Lecture Topics. Doppler CW Radar System, FM-CW Radar System, Moving Target Indication Radar System, and Pulsed Doppler Radar System

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1 Lecture Topics Doppler CW Radar System, FM-CW Radar System, Moving Target Indication Radar System, and Pulsed Doppler Radar System 1

2 Remember that: An EM wave is a function of both space and time e.g. The electric field strength E(x, y, z, t) v = f = v / f v = 3 x 10 8 m/s v : is in metre/second f : is in cycle/second : is? f metre second second cycle metre cycle An EM wave will go through one cycle in a distance equal to one wavelength 2

3 Interpretation As an example, for a frequency f = 900 MHz, the wavelength = 1/3 m, and the period T = 1.11 x 10-9 sec. t 1 m The wave will travel 1/3 m per cycle 3

4 Phasor Representation A (t) Imaginary A i Real t ( t) ( ) d 0 i 0 4

5 Instantaneous Frequency Taking the derivatives of both side of the equation: the result is: ( t) ( ) d d i dt t 0 i (t) 0 The instantaneous frequency of a sinusoidal signal is given by the time derivative of its phase. 5

6 Fixed and Moving Objects (straight line) Moving Object R 3 R 2 R 1 R 1 R 2 R 3 Fixed Object 6

7 Fixed and Moving Objects (circular path) Moving Object R 3 R 2 R 1 R 1 = R 2 = R 3 Fixed Object 7

8 Doppler CW Radar (Simplified) f t CW Tx f t Dup Dup f t + f r f t - f r f r Frequency Counter f d Amp f d Det CW: Continuous wave 8

9 Characteristics of CW Radar Transmit unmodulated continuous sinusoidal carrier. Echoes will also be unmodulated continuous sinusoidal carrier. Time difference between the transmitted and returned echoes cannot be detected. Echoed radio energy from a moving target differs in frequency from that transmitted by the radar producing a beat frequency that can be detected. CW Radar Utilise Doppler Frequency Shift for detecting and measuring the radial velocity of moving targets. 9

10 Doppler Frequency The total number of wavelengths of the two-way path between the Radar and Target is given by: 2R / Since a wavelength correspond to an angular excursion of 2 radians, the returned echo will have a phase difference given by: = (2R / ) 2 4 R / radians Substituting c / f t for = 4 R f t / c radians Where f t is the radar transmitted frequency, and c the speed of radio waves. 10

11 Angular Frequency For a moving target, R and are functions of time. t = 4 R(t) f t /c radians Differentiating R and with respect to time, but, d dt d dt = 4 f t /c dr dt (a) d = 2 f d (b) angular Doppler frequency and dr dt = v r (c) target relative velocity 11

12 Equation of Doppler Frequency Substituting (b) and (c) in (a) and rearranging: 2 f d = (4 f t / c) v r f d = 2 v r f t / c f d v r f t c : Doppler Frequency : Target relative velocity : Radar transmit frequency : 300 x 10 6 m/s 12

13 Bandwidth Consideration A wide bandwidth amplifier is required for the expected range of Doppler frequencies. Receiver noise increases with bandwidth, resulting in decrease of receiver sensitivity. Use of multiple narrowband filters at the baseband or IF frequencies. Use of Phase-Locked-Loop to keep track of the varying Doppler frequency. 13

14 IF Doppler Filter Bank Filter No.1 Filter No.1 Det. Det. Filter No.2 Filter No.2 Det Det Mixer Mixer IF Amp IF Amp Filter No.3 Filter No.3 Det Det Indicator Filter No.4 Filter No.4 Det Det Filter No.n Filter No.n Det Det 14

15 Frequency Response Characteristics IF bandwidth Response f 1 f 2 f 3 f 4 fn Frequency 15

16 Radial Velocity Sign Detection Transmit Antenna f t CW Trans. 2 Channel A Receive Antenna f t + f d f t - f d Mix A Mix B LPF LPF Synch Motor Indicator Channel B 16

17 Spectra of Received Signals No Doppler shift Amplitude f t Frequency Approaching target Amplitude f t f d Frequency Receding target Amplitude f d f t Frequency 17

18 Signal Representation Let the transmitted signal be: E t = E o cos o t For an approaching target, the echo signal will be: E r = k 1 E o cos [( o + d )t] For a receding target, the echo signal will be: E r = k 1 E o cos [( o - d )t] Note: k 1 is a scaling factor 18

19 Signal Analysis The output of the Mixer is obtained by multiplying the transmitted and echo signals and using the following trigonometric identity. cos A cos B = 0.5 cos (A-B) cos (A+B) 19

20 Mixer Output (the answer) If the target is approaching, the output of channels A and B: E A = k 2 E o cos ( ( d t) E B = k 2 E o cos ( ( d t + /2 ) Velocity Direction If the target is receding, the output of channels A and B: E A = k 2 E o cos ( ( d t) E B = k 2 E o cos ( ( d t - /2 ) Velocity Direction 20

21 Calculations Echo Signal For an approaching target, E r = k 1 E o cos [( o + d )t] E r = k 1 E o cos [( o + d )t] For a receding target, E r = k 1 E o cos [( o - d )t] E r = k 1 E o cos [( o - d )t] x x x x Local Oscillator E t = E o cos o t E t = E o cos( o t - /2) E t = E o cos o t E t = E o cos( o t - /2) 21

22 Output of A Mixer (approaching target) E r = k 1 E o cos [( o + d )t] Ignoring magnitude for now, E A = cos [( o + d )t] cos o t x E t = E o cos o t E A = 0.5 cos [( o + d - o )t] cos [( o + d + o )t] E A = 0.5 cos ( d t) cos [(2 o + d )t] The term cos [(2 o + d )t] is double the RF frequency and hence it is filtered out Then the out put of the mixer A is: E A = 0.5 cos ( d t) 22

23 Output of B Mixer (approaching target) E r = k 1 E o cos [( o + d )t] x E t = E o cos( o t - /2) E B = cos [( o + d )t] cos( o t - /2) E B = 0.5 cos [( o + d - o )t + /2] cos [( o + d + o )t - /2] E B = 0.5 cos [( d )t + /2] cos [(2 o + d )t - /2] The term cos [(2 o + d )t - /2] is double the RF frequency and hence it is filtered out Then the out put of the mixer A is: E B = 0.5 cos [( d )t + /2] 23

24 FM - CW Radar Systems 24

25 FM- CW Radar Systems CW Radar Systems do not give target range information. Doppler frequency is zero for stationary targets. A version of CW Radar provides range information by incorporating Frequency Modulation (FM) technique. FM-CW Radar can employ linear or non-linear frequency modulation. Linear Modulation is achieved by Triangular modulating waveform, while Non-Linear Modulation is achieved by Sinusoidal modulating waveform. 25

26 Frequency-Time Relationship Frequency f o transmitted f t = 2R/c received time The frequency Rate of Change:. f o = f t Hz / second 26

27 Linear Modulation. If the frequency is being increased linearly at the rate f o Hz/sec, then during the time t = 2R/c the transmitted frequency would have increased by:. f = f o t Substituting 2R/c for t and f b for f. f b = f o 2R/c 27

28 Range Calculation If the transmitted frequency is f t, then the received frequency is given by: f t + f b The difference between the transmitted and received frequencies is called the Beat Frequency f b. The range R is then given by: R = c f. b 2 f o where. f o = f t 28

29 Linear Modulation Waveform Frequency transmitted received f r t = 2R/c time Frequency f b time 29

30 Triangular Modulation Practically, the frequency cannot be increased indefinitely and the target may not be stationary. The modulating signal waveform used is Triangular, linearly increasing and decreasing (positive and negative slopes). Let the frequency of the triangular waveform be f m, and the peak-to-peak frequency deviation 2 f (FM modulation), then the transmitted frequency is linearly increasing and decreasing by the rate: f f f 0 4 m see FM theory 30

31 Frequency Rate of Change The modulating frequency f m = 1 / T Frequency f o T/4 f time T The frequency rate of change (slope) = f / t t = T / 4 = 1 / 4f m 31

32 Stationary Target The beat frequency is given by:. Substituting f o = 4 f m f. f b = f o 2 R / c f b = 8 f m f R / c The range is given by: R = c f b / ( 8 f m f ) 32

33 Stationary Target Waveform Frequency f o t = 2R c f time Frequency f b time 33

34 Moving Target When the target is moving Doppler Effect takes place and the frequency is shifted accordingly. f d Frequency f o time f d = 2 v r f t / c 34

35 Moving Target Waveform Frequency f o time Frequency f b time 35

36 Beat Frequency for Moving Target For a moving target, the beat frequency will now include an additional component due to Doppler frequency shift. The positive and negative frequency slopes will be: f up = f r -f d f down = f r + f d 36

37 Beat Frequency Waveform Frequency f r -f d f r + f d time 37

38 FM-CW Radar Block Diagram Transmit Antenna FM Transmitter Modulator Indicator Receive Antenna Mixer Amp Limiter Frequency Counter 38

39 MTI & Pulsed Doppler Radar System 39

40 Introduction So far we examined the functionality of a number of radar systems, Pulsed Radar, CW Radar, and FM-CW Radar Systems. Pulsed Radar System provides range (distance) information. Doppler CW Radar System provides the relative velocity of a moving object. FM-CW Radar System provides range information. Is it possible to obtain both range and velocity of a moving object using one radar system? 40

41 Waveform (Wide Pulse) CW Modulating Signal Pulsed CW Long enough to detect velocity! 41

42 Waveform (Narrow Pulse) CW Modulating Signal Pulsed CW Far enough to detect range! 42

43 Waveform (Medium Pulse) CW Modulating Signal Pulsed CW Good enough to detect both range and velocity! 43

44 MTI Radar (measures range) The purpose of MTI Radar is to reject signals from fixed or slow-moving unwanted targets and display signals from fast-moving wanted targets. Examples of slow-moving targets: buildings, hills, trees sea waves, and rainfall. A flying aircraft is an example of fast-moving targets. 44

45 Pulsed Doppler Radar (measures velocity) Optimised for speed measurement, the range need not be accurate. Pulsed Doppler Radar operates with unambiguous Doppler measurement but with ambiguous range measurement. 45

46 Purpose & Characteristics MTI and Pulsed Doppler Radar systems are used to detect moving targets in severe clutter environment. Unambiguous Range MTI PD Velocity Ambiguous Low Medium High PRF PRF : Pulse Repetition Frequency 46

47 Purpose and Definition Both the MTI and Pulsed Doppler Radar systems are based on the same physical principle, but in practice there are generally recognisable differences between them. mainly for range but with some knowledge on speed MTI Radar operates with ambiguous Doppler Measurement but with unambiguous Range Measurement. Pulsed Doppler Radar operates with unambiguous Doppler Measurement but with ambiguous Range Measurement. mainly for speed but with some knowledge on range 47

48 Operational Limits Combing the features of Pulsed and CW radar systems to obtain target Range and Speed information. Unambiguous Range Measurement is inversely proportional to the pulse repetition rate. Unambiguous Speed Measurement by Doppler frequency shift method requires a long enough pulse width. A compromise must be made on which measurement is to be unambiguous, Rang or Speed. 48

49 Coherent MTI Radar System Pulsed f t Dup Phase Detector PRI Memory - Pulsed f t CW + Pulsed Amplifier CW RF Oscillator PRI : Pulse Repetition Interval 49

50 Simple CW Radar Transmit Antenna f t CW Oscillator f t Receive Antenna f t + f d f t -f d Receiver f d Indicator 50

51 Pulsed-Doppler Radar Pulse Modulator Transmit Antenna Pulsed f t Power Amplifier f t CW Oscillator Pulsed f t Receive Antenna f t + f d f t -f d Receiver f d Indicator 51

52 Waveform Equations The transmitted carrier = A 1 sin (2 f o t) The reference carrier = A 2 sin (2 f o t) The returned echo = A 3 sin [2 f o +/- f d ) t - 4 f o R / c] The result of mixing returned echo and reference carrier is : V diff = A 4 sin ( 2 f d t - 4 f o R / c ) 52

1. Explain how Doppler direction is identified with FMCW radar. Fig Block diagram of FM-CW radar. f b (up) = f r - f d. f b (down) = f r + f d

1. Explain how Doppler direction is identified with FMCW radar. A block diagram illustrating the principle of the FM-CW radar is shown in Fig. 4.1.1 A portion of the transmitter signal acts as the reference