Naval Postgraduate School Microwave Devices & Radar Distance Learning Microwave Devices & Radar LECTURE NOTES VOLUME I by Professor David Jenn Contributors: Professors F. Levien, G. Gill, J. Knorr, P. Pace and J. Lebaric Ver7.2 Naval Postgraduate School Microwave Devices & Radar Distance Learning Radio Detection and Ranging (Radar) Traditional radar functions: R, range obtained from pulse time delay vr , relative radial velocity obtained from the Doppler frequency shift fd (if the target or radar is moving) angles or (or both) of the target obtained from antenna pointing Signature analysis, inverse scattering, and imaging: target size from magnitude of return target shape and components (return as a function of direction) moving parts (modulation of the return) material composition The complexity (i.e., cost, weight and size) of the radar increases with the extent of the functions that the radar performs. 1 Naval Postgraduate School Microwave Devices & Radar Distance Learning Radar Operational Environment INTERFERENCE FROM OTHER EMITTERS RADAR TARGET SYSTEM TH PA RECT DI H T TX A IP T L U M RX CLU TTER GROUND CLUTTER Radar return depends on: target orientation (aspect angle) and distance (range) target environment (other objects nearby; location relative to the earth's surface) propagation characteristics of the path (rain, snow or foliage attenuation) antenna characteristics (polarization, beamwidth, sidelobe level) transmitter (Tx) and receiver (Rx) characteristics 2 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (1) Radar is based on the sensing of electromagnetic (EM) waves reflected from objects. Energy is emitted from a source (antenna) and propagates outward. A point on the wave travels with a phase velocity up, which depends on the electronic properties of the medium in which the wave is propagating. From antenna theory: if the observer is sufficiently far from the source, then the surfaces of constant phase (wave fronts) are spherical. At even larger distances the wave fronts become approximately planar. SPHERICAL WAVE FRONTS PLANE WAVE FRONTS RAYS 3 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (2) Snapshots of propagating waves at time t 0. Plane wave propagating in the y Spherical wave propagating outward from the direction origin E E (R,t) ˆ o cos(t R) E (y,t) zˆ E o cos(t y) R 4 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (3) Electrical properties of a medium are specified by its constitutive parameters: 7 permeability, or (for free space, o 4 10 H/m) 12 permittivity, or (for free space, o 8.85 10 F/m) conductivity, (for a metal, ~ 107 S/m) Electric and magnetic field intensities: E (x, y, z,t) V/m and H (x, y,z,t) A/m vector functions of location in space and time, e.g., in Cartesian coordinates ˆ ˆ ˆ E (x, y, z,t) xE x (x, y, z,t) yE y(x, y, z,t) z Ez(x, y, z,t) similar expressions for other coordinates systems the fields arise from current J and charge v on the source (J is the volume 2 3 current density in A/m and v is volume charge density in C/m ) Electromagnetic fields are completely described by Maxwell’s equations: H (1) E (3) H 0 t E (2) H J (4) E v / t 5 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (4) The wave equations are derived from Maxwell’s equations: 1 2 E 1 2H 2 E 0 2 H 0 u2 t 2 u2 t2 p p 8 The phase velocity is up . In free space up c 2.99810 m/s. The simplest solutions to the wave equations are plane waves. An example for a plane wave propagating in the z direction is: z E (z,t) xˆ Eoe cos( t z) attenuation constant (Np/m); 2 / phase constant (rad/m) up wavelength; 2 f (rad/sec); f frequency (Hz); f Features of this plane wave: propagating in the z direction x polarized (direction of electric field vector is xˆ ) amplitude of the wave is Eo 6 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (5) Time-harmonic sources, currents, and fields: sinusoidal variation in time and space. Suppress the time dependence for convenience and work with time independent quantities called phasors. A time-harmonic plane wave is represented by the phasor E (z) () jzjt jt Ezt(,) Re xEeˆ o e Re Eze () E (z) is the phasor representation; E(z,t) is the instantaneous quantity Re is the real operator (i.e., “take the real part of”) j 1 Since the time dependence varies as e j t , the time derivatives in Maxwell’s equations are replaced by /:t j (1) E jH (3) H 0 (2) H J jE (4) E v / The wave equations are derived from Maxwell’s equations: 2E 2E 0 2 2 H H 0 where j is the propagation constant. 7 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (6) Plane and spherical waves belong to a class called transverse electromagnetic (TEM) waves. They have the following features: ˆ 1. E , H and the direction of propagation k are mutually orthogonal 2. E and H are related by the intrinsic impedance of the medium o 377 for free space ( j / ) o o kˆ E The above relationships are expressed in the vector equation H The time-averaged power propagating in the plane wave is given by the Poynting vector: 1 * 2 W ReE H W/m 2 1 E 2 For a plane wave: W (z) o zˆ 2 2 1 Eo ˆ For a spherical wave: W (R) 2 R (inverse square law for power spreading) 2 R 8 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (7) A material’s conductivity causes attenuation of a wave as it propagates through the medium. Energy is extracted from the wave and dissipated as heat (ohmic loss). The attenuation constant determines the rate of decay of the wave. In general: 1/ 2 1/ 2 2 2 1 1 1 1 2 2 For lossless media 0 0. Traditionally, for lossless cases, k is used rather than . For good conductors ( / 1), f , and the wave decays rapidly with distance into the material. 1 0.8 0.6 0.4 0.2 0 -0.2 Sample plot of field vs. distance -0.4 -0.6 -0.8 ELECTRIC FIELD STRENGTH (V/m) -1 0 1 2 3 4 5 DEPTH INTO MATERIAL (m) 9 Naval Postgraduate School Microwave Devices & Radar Distance Learning EM Refresher (8) For good conductors the current is concentrated near the surface. The current can be approximated by an infinitely thin current sheet, or surface current, J s A/m and surface charge, s C/m Current in a good conductor Surface current approximation Ei Ei ˆ ˆ ki BOUNDARY ki BOUNDARY J J s At an interface between two media the boundary conditions must be satisfied: (1)n ˆ (E E ) 0(3)ˆn (E E ) / 21 1 2 21 1 2 s (2)n ˆ21 (H1 H 2 ) J s (4)n ˆ21 (H1 H2 ) 0 ˆ REGION 1 n21 Js s INTERFACE REGION 2 This is important for predicting the reflections from the ground, water, and man-made objects. 10 Naval Postgraduate School Microwave Devices & Radar Distance Learning Wave Reflection (1) For the purposes of applying boundary conditions, the electric field vector is decomposed into parallel and perpendicular components E E E|| E is perpendicular to the plane of incidence E|| lies in the plane of incidence ˆ The plane of incidence is defined by the vectors ki and nˆ DECOMPOSITON OF AN ELECTRIC FIELD PLANE WAVE INCIDENT ON AN VECTOR INTO PARALLEL AND INTERFACE BETWEEN TWO DIELECTRICS PERPENDICULAR COMPONENTS TRANSMITTED z t E MEDIUM 2 E , || 2 2 INTERFACE E , 1 1 ˆ MEDIUM 1 n i r i ˆ k i NORMAL y INCIDENT REFLECTED x 11 Naval Postgraduate School Microwave Devices & Radar Distance Learning Wave Reflection (2) Plane wave incident on an interface Reflection and transmission coefficients:* between free space and a dielectric Perpendicular polarization: REGION 1 REGION 2 cosi 0 cost FREE SPACE cosi 0 cost o o DIELECTRIC 2cosi r r kˆ i cosi 0 cost Er Ei and Et Ei i nˆ Parallel polarization: r t cos cos t 0 i || cos cos ˆ t 0 i kr INTERFACE 2cosi || sin sin sin cos cos i r r r t t 0 i E E and E E r|| || i|| t|| || i|| o ro r o and o o ro r *See your undergraduate EM textbook for details (e.g., Ulaby, Fundamentals of Applied Electromagnetics) 12 Naval Postgraduate School Microwave Devices & Radar Distance Learning Wave Reflection (3) Example: A plane wave incident on a boundary between air and glass (r 4,i 45 ). Reflections that satisfy Snell’s Law (most of the energy goes in the direction ri ) are called specular reflections. INCIDENT WAVE 10 8 i 45 ,f 100 MHz TRANSMITTED 6 4 t GLASS 2 BOUNDARY 0 z (m) z (m) ˆ ki AIR -2 i r i nˆ NORMAL -4 -6 Wavefront INCIDENT REFLECTED -8 o 3 m -10 -10 -5 0 5 10 x (m) 13 Naval Postgraduate School Microwave Devices & Radar Distance Learning Wave Reflection (4) Example of a plane wave reflection: reflected and transmitted waves (r 4,i 45 ) REFLECTED WAVE TRANSMITTED WAVE 10 10 8 8 i 45 ,f 100 MHz 6 6 1.5 m 4 4 nˆ kˆ t t 2 2 BOUNDARY 0 0 z (m) z (m) z (m) z (m) z (m) BOUNDARY -2 -2 r nˆ kˆ -4 r -4 45 ,f 100 MHz, 4, 20.7 -6 -6 irt Wavefront o 3 m -8 -8 -10 -10 -10 -5 0 5 10 -10 -5 0 5 10 x (m) x (m) 14 Naval Postgraduate School Microwave Devices & Radar Distance Learning Wave Reflection (5) Example of a plane wave reflection: total field irt45 ,f 100 MHz, 4, 20.7 10 The total field in region 1 is the sum of the 8 incident and reflected fields 6 ˆ kt The incident and reflected field add 4 ˆ constructively and destructively to form n t 2 maxima and minima BOUNDARY 0 z (m) z (m) ˆ ki If region 2 is more dense than region 1 -2 i r nˆ ˆ (i.e.,