series of phase contours surrounding the corresponding source location. Even though the sampled scanning field was obtained sparsely, the reconstructed image has a

**Figure 22.**

*(a) Validation DUT with 16 optical transceiver modules (numbered by pairs). (b) 15 radiation peaks from the DUT around 10.3125 GHz [10].*

continuous distribution due to Fourier transform and inverse Fourier transform in Eq. (1). **Figure 23(d)** shows the convergence of radiated power as more scanning points were sampled. The converged radiated power is approximately 83.4 dBm.

One more experiment was implemented to validate the identified radiation module in **Figure 23** by removing radiation pair # 3 from the DUT and performing another ESM scan. The result is shown in **Figure 24**. The measured scanning field, the reconstructed source field, and the calculated radiated power were significantly reduced. After removing the radiation module for frequency # 11, there is some radiation from the same location. The reason is that the physical layer interface IC beneath the optical module is still radiating.

Furthermore, the total radiated power (TRP) for the two cases in **Figures 23** and **24** was measured in a reverberation chamber (RC) for comparison, and the result is listed in **Table 3**. After removing radiated pair # 3, the TRP value is reduced by 14.1 dB, which is close to the 13.5 dB reduction estimated by the sparse ESM scanning.

The above experiments demonstrate that the sparse ESM is a reliable technique to identify the locations and quantify the radiated power of dominant sources at high frequencies. As a commonly used product in data communication systems, optical transceiver modules were used as the DUT. The sparse ESM method can be applied to identify the radiating modules rapidly.

However, the measurement for the sparse ESM method mentioned above was performed manually, which was user-unfriendly. Also, the image quality can be degraded by operators'subjective decisions and perceptions. An approach based on Gaussian process regression was proposed to achieve automatic scanning to address this issue [16]. The Gaussian process is used to estimate the amplitude variation of the scanned field and its uncertainty to focus on the most relevant scanning area. Thus, compared with pure random scanning, the proposed approach can save the number of scanning samples.

#### **Figure 23.**

*Scanning result at frequency # 11. (a) E field on the scanning plane. (b) the magnitude of the reconstructed image on the DUT plane. (c) the phase of the reconstructed image on the DUT plane. (d) the convergence of calculated radiated power [10].*

**150**

#### **Figure 24.**

*Scanning result at frequency # 11 after removing the corresponding radiated pair # 3. (a) E field on scanning plane. (b) the magnitude of the reconstructed image on the DUT plane. (c) the phase of the reconstructed image on the DUT plane. (d) the convergence of calculated radiated power with the increase of the number of samples [10].*


**Table 3.**

*Power comparison at frequency # 11 [10].*

#### **4. Multiple EMI radiators**

Measuring the maximum E field emission for a complex system with numerous optical modules requires exhaustive hardware testing. **Figure 25** illustrates a large network router with many optical modules. The 3D radiation pattern of a single optical module was measured as depicted in **Figure 25(b)**. Statistical analysis and simulation were then performed to fast estimate the E field emission from multiple radiators without running actual hardware testing [12, 13].

The phased array antenna theory and Monte Carlo simulation were utilized to perform the statistical analysis [12]. A tendency of 10*logN* (dB) was found for the maximum electric field emission from a system with radiators at the same frequency with random phase distribution, where *N* is the number of radiators. Also, it was found that when multiple radiators with the same magnitude and random distribution contribute simultaneously, the maximum E field follows a normal distribution. Hence, a cumulative distribution function (CDF) can be obtained, and a level of certainty for the E field estimation can be provided.

**Figure 25.**

*(a) A large network router consisting of numerous optical modules radiating at 10.31 GHz. (b) a typical optical module and its 3D radiation pattern from the seams [12].*

**Figure 26.** *Emax comparison between measurement and prediction as the number of line cards increases [12].*

**Figure 26** compares the *Emax* between the measurement, simulation, and estimation when the number of line cards increases. "Adding field" means using the same frequency for all line cards, while "adding power" means using different frequencies for each line card. It is shown in **Figure 26** that adding power intensities instead of adding fields has a slower slope than 10*logN* (dB) tendency. From **Figure 26**, it can be concluded that the simulation and measurement results can agree reasonably well with the 10*logN* (dB) tendency. When the number of line cards increases, the measurement result starts to deviate slightly from the estimation. The reason given in [12] is that more line cards meant a higher probability of missing the maximum electric field in the measurement, depending on the radiation pattern of the receiving horn antenna.

More experiments were implemented in [13] to validate the 10*logN* tendency by using patch antennas to mimic the radiation of optical modules. The same agreement between measurement and estimation was observed. **Figure 27** shows the CDF distribution for 15 and 30 patch antennas with random phase excitation. The measured *Emax* under different phase randomizations fell into the 40–90% range. Therefore, it can be concluded from the experiment that the statistical model can reliably estimate the worst E field emission from multiple radiators with random phase distribution. By adopting the 10*logN* (dB) tendency and the CDF of normal distribution, one can easily estimate the likelihood of passing an EMC regulation

*High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

**Figure 27.** *Measurement samples and prediction of the CDF for two different number of patch antennas [13].*

without running exhaustive hardware testing with more radiation modules to be installed.

#### **5. Conclusion**

In this chapter, some effective diagnostic approaches for industrial products at high frequencies are reviewed. First, the study of an explicit optical transceiver module is presented to investigate the internal EMI coupling mechanism. An accurate simulation model for the optical subassembly (OSA) module was constructed by correlating the total radiated power of simulation and measurement. More simulations and measurements were performed to identify the dominant radiation modules and coupling paths. An intuitive visualization method for EMI coupling paths was also adopted. According to the EMI coupling paths, mitigation solutions were correspondingly proposed and demonstrated to work effectively in real product applications. Subsequently, an emission source microscopy (ESM) method that can efficiently localize far field radiation sources is introduced. Using the ESM technique, the dominant radiation modules among multiple optical modules can be rapidly identified. Moreover, for numerous sources radiating at the same frequency with random phase distribution, the maximum electric field emission has a 10*logN* (dB) tendency, where *N* is the number of sources. Thus, the probability of passing an EMC regulation can be fast estimated without running exhaustive hardware testing. This chapter reviews and summarizes an insightful and systematic approach for high-frequency EMI diagnostics for industrial products.

#### **Acknowledgements**

The authors would like to thank Prof. James Drewniak, Prof. David Pommerenke, Prof. Victor Khilkevich, Dr. Kyoungchoul Koo, Dr. Jing Li, Dr. Alpesh Bhobe, Xiao Li, Xiangyang Jiao, and Sukhjinder Toor for their kind help and support on the related research.

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Author details**

Ling Zhang<sup>1</sup> \*, Yuru Feng<sup>1</sup> , Jun Fan<sup>2</sup> and Er-Ping Li<sup>1</sup>


<sup>© 2021</sup> The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*High-Frequency Electromagnetic Interference Diagnostics DOI: http://dx.doi.org/10.5772/intechopen.97613*

#### **References**

[1] L. Zhang et al., "EMI Coupling Paths and Mitigation in Optical Transceiver Modules," in IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 6, pp. 1848–1855, Dec. 2017, DOI: 10.1109/TEMC.2017.2697761.

[2] J. Li et al., "EMI coupling paths in silicon optical sub-assembly package," 2016 IEEE International Symposium on Electromagnetic Compatibility (EMC), Ottawa, ON, Canada, 2016, pp. 890– 895, DOI: 10.1109/ISEMC.2016.7571768.

[3] J. Li, S. Toor, A. Bhobe, J. L. Drewniak and J. Fan, "Radiation physics and EMI coupling path determination for optical links," 2014 IEEE International Symposium on Electromagnetic Compatibility (EMC), Raleigh, NC, USA, 2014, pp. 576-581, DOI: 10.1109/ISEMC.2014.6899037.

[4] J. Li, X. Li, S. Toor, H. Fan, A. U. Bhobe, J. Fan, and J. L. Drewniak, "EMI Coupling Paths and Mitigation in a Board-to-Board Connector," in IEEE Transactions on Electromagnetic Compatibility, vol. 57, no. 4, pp. 771–779, Aug. 2015.

[5] A. Talebzadeh, P. C. Sochoux, J. Li, Q. Liu, K. Ghosh, and D. Pommerenke, "Shielding Effectiveness, Coupling Path, and EMI Mitigation for QSFP Cages With Heatsink," in IEEE Transactions on Electromagnetic Compatibility, vol. 60, no. 5, pp. 1254–1262, Oct. 2018, DOI: 10.1109/TEMC.2018.2813889.

[6] A. Talebzadeh et al., "Coupling Path Visualization and EMI Mitigation for Flyover QSFP Connectors," in IEEE Transactions on Electromagnetic Compatibility, vol. 62, no. 4, pp. 1037– 1044, Aug. 2020, DOI: 10.1109/ TEMC.2019.2943290.

[7] D. Baudry, C. Arcambal, A. Louis, B. Mazari, and P. Eudeline, "Applications of the Near-Field Techniques in EMC Investigations," in IEEE Transactions on Electromagnetic Compatibility, vol. 49, no. 3, pp. 485–493, Aug. 2007, DOI: 10.1109/TEMC.2007.902194.

[8] J. J. H. Wang, "An examination of the theory and practices of planar near-field measurement," in IEEE Transactions on Antennas and Propagation, vol. 36, no. 6, pp. 746–753, June 1988, DOI: 10.1109/ 8.1176.

[9] P. Maheshwari, H. Kajbaf, V. V. Khilkevich, and D. Pommerenke, "Emission Source Microscopy Technique for EMI Source Localization," in IEEE Transactions on Electromagnetic Compatibility, vol. 58, no. 3, pp. 729–737, June 2016, DOI: 10.1109/TEMC.2016.2524594.

[10] L. Zhang et al., "Sparse Emission Source Microscopy for Rapid Emission Source Imaging," in IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 2, pp. 729–738, April 2017. DOI: 10.1109/TEMC.2016.2639526.

[11] X. Jiao et al., "EMI mitigation with lossy material at 10 GHz," 2014 IEEE International Symposium on Electromagnetic Compatibility (EMC), Raleigh, NC, USA, 2014, pp. 150–154, DOI: 10.1109/ISEMC.2014.6898960.

[12] J. Meiguni et al., "EMI Prediction of Multiple Radiators," in IEEE Transactions on Electromagnetic Compatibility, vol. 62, no. 2, pp. 415–424, April 2020, DOI: 10.1109/ TEMC.2019.2914240.

[13] W. Zhang et al., "System-Level EMI of an Artificial Router System With Multiple Radiators: Prediction and Validation," in IEEE Transactions on Electromagnetic Compatibility, vol. 62, no. 4, pp. 1601–1610, Aug. 2020, DOI: 10.1109/TEMC.2020.3006517.

[14] H. Li, V. V. Khilkevich and D. Pommerenke, "Identification and

Visualization of Coupling Paths—Part I: Energy Parcel and Its Trajectory," in IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 3, pp. 622– 629, 1 June 2014, DOI: 10.1109/ TEMC.2014.2314645.

[15] H. Li, V. V. Khilkevich and D. Pommerenke, "Identification and Visualization of Coupling Paths-–Part II: Practical Application," in IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 3, pp. 630–637, 1 June 2014, DOI: 10.1109/ TEMC.2014.2314660.

[16] J. Li, J. Zhou, S. Yong, Y. Liu, and V. Khilkevich, "Automatic sparse ESM scan using Gaussian process regression," 2020 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI), Reno, NV, USA, 2020, pp. 671–675, DOI: 10.1109/EMCSI38923.2020.9191463.

#### **Chapter 8**

## UHF RFID in a Metallic Harsh Environment

*Renata Rampim and Ivan de Pieri Baladei*

#### **Abstract**

The use of the UHF RFID system in a warehouse that contains steel coils is a challenge for the technology itself since there are countless reflections of the radio frequency waves in the environment causing the multipath effect, which represents one of the most complex problems for wireless communication. Thus, this effect must be managed with the hardware, such as the antenna radiation diagram, and with the software, in the middleware, the software developed for the application. In this chapter, an application of RFID in metallic items will be discussed, tracking them since the product's hot rolling, controlling the receiving process, shipping, and inventory, working together with equipment such as overhead crane.

**Keywords:** RFID, UHF RFID system, logistic, harsh environment, RFID in metallic

#### **1. Introduction**

RFID (Radio Frequency Identification) is an identification technology that uses a magnetic field or electromagnetic waves to access data stored in a microchip that is connected to a small antenna attached to an object.

The RFID system uses the magnetic field at LF (125 kHz) or HF (13.56 MHz) frequencies for communication between the transmitter and receiver. This communication typically has a maximum range of 20 cm, named NFC (Near Field Communication), that is, it is a short-range wireless connectivity technology, which transfers energy to the tag through inductive coupling.

However, for the frequencies used in the RFID system in the UHF band (860 MHz - 960 MHz) there is also a magnetic field constituted near the transmission antenna (near field), which is well defined at this distance. As the magnetic field spreads, an electric field develops. These fields, magnetic (near field) and electric (developed), add up orthogonally and the result is an electromagnetic field. This electromagnetic field has the property of propagation and propagates in the form of an electromagnetic wave, moving away from the transmitting antenna. In this way, when a UHF RFID tag is hit by this electromagnetic wave, coupling occurs. In other words, the energy of the electromagnetic wave captured by the RFID tag antenna energizes the microchip (IC - Integrated Circuit). With this, the IC internally performs its functions and returns its data, object identification and other information that are stored in its memory, to the RFID UHF reader through another electromagnetic wave created by the IC. This description refers to a backscatter coupling.

Typically, due to physical properties, the RFID system at LF and HF frequencies have an easier time reading their tags when they are on objects containing metal, liquids, wood and due to their type of coupling (inductive coupling), which does

**Figure 1.** *Overview of an RFID system with backscatter coupling.*

not occur with the UHF RFID system. The electromagnetic wave that propagates is strongly influenced by the environment in which the RFID system is implemented and is dominated by the same phenomena that characterize any radio signal, that is, reflection, diffraction, and refraction. These phenomena can alter the amplitude, phase or frequency characteristics of the electromagnetic wave and cause signals of multiple paths, making it difficult to implement the UHF RFID system.

The great challenge of implementing a UHF RFID system in a metallic environment is to control these multipath signals, in which the variables in the environment are numerous and which cause a very unstable signal level, both from the reader to the tag and from the tag to the reader.

#### **1.1 Overview of a UHF RFID system**

The overview of an RFID system with backscatter coupling is shown in **Figure 1** [1]. In this figure, at the beginning of the process (1), the RFID reader creates an electromagnetic wave and transmits it.

When the electromagnetic wave meets an RFID tag, the backscatter coupling occurs (2). With the energy resulting from the coupling, the microchip (IC) performs its functions and sends the contents of its memory to the reader through another wave created by it (3).

Upon receiving the wave with the IC memory, the reader demodulates the signal and obtains the data and amplifies them to send to the computer (4).

With this data, the computer performs its functions, such as grouping, filtering and, in this way, prepares them for the application (5).

#### **2. UHF RFID system in a metallic environment**

A typical RFID system is divided into two layers: physical and software.

In the physical layer, there are readers, also called interrogators, which functions are: to generate radio frequency energy and query signals and send them through one or more antennas; receiving replies to the queries from RFID tags, amplifying and demodulating these signals; organizing the data received from the RFID tags and, finally, sending them to a computer or a network.

#### *UHF RFID in a Metallic Harsh Environment DOI: http://dx.doi.org/10.5772/intechopen.95611*

In this way, a reader must have at least one antenna, which is the communication interface with an RFID tag, and an interface for communication with the computer, which can be a serial or USB output, an Ethernet output, Wi-Fi, Bluetooth, 3G.

RFID tags also belong to the physical layer and consist of an inlay, which, in turn, consists of: a microchip or integrated circuit (IC). The data, the unique identification of the object and other information, are stored in the memory of this IC, which is also responsible for several essential processes for communication with the reader to occur; antenna: responsible for receiving and sending radio frequency waves. The shape of the antenna depends on the frequency of operation of the system; connectors: connect the IC to the antenna; substrate: the support base of the antenna, the IC and the connectors. It contains electrical characteristics that are considered in the design of the antenna.

The inlay can be encapsulated or not. Both the material to be used for the encapsulation and its format will be defined according to the characteristics of the application. Thus, an RFID tag can be provided in many shapes, types and sizes.

Still belonging to the physical layer it is the interrogation zone. The interrogation zone represents the area in which the RFID reader is able to activate and obtain an answer from an RFID tag, one of the crucial points for any implantation.

The RFID software layer, named middleware, goes beyond simply connecting devices. It allows all necessary applications for the RFID system, as filttering, giving hability to manage data and other applications for the user.

#### **3. Attributes for the implementation of the RFID system**

The key attributes for implementing the RFID system in a metallic environment and achieving success with the system are: process vision; requirements for implementing the RFID system within the existing process; the necessary resources for the implementation of the RFID system and; finally, the implementation action plan.

#### **3.1 Process view**

The entirely process understanding and knowledge of its features in which the RFID system will be implemented is as important as the RFID technology itself. Understanding the challenges of the process and, consequently, make them suitable for the specific application and determine the best RFID system for this process is crucial. Without this essential view of the process, a mistake in the results of the implementation of the RFID system could occur and, consequently, wrong deliveries to the customer.

For example, the RFID system will be used to identify steel coils (steel wire rod), **Figure 2**.

The steel coils are produced in the rolling mill, where they receive a label for their identification of batch and type of material. The identification tag is attached to the coil manually. After weighing and printing the label with the identification, an operator fixes it to the coil by means of a clamp on one of the coil's ties.

Inside the laminator, the rollers are transported by a type C hook until unloading to the transfer carriage. After labeling, the rollers continue, taken by the hook, towards the transfer cart and finally deposited on the bed. The bed is the delivery point of the rolls for logistics. When the rollers are in bed, it is already the responsibility of the logistics department.

The coils, under the responsibility of logistics, are stored internally in a warehouse and transported through an overhead crane, as outlined in **Figure 3**.

The destination of the stored coils is for sale to the foreign market, so their transportation is done by trucks or train cars.

In short, the RFID system will be used for storage management. The storage management comprises the flow of the coils, their movement, storage, until the order is picking and shipment [2]. However, with the RFID system, picking is a step that will be eliminated, as the system allows the coils to be removed from the storage position and to be directly shipped for transportation, as shown in the flow in **Figure 4**.

#### **3.2 RFID system implementation requirements**

After analyzing the process in depth, a thorough approach to analyze the specific need to use the RFID system and is necessary. After this step, design the system architecture solution with the best cost–benefit ratio. Without these basic requirements there may be an unrealistic expectation in the delivery of the RFID project.

Below are some important aspects of the application:


**Figure 3.** *Storage of steel wire rods.*


#### **3.3 Resources for implementing the RFID system**

The resources for the implementation must be mapped so that there is no frustration with the RFID system. The resources are divided into financial and human resources.

#### *Electromagnetic Wave Propagation for Industry and Biomedical Applications*

**Figure 5.** *Coil temperature at the hot rolling process outlet at* 113*:*5*oC.*

#### *3.3.1 Financial resources*

The financial resource is an estimate of the necessary amount of financial resources for the project. The estimated budget is obtained through a business plan based on the architecture of the solution and aligned with the objectives that justify the implementation of the RFID system attending the expected project goals.

The business plan helps to obtain the correct investment decisions and must be focused on defining the problem that the RFID system will solve, considering the objectives and risks that the organization will face when implementing this technology. The definition of objectives at the beginning of the process will ensure that the design of the solution is monitored both during implementation and at the conclusion of the steps and their deliveries; consequently, it will bring subsidies to monitor the evolution of the implementation of the RFID system.

For a steel industry, improving the working conditions and protecting healthcare of their operators are the main objectives for the implementation of the RFID system in coil storage, i.e. the focus is on work safety of their employees. The automatic collection of the coil identification removes the operator from the storage area and considerably reduces the risk of accidents with the coil falling during its transport on the overhead crane.

Business performance can also be scored and should consider: the efficiency of steel coil circulation, inventory management, more effective inventory control, improving operational productivity by reducing management costs, reducing lead times coil loading for road or rail transport.

#### *3.3.2 Human resource*

The human resource is the project team needed for the implementation. The RFID system is a complex system and involves hardware and software, so the team must consist of at least:


#### **3.4 Action plan for the RFID implementation**

An inadequate action plan leads to a false start in the implementation, and as a result, mismatched and uncertain delivery dates. For this reason the action plan must be carefully elaborated and must provide details of all activities involved as who will be in charge and how the piece of necessary information is going to be provided.

The action plan can be divided into four stages: conceptual phase, which describes the initial vision and the basic objectives of the project and the business plan itself; planning phase, which consists of an analytical structure of projects carried out by the project manager, involving responsibility for the work and interrelated tasks; installation phase, which is the stage in which it is possible to identify and purchase all the equipment and software that will be part of the solution. The installation phase will remain until all software and hardware installations in the approval environment are completed, for testing and validation, and later, the turn to the production environment. In this phase, the project manager transfers the project to the operating personnel along with all project documentation, including the service and governance plan.

#### **4. Solution design**

In order to analyze the feasibility of implementing the RFID system for identification in steel coils, a proof of concept is required. Proof of concept (POC) is an activity that demonstrates, in the installation environment itself, electromagnetic interference in real conditions and the most appropriate RFID tag for the operation, consequently, the POC identifies the challenges that the implementation of the RFID system will face in this hostile environment for radio frequency.

#### **4.1 The physical layer**

#### *4.1.1 RFID tag*

The temperature in the steel coils is a variable analyzed in the proof of concept, as it will determine the type of RFID tag for the system.

A coil has three sectors divided into head, middle and tail. The RFID tag must be placed on its tail and on the inside part, named as the cold zone. For this reason, the temperature measurement in the POC must be performed on the steel coil on its tail and inside it at the time of the hot rolling process exit after cooling, according to the points indicated in **Figure 6**, using a FLUKE thermometer.

**Table 1** shows the temperatures measured at the exit of the laminator at measuring points 1, 2, 3 and 4, as shown in **Figure 6**, performed at an ambient temperature of 23*<sup>o</sup> C*.

In addition to the measurement shown in **Table 1**, the coil temperatures must be recorded during the storage process, that is, on the scale, in the storage place after transportation with the overhead crane and after 40 minutes of storage. As an example, the following coil gauges were chosen for measurement: 31.75 mm and 7 mm, as the gauge directly influences the temperature, as well as the chemical



#### **Table 1.**

*Temperature in the coils at the measuring points at the power plant exit.*

composition of the steel, among other factors, however, these characteristics were not considered in this work.

After the first 20 laminated pieces, it is suggested to start measuring the temperature of the 04 posterior coils, named X1, X2, X3 and X4, in point 1, to check if there will be a higher temperature in relation to the other measured points, which could occur. **Table 2** shows the coil temperatures of 31.75 mm during the storage process of 04 (four) coils, referring to the location where the coil was during the measurement, the coil and the respective temperature *oC*. **Table 3** shows the coil temperatures of 7.0 mm.

Looking at **Tables 2** and **3**, it can be seen that 100% of the 31,75 mm and 7 mm gauge coils are above the maximum operating temperature desired for the RFID system in all storage locations, as can be seen in the graph of **Figure 7** and this is a challenge for the implementation of the RFID system, as these conditions can affect the reading distance and the reading rates.

The functional and performance requirements of an RFID tag are influenced by the temperature at which it is submitted. An example can be seen in **Table 4** presented in the technical specifications of the Impinj Monza 4 RFID Tag IC [3].


#### **Table 2.**

*Coil temperatures of 31.75 mm during storage process.*


#### **Table 3.**

*Coil temperatures of 7.0 mm during storage process.*

#### **Figure 7.**

*Temperature of coils X1, X2, X3 and X4 (31.7 mm) and X5, X6, X7 and X8 (7 mm) in the different storage locations and the operating temperature of the RFID system.*


#### **Table 4.**

*Temperature parameters – Impinj Monza 4 tag Chip.*

A solution to the high temperatures of the product is to use RFID tags developed by several suppliers of special tags. **Table 5** presents the specification of some High Temperature UHF RFID Tags developed by some worldwide recognized manufacturers that would the possible to be used in the mentioned RFID application.

However this solution makes the project unfeasible due to the price of these tags, due to the current Brazilian market complex tax system as import duties, taxes, shipping fees, and a few other costs applied when importing goods to Brazil.

Another solution for high temperature is to encapsulate the tag to protect it and prevent damage to the IC or to the connector that connects the antenna to the IC. This solution was designed specifically for the characteristics of the project and developed in the country itself, with no import cost. This was the recommended solution as it enabled the project in the RFID tag requisite.

#### *4.1.2 RFID reader*

The RFID reader is a device that reads, writes and processes the data on the tags and sends them to an application. Finally, it is responsible for remotely energizing

#### *UHF RFID in a Metallic Harsh Environment DOI: http://dx.doi.org/10.5772/intechopen.95611*


#### **Table 5.**

*Physical specifications - UHF RFID tag - High Temperature.*

**Figure 8.** *RFID reader at the output of the laminator.*

RFID tags and obtaining the data contained in them. The reader can also perform filtering and data collection functions, and manage equipment input and output.

The reading of the RFID tags on the bed is performed by a fixed reader with an antenna, as shown in **Figure 8**.

The reader must be installed in a metallic distribution board of overlapping NEMA Norm category 4 with ventilation. This protection will prevent the conditions of the environment, high temperatures coming from the laminator, and dust, do not cause the interruption of its operation due to the temperature control. Reinforcing that the RFID reader is an electronic equipment and requires operating temperatures between �20*<sup>o</sup> <sup>C</sup>* to <sup>þ</sup>50*<sup>o</sup> C* [7].

The automatic receipt of the identification of the coils through the RFID system allows the status of the entry in the logistics sector to be more assertive, with verification of the material of the coil with which it was requested for hot rolling process, in addition to the analysis of the return of non-compliant materials, together with the integration of the WMS system (Warehouse Management System), increasing the quality and speed of the information in order to rationalize and optimize the storage logistics and the management of coil stocks.

Leaving the hot rolling process, in the movement stage, the identification of the coils by the RFID system must be performed by a reader installed on the electromagnet overhead crane itself.

#### **4.2 Environment**

#### *4.2.1 Electromagnet overhead crane*

A feasibility test of the RFID system must be carried out on the electromagnet overhead crane for the movement of steel coils in the storage area. For this, an RFID antenna must be attached to the overhead crane connected to a fixed RFID reader, in order to the performance tests of reading the RFID tags attached to the steel coil. The number of coils for the test must be according to the number of coils that the bridge's electromagnet car supports. For two coils, the RFID tag reading must be analyzed for these two coils, for four coils, the reading must be analyzed for four coils, and so on. Assuming the reading for two coils, the tests are carried out on two steel coils moved simultaneously with activation of the electromagnet. In this way, the RFID tags of the two coils are read with the system in a static way and with the system in motion.

In order to simulate a real situation, RFID tags must be fixed by the operator himself and in accordance to the process already used for this purpose. Thus, the RFID tags are inside the wire rod as shown in **Figure 9**.

With the system activated, consequently, the electromagnet turned on, **Figure 10**, the analysis of the frequency behavior through a spectrum analyzer occurs, **Figure 11**. Simultaneously, the reading of the RFID tags is obtained. The RFID tag must be read with both in the static and in motion systems.

It is verified in the spectrum analyzer that the magnetic field emitted by the electromagnet of the overhead crane is superimposed on the electromagnetic field of the RFID system. The magnetic field does not interfere with the electromagnetic field of the RFID system.

In **Figure 11** it is also possible to see the hopping channels of the Frequency Hopping Spread-Spectrum (FHSS) technology used in the RFID system according to the rules of the Brazilian regulation established by ANATEL (National Telecommunications Agency). It is important to note that the technology Frequency Hopping (FH) operates with a number of fixed channels stipulated by the country's regulatory agency. In the case of Brazil, 35 hop channels for the RFID system are used in the frequency range of 902 to 907.5 MHz and 915 to 928 MHz.

The FH technology uses these channels to send and receive the signals from the RFID system during a time interval established by the standard and in a sequence of use of each pseudo-random channel, thus reducing the probability of interference from other systems that use the same band of frequency.

Results: there is no interference of the magnetic field in the electromagnetic signal of the RFID system and the reading of the RFID tag is performed successfully, as shown in **Figure 11**. Therefore, the test results are positive in this scenario and the movement of the coils can be carried out by the overhead crane in the inner courtyard. Thus, it completes the storage management cycle by supporting the storage and shipping steps with the RFID system by sending the coil identifications to the logistics management system that the organization uses.

#### **4.3 Software layer**

The software layer consists of the RFID Middleware. It is a set of software components that act as a bridge between the components of the RFID system (in *UHF RFID in a Metallic Harsh Environment DOI: http://dx.doi.org/10.5772/intechopen.95611*

#### **Figure 9.** *RFID antenna installed on the overhead crane for the RFID tag reading tests.*

this case, RFID readers) and the application (logistics management system) of the organization that will receive the events generated by the RFID system. It needs to provide two main functions: monitoring the health and status of RFID devices, readers and reader antennas; and, manage the infrastructure and data flow specific to the RFID system.

For the system proposed in this chapter, the development of the RFID middleware considers: centralization of the reception of events generated by RFID readers in each equipment in which the RFID system will be installed, overhead crane and laminator bed; filtering and processing messages; interpretation of the message sequence according to the needs of the storage management system; forwarding messages to the storage management system. In addition, a system for monitoring the entire RFID system, including the monitoring of readers and their respective antennas, should also be considered.

The big challenge is to mitigate interference. The interference in the proposed system is considered when there is a reading of the identification of the steel coils that are not the desired ones, called unwanted coils. The interference occurs when there is reflection of the radiofrequency wave signal in the coils stored in the storage area and, consequently, the identification of unwanted coils is read by the RFID system installed on the bridge. This phenomenon is more evident when the overhead crane moves over the high stock, that is, many coils stored with stacking them in several overlapping layers.

*Electromagnetic Wave Propagation for Industry and Biomedical Applications*

#### **Figure 11.**

*Spectrum analyzer measuring the frequencies radiated in the environment during the RFID reading tests with the electromagnetic overhead crane connected.*

#### *4.3.1 Mitigation of interference*

The mitigation of interference must be performed at the hardware layer and at the software layer.

#### *UHF RFID in a Metallic Harsh Environment DOI: http://dx.doi.org/10.5772/intechopen.95611*

In the hardware layer, the interference is mitigated by adjusting the minimum power required to read the identification of the desired steel coils. This is done by adjusting the reader power of each RFID antenna with the static system, overhead crane stopped, loading the coils and positioned on top of the stock.

The software layer, on the other hand, must be responsible to solve the interference that still resulted with the power adjustments. For this, the development of the middleware must contain an established result interpretation logic that eliminates the reading of unwanted coils during the movement of the overhead crane.

The readings that occur in the movement of the overhead crane over the high stock, with the desired coils hoisted by the electromagnet. These readings always contain the identification of the desired coils. However, the reading of the identification of unwanted coils is shown punctually during movement, being eliminated during the journey. The problem is when the route is not long enough for these readings to disappear and not be sent to the management system improperly, and thus, the need for the logic of interpretation of the results. The problem occurs when the path is not long enough for these readings disappear and not be sent to the management system improperly, and thus, there is a need for the logic of interpretation of the results.

The logic of interpretation of the results must be analyzed for each situation of the RFID system, that is, not only when it comes to the RFID solution in overhead crane, but also a logic for each RFID system installed in environments such as the one mentioned in this chapter, a logic for the receiving RFID system, reader installed in the laminator bed and a totally different logic for the RFID system on the overhead crane, which will be true when the system is installed on forklifts, for example.

Therefore, the logic of interpretation of the results must be analyzed case by case when implementing the RFID system in metallic environments and this logic will be responsible for the quality of the delivery of events that are generated by the RFID system and delivered to the storage management system.

#### **5. Conclusions**

The implementation of the RFID system is possible in a warehouse that contains steel coils, since the necessary attributes for the successful use of this technology are observed. The attributes are divided into four stages: view of the process; requirements for implementation; the necessary resources; and the mapping of the action plan.

The vision of the process is the first step, and it must occur even before the implementation. It represents one of the most important factors in the whole process, as it presents all the challenges that the RFID system will face and serves as a foundation for the other steps. After analyzing the process, the requirements must be very well mapped for a successful implementation. They must contain the most important aspects for the application of the RFID system, such as: the logistical processes that the RFID system will support; the intrinsic variables of the process, item temperature, storage conditions, for example; type of transport that the item will use; safety conditions for the employees; etc.

Resources are divided into two sectors: financial and human. Without the necessary resources for the implementation of the RFID system, especially in a harsh environment, such as the storage of steel coils, the RFID system, during its implementation, can bring some frustration in the deliveries since there will not be trained people available nor financial support for the project on how to proceed correctly. The last step of the attributes is the action plan. The action plan includes the design of the project, the approvals, both of software and hardware in a test environment and, finally, the delivery of the solution in a production environment.

In case there is high temperature in the item that will use the RFID system, the RFID tag must be carefully studied. There are many market solutions for tags for these items, however, the cost can turn the RFID implementation unfeasible and another effective solution should be studied so that the RFID tag is able to support the variables that involve this type of application.

The RFID Middleware, i.e., the software that has the native function of collecting, filtering and grouping raw data sent from RFID tags and collected by the RFID readers, will also insert some business rules necessary for the implementation. The Middleware is also in charge of dealing with the interference arising from the environment so that a successful RFID implementation may occur. In short, the RFID Middleware plays an extremely important role in the whole context making possible to get success in the RFID implemented system in such a harsh environment when dealing with a technology that uses radio frequency at the frequency of 900 MHz.

#### **Abbreviations**


### **Author details**

Renata Rampim1,2\* and Ivan de Pieri Baladei2

1 RF Consulting, Sorocaba, Brazil

2 FAAP, São Paulo, Brazil

\*Address all correspondence to: renata@rfconsulting.com.br

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*UHF RFID in a Metallic Harsh Environment DOI: http://dx.doi.org/10.5772/intechopen.95611*

#### **References**

[1] Rampim R., Internet das coisas sem mistérios: uma nova inteligência para os negócios. 1nd ed. NETPRESS BOOKS; 2016. 127 p. ISBN 978–85–65794-02-2

[2] Rampim R. [et al.], Implementando RFID na cadeia de negócios: tecnologia a serviço da excelência. 3nd ed. EDIPUCRS; 2014. 344 p. ISBN 978–85–397-0350-0

[3] Impinj, Monza 4 Tag Chip Datasheet IPJ-W1510, IPJ-W1512, IPJ-W1513, IPJ-W1535. Impinj, Inc; Version 10.0; 2016.

[4] HID High Temperature Label 2020 https://www.hidglobal.com.br/node/ 23371 [Accessed: 21 December 2020].

[5] IQ 400P HT 2020 https://omni-id. com/datasheet/781/ [Accessed: 21 December 2020].

[6] Product Datasheet Confidex Heatwave Flag 2020 https://www. confidex.com/wp-content/uploads/ Confidex-Heatwave-Flag-Datasheet.pdf [Accessed: 21 December 2020].

[7] Impinj, SpeedwayR Installation and Operations Guide Version 6.4. Impinj, Inc; Version 6.4; 2020.

## **Chapter 9** RFID Applications in Retail

*Narges Kasiri*

### **Abstract**

Radio Frequency Identification (RFID) technology is one of the latest product tracking technologies being utilized by retailers. Operations management improvements were among the first recognized applications of this technology earlier in the century. RFID applications in managing retail operations, such as inventory management and control, lead to significant benefits. However, RFID applications are not limited to operations management and go beyond the operations side to offer improvements in other areas in retail such as marketing and managing customers' shopping experiences. In this research, we review the applications of RFID technology in retail since its introduction and how those applications have evolved over the last two decades to help retailers provide omnichannel services to their customers in the current market. We will demonstrate what strategic and tactical factors have helped retailers implement this technology and what factors have slowed down the process of adoption. We will also report on the latest status of the utilization of RFID in the retail sector.

**Keywords:** RFID, RFID applications, RFID in retail, Retail sector, RFID in retail operations

### **1. Introduction**

Retail stores manage millions of items on a day to day basis to deliver to their customers. Point of Sales (POS) systems with barcodes were among the first technologies used to track products across the supply chain and in stores. Barcodes, as an identification technology, are not utilized at item-level but usually represent a group of products. Retailers need to scan products at pallet level at the point of receiving shipments, in inventories entrance and exit places, and at the POS to keep track of what is coming into and leaving stores [1]. With barcode systems, inventory inaccuracy is created because stores barcode scanning are not always performed at the right time and the right location. This inventory inaccuracy leads to a significant loss at retailers. Retailers needed to explore new ways of tracking their items to lower the inventory inaccuracy and prevent consequent losses. Radio Frequency Identification (RFID) technology appears to be the new technology solution that could improve the inventory record accuracy of stores for various items.

RFID technology applications have been recognized in many areas such as healthcare, finance, manufacturing, and retail. The share of the RFID market in retail is projected to be the largest of all sectors with about 34% by 2026, followed by transportation sector (25%), financial and security services (22%), and other industries such as healthcare and manufacturing at smaller portions [2]. RFID tags can store more information about each item at real time and can have individualized identification for items versus barcodes with a small data storage capacity that can only identify a group of items. RFID readers do not need to be on the line of sight to

read RFID tags information which means items can be scanned more frequently and faster at any movement. These capabilities allow little mistakes in tracking records and largely eliminates inventory inaccuracy.

RFID technology's benefits to retailers were identified early at the beginning of the 21st century. However, RFID's applications in retail stores on a large scale took a while to be implemented. This paper reviews utilizing RFID, as an ideal solution to retail operations, since earlier this century and will cover a twenty-year horizon (2001–2020) divided into three equally long periods of 2001–2007, 2008–2014, and 2015–2020.

#### **2. Early introduction and utilization of RFID (2001–2007)**

In studies done earlier in this century, RFID was recognized as the next major identification technology to replace barcode systems in the retail industry [3–7]. Barcode systems have been used to track customer purchases, to manage inventory records, and to offer promotion and advertising in retail since 1970 [8]. Barcode tags, however, need to be on the line of readers to be read, a requirement that makes physical inventory counting a labor-intensive task and prevents stores from updating their inventory records frequently and on time. Therefore, with barcode systems, inventory inaccuracy is significant [9]. Inventory inaccuracy refers to the difference between inventory on record and the actual number of items on hand in stores. Inventory inaccuracy is caused by many factors such as transaction errors in the POS system, or shrinkage caused by possible employee/ customer theft. Inventory inaccuracy means that stores may not be able to place inventory orders on time, resulting in out-of- stock conditions and consequently losing sales and hurting customer shopping experience. RFID technology, on the other hand, enhances product visibility in store operations and across the supply chain through the ease of reading RFID tag information and updating inventory records on a real-time basis.

Studies have investigated RFID benefits in different areas of retail operations, such as supply chain management, and show how inventory inaccuracy and consequently out-of-stock conditions are improved with the implementation of RFID across the supply chain [10–12]. Enhanced information visibility, provided by RFID in the supply chain, decreases uncertainties and lowers high inventory costs associated with the uncertainties [13, 14].

Many pilot studies during this period investigated and explored the applications of this technology at the pallet level, case level, and item levels in stores [1, 6, 12, 15, 16]. Bottani and Rizzi [1] conducted a case study in 2005 to analyze pallet and case-level implementation of RFID and enhanced visibility generated at the receiving gates and entrance doors from backstore to sales floors. They demonstrated that safety stock and inventory holdings can be significantly reduced and RFID benefits are broad, ranging from labor efficiencies to inventory management improvements. Cost–benefit analyses in this period showed that pallet-level implementations of RFID were more cost effective than case-level implementations.

Metro Group in Germany conducted some case studies in their stores to show item-level RFID applications can improve customers' shopping experiences as well. They introduced some tools provided by RFID technology such as automatic checkout, smart carts that help customers navigate stores and find their items easier and faster, and smart dressing rooms that help customers find their desired apparel items more conveniently [6, 16]. They demonstrated that utilizing these tools significantly enhances customers' shopping experience.

Walmart retail stores in the US were the first retailers that decided to mandate the implementation of RFID at pallet and case level across some of their supply

#### *RFID Applications in Retail DOI: http://dx.doi.org/10.5772/intechopen.95787*

chain in 2005. Walmart also did a pilot study with 24 stores over a period of around 6 months to measure how RFID can improve inventory management. They demonstrated out-of-stock conditions were significantly reduced with the implementation of RFID technology [12].

In Asia, two Singaporean fashion retailers piloted item-level RFID on their apparel stores and reported significant reduction in stocking time from hours to minutes that consequently increased the frequency of counting items with handheld readers and improved inventory accuracy [17].

#### **3. Delays and reflection time on implementing RFID solutions (2008-2014)**

Financial crises and the great recession that started in 2008 did not work to the advantage of retailers that were planning to implement RFID applications in their stores. During financial crises, businesses tend to adopt strategies that could help them sustain and survive by spending low and investing less. RFID technology implementation plans were mostly postponed or slowed down during the financial crises. However, this period was the best time to develop some foundations with respect to policies, regulations, and standardization of the technology.

Privacy issues raised by consumer protection agencies and standardization issues across different platforms put forward by case studies and pilot projects led to the development of some regulations and privacy policies by governments, institutions, and businesses. European Commission (EC) took an active role by funding many initiatives across Europe [18]. Initiatives such as Coordinating European efforts for promoting the European RFID value chain (CE RFID) [19] and Building Radio frequency Identification solutions for the Global Environment (BRIDGE) [20], conducted from 2006 to 2009, highlighted that wide implementation of RFID technology needs some regulations, standardizations, and privacy policies in place. For example, the BRIDGE project, coordinated by GS1, helped the industry to develop standardizations such as establishing a common format for the data stored on RFID tags, or the availability of possible frequency bands.

RFID tags can store identifiable consumers' private data, which need to be protected. Therefore, EU members signed an agreement on the Privacy Impact Assessment framework in order to protect consumer privacy [21–23]. This agreement established some rules to be followed in the design of smart chips such as RFID tags to protect the privacy of consumers' data. Consumers should be informed if RFID tags are utilized in stores. In addition, tags must be deactivated at the point of sales at no cost [24]. This framework was later expanded to cover some rules for smart meters as well. In the United States, lawsuits against RFID application patents as well as privacy issues in 2011–2013 were setbacks for largescale implementations of the technology. The National Institute of Standards and Technology (NIST) in the US has helped to establish some guidelines to help retailers; however, most of the development of policies and standardizations have been initiated by corporations in the US.

In addition to developing policies and standardizations, businesses had more chances to identify and learn broader applications of RFID technology in retail. The focus of most of earlier pilot studies was how this new tracking technology helps manage inventories better in order to avoid out-of-stock conditions. However, the applications of the technology go beyond only inventory management and tracking items throughout the supply chain. As shown in the balanced scorecard developed in [25], RFID benefits extend to marketing and merchandising operations in retail as well (**Figure 1**).

#### **Figure 1.**

*Balanced scorecard for RFID applications in retail.*

In marketing, stores can monitor the behavior of consumers better when customers use tools such as smart carts or smart dressing rooms provided by RFID. Retailers can learn about consumers' preferences and reflect that in the promotion and advertising offered to customers in real time while they shop. The available tools such as smart dressing rooms and smart carts also enhance customer shopping experience. Use of these tools enables customers to find their desired items more conveniently and faster, which eventually leads to higher customer satisfaction and increase in sales.

In merchandising, enhanced visibility on consumer behavior in stores provided by RFID can help retailers identify better assortments of products. In addition, an enhanced visibility means better shelf-replenishment; that is stores can reduce the shelf space since enhanced visibility on shelves allows retailers to replenish them as soon as they become emptied. Less shelf space leads to holding less number of items on shelves at any given time and consequently less inventory and capital held in stores, which allows retailers to invest in carrying more variety for products in stores.

There were also more studies during this period conducting cost–benefit analysis of the implementation of the technology. The fixed cost of implementation includes middleware, fixed antennas, sensors, and readers and the variable cost includes the cost of tags per item. The cost of tags can be added to the cost of each product but then the big question is who has to pay for that cost. Should the cost be transferred to consumers or should that be shared between retailers and manufacturers? The tag cost as the variable cost of utilizing the technology is huge and cost–benefit analysis studies have shown it to be a major barrier to the implementation of the technology during this period. Kasiri and Sharda [26] showed that the cost of tags in item-level implementation of RFID, as the variable cost, is cumbersome. Moreover, the cost can exceed the benefits in some cases depending

on the extent to which stores implement RFID applications. The cost barrier was expected to weigh less as the cost of tags became lower over time.

### **4. Large-scale implementation of RFID (2015-2020)**

Surveys of businesses show the implementation of RFID has picked up in this period. A survey of 60 retail executives throughout the United States and Europe showed about 73% of retailers had plans to implement RFID in 2016 [27]. Another survey in 2018 [28], however, showed that 92% of retailers in North America plan on implementing RFID, which is about a 20% increase from the 2016 results.

The cost of implementation has been decreasing over time, as expected, and at the same time retailers have learned how to partially implement the technology. Retailers realized that they do not need to fully implement the technology. In some cases, only tags and hand-held readers are used to add visibility of items in stores without many of the infrastructures such as antennas. Cloud services, on the other hand, have allowed retailers to eliminate some of the middleware cost as well. The leading European fashion stores C & A is one of many retailers that explored lower cost implementations with partial utilization of the technology [29].

RFID platforms can generate big data that are the records of tracking items throughout the supply chain and stores in real time. Businesses need big data and business analytics capabilities to fully utilize technologies [30]. The results of the analysis of such data can help retailers improve their processes such as shelfreplenishment process as well as variety and assortment planning that have been used in the same format for many years. A new timely replenishment process can result in better management of physical space, layouts, and lowering holding costs in stores. Furthermore, a better variety and assortment planning means fulfilling customers' expectations and eliminating unpopular items that releases some capital and allow investment opportunities in other areas in retail.

Competing technologies to RFID have been developed and utilized over time as well. For example, Quick Response (QR) codes give retailers better ability to manage items compared to barcodes, Near-Field Communication (NFC) technology has some capabilities compared to UHF RFID, and most recently Amazon's cameras increase product visibilities in stores for fast checkouts. In addition, retailers have different priorities in investing in new technologies and there is competition for dollars invested in various technologies by retailers. For instance, a retail chain can focus on improving inventory operations, but another retailer may be focused on improving marketing operations and customer shopping experience in stores by developing new apps that can assist customers make decisions during their shopping time in stores. In a different example, Gucci as an Italian luxury brand name does not suffer from inventory inaccuracy issues but their priority is customer shopping experience and they have utilized RFID tags to protect customers against counterfeiting across the supply chain until products reach their customers [31].

Omnichannel retail has been widely available during this period of time. Retailers' customers can shop at any time, in any place, and via any shopping channel. Omnichannel retailing needs accurate inventories and enhanced product visibility more than any other time. Item-level RFID can, therefore, accommodate the needs of omnichannel retail more than other technologies available [32]. In addition, blockchain as the latest technology in retail can provide automatic exchange of product data carried by RFID tags between different partners across the supply chain. The blockchain in retail solutions are currently being studied in a consortium of large retailers such as Nike, Macy's, and Dillard's in an RFID lab at Auburn University [33].

#### *Electromagnetic Wave Propagation for Industry and Biomedical Applications*

**Figure 2.** *3-S model for RFID retail adoption.*

The 3-S model (substitution, scale, and structure) introduced in [34] discussed and projected different phases of the adoption of RFID earlier when this technology was introduced. Later the 3-S model was adapted by [35] to describe the current stage of retailers' implementation of RFID applications in retail (**Figure 2**). The substitution and scale stages are covering mostly what has been achieved during the three periods discussed in this paper. In the substitution phase, the RFID technology was utilized to replace the applications of barcode systems in tracking products. In the scale phase, the RFID applications are enabling retailers to manage their operations with more accuracy, efficiencies, and at a higher speed and scale. The structure phase, that is re-engineering processes and completely overhauling retail operations, is still underway. The RFID technology will enable retailers to accomplish things they could not imagine before and allows retailers to tap into completely new domains and applications.

#### **5. Conclusion**

Retailers have different needs based on the way they operate in stores. Some retailers must manage large inventories in stores. An enhanced visibility on their products help them improve inventory accuracies and avoid out-of-stock and increase their efficiencies. On the other hand, some retailers have small backstore inventories and every item they receive is put directly on their shelves and available to their customers. Inventory management is not their priority, but they need to focus more on customer shopping experience. Therefore, the enhanced visibility of items in stores is expected to promote retailers' marketing operations. Depending on the way retailers operate and what their priorities are, retailers have to plan on implementing appropriate applications of RFID technology.

As discussed in this paper, RFID has been utilized broadly with various applications. As a revolutionary technology, RFID's implementation can go beyond improving the current processes in retail operations. The current processes can innovatively change to debut completely new applications that are only possible with the enhanced visibility of items in real time. The ensuing big data that is derived from the visibility provided by RFID tags can be analyzed, leading to innovations in retail operations.

Implementing item-level RFID needs to be part of omnichannel strategy in the retail sector. With the wide-spread usage of online retail services such as Amazon, the competition in retail is tougher than ever before. In omnichannel services, retailers need to grant their customers easy access via different channels and make their products available in a variety of delivery services. The accessibility and fast delivery will not be possible with the level of visibility provided by barcode systems. Utilization of technology in retail is evolving quickly and RFID technology is the one that can definitely help retailers win in this overhaul.

*RFID Applications in Retail DOI: http://dx.doi.org/10.5772/intechopen.95787*

#### **Author details**

Narges Kasiri School of Business, Ithaca College, Ithaca, NY, USA

\*Address all correspondence to: nkasiri@ithaca.edu

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[10] Atali, A., Lee, H., and ÖlpOzer, O. If the inventory manager knew: Value of RFID under imperfect inventory information. White paper, Stanford University, 2005.

[11] Heese, H. S. Inventory record inaccuracy, double marginalization and RFID adoption. Production and Operations Management,2007, 16(5), 542-553.

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### *Edited by Lulu Wang*

This book highlights original research and high-quality technical briefs on electromagnetic wave propagation, radiation, and scattering, and their applications in industry and biomedical engineering. It also presents recent research achievements in the theoretical, computational, and experimental aspects of electromagnetic wave propagation, radiation, and scattering. The book is divided into three sections. Section 1 consists of chapters with general mathematical methods and approaches to the forward and inverse problems of wave propagation. Section 2 presents the problems of wave propagation in superconducting materials and porous media. Finally, Section 3 discusses various industry and biomedical applications of electromagnetic wave propagation, radiation, and scattering.

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