# 10.5 Radar Sensors

The term radar is a contracted form of the phrase radio detection and ranging, which conveys some—not all—of the features of a modern radar system. Historically, radar systems were first developed and used at radio frequencies, including the microwave band, but we now also have light radars or lidars that operate at optical wavelengths. Over the years, the name radar has lost its original meaning and has come to signify any active electromagnetic sensor that uses its own source to illuminate a region of space and then measure the echoes generated by reflecting objects contained in that region. In addition to detecting the presence of a reflecting object and determining its range by measuring the time delay of short-duration pulses transmitted by the radar, a radar is also capable of specifying the position of the target and its radial velocity. Measurement of the radial velocity of a moving object is realized by measuring the Doppler frequency shift produced by the object. Also, the strength and shape of the reflected pulse carry information about the shape and material properties of the reflecting object.

Radar is used for a wide range of civilian and military applications, including air traffic control, aircraft navigation, law enforcement, control and guidance of weapon systems, remote sensing of Earth’s environment, weather observation, astronomy, and collision avoidance for automobiles. The frequency bands used for the various types of radar applications extend from the megahertz region to frequencies as high as 225 GHz.

# 10.5.1 Basic Operation of a Radar System

The block diagram shown in Fig. 10-9 contains the basic functional elements of a pulse radar system. The synchronizer–modulator unit serves to synchronize the operation of the transmitter and the videoprocessor–display unit; it does so by generating a train of direct-current (dc) narrow-duration, evenly spaced pulses. These pulses, which are supplied to both the transmitter, and the videoprocessor–display unit, specify the times at which radar pulses are transmitted. The transmitter contains a high-power radio-frequency (RF) oscillator with an on/off control voltage actuated by the pulses supplied by the synchronizer–modulator unit. Hence, the transmitter generates pulses of RF energy equal in duration and spacing to the dc pulses generated by the synchronizer–modulator unit. Each pulse is supplied to the antenna through a duplexer, which allows the antenna to be shared between the transmitter and the receiver. The duplexer, which often is called the transmitter/receiver (/R) switch, first connects the transmitter to the antenna for the duration of the pulse and then connects the antenna to the receiver for the remaining period until the start of a new pulse. Some duplexers, however, are passive devices that perform the sharing and isolation functions continuously. The circulator shown in Fig. 10-5 is an example of a passive duplexer. After transmission by the antenna, a portion of the transmitted signal is intercepted by a reflecting object (often called a target) and scattered in many directions. The energy reradiated by the target back toward the radar is collected by the antenna and delivered to the receiver, which processes the signal to detect the presence of the target and to extract information on its location and velocity. The receiver converts the reflected RF signals into lower-frequency video signals and supplies them to the videoprocessor–display unit, which displays the extracted information in a format suitable for the intended application. The servo unit positions the orientation of the antenna beam in response to control signals provided by either an operator, a control unit with preset functions, or a control unit commanded by another system. The control unit of an air-traffic-control radar, for example, commands the servo to rotate the antenna in azimuth continuously. In contrast, the radar antenna placed in the nose of an aircraft is made to scan back and forth over only a specified angular sector.

# Figure 10-9 Basic block diagram of a radar system.

Figure 10 9 Full Alternative Text

# 10.5.2 Unambiguous Range

The collective features of the energy transmitted by a radar are called the signal waveform. For a pulse radar, these features include (1) the carrier frequency f, (2) the pulse length τ, (3) the pulse repetition frequency f p (number of pulses per second) or equivalently the interpulse period T p=1/f p, and (4) the modulation (if any) within the pulses. Three of these features are illustrated in Fig. 10-10. Modulation, which refers to control of the amplitude, frequency, or phase of the signal, is beyond the level of the present treatment.

# Figure 10-10 A pulse radar transmits a continuous train of RF pulses at a pulse repetition frequency f p.

Figure 10 10 Full Alternative Text

The range of a target is determined by measuring the time delay T taken by the pulse to travel to the target and back. For a target at range R,

T=2 R c, (10.13)

where c=3×10 8 m/s is the speed of light and the factor 2 accounts for the two-way propagation. The maximum target range that a radar can measure unambiguously, called the unambiguous range R u, is determined by the interpulse period T p and is given by

The range R u corresponds to the maximum range that a target can have such that its echo is received before the transmission of the next pulse. If T p is too short, an echo signal due to a given pulse might arrive after the transmission of the next pulse, in which case the target would appear to be at a much shorter range than it actually is.

According to Eq. (10.14), if a radar is to be used to detect targets that are as far away as 100 km, for example, then f p should be less than 1.5 kHz, and the higher the pulse repetition frequency (PRF), the shorter is the unambiguous range R u. Consideration of R u alone suggests selecting a low PRF, but other considerations suggest selecting a very high PRF. As we will see later in Section 10-6, the signal-to-noise ratio of the radar receiver is directly proportional to f p. Hence, it would be advantageous to select a PRF as high as possible. Moreover, in addition to determining the maximum unambiguous range R u, the PRF also determines the maximum Doppler frequency (hence, the target’s maximum radial velocity) that the radar can measure unambiguously. If the requirements on maximum range and velocity cannot be met by the same PRF, then some compromise may be necessary. Alternatively, it is possible to use a multiple-PRF radar system that transmits a few pulses at one PRF followed by another series of pulses at another PRF. Then the two sets of received pulses are processed together to remove the ambiguities that would have been present with either PRF alone.

# 10.5.3 Range and Angular Resolutions

Consider a radar observing two targets located at ranges R 1 and R 2, as shown in Fig. 10-11. Let t=0 denote the time corresponding to the start of the transmitted pulse. The pulse length is τ. The return due to target 1 will arrive at T 1=2 R 1/c and will have a length τ (assuming that the pulse length in space is much greater than the radial extent of the target). Similarly, the return due to target 2 will arrive at T 2=2 R 2/c. The two targets are resolvable as distinct targets so long as T 2≥T 1+τ or, equivalently,

2 R 2 c≥2 R 1 c+τ. (10.15)

# Figure 10-11 Radar beam viewing two targets at ranges R 1 and R 2.

The range resolution of the radar, Δ R, is defined as the minimum spacing between two targets necessary to avoid overlap between the echoes from the two targets. From Eq. (10.15), this occurs when

Some radars are capable of transmitting pulses as short as 1 ns in duration or even shorter. For τ=1 ns, Δ R=15 cm.

The basic angular resolution of a radar system is determined by its antenna beamwidth β, as shown in Fig. 10-12. The corresponding azimuth resolution Δ x at a range R is given by

0 0 Δ x=β R, (10.17)

where β is in radians. In some cases, special techniques are used to improve the angular resolution down to a fraction of the beamwidth. One example is the monopulse tracking radar described in Section 10-8.

# Figure 10-12 The azimuth resolution Δ x at a range R is equal to β R.