An Introduction to Communication Antennas Proceedings Paper for Engineering 302 Spring 2004

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Abstract- This paper explores many angles of communication antennas such as origin, types, applications, material makeup, and fundamental equations. The purpose is to give the reader a brief history on radio communications as well as a look into the electromagnetics of how antennas operate. Index Terms—Antenna, Dipole, Maxwell, Waveguide,

I. INTRODUCTION ommunication antennas are all around us and a major part of the way we live our lives. Chances are that you have a cell phone or wireless PDA on your person right now. A drive down most any road will likely take you past a radio tower or cell station array. So why are antennas so important and worth studying? The answer lies in the fact that they are essential to modern day human communication. Many believe that the ability to talk across the world with a transmitter and a piece of wire is amazing and almost magical. There are many purposes to this paper. We will start by exploring the origin of wireless communication, then explore the different types and parts of antennas, and then finally explore the fundamental equations behind antenna functionality.

II. ORIGIN OF WIRELESS COMMUNICATION Antennas go back to the mid 1800s and much evolution has occurred since. The first experiments with wireless communication are on record in 1867 but little details are available. A major breakthrough is noted for Guglielmo Marconi with a wireless call that traveled to boats across the Atlantic Ocean. Previous to this feat radio transitions had a very limited range such that houses or boats very close could talk to each other, but communication over great distances was unlikely. Radio communication was only a series of tones, know as mores code, but it now provided the ship industry with an element of safety that it didn’t have before Marconi.

The next breakthrough was in 1916 when operators at Radio Arlington were able to transmit the sound of a human voice up and down the Atlantic coast. This was a major breakthrough and the beginning of AM (Amplitude Modulation) radio. This sparked an interest in radio and during the mid 1920s many citizens were putting wire array antennas on their roofs to talk to other people nearby. The frequencies used by citizens were in the high frequency range lower than 200 meters wavelength. Because of this people who use this band are know and shortwave or “ham” operators. People quickly realized that the shorter the wave the further it propagates through space. Therefore people operating in the range below 50 meters were able to make contact around the world in the early 1920s [2].

III. RADIO WAVE PROPAGATION Radio waves are similar to light waves but they vary in several aspects. Radio waves do not always follow the inverse square law as their light wave counterpart. There are many external conditions that affect a radio wave such as atmospheric conditions. Discovery of radio signals as electromagnetic waves is attributed to Heinrich Hertz. Before Hertz carried out various experiments the knowledge of induction fields among current carrying wires was used in the development of electric motors. In radio applications there is a radiated field that leaves the conductor and travels through space. Antennas create a series of oscillation waves with specified frequencies and wavelengths. The electromagnetic wave travels away from the antenna up to a distance where the energy is completely damped by the environment.

IV. RADIO WAVES AS ELECTROMAGNETIC FIELDS Radio signals are very much like light signals except that they have additional components of frequency. All radio waves are called transverse

Kyle Israels, Student Member IEEE, Engineering 302 Proceedings

P distanceP antenna

4 π d2.Eq 1

P loadP distance λ wavelength

2.

4 π( )2 d2Eq 2

Loss dB 10 LogP antenna

P load. Eq 3

electromagnetic (TEM) waves because they consist of two fields, offset by 90 degrees along the propagating axis. Fig. 1 shows this phenomenon. The direction of the fields can be oriented by the transmitting antenna. Thus antenna are therefore “polarized”. An antenna is classified as vertically or horizontally polarized based on the direction in which the electric field radiates from the antenna. Most radio antennas are vertically polarized It is important that a pair of antennas has the same orientations or signal loss on the order of 20 dB can be expected.

Fig.1 Diagram showing the electric and magnetic fields radiating from a point charge Radio waves are attenuated by the inverse square law. This is due to the energy being emitted from a point out into a spherical pattern. The power density of a radio wave is measured in watts per meter squared (W/m^2). Due to the inverse square law the power intensity at a distance d from the antenna can be described as in equations 1 below (isotropic conditions) where d is the distance from the antenna to the point of measurement. The power delivered to the load (receiving antenna) is the product of the aperture gain and the transmitted power. Aperture gain is gain which is attributed to the antennas reflector if present. Equation 2 shows this formula. Given the equations above the losses due to space propagation (dB) can be determined using equation 3.

V. RADIO WAVE PROPAGATION ON EARTH TEM waves do not rely on an atmosphere for travel, but they are affected by atmospheric conditions. Radio waves travel best though bands of atmosphere with low air densities. Thus waves that travel in the upper atmospheric layers are the waves that travel the furthest along the radio horizon. Air is less dense when it is cold, therefore waves travel the greatest distances at night. This is a common phenomenon with AM radio stations at night. You are much more likely to receive distant AM stations on a summer night than a winter day. Fig 3 shows a very detailed of TEM wave interactions with the atmosphere. High frequencies, those operating in the VHF and UHF bands, are very susceptible to multipath phenomena and line of sight reception. Thus radio communications operating in this range need to have a line of sight between the transmitter and receiver. Typically signal range in this band is within 100 miles of the antenna. Multipath phenomena is when a signal is distorted by the interaction with the genuine signal and a delayed signal which has been reflected upon its path. This phenomena results in a “ghost” image on the television, and causes cell phones to occasionally drop calls. Radio signals in the VHF and UHF bands are limited to line of sight from the antenna to the horizon. Refraction by the atmosphere can affect the magnetic fields so that the actual signal range is increased by unto 20 %. A diagram of this phenomena is shown in fig. 2 Fig.3 Radio horizon path can be further away from point source compared to normal l ine of sight. [!]

Fig.3 Diagram showing wave propagation affected by atmospheric condit ions.[2] When a signal enters into the atmosphere is interacts with the ions and as a result the signal is “bent” back in the direction of the ground. This ionization allows for the signal skip phenomenon. Waves are also affected by reflection and refraction. When a signal hits an object it is reflected at a complimentary angle, angle of reflection to the angle at which it hit the object, the angle of incidence. If a signal strikes an object it creates a shadow zone behind it where radio communication is blocked. An example of this could be a lack of signal in a basement, or behind the moon. Figures 4 and 5 show these phenomena.

Fig. 4 Radio wave being blocked by a foreign object [3]

Fig. 5 Wave reflection off solid object [2]

VI. ANTENNAS MODELED AS A CAPACITOR Before we go much further it is necessary to talk about how the transmitting antenna develops a TEM wave. The antenna is supplied by an AC current and voltage from a transmitter operating at a specified frequency. The antenna acts as a capacitor developing magnetic and electric fields between the poles. Unlike electrical capacitors, which have a dielectric material between the plates, antennas have poles that are separated but usually on axis with each other. A common example that will be explored later is the dipole antenna. When a signal is applied to an antenna the voltage lags the current by 90 degrees. This is what caused the electric and magnetic fields to also be out of phase with each other. As the current flows in the antenna the electric field goes to a minimum level and the magnetic field rises to its maximum level. Once the current supply is stopped a voltage differential is generated in the antenna and the electric field builds to its maximum level. Fig 6 shows a graphical representation of this procedure.

Fig. 6 Voltage and Current density in a dipole antenna. Feed point is in center of horizontal axis [2]. When the current is abruptly stopped the result on an antenna is a voltage buildup at the ends. This causes a wave to travel backwards towards the transmitter. This wave is known as a reflected wave and can aid or harm the overall antenna efficiency. The reflected wave is summed with the wave generated by the transmitter and the resultant is called a standing wave. The standing wave can be twice the magnitude of the transmitter input if the waves are in phase. The standing wave can have a very small magnitude if the waves are out of phase with each other. The standing wave is determined directly by the length of the antenna.

Figure 7 Shows phase addition theorems. These theorems are not only applied to transmitting antennas with standing waves but also receiving antennas experiencing delayed signals. Fig 7a shows two signals in phase with each other. 7b shows two waves out of phase causing cancellation. There are a couple variations in devices which allow electromagnetic waves to propagate through a medium. The two most common of devices are waveguides and antennas. A waveguide is described as a device which moves electromagnetic waves between two direct points allowing very little energy outside of the path. An example of a wave guide might be a piece of coax cable between a transmitter and its antenna. An antenna allows the electromagnetic waves to propagate in all directions into space (depending on type of antenna). Waveguides come in many different varieties as shown in figure 9. For means of explorations consider the parallel plate waveguide. In order for the wave guide to work a voltage differential is applied between the two conducting plates. Current flows in the z direction and therefore the magnetic field in developed in the y direction, 90 degrees off axis. The wave is guided

Fig. 9 Typical waveguides. A)square guide, B)circuilar guide, C)Dielectric plate, D)Coaxial guide. C and D are capacit ive in nature. [3]

Fig 10. Signal propagation in a waveguide [3] along the medium in a “zig-zag” motion between the two plates. The wave vectors are equal in magnitudes as shown in figure 10. This figure show a TEM (traverse electric magnetic) wave as it travels down a transmission line.

VII. APPLICATIONS OF MAXWELL’S EQUATIONS. In order to understand antennas it is necessary to understand the math behind their fundamentals. Maxwell’s equations state that in order to create electromagnetic fields a time varying current source is needed. The fields must satisfy the four Maxwell’s equations in a region containing time-varying charge and current sources. Maxwell’s equations in a lossless (dielectric), linear, isotropic, and homogeneous medium in time dependent form are stated below: [

tBE∂∂

−=×∇ Eq 4

tBJH∂∂

+=×∇ Eq 5

0=⋅∇ B Eq 6

ρ=⋅∇ D Eq 7 ρ and J are the volume charge and volume current densities that exist in the medium as time-varying sources. Field B is a continuous field expressed in terms of field A, which is the magnetic potential vector.

AB ×∇= Eq 8 The electric field can be determined by taking the derivative of the magnetic potential field. Both A and E are time varying.

tAVE∂∂

−−∇= Eq 9

The time varying magnetic field can be modeled with the following simplified equation:

∂∂

−∇−∂∂

µε+µ=×∇×∇tAV

tJA

Eq 10 where u is the permeability of the dielectric insulator. Applying the uniqueness theorem and a couple of simplifications yields the Helmholtz equations

JAA µ−=β+∇ 22 Eq 11

where Beta is defined as

µεω=β Eq 12 The phase velocity, or speed of the wave is defined as U=w/B Eq 13 where w is the frequency of the signal It is important to note that the maximum wave speed is 3x10^8 m/s, the speed of light. Given all of these equations the Voltage potential of a radio wave as a function of time and distance from source (r) is: Eq 14

VIII. THE DIPOLE ANTENNA One of the simplest and oldest type of antennas is the Dipole of Hertzian antenna. This type of antenna is characterized by two radiators placed in line with each other. This antenna was first used by Heinrich Hertz who is considered to be the father of modern day radio. The length of the radiators is determined by the wavelength. Each wavelength must be ¼ of the desired frequency for optimal power delivery. Therefore the length of each radiator is determined by equation 15 where f is the frequency in MHz and L is the radiator length in feet.

L 468 ftf

L 468 ft

f Eq 15 The length is not the only feature of interest in making an efficient antenna. Antennas act as a RLC network with varying impedances dependent on the frequency of interest. At some frequencies the antenna acts as an inductor and at others it acts as a capacitor. The perfect antenna will be one in which the capacitance and inductive characteristics will cancel each other out. This is called a resonant antenna. An efficient antenna is one which is resistive and resonant. Dipoles antennas are coupled to transmitters by a transmission line which is connected between the radiators. As shown in figure 11 the center is a point at which the Current is prominent and the

voltage is at a minimum. This also equates to an electric field intensity which is close to zero. This point on the antenna also has the lowest input resistance making it ideal as the input signal point for the transmitter. Fig 11. Voltage and Current density along a dipole. The feed point is in the center of the horizontal axis. [2] The input of an antenna can be easily calculated using the power law derived from Ohms law. Eq 16 It is essential to match the antenna input resistance with both the transmission line and the transmitter output. Typical input resistances for dipole antennas are between 60 and 90 ohms, but it is interesting to note that the antenna resistance will vary with outside conditions such as weather and nearby objects. A graph showing the relationship between the height of an antenna above the ground and its resistance is shown below in figure 12. Fig 12. Input resistance as a function of antenna distance from the ground. [2]

V r t,( ) Qcos ωt θ( )4 π i. e. r.

R P

I2

The magnetic field in a dipole can be modeled using equation 17.

dzerIA rj

Czβ−∫π

µ=

4 Eq. 17 where I is the current along the antenna defined as in equation 18.

qjI ω= Eq. 18 Variable r represents the distance line of sight from the antenna to the receiver. This indicates that a radiated field from an antenna decreases proportionally as the distance increases.

IX. STANDING WAVES IN DIPOLE ANTENNAS In the previous section I outlined how to make an antenna resonant. If this can’t be achieved by physical placement of the feed point and the antennas height additional measures must be taken. The simplest fix is to use a matching transformer to match the transmission line to the antenna input. If there is a large difference between these two features a phenomena called standing waves will occur on the lines. A measure of the standing wave ratio (SWR) is calculated by taking a ratio of Zo, the transmission line resistance, and R, the antenna resistance.

SWRZ 0R Eq. 19

Figure 13 shows a tuning plot for an antenna based on the SWR value. In the plot trace A indicates a short in the antenna. Traces B and C are ideal for the given frequency, and traces D and E indicate an antenna that is tuned to frequencies higher and lower than the specified design frequency.

Fig 13. SWR Tuning plots for various frequencies.[2]

X. RADIATION IN A QUARTER-WAVE DIPOLE ANTENNA The dipole antenna acts as an isotropic point source, radiating its energy in all directions. This characteristic makes the antenna omni directional in respect to coverage area of the radiated signal. Figure 14 shows an idealized diagram of dipole antenna radiation. As shown the energy is directed in all directions around the antenna axis (B), the signal is radiated from approximately 45 degrees off axis in the direction perpendicular to the antenna axis (C). Fig 14. Dipole Radiation patterns. [2] Radiation and directivity can be expressed as directive gain which is the ratio of the power density that is radiated by the antenna to the average power density. This is determined by equation 20.

( )radPSrG

24π=

Eq. 20 The gain for a dipole can be simplified further to

θ= 2sin5.1G Eq. 21 By applying simple trigonometry to this equation it is easy to see that the maximum gain from a dipole antenna is 1.5, or 1.76dB.

XI. EFFICIENCY OF AN ANTENNA The efficiency of an antenna is directly related to its total resistance and the power which is delivered to it. The total resistance is the sum of the connector resistance as well as the resistance due to radiation. The power delivered to the antenna is defined in equation 22 where I is the current delivered and Rrad is the total antenna resistance. The power radiated by the antenna is related to the resistance of radiation.

radrad RIP 2

21

= Eq. 23

The efficiency of the antenna is the ratio of power radiated vs the power delivered to the antenna.

radC

rad

a

rad

in

rade RR

RRR

PP

+===η Eq. 23

XII. RADIATION IN HALF-WAVE DIPOLE ANTENNA When more power is needed to be dissipated by the antenna a half wave or full wave antenna is appropriate. Increasing the antenna length also increases the amount of current that can be supplied to the center tap.

XIII. DIRECTIONAL ANTENNAS

Sometimes radio signals need only be focused in a single direction. When this is the application a directional antenna rather than an omni directional antenna is better suited for the job. The most common directional antenna is called a Yagi-Uda antenna because it is very effective at radiating energy in a single direction. The Yagi antenna is typically a half wavelength type and has three radiating elements instead of a single dipole radiating element. The antenna has a single driver that is fed at a center tap similar to a dipole. In addition there are a minimum of two additional elements couples to the driver. These elements act as reflectors which absorb energy from the main radiating element and channel it back to the feed point to be redirected in the desired direction. The reflector elements are typically 5 % longer than the length of the main radiating element. The spacing between the radiator and the reflectors is typically .2 wavelengths. Figure 14 shows a directivity graph that would be typical of the performance of a Yagi antenna. In the figure the angle a between the line of propagation to the beam edge is the angle of directionality, or the angle between 0 and -3dB. The main

lobe of radiation is much greater than the secondary or side lobes. Depending on the efficiency of the antenna the main lobe can be between 20 and 40 dB higher than the omni directional equivalent.

Fig. 14 Directionality and gain of a Yagi antenna. [1]

XIV. WIRE LOOP ANTENNAS

A third common type of antenna is a wire loop. This antenna differs from both dipole and directional in that it is less efficient, but it has some unique characteristics that allow it to be used for specific applications. Wire loop antennas are classified as being large or small depending on the size of the loops. A small loop antenna refers to an antenna in which the length or a single loop is less than .2 wavelengths in length. A large loop antenna is therefore any antenna with a loop larger than .2 wavelengths. The main difference between the loop antennas in terms of electromagnetics is that the current varies along the wire of a large loop antenna. Also because the large loop antenna is typically one wire in density the feed point is at a point where the voltage potential is a maximum. This results in a feed point with a resistance in the order of 1 kilo ohm. Wire loop antennas generate and receive magnetic flux around the outside of their coils as shown in figure 15. This characteristic allows the antennas to be directional, or used to determine the direction in which a signal is being received. The figure also shows two nulls on either side of the loop. The sensitivity of these nulls can be -30 dB from the maximum reception areas. Taking advantage of this electromagnetic characteristic allows this antenna to reject noise or track a signal when used on a receiver or send a semi-directional signal in a compact environment when used on a transmitter.

Fig.15 Effective plot of a small wire loop antenna

XV. REFERENCES [1] “Antenna Fundementals: chapter 5” University of South

Carolina,http://www.ece.sc.edu/classes/ Spring01/elct362/Ch5_362.doc [2] Carr, Joeseph J. “Practical Antenna Handbook”, McGraw

Hill publishers, 3rd edition, 1998. [3] Hayt, William H and John Buck, “Engineering Electromagnetics” McGraw Hill, 6th edition, 2001. [4] Imberi, Jonathan and Sara. “Ham-shack.com”

http://www.ham-shack.com/propagation.html. [5] Siwiak, Kazimierz. “Radiowave Propagation and antennas

for personal communications” Artech House Publishers, 1995.

[6] Vizmuller, Peter. “RF Design Guide: systems, circuits, and equations” Artech House Publishers, 1995

[7] Wade, Paul “Antenna Fundamentals”, 1998