# Introduction to Microwaves

#### From the book "Microwaves and Wireless Simplified" by Thomas S. Laverghetta by Artech House

## Defining Microwaves

Microwaves are used in radar, radio transmission, cooking and other applications that have become essential in our modern society. Microwaves are electromagnetic waves^{[1]} generally defined as lying within the frequency range of 100 MHz (3 m wavelength) to 300 GHz^{[2]} (1 mm wavelength).^{[i]} Above 30 GHz, because wavelengths are measured in mm, it is the convention to call them mmWaves. The optical frequency regime begins above 300 GHz with infrared. The radio frequency range extends down from the microwave region to as low as 3 KHz (100,000 m wavelength). It is important to understand that these are all electromagnetic waves that obey the same classical laws.

Because the dimensions of common discrete electrical components (e.g. carbon resistors, mica capacitors, wire-wound inductors) and the wires connecting them become large relative to a wavelength at microwave frequencies and above, they are no longer suitable for the construction of microwave circuits. Distributed “printed” circuit components, waveguide and specialized active components (i.e. amplifiers) with microscopic internal dimensions are used instead, until wavelengths become so small that optical techniques, such as the use of lenses and mirrors, are employed.

## Skin Effect at Microwave Frequencies

Another reason common lower frequency discrete components and connecting wires cannot be used at microwave frequencies is a phenomenon called skin effect, which is the concept that high frequency energy travels only on the outside skin of a conductor and does not penetrate into it for any great distance. The concept of skin effect can best be understood by the following example. If you tie a string to a ball and then twirl the ball around your head at a slow speed, you will see that the ball stays fairly close to your body as you spin it around. As you spin it faster, it stretches further away from your head and body and at a high enough speed it stretches straight out. The force that causes that to happen is centrifugal force.

Relating the speed of the ball to frequency (slow speed is low frequency, high speed is high frequency), as the frequency gets higher, an increasing centrifugal force arises. The force is inductance that is set up in the transmission line simply because a current is flowing. This force, which we refer to as a microwave centrifugal force, keeps the energy from penetrating the surface of the transmission line and makes it follow a path along the skin of the line rather than down into the entire cross-sectional area, as in low-frequency circuits; thus, a skin effect determines the properties of microwave signals.

Corresponding to the skin effect is a term called skin depth. This is how far the microwave energy actually penetrates into a conductor, and is dependent upon the material being used and on the frequency of operation. For example, the skin depth in copper at 10 GHz is 0.000025 in.; for aluminum at 10 GHz, it is 0.000031 in.; for silver, it is 0.000023 in.; and for gold, it is 0.000019 in. Thus, it can be seen that the energy truly does travel along the outer edge of the metal. This is emphasized even more when considering that for a microwave circuit board with copper cladding, the thickness of the copper is typically 0.0014 in.

Since transmission lines do not allow high frequency energy to penetrate very far into a conductor, it makes no sense to have round (radial) wire leads on components for microwave applications. The energy would travel only on the skin of the lead and be very inefficient. That is why there are ribbon leads or no leads with only solder termination points on most microwave components. It also is why there are relatively few physical components on a microwave circuit board. They are there, but they are distributed over a large, thin area with values equivalent to discrete devices used at lower frequencies; hence, the term distributed element components. This is what prompts many people to look at a microwave circuit and ask, “Where are all the parts?” Microwave circuits require special design and fabrication techniques.

###### [1] Simultaneous periodic variations of electric and magnetic fields that radiate through space.

###### [2] The terms *megahertz *(MHz) and *gigahertz *(GHz) indicate frequency in cycles per second (hertz). The term *mega *(designated as 106) means that the signal amplitude changes over a full cycle at a certain number of million times per second. The term *giga *(designated as 109) means the signal amplitude change by a full cycle at a certain number of billion times per second.

###### [i] “United States Frequency Allocations, the Radio Spectrum,” https://www.ntia.doc.gov/files/ntia/publications/2003-allochrt.pdf.

## Terminology

With microwaves defined, the following is an introduction to some of the basic terminology associated with microwaves and wireless technology, i.e. the jargon and the buzz words used by those in the microwave field. This list will be expanded and further refined as subsequent topics are introduced.

**Decibel (dB).** dB, a relative term with no units, is a ratio of two powers (or voltages). The decibel value can be positive (gain) or negative (loss). If an output power and an output power of a device (or system) is measured, the log of the ratio of the two taken, multiplied by 10 results in a decibel value for gain or loss. When using voltages, the multiplication factor is 20, since power is proportional to the square of voltage. It represents only how much the power or voltage level increases or decreases. It does not, by itself, provide a measure of the actual power or voltage level. It is valuable in determining a system’s overall gain or loss. For example, a filter with a 2 dB loss, an amplifier with a 20 dB gain, an attenuator with a 6 dB loss and another amplifier with a 12 dB gain, has an overall setup (or system) gain of +24 dB (see

*). The value is found by adding the positive decibels (+32) and the negative decibels (-8), and taking the difference (+24).*

**Figure 1****Decibels Referred to Milliwatts (dBm).** Where dB is a relative term, dBm is an absolute number, that is, decibels referred to milliwatts (mW) are specific powers (mW, W and so forth). To determine decibels referred to mW, only one power is needed. For example, given a power of 10 mW (0.010 W), divide it by 1 mW, take the log of the result, and multiply it by 10 (+10 dBm, in this case). The value of +10 dBm means that 10 mW of power are available from a source or are being read at a specific point. That differs greatly from +10 dB, which means only that there is a gain of 10 dB (gain of 10). So, whenever absolute power readings are required, use decibels referred to mW. To help to understand decibels referred to mW and related powers, see

*. The table shows five values of decibels referred to mW and the powers associated with them.*

**Table 1**Power |
10 µW | 100 µW | 1 mW | 10 mW | 100 mW |
---|---|---|---|---|---|

dBm |
-20 | -10 | 0 | +10 | +20 |

The terms decibels and decibels referred to mW can be used together, as illustrated in * Figure 2*. In the figure, there is an overall gain of +14 dB. One can also see that a +10 dBm signal is applied at the input. Following the decibel and decibel-referred-to-mW levels throughout, one can see that the output is +24 dBm, which is exactly 14 dB higher than the input. Thus, it is shown that decibels and decibels referred to mW can be used together.

**Characteristic Impedance.** When thinking of impedance, think of something in the way. A running back in football is impeded by a group of 300-pound defensive linemen; an accident on the freeway impedes the flow of traffic; and alcohol impedes one’s driving skills. All these examples show some parameter in the way of normal operations. A characteristic impedance is an impedance (in ohms) that determines the flow of high frequency energy in a system or through a transmission line. The characteristic impedance most often used in high-frequency applications is 50 ohms. This value is a

*dynamic impedance*in that it is not a value measured with an ohmmeter but rather an

*alternating-current*(ac) impedance, which depends on the characteristics of the transmission line or component being used. An ohmmeter placed between the center conductor and the outer shield of a coaxial cable would not measure anything but an open circuit.

^{[3]}Similarly, measuring with an ohmmeter from the conductor of a microstrip transmission line to its ground plane would yield the same result.

^{[4]}This should reinforce the understanding that characteristic impedance is not a direct-current (dc) parameter but one that quantitatively describes the system or the transmission line at the frequencies at which it is designed to work.

As previously mentioned, the characteristic impedance most often used in high frequency applications is 50 ohms. To understand how this value is determined, see * Figure 3*. It can be seen from this chart that the maximum theoretical power handling capability of a transmission line occurs at 30 ohms, while the lowest attenuation occurs at 77 ohms. The “ideal” characteristic impedance is a compromise between these two values, or 50 ohms. Note also that the characteristic impedance is the same at the input of a transmission line or device as it is 30 cm away, 1 m away, or 1 km away. It is a constant that can be relied upon to produce predictable results in a system.

__Voltage Standing Wave Ratio ____(VSWR)__**.** VSWR is used to characterize many aspects of microwave circuits. It is a number between 1.0 and infinity. The ideal value for VSWR is 1:1 (it is expressed as a ratio), which is termed a matched condition. A matched condition is one in which systems have the same impedance, i.e. all energy transmitted by a source travels forward through a transmission media to a load; there is no energy reflected back to the source. To understand the concept of a standing wave, consider a rope tied to a post. If you hold the rope in your hand and flip your wrist up and down, you see a wave going down the rope to the post. If the post and the rope were matched to each other, the wave going down the rope would be completely absorbed by the post and not seen again, i.e. all energy from the wrist is transmitted to the post via the rope. In reality, however, the post and the rope are not matched to each other and the wave comes right back to your hand. If you could move the rope at a high enough rate, you would have one wave going down the rope and one coming back at the same time, adding at some points and subtracting at others. This results in a wave on the line that is “standing still,” which is where the term standing wave* *comes from.

VSWR is the peak amplitude of the standing wave voltage maximum divided by its peak voltage minimum. It depends on the value of the impedance at the output of a transmission line compared to the characteristic impedance of the transmission line. It also can be shown that the standing wave ratio is a comparison of the impedance at the input of a device compared to the impedance at the output of the device that is driving it. A perfect match is indicated by no standing waves. A drastic mismatch, such as an open circuit or a short circuit, results in a large amplitude standing wave on the transmission line or device. This indicates a very large mismatch between devices or between the transmission line and the load at its output. The larger the mismatch, the higher the VSWR on the transmission line, or at the input or the output of a device. Conversely, a smaller mismatch results in a lower VSWR. The lowest possible VSWR, a value of 1:1 occurs with a perfect match.

###### [3] A coaxial cable is a transmission line with a center conductor surrounded by an outer conducting shield separated by an insulating dielectric material.

###### [4] A microstrip transmission line is a printed conductive line on one side of a planar dielectric board with a complete conductive ground plane plated on the other side.

## Terminology cont.

__Return loss__* .* Related to VSWR, return loss (in decibels) indicates the level of power reflected from a device due to a mismatch. With a perfect match between a transmission line and a load at its output, very little, if any, power is reflected, and the difference between the input level and the reflected power is a large number of decibels. If there is a short circuit or an open circuit at the output of the transmission line, all the incident power is reflected back, and there is very little difference in decibels between the two. It is important to understand that a much better match in a circuit (a more desirable condition) is represented by a higher value of return loss as well as a lower VSWR.

__Reflection coefficient__* .* The reflection coefficient is the ratio of the amplitude of the reflected wave to the incident wave at the end of a transmission line or at the input or output of a circuit. It is related to VSWR as well. The magnitude of this ratio squared and multiplied by 100 represents the percentage of power reflected from a mismatch. If there is a perfectly matched condition, the reflection coefficient is 0 (0 percent); if there is an open circuit or a short circuit at the end of a transmission line, the reflection coefficient is 1 (100 percent). Any mismatched condition between those two extremes is between 0 and 1. The designation for the reflection coefficient is either ρ or G, depending on the publication. A low reflection coefficient represents a good match. A high reflection coefficient is an indication of a large mismatch and, consequently, a high VSWR and low return loss.

__Wavelength__** .** A wavelength is the length of one cycle of a signal, as illustrated in

*. Wavelength is designated by the symbol λ. One wavelength is the distance between two adjacent points with the same amplitude. If, for example, we measure 0.1 V at one point on the wave, one wavelength will be where the wave is 0.1 V again. Values commonly used in high frequency applications are λ/2 (half wavelength) and λ/4 (quarter wavelength).*

**Figure 4**__Frequency__** .** This simply means how many times an electromagnetic wave repeats itself (i.e completes one full cycle) in 1 second. One cycle per second is defined as 1 Hz. For example, 1 GHz means that the wave repeats itself 1,000 million times in 1 second (1 billion times per second).

__Short circuit__** .** For high-frequency work, a short circuit is often an intentional condition, i.e. an actual short circuit with a value of 0 ohms if measured with an ohmmeter. A short circuit is useful to establish a defined reference point along a transmission line. Care must be taken in the use of a short circuit for any application; it is a short to DC as well as microwaves and will shunt DC current to ground.

__Wireless__** .** In a wireless communications system, there is no physical connection between the transmitter and the receiver. Although wireless technology is now a very large business, there is nothing new about the concept, which dates back to the days of Tesla and Marconi. We have come a long way since then; today, wireless local area networks (LAN), personal communication systems (PCS) and many other systems that have no connecting wires are commonplace. Three terms are associated with many wireless applications: time division multiple access (TDMA), frequency division multiple access (FDMA) and code division multiple access (CDMA).

**TDMA** is a time-sharing scheme in which stations are allocated specific time slots in which to operate. * Figure 5* shows the relationship of time and frequency for TDMA operation. It can be seen that there are specific times for each system, with guard times between so there is no interaction between stations. In a TDMA scheme, each channel is assigned specific times to transmit and to receive. During the times not allotted to them, they cannot perform their assigned functions. This may seem problematic, but these are short times, on the order of millisecond and microseconds, where interruptions in transmission or reception are not noticed.

**FDMA** is illustrated in * Figure 6*. Each station is on all the time but is assigned certain frequencies in which to operate. There also are spaces between stations in this scheme, called guard bands, which serve the same purpose as the guard times in TDMA. FDMA is the method with which most people are familiar (although they may not realize it), because it is used in AM and FM radio and television. Each station, or channel, is assigned a specific frequency on which to transmit. The stations are on all the time at their assigned frequencies. There also are bands between stations so that an easy listening radio station does not interfere with a rock station or a television sitcom does not interfere with the evening news.

## Terminology cont.

**CDMA** is used for spread spectrum secure communications systems. * Figure 7* shows that CDMA assigns both time and frequency according to a code. These time/frequency allocations are called

*chips*. Usually, a pseudorandom code is established at the transmitter and is received only by those receivers that have the same code; only they can receive the signal and demodulate it. This is the operating principle behind 3G cellular telephone network, ensuring the security of conversations.

Finally, a form of FDMA, called orthogonal frequency division multiple access (**OFDMA**) has been adopted in recent years for use in 4G of cellular communications. It splits a serial data stream into several parallel streams transmitted through separate closely-spaced narrowband channels. These frequency channels can be closely packed in an efficient manner because their spectrums are orthogonal, or independent of each other. This has the effect of reducing interference and crosstalk without sacrificing throughput. This form of modulation and signal processing has found favor over CDMA in modern networks because of its resilience to fading and interference, and its spectral efficiency.

*Radar*** . **The earliest systems for

**Ra**dio

**D**etection

**a**nd

**R**anging were developed just before and during WWII for the detection, characterization and tracking of airborne threats. Current applications are more diverse to include air and terrestrial traffic control, navigation, radar astronomy, ground mapping, weather prediction and more. Radar employs complex modulations superimposed on transmitted electromagnetic waves at microwave frequencies and higher. These are aimed and focused through sophisticated antenna systems in order to detect, characterize and track targets and subjects of interest with high accuracy and precision by reflecting the transmitted energy back to sensitive receivers with sophisticated signal processors.

## Summary

This brief introduction and definition of some fundamental terms should provide a basis for subsequent discussions that address topics such as transmission media, components, solid state device, materials and measurements.