Chapter 2

Energy Fundamentals 1 1 Naval Weapons Systems



The first requirement of any weapon system is that it have some means of detecting a target. This function of the Fire Control Problem, as well as several others, is accomplished by the weapon system sensor. In order to detect, track and eventually nuetralize a target, the weapon system must be capable of sensing some unique characteristic that differentiates or identifies it as a target. One such characteristic is the energy that is either emitted or reflected by the target. Once the energy is detected the weapon system sensor can perform some of the other functions of the Fire Control Problem, namely the localization, identification and tracking of the target. The information thus obtained by the sensor can then be furnished to the other components of the weapons system.

This section is heavily directed toward the properties of radar energy, but the principles presented in Chapter 2 are the same for all other types of electromagnetic energy--such as radio, infrared, visible light, and X-rays. Sound energy, though not electromagnetic, also exhibits many of these same properties, as will be described later in this section. It is imperative that a solid foundation in the principles of energy transmission and propagation be acquired in order to fully understand the design and use of the various types of modern weapons-system sensors.



Energy Fundamentals


1. Understand the relationship between wavelength and the speed of wave propagation.

2. Understand the concept of the generation of electromagnetic energy and the relationship between the E and H fields in an electromagnetic wave.

3. Be acquainted with the concepts of time and distance as they affect wave phase angle and constructive and destructive interference.

4. Understand the principles of reflection, refraction, ducting and polarization.

5. Know how antenna and target height affect detection range.

6. Know the relationship between frequency and wave propagation path.


The Nature of Waves

The detection of a target at tactically advantageous ranges can only be accomplished by exploiting energy that is either emitted by or reflected from the target. The form of energy that has proven to be the most suitable is energy wzves. This type of energy radiates or propagates from a source in waves, in much the same way as waves spread out concentrically from the point of impact of a pebble dropped in water. A small portion of the surface is elevated above the normal level of the pond by the force of pebble impact. This elevated portion is immediately followed by another portion that is below the normal level of the pond, conserving the water medium. Together the two parts appear as a small portion of a sine wave function that is perpendicular to the surface of the pond. The disturbance seems to move equally in all directions, and at a constant speed away from the point of impact. This type of activity is known as a transverse travelling wave.

While the waves created by this familiar example are two-dimensional, electromagnetic energy radiated from a point in a vacuum travels in three-dimensional waves--i.e., concentric spheres. The fact that, unlike sound, electromagnetic waves travel through a vacuum reminds us that the wave does not depend upon a substantive medium, but rather upon "fields" of potential force, that is the electric and magnetic fields that make up the electromagnetic wave. In the study of radiated energy, it is often difficult to envision expanding spheres of concentric wave fronts as they propagate through space. To model the wave and keep track of its progress, it is convenient to trace the two dimensional ray paths rather than the waves. A ray is formed by tracing the path of a hypothetical point on the surface of a wave front as it propagates through a medium. This trace forms a sinusoid and models a transverse travelling wave. No matter what type of weapon system is being discussed, energy waves are usually involved at some point in the detection, tracking, and nuetralization of the target. It is therefore very important to understand some fundamental concepts and descriptive properties of energy waves, because it is fundamental to all our modern weapons systems.


Perhaps the single most important property that distinguishes between the different forms of radaited energy is frequency. Nearly all wave activity is periodic, menaing that the disturbance forming the wave happens over an over again in usually rapid succession. If the number of disturbances that occur over a given time (usually one second) are counted, then we have a measure that describes the periodic structure or frequency of that wave. As mentioned previously, a wave disturbance produces a maximum (crest) followed by a minimum (trough) value. By counting the number of maximums and minimums per second gives us the frequency which is measured in cycles per second or hertz (Hz), named in honor of Heinrich Hertz who in 1887 was the first to produce and detect electromagnetic waves in the radio frequency range. In the case of sound, frequency is the rate at which the medium is successively compressed and expanded by the source. For electromagnetic energy such as radio, radar, and light, it is the rate at which the electric and magnetic fields of a propagating wave increase and decrease in intensity. Since radiated energy is composed of periodic waves, these potential force fields can be represented by sine or cosine waves.

To help understand the significance of frequency as a descriptive parameter, it may be helpful to know that the push tones on your telephone, radio waves, heat, light, x-rays and gamma radiation may all be described as radiated sinusoidal waves. It is the frequency that distinguishes one of these energy forms from the other. Discriminating one form of radiated energy from another on the basis of frequency alone is called a spectrum. Figure 2.1 shows how the various forms of wave energy relate to frequency. Audio frequencies are low numbers, ranging from about 10 to 20,000 Hz. At about 20,000 Hz the nature of waves change from the more mechanical sound waves to electromagnetic waves, which comprise the remainder of the spectrum. At the lower frequencies are radio, television, radar and microwave ransmissions. This radio band is very wide ranging from 20 thousand (kilo) to about 200 million (Mega) Hz fro radio and television, and to 100 billion (Giga) Hz for radar and microwaves. At yet higher frequencies the energy forms become heat, then visible light, followed by x-rays and finally gamma radiation. The entire spectrum has covered 20 orders of mamgnitude, and yet the sinusoidal wave form of the radaited energy has remained the same!


The velocity that waves spread from their source can vary dramatically with the form of the energy and with the medium the energy is spreading through. The velocity at which the energy propagates can vary from a few meters per second as in the case of the wave on the surface of the pond to 300 million (3x108) meters per second for the velocity of an electromagnetic wave in a vacuum. For an electromagnetic wave travelling in other mediums the speed may be substantianally reduced. For example, electromagnetic energy flowing alog a wire, or light passing though a lens may have a velocity that is only about 3/4 that of the velocity in a vacuum.

As a wave passes through mediums with different propagation velocities, the path of the wave may be significantly altered. It is therefore useful to have a relative measure of the effect of different mediums and materials on wave speed. The measure of this difference in propagation velocity is called the index of refraction. The index of refraction is simply the ratio of a wave in a standard medium or material (usually designated as c) divided by the velocity of the wave in the medium being examined. For sound waves the standard velocity is usually the velocity in a standard volume of air or seawater. For electromagnetic waves, the standard is the propagation velocity in a vacuum. As an example, if the velocity of light in a galss lens were 3/4 of the velocity in a vacuum, the index of refraction would be 3x108 m/sec divided 2.25x108 m/sec, giving an index of refraction of 1.33. For radar frequencies and above, the index of refraction of air is very close to 1.0 and therefore the velocity difference in the two mediums is usually ignored in the timing of radar echoes to determine target range.


We have seen that all travelling waves consist of a periodically repeating structure, and that the wave propagates at some idetifiable velocity. A new descriptive parameter that combines the two measurements of frequency and velocity will now be examined. If the distance between two easily identifiable portions of adjacent waves, such as the crests, is measured, then we have measured the the wave travels during one complete wave cycle. This distance is known as wavelength (). Notice that the wavelength depends on how fast the wave is moving (wave velocity) and how often the the disturbances are coming (wave frequency). From physics we know that distance (wavelength) equals velocity (c) multiplied by time. Figure 2.2 shows a wave as it would exist at any one instant in time over a distance r, in the direction of propagation. The time interval required for the wave to travel exactly one wavelength, that is for the displacement at point r4 to return to the same value as it had at the beginning of that time interval, is known as the period and is given the symbol T. This time period is also equal to the reciprocal of the frequency of oscillation. From these observations, an inverse relationship between frequency and wavelength can be written, as seen below:


c = Wave propagation velocity in a particular medium (meters/sec)

= wavelength (meters)

f = frequency (Hz)

T= period (sec)

Wavelength is very important in the design of radio and radar antennas, because of its relationship to antenna size. Referring to figure 2.1 radio frequency wavelengths range from thousands of meters at the low end of the spectrum to fractions of a centimeter at the high frequency end. Infrared and light energ have ver small wavelengths in the nanmeter (1x10-9 m) range. X-rays and gamma rays have wavelengths even smaller, in the picometer (1x10-12 m) to femtometer (1x10-15 m) range. Both the efficiency of a radar or radio antenna and its ability to focus energy depends on the wavelength since the antenna's ability to form a narrow beam (its directivity) is directly related to the antenna size measured in wavelengths. That is, a physically small antenna will have very good directivity when used at a high frequency (short wavelength), but would not be able to form as narrow a beam if used to transmit at a lower frequency. In addition, the size of the antenna is directly proportional to the wavelength of the energy being transmitted.


Amplitude may be defined as the maximum displacement of any point on the wave from a constant reference value. It is easy to picture the amplitude of say waves on the surface of the water. It would be the height of the water at a crest of a wave above the average level of the water, or the level of the water when it is still. The amplitude of an electromagnetic wave is more complicated, but it is sufficient to think of it as associated with the intensity of the two fields that compose it, the electric and magnetic. When depicting an electromagnetic wave as a sine wave it is the electric field intensity, in volts per meter (v/m) that is plotted. In figure 2.2 the amplitude varies from +A to -A. The stronger the electromagnetic wave (i.e. the radio signal) the greater the field intensity. The power of the electromagnetic wave is directly proportional to the square of the electric field intensity. The crests and troughs of the wave are simply reversals of the polarity (the positive to negative voltage direction in space) of the electric field.


The final property of a wave to be discussed is its phase. Phase is simply how far into a cycle a wave has moved from a reference point. Phase is commonly expressed in degrees or radians, 360 degrees or 2 radians corresponding to a complete cycle of the wave. Referring back to figure 2.2 as an illustration, there is no field intensity at the origin, at the instant in time for which the wave is drawn. At the same instant in time, a crest or peak in field intensity is being experienced at point r1 , a trough or oppositely directed peak intensity at point r2 , another "positive zero crossing" at r3 and another crest at r4. The wave at r1 is one quarter cycle out of phase with that at the origin, three quarters of a cycle out of phase at r2, and back in phase at r3. Points that are separated by one wavelength (r3 and the origin, r4 and r1) experience in phase signals as the propagating wave passes by. Based on the way in which phase is measured, we can say that the signal seen at r1 is 90o out of phase with the origin.

Now consider a wave propagating to the right. Figure 2.3 illustrates a propagating sine wave by showing, in three steps in time, the wave passing four observation points along the r axis. The increments of time shown are equal to one quarter of the period of a cycle, t = T/4. Just as we can plot a wave by looking at it as the wave exists at some instant in time, we can also plot a propagating wave as a function of time as seen at one point in space. Figure 2.4 illustrates this by showing the position of the wave at points r4, r2 and r1. The signals at r4 and r1 are in phase, whereas the signal at r2 is out of phase with the signal at r4 by 90o.

The signal at r2 is also said to lead the signal at r4. This is because the waveform at r2 crosses the horizontal axis (at t2) and reaches its peaks (at t3) before the waveform at r4. Similarily, we can say that the signal at r4 lags the signal at r2 by 180o.

A sine wave can also be thought of as being generated by a rotating vector or phasor as shown in figure 2.5(a). At the left is a vector whose length is the amplitude of the sine wave and which rotates counter clockwise at a rotation rate () of 360o or 2 radians each cycle of the wave. This rotating vector representation is very useful when it is necessary to add the intensities of the fields (amplitudes) of multiple waves arriving at a point. This method of adding two or more rotating vectors is known as phasor algebra and is illustrated in figure 2.5(b). In figure 2.5(b), two vectors of equal amplitude and rotation rate, with vector one leading vector two by 30o, are shown. The resultant is the vector addition of the two vectors/waves and is illustrated by the dashed vector/waveform. When multiple waves are involved, as in most radar applications, it is easier to add the vectors together to create a new vector, the resultant, than to add the waves themselves.


Any pure energy that has a single frequency will have the waveform of a sinusoid and is termed coherent energy. In addition any waveform which is composed of multiple frequencies and whose phase relationships remain constant with time is also termed coherent. For pulses of electromagnetic energy (as in radar) coherence is a consistency in the phase of a one pulse to the next. That is, the first wavefront in each pulse is separated from the last wavefront of the preceeding pulse by an integer number of wavelengths (figure 2.6). Examples of coherent signals used in radar are:

- a short pulse of a constant frequency signal.

- a short pulse of a frequency modulated signal.

- the series or "train" of such pulses used over a long period of time.

Noncoherent energy is that which involves many frequency components with random or unknown phase relationships among them. Sunlight and the light emitted by an incandescent light are examples of noncoherent energy. Both are white light, that is they contain numerous frequencies, are random in nature and the phase relationships among them change with time. Coherent energy has two major advantages over noncoherent energy when employed in radars. These advantages will be addressed and explained later in this section under the Radar Equation topic. Radars of older design used noncoherent signals, since at the time of their development, the technology was not available to produce a sufficiently powerful coherent signal. The high performance radars used today make use of coherent signals.

The Wave Equation

In order to derive an equation that completely defines the amplitude and hence the strength of the electric field in terms of time and distance, it is helpful to begin by investigating the simplified example of a sine wave at a single instant in time (figure 2.2). The displacement of the wave in the y direction can be expressed as a function of the distance from the source (r) and the maximum amplitude (A).

The y displacement is solely a function of the lateral (r) displacement from the origin since the sine wave is shown at one instant in time.

In figure 2.3 the wave is propagating to the right and the displacement is seen at different points along the r axis as the time changes. At any given point along the r axis (for example r4) the displacement varies as the frequency of oscillation. The number of cycles that pass by any point during an elapsed time t is equal to the frequency multiplied by the elapsed time. To determine the actual change in phase angle that has occurred at this point after a time t the full cycle of oscillation is equal to 360o or 2 radians must be also taken into consideration. This change in phase is expressed by:

It is now possible to express the displacement in y of this propagating sine wave as a function of distance from the source (r), elapsed time (t), frequency (f) and the maximum amplitude (A):

Substituting in the relationship of equation 2-1, equation 2-4 becomes:



Maxwell's Theory

Maxwell's Equations state that an alternating electric field will generate a time-varying magnetic field. Conversely, a time-varying magnetic field will generate a time-varying electric field. Thus, a changing electric field produces a changing magnetic field that produces a changing electric field and so on. This means that some kind of energy transfer is taking place in which energy is transferred from an electric field to a magnetic field to an electric field and so on indefinitely. This energy transfer process also propagates through space as it occurs. Propagation occurs because the changing electric field creates a magnetic field that is not confined to precisely the same location in space, but extends beyond the limit of the electric field. Then the electric energy created by this magnetic field extends somewhat farther into space than the magnetic field. The result is a traveling wave of electromagnetic energy. It is important to note that these fields represent potential forces and differ from mechanical waves (i.e. ocean waves or sound) in that they do not require a medium to propagate. As such they are capable of propagating in a vacuum.

Generation of Electromagnetic Waves

An elementary dipole antenna is formed by a linear arrangement of suitable conducting material. When an alternating electric voltage is applied to the dipole, several phenomena occur that result in electromagnetic radiation. An electric field that varies sinusoidally at the same frequency as the alternating current is generated in the plane of the conductor. The maximum intensity of the generated electric field occurs at the instant of maximum voltage.

It was stated at the beginning of this section that an alternating electric field will produce a magnetic field. The dipole antenna just described must therefore be surrounded by a magnetic field as well as an electric one. A graphical illustration of this field is shown in figure 2.7. Since the current is maximum at the center of the dipole, the magnetic field is strongest at this point. The magnetic field is oriented in a plane at right angles to the plane of the electric field and using the right-hand rule, the direction of the magnetic field can be determined as illustrated in figure 2.7.

The elementary dipole antenna of the foregoing discussion is the basic radiating element of electromagnetic energy. The constantly changing electric field about the dipole generates a changing magnetic field, which in turn generates an electric field, and so on. This transfer of energy between the electric field and the magnetic field causes the energy to be propagated outward. As this action continues a wave of electromagnetic energy is transmitted.

The Electromagnetic Wave

In order to provide further insight into the nature of electromagnetic radiation, a sequential approach to the graphical representation of electromagnetic fields will be undertaken.

Figure 2.8 illustrates the waveform of both the electric (E) and magnetic (H) fields, at some distance from the dipole, as they are mutually oriented in space. The frequency of these waves will be identical to the frequency of the voltage applied to the dipole. From previously developed relationships, the electric and magnetic field strengths at any distance r and time may be defined as:



Eo = maximum electric field strength

Ho = maximum magnetic field strength

c = speed of light = 3 X 108 meters/sec

r = distance from the origin

t = time since origination (or some reference)

Phase Shifted Equation

Consider two dipole antennas, each of which is operating at the same frequency, but located such that one antenna is a quarter of the wavelength farther away from a common reference point as shown in figure 2.9. For simplicity, only the E field from each antenna is shown. The electric field strength at point P from antenna one is depicted in equation 2-7(a). In this particular case the wave from antenna one leads antenna two by the distance they are seperated, 1/4 wavelength or 90o. For antenna number two, the field strength equation becomes:

which can be further reduced to:

E~=~E_o~sin~ LEFT