The publication of the first edition of Modern Radar Systems, in 2001, provided the radar community with a valuable resource for understanding the principles of radar systems and their various subsystems. Additional data on discrete phase codes, including the polyphase codes, have been added to the material from the first edition.
The radar and its ground environment
PRIMARY AND SECONDARY RADAR
- Other types of radar
The pulses from the interrogator are decoded and the code, if any, for the state is sent to the encoder. The signal from continuous wave radars must be frequency modulated to measure range as in figure 1.4. a) Cross section of buried objects (b) B-scope view of data collected in (a) Radar.
COORDINATE SYSTEMS AND RANGE
The pulse repetition rate of pulse radars limits the range of Doppler frequencies that can be uniquely identified (see Chapter 9, Detectors). The pulses are a form of sampling and this limits the determination of the Doppler frequency to a range of the pulse repetition frequency (see Chapter 11, Signal Processing).
MAIN MONOSTATIC RADAR COMPONENTS
- Transmitter
- Waveguide or transmission line system
- Diplexer
- Antenna
- Factors external to the radar
- Receiver
- Matched and matching filters
- Detector
- Analogue-to-digital converter
- Signal processor
- Threshold
- Determination of position
This reduces the probability of detection for the radar, and the increase in signal-to-noise ratio needed to bring the probability of detection back to the specified value is called the eclipse loss. An example of the signal-to-noise ratio for a spreader of one square meter is shown in Figure 1.12.
SECONDARY RADAR
PIR is the interrogator-receiver sensitivity to the required probability of decoding a response;. The transponder antenna is quasi-omnidirectional and the gain is assumed to be close to 0 dB.
RADARS WITH SEPARATELY LOCATED TRANSMITTERS AND RECEIVERS
- Elliptical coordinates
- Bistatic radar maximum range
Ellipses with the major axis along the x-axis are commonly defined by two of the following. The ellipticity is the ratio of the distance between the foci to the length of the major axis, or c/a.
PERFORMANCE
- Effects on range
- Resolution
- Accuracy
- Stability
Performance margins must be estimated to compensate for the losses in the system, and most of the factors listed under performance reduce the signal-to-noise ratio, thereby reducing maximum range and accuracy. During the signal's path from the transmitter back to the point where signals are extracted or displayed, the pulse is stretched in range and angle (azimuth and elevation), and the main stages are shown in Table 1.8.
Usual and unusual concepts
AN EXAMPLE OF THREE-DIMENSIONAL REPRESENTATION: THE WIEN BRIDGE OSCILLATOR The Wien bridge oscillator in Figure is well known
Traditionally, Bode diagrams, showing the gain and phase shift around the loop at point A, are drawn as in Figure 2.2. Here it is clear that there is only one frequency of oscillation where the operating point intersects the frequency axis, as shown in the enlarged views.
VECTOR REPRESENTATION
In this representation of complex operating point versus frequency there is no discontinuity and nature feels much better. The conjugate of a complex quantity is the quantity with the sign of the imaginary part reversed.
ORDER OF LINEAR PROCESSING
The calculation of power is performed by multiplying the voltage by the complex conjugate of the current. The calculation of power is also used for the correlation of two waveforms in Chapter 8, Matching and Pass Filters, and Chapter 11, Signal Processing.
POLYPHASE MODULATION AND DEMODULATION
The power supplied by a three-phase power circuit is the sum of the powers in each of the individual phases. In AC and polyphase systems, the power is the voltage times the conjugate of the current.
SYMMETRICAL COMPONENTS IN POLYPHASE CIRCUITS
The direction the egg is pointing is given by the phase angle, 2, of the negative component, as illustrated in Figure 2-15. The negative and zero phase sequence components are interfering by-products and are discussed in the description of the errors of Cartesian detectors.
HARMONICS IN BALANCED POLYPHASE CIRCUITS
POLYPHASE, OR BOTTLE-BRUSH, NOISE
The amplitude output of the polar detector is the radius, r, of the noise pattern in Figure 2.22. Median of the Rayleigh distribution (half of the points are inside this radius and half are outside).
TIME AND SPECTRAL DOMAINS, HELICAL SPECTRA
- Convolution and correlation
The convention in Figure 2.27 and the direction of the axes are common throughout this book. The inverse transform, Figure 2.31(h), yields an impulse with a delay of 2 and a variance of the sum of the variances of the original curves, 2 (standard deviation /2).
GAUSSIAN PULSES, SPECTRA, AND BEAM SHAPES
- Gaussian pulses and spectra
- Gaussian beam shapes
- Gaussian illumination functions
The spectrum of a Gaussian time pulse is itself a Gaussian or bell shape, which is the reason for its usefulness. Gaussian illumination is finite and is cut off (cut off) at the sides of the reflector giving side lobes. The values of n determine how much of the central part of the Gaussian function is used to illuminate the aperture.
USE OF BRACKETS AND OTHER SYMBOLS
Transmitters
TRANSMITTER POWER
POWER OUTPUT STAGE
- Semiconductor transmitters
Increased pulse width is sometimes used to reduce peak power in the waveguide to prevent arcing. Power recombination can be avoided by dividing the transmitter elements into separate transceiver modules in the antenna, each behind its separate element or line of elements, in a planar (or otherwise shaped) array. The spectrum of the transmitter, or range of transmitters, depends on how it is modulated, and pulse compression, described in section 3.4, is often used to drive enough power into the pulse.
SPECTRUM AND SIDEBANDS
- Trapezoidal edges
- Cosine and cosine squared edges
The spectra of the pulse waveforms can be constructed from the sum of the component spectra. The waveforms of the edges are shifted in time to fit the leading and trailing edges of the center section. Cosine edges remove the corners at the top of the waveform, and cosine squared edges also remove the corners at the bottom, as shown in Figure 3-5.
PULSE COMPRESSION
- Linear frequency modulation
- Simple phase modulation
- Other types of modulation and their spectra
The complex plot (amplitude and phase) of the center of the spectrum with the time waveform centered at zero is shown in Figure 3.16. Joining the points of the phase vectors shows its relationship with the P3 code and is shown in Figure 3.30. The spectrum of the signal resembles linear frequency modulation with additional sidebands for the frequency switching function.
HARMONICS FROM THE TRANSMITTER
Barker codes can be nested, but they can have awkward topside loops, whereas examples of polyphase barker codes can be found in [3, p. Costas codes are the result of rearranging the order of the frequency steps in stepped-frequency linear frequency modulation [ 3] so that the parts can be recombined to give a thumb ambiguity function. The transmitter must amplify the full signal bandwidth with minimal distortion in amplitude and phase so that when the expanded pulses are passed through a compression filter, the original narrow pulse is restored with the resolution within range.
FIGURES AFFECTING RADAR PERFORMANCE
- Range
- Resolution
- Accuracy
- Stability
- Interference to neighboring systems
The jitter effect is the displacement of the modulator pulse relative to the RF driver pulse. This phase error limits the cancellation ratio as .. where )N is the standard deviation of the phase error in radians between pulses. The output stages thus give amplitude and phase errors that limit the radar cancellation ratio.
Microwave waveguide and transmission line system
- MISMATCH
- COMPONENTS
- Coaxial cables
- Waveguides
- Striplines or microstrip lines
- Microwave passive components
- MONITORING
- Power level
- Voltage standing wave ratio (VSWR)
- EFFECT ON RADAR PERFORMANCE
- Effects on maximum range
- Effects on stability
On the rotary side of the rotary joint, the waveguide goes into the antenna feed system. Circuit breakers are used to direct the transmitter pulses to the antenna and the echo return signals to the receiver. The amount of power point that passes to the receiver when the tube starts to light;.
Antennas
LINEAR AND RECTANGULAR RADIATORS
- Tapering the illumination function to reduce sidelobes
- Uniform, trapezoidal, and triangular illumination tapering
- Simply tapered illumination functions
- Low-sidelobe tapering functions
- General rules for tapering
The illumination function and the beam pattern are the product of the line patterns in the two dimensions (see section 5.1.1). Alternatively, the antenna in Figure 5-12 can be assumed to have the area D² S at the base of the cone. Equation (5.32) describes a central beam with amplitude A and side lobes with amplitude 1. The zeros of the side lobes are at.
RADIATION FROM CIRCULAR APERTURES
- Circular Taylor low-sidelobe tapering function
The normalized power characteristic in decibels is shown in Figure 5.20 with a linear angle scale, while the antenna pattern is actually polar and the polar plot is shown in Figure 5.21. If a circle is cut by a square and the excitation in the y direction is summed to a diameter in the x direction, the function represents a narrowed illumination of a line source in the x direction. As with linear luminance functions, there are a number of luminances defined by distance from the center of a circular directory.
MONOPULSE RADAR ANTENNAS
- Tapering functions for monopulse antennas with low sidelobes
The combined view shows the fact that an odd antenna pattern requires an imaginary aperture function, as shown in Figure 5-25. Many of the derivatives of sum patterns can be used to form difference patterns and the Taylor derivative [4, p. Figure 5.28 Taylor-derived antenna characteristic in decibels. The side lobe ratio is determined by the value at x = x and depends on n, and Figure 5-30 gives the values from k to 2 to achieve this.
ARRAYS OF DISCRETE RADIATORS
- Tapered illumination functions
- Ways of driving discrete elements
- Grating effects
- Beam-steering quantization effects
The components of the wavefront all have the same phase, so that the phase shift represented by the distance X in Figure 5.40 is. The steering of the main beam away from the broadside increases the appearance of grid patches as shown in Figure 5.39. The height of the steps is the actual phase error between the elements, which is always less than the continuous form shown in Figure 5.47.
CREATING SHAPED BEAMS
- The Woodward-Lawson method
The synthesized antenna pattern is the sum of these elementary patterns and is shown in the traditional angle versus decibel form in Figure 5.54. It is calculated from the inverse Fourier transforms of each sample, one of which is shown in Figure 5.57. The illumination function is the sum of the Fourier transforms of the individual sink functions in Figure 5.53.
CIRCULAR POLARIZATION
- Circular polarizer for horn feeds
- Reflecting polarizers
- Transmission polarizers
- Phased array polarization
- Engineers’ and physicists’ conventions
- Ellipticity or the quality of circular polarization
- Rain echo suppression
Although there is a phase shift in the principal mode, there is no transition to circular polarization. If the waves in the waveguide in Figure 5.62 are horizontally polarized, the delay occurs in the opposite order and right circular polarization is produced. The quality of circular polarization is measured using a rotating dipole as a transmitting antenna during antenna testing.
ANTENNA HARDWARE LOSSES
- Illumination function loss
- Blocking loss
- Spillover loss
- Surface tolerance loss
- Losses in power dividers, phase shifters, and other beam-forming network components
- Other effects giving losses
The antenna gain can be restored to the desired value by enlarging the antenna or changing the lighting function. For structures that are short along the antenna axis, the area and shape of the blocking structure can be used. Some of the energy passes around the edges and is called the spillover, causing additional noise when the echoes enter the horn via the same path.
BEAM SHAPE LOSS
- Coherent integration
- Noncoherent integration
- Small numbers of pulses
Output signal-to-noise ratio 'n Sin k T B. Figure 5.77 Bilateral scan loss for a surveillance radar with a beamwidth of 0.5 degrees rotating at 6 rpm THE EQUIVALENCE OF DIFFERENT SIGNAL COMBINATION SYSTEMS. Neglecting the cosmic noise and antenna loss noise, the signal-to-noise ratio at the output of the radio frequency amplifier, gain A, fed by the radio frequency combiner, is isrf. Output signal-to-noise ratio, each amplifier ' Sin k TB. Output signal-to-noise ratio, all amplifiers ' n² n. Figure 5.78 Radio frequency, intermediate frequency, and digital beamforming systems.
NOISE RECEIVED FROM AN ANTENNA
If the source temperature is 0 K, the noise power delivered to the load is generated entirely in the attenuator. Referring to the noise temperature of the input [1], the load believes that the effective source temperature T is. The noise contributions for a ground radar from cosmic noise, the sun, the ground and the antenna are shown in Figure 5.83 [27].
SIDELOBE CANCELERS AND ADAPTIVE BEAM FORMING
The noise arriving at the output is attenuated by resistive losses in the reflector, feed system and beamforming grids, and the waveguide or coaxial line leading to the output flange where the antenna gain measurement was made. In addition, the echo signals received through the main beam are much larger than the echo signals received through the auxiliary antenna, and these two characteristics prevent the canceler from canceling the desired echo signals. The circuit shown in Fig. 5.87 can only cancel signals from one or the strongest jammer, and each additional jammer to be canceled requires an additional auxiliary antenna and cancellation loop.
ANTENNAS MOUNTED ON AIRCRAFT
- Mapping
- Radars on satellites
- Other considerations
Although the range resolution can be improved by using shorter pulses, the azimuth resolution depends on the antenna beamwidth. The pattern of the ground-illuminating aircraft-mounted antenna is determined in beam by the vertical beamwidth. The standard physical antenna beamwidth of width, w, is 8/w and covers a ground length of R8/w.
FIGURES AFFECTING RADAR PERFORMANCE
- Range
- Resolution
- Accuracy
- Stability
The angle of the antenna was set to give bandwidths of the order of 50 to 100 km and the resolutions were of the order of 15 m to 100 m. For military radars, high sidelobes allow energy from jammers to enter the receiving system, augmented by the gain of the sidelobe. The beamwidth of the antenna defines the resolution of two echoes on exactly the same range in the appropriate azimuth or elevation direction.
