Chapter 1 Introduction

Chapter 1 Introduction This book is intended to provide a sound knowledge and thorough understanding of microwave engineering from a practical and theoretical point of view. In the process we will answer the questions of what it is all about and where and how it is employed. Microwave engineering is a tool to help understand (characterize, analyze and design) circuits whose sizes are comparable to or larger than the wavelength of the signal of operation. To understand this, it is necessary to define wavelength and to relate it to the frequency of operation. WAVELENGTH is a distance a single frequency wave propagates during its complete cycle (=period T), i.e, λ[cm] = v[cm/sec] × T [sec]

(1.1)

Now, we need to answer the question why we need to come up with a new tool to deal with such circuits, and what is wrong with the traditional AC circuit theory. The answer to these questions can be clarified with the following example: Example 1.1. Let us take a carbon resistor with its insulating shell (on which the color code of the resistor is printed) as shown in Fig. 1.1. Basic assumption of the conventional AC theory is that the current entering the resistor, I1 , must be equal to the current exiting the resistor, I2 , both in magnitude and phase.

l I1

I2

Insulating shell

Carbon

Figure 1.1: A carbon resistor 1

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CHAPTER 1. INTRODUCTION However, for a time dependence of ejωt , the input and output currents are written as I1 = I 1 6 0 ◦ I2 = I1 6 θd = I1 6 ωtd

(1.2) (1.3)

where td (=l/v) is the time delay of the electrical current to reach to the output of the resistor, meaning that there is a finite amount of phase difference between the output and the input currents: θd = ωtd =

l 2π l = 2π . T v λ

(1.4)

From Eq. (1.4), it can be concluded that if the length of the resistor l is much less than the wavelength of the signal, the phase difference can be assumed to be negligible. To give a numerical value, let the length of the resistor be 1 cm, and the signal frequency be 1 MHz and 1 GHz. Assuming that the signal propagates along the carbon resistor with the speed of light (c ' 3 × 1010 cm/sec), the wavelengths corresponding to 1 MHz and 1 GHz are c = 30000cm ; f c λ(f = 1 × 109 Hz) = = 30cm ; f

λ(f = 1 × 106 Hz) =

2π 30000 2π θd = 30 θd =

(1.5) (1.6)

It is obvious that the phase difference 2π/30 000 is extremely small and can be neglected while the phase difference 2π/30 (=12 degrees) is significant. As a conclusion from this example, the traditional AC circuit theory can not be used for the analysis and design of such circuits. Then, a natural question arises, “ why do we need microwave frequencies ?” if it makes life more complicated for us. The answer is quite simple because systems designed in microwave frequencies have unique features that can not be replaced by the low-frequency counterparts, which are; • More bandwidth: Note that the frequency range 109 –1012 contains 1000 × (0–109 ). A 1% bandwidth at 600 MHz is 6 MHz (the bandwidth of one television channel), while at 60 GHz a 1% bandwidth is 600 MHz (about 100 television channels). • Line-of-Sight Communication: Microwave signals are not bent by the ionosphere as are lower frequency signals. Therefore, in satellite communication systems, the microwave frequency signals are used to achieve high capacity communication. Note that the signals at millimeter wave frequencies are highly attenuated by the atmosphere. • Minimum sky noise: The electromagnetic noise power picked up by an antenna used in satellite communication systems, in addition to the noise caused

1.1. FREQUENCY SPECTRUM, PREFIXES AND SYMBOLS

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by electronic processes, is due to extra-terrestrial radiation (sky noise). This noise component is most intense between about 10 and 300 MHz and around the frequencies of 20-60 GHz. This is of course one of the reasons why frequencies in the 1-10 GHz range are used for satellite communications. • More antenna gain: Antenna gain is proportional to the electrical size (in terms of wavelength) of the antenna. Therefore, larger antenna gain can be achieved at higher frequencies for a given size of the antenna. • Radar applications: The effective reflection area (radar cross-section) of a radar target is usually proportional to the target’s electrical size. This fact, coupled with the characteristics of antenna gain, often make microwave frequencies the preferred band for radar applications. Radar (RAdio Detection And Ranging) systems are used for detecting and locating air, ground, or see-going targets, by airport traffic-control radars, missile tracking radars, fire-control radars, and other weapons systems. Radar is also used for weather prediction and remote sensing applications. It seems that the systems designed in microwave frequencies are indispensable parts of modern commercial and military technologies, and moreover the well-established low frequency circuit theory can not be applied directly to the characterization of such systems. Therefore, we need to develop a different approach for efficient and accurate analysis and design of microwave circuits and systems, which is called Microwave Theory and Techniques. Since the traditional circuit theory is an approximation or a special case of the theory of Electromagnetics, microwave theory and techniques help us to work on a problem in terms of electric and magnetic fields. If briefly stated; microwave engineering can be defined as applied electromagnetic fields engineering. Therefore, we must begin with Maxwell’s equations and find their solutions in a given structure in terms of electric and magnetic fields. But since the interest of engineers lays in the quantities pertinent to the ports of the network, such as power, voltage, current and impedance values, the field quantities will be converted to (or approximated by) the voltages and currents, wherever it is possible.

1.1

Frequency Spectrum, Prefixes and Symbols

The frequency spectrum starts below 30 Hz in the sub-audio region and extends in frequency to around 1 × 1028 Hz in the cosmic ray region, a part of which is given in Table 1.1 with their classifications. Originally the microwave band was designated to the frequencies between 1 and 40 GHz, but today it is better defined from 1 to above 100 GHz, a part of which is defined as the millimeter wave band. The main reason for this definition is because the microwave theory and techniques, that will be developed throughout this book, are applied to the analysis and design of information-handling systems in this frequency range. At higher frequencies, i.e., shorter wavelengths, some techniques developed from classical optical techniques are employed in the characterization of systems,

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CHAPTER 1. INTRODUCTION Table 1.1: Frequency spectrum Frequency Range 3-30 KHz 30-300 KHz 300-3000 KHz 3-30 MHz 30-300 MHz 300-3000 MHz 3-30 GHz 30-300 GHz

Band Designation Remarks Very Low Frequency (VLF) Navigation, Sonar Low Frequency (LF) Radio beacons Medium Frequency (MF) AM broadcast High Frequency (HF) Telephone, FAX Very High Frequency (VHF) TV, FM broadcast UltraHigh Frequency (UHF) Microwave band SuperHigh Frequency (SHF) Extreme High Frequency (EHF) Millimeter wave band

therefore, this is the range where optical engineering takes over. The microwave frequency band is further split into subbands with letter designations, known as IEEE Microwave Bands, for frequencies from 1 GHz to 40 GHz as described in Table 1.2. The use of the letters probably dates back to World War II as a form of short-hand

Table 1.2: IEEE Microwave Bands Band Frequency Range L 1.00-2.00 GHz

Remarks Mobile satellite service (MSS), UHF TV, Terrestrial microwave links, Cellular phone

S

2.00-4.00 GHz

MSS, NASA and deep space research

C

4.00-8.00 GHz

Fixed satellite service (FSS), Fixed service terrestrial microwave

X

8.00-12.50 GHz

FSS military comm., Fixed service terrestrial, Earth exploration and meteorological satellites

Ku

12.50-18.00 GHz

FSS, Broadcast satellite service (BSS), Fixed service terrestrial microwave

K

18.00-26.50 GHz

BSS, FSS, Fixed service terrestrial microwave

Ka

26.50-40.00 GHz

FSS, Fixed service terrestrial microwave

and simple code for developers of early microwave circuits. Here are some examples of frequencies or frequency bands that find applications in our daily lives:

1.1. FREQUENCY SPECTRUM, PREFIXES AND SYMBOLS

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Typical Frequencies AM broadcast band Shortwave radio FM broadcast band VHF TV (2-4) VHF TV (5-6) UHF TV (7-13) UHF TV (14-83) Microwave ovens Cellular system–GSM

535-1605 KHz 3-30 MHz 88-108 MHz 54-72 MHz 76-88 MHz 174-216 MHz 470-890 MHz 2.45 GHz 890-960 MHz

Current DIGITAL CELLULAR SYSTEMS use one of three standards: • Western Europe–Global System for Mobile Communications (GSM) • North American Electronic Industry Association Standards IS-54 • Japanese Digital Cellular (JDC)

Even in Introduction, we have used several prefixes and Greek symbols that are the integral part of engineering jargon, especially of microwave and optical engineering. Therefore, it would be nice to provide them here once and for all, for later references.

Table 1.3: Table of Prefixes Prefix exa peta tera giga mega kilo

Power of Ten 1018 1015 1012 109 106 103

Prefix Power of Ten basic unit 1 milli 10−3 micro 10−6 nano 10−9 pico 10−12 femto 10−15

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CHAPTER 1. INTRODUCTION Table 1.4: Lower Case Greek letters and Commonly Used Capitals alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu

α β γ δ  ζ η θ ι κ λ µ

nu ν xi(ksi) ξ Γ omicron o π ∆ pi rho ρ sigma σ tau τ Θ upsilon υ phi φ chi(khi) χ ψ Λ psi omega ω

Ξ Π Σ Υ Φ Ψ Ω

REFERENCES 1.1 Robert S. Elliott, An Introduction to Guided Waves and Microwave Circuits, Prentice-Hall International, Inc. 1993. 1.2 D. M. Pozar, Microwave Engineering, Addison-Wesley Publishing Company, 1990. 1.3 Peter A. Rizzi, Microwave Engineering, Prentice-Hall International, Inc. 1988. 1.4 R. E. Collin, Foundations for Microwave Engineering, 2nd Edition, McGrawHill Book Company, 1992. 1.5 Edgar Hund, Microwave Communications: components and circuits, McGrawHill Book Company, 1989. 1.6 Fred Gardiol, Microstrip Circuits, John Wiley & Sons, Inc. 1994.