3.5 APPLICATIONS OF CW RADARS

Transcription

1 Keywords. CW radars, FM-CW radars 3.5 APPLICATIONS OF CW RADARS The chief use of the simple unmodulated CW radar is for the measurement of the relative velocity of a moving target. The principal advantage of a CW doppler radar over other non-radar methods of measurement of speed is that there need not be any physical contact between the measuring device and the object whose speed is being measured. Another advantage is that the CW radar, when used for short or moderate ranges, is characterized by simpler equipment than a pulse radar. Among its disadvantages is the fact that the amplitude of the signal that can be transmitted by a CW radar is dependent on the isolation that can be achieved between the transmitter and the receiver since the transmitter noise that finds its way into the receiver limits the receiver sensitivity. This limits the maximum range of the radar. The pulse radar has no similar limitations to its maximum range because the transmitter is not operative when the receiver is turned on. One of the greatest shortcomings of the simple CW radar is its inability to obtain a measurement of range. This limitation can be overcome by modulating the CW carrier, as in the frequency-modulated radar described in the next section. 44

2 3.6 FREQUENCY MODULATED CW RADAR (FM-CW) From the principle of CW radars we see that the Doppler frequency shift can be used to determine the presence of a moving target and its relative velocity along the LOS. In chapter 2 we had mentioned that one of the primary functions of a radar is to measure the range to an object. This does not appear to be possible in a CW radar since we have no way of determining the time after which a particular part of the transmitted waveform comes back in the form of an echo. This is so since it is impossible to distinguish one part of a continuous signal waveform from another. In pulse radars there is considerable gap between one pulse and the next and so it was easy to associate or identify a pulse with its echo. Recall that even there this identification became difficult when the gap between pulses was small (or the target was at a large distance), giving rise to second-time-around echoes. In CW radars an exactly similar effect, though of a more serious nature, occurs thus making it impossible to identify a part of and echo waveform with its original transmitted waveform. This is the reason why an ordinary radar is incapable of measuring range to an object. A solution to this problem can be obtained by using frequency modulation. A simple way to do this is to vary the transmitted frequency over a certain range. Then the transit time is proportional to the difference in frequency between the echo signal and the transmitter signal (for a stationary target). The greater the transmitter frequency deviation in a given time interval, the more accurate the measurement of the transit time. Radars which use this mode of operation are called frequency modulated continuous wave (FM-CW) radars. Below we will describe how range measurement is done in FM-CW radars. In FM-CW, the transmitted signal frequency is varied as a function of 45

3 Figure 3.5: Linear frequency modulation in FM-CW radars time. Suppose it increases linearly with time, then we will have a variation as shown in Fig 3.5. Here,f b is the beat frequency which is defined as the difference between the transmitted and received frequency. Since the beat (or difference frequency) is caused only by the target s range (as the target is stationary) it is also denoted by f r. Consider the transmitter CW signal at time t A, having frequency f a. This signal hits the stationary target and comes back to the radar at time t B when the frequency of the transmitted signal would have increased to f c. Hence, the increase in the transmitted frequency during the to-and-fro transit time T of a signal is (f c f a ) and is the beat frequency. Thus, at any given instant in time the difference between the currently trans- 46

4 mitted signal frequency and the currently received signal is a measure of the to-and-fro transit time of the transmitted signal. We extract range information from a measurement of f) b as follows: Let the slope of the curve shown Fig.3.5 be f 0, the rate of change of frequency, or the modulation rate. Note that this is a known quantity since the modulation rate is chosen by the designer at the radar end. Then, f b = f r = f 0 T = f 0 2R c where, R is the distance to the target and so T = 2R c get. From the above we R = f bc 2f o (3.18) The above analysis shows that measurement of f b and the knowledge the frequency modulation rate is sufficient to obtain the required range information. The obvious flaw in the above scheme is that the transmitted frequency cannot go on increasing indefinitely. A solution is to use a periodic change in the frequency. A particular case is the triangular-frequency modulation waveform. This is shown in Fig. 3.6 below where both the frequency modulation scheme and the resulting beat frequency curve is given. Note that the sign of the beat frequency is not preserved and hence it always appears as a positive frequency. Here, the beat frequency is given by f r at all points except in the neighbourhood of the peaks of the transmitted signal. Note that the frequency of the triangular modulation waveform is f m and hence its time period is given by 1 f m. This is shown in the figure. Thus we have, f r = 2R c f 0 = 2R c. f/2 1/(4f m ) = 4Rf m f c (3.19) 47

5 Figure 3.6: Triangular frequency modulation in FM-CW radars Hence, the measurement of beat frequency measure the range as, R = cf [ r 4f m f = c 4f m f ] f r = kf r (3.20) where, k =[c/(4f m f)] can be used for callibrating the frequency counter. A simplified block diagram of the FM-CW radar is given in Fig.3.7. In the above analysis the target was assumed to be stationary. Suppose it is not. Then there will be another frequency change due to the doppler frequency shift. This is denoted by f d and the beat (difference) frequency 48

6 Figure 3.7: Block diagram of a FM-CW radar will now be f b = f r ± f d This will become clearer from the figures given below. First consider an approaching target. The corresponding waveforms are shown in Fig.3.8. The figure is self-explanatory. The only feature to note here is that the beat frequency is lower during the increasing portion of the transmitted frequency and higher during the decreasing portion of the transmitted frequency. Now consider the case for receding targets. This is shown in Fig.3.9. Note that here the beat frequency during the increasing portion of the transmitted frequency is higher than during the decreasing portion. However, essentially 49

7 Figure 3.8: Approaching target there is no distinction between the two beat frequency curves shown in Fig.3.8 and 3.9, if they are considered in isolation. The direction of movement of the target (i.e., wheter it is approaching or receding)has to be determined by other means. For approaching targets, let us denote f b (up) = f r f d f b (down) =f r + f d The words up and down refer to the increasing and decreasing portions of the transmitted frequency i.e., when the frequency is increasing (or going up )or decreasing (or going down )with time. For receding targets, we have, 50

8 Figure 3.9: Receding target f b (up) =f r + f d, f b (down) = f r f d By taking the average frequency, the range frequency f r follows (if f r f d ) can be found as f r =(1/2)[f b (up)+f b (down)] The difference between them will yield the doppler frequency as (if f r f d ) 51

9 f d =(1/2) [f b (up) f b (down)] Using f r in (3.18) yields the range and using f d we can find the target relative velocity along the LOS. The above analysis is true if f r f d. If f r <f d then (3.22)will yield doppler frequency and (3.23) will yield range frequency. Example 3.2:In a FM-CW radar, transmitting at an average frequency of 100 MHz, the rate of triangular frequency variation is 20 KHz. Calculate the beat frequencies during the increasing and decreasing portions of the FM cycle. The radar-target configuration is as shown below. ANSWERS Refer to Fig 3.6 for explanation of the terms used below. The average 52

10 transmission frequency =f=100 MHz = 100x10 6 Hz. The peak-to peak frequency variation =Δf=20KHz=20x10 3 Hz. The rate of triangular frequency modulation = f m = 20 Hz. Then the slope of the variation in frequency, given by Å, is Å = f/2 1/(4f m ) = /2 1/(4 20) =8 105 Hz/Sec (3.21) Distance of the target = R = 50 km = 50 x 10 3 m. Then, the beat frequency due to range only is f r = 2RÅ c = 2 ( ) ( ) = Hz. (3.22) From the figure we see that the target is a receding one with relative velocity v r = 400cos60 0 = 200 m/sec. Then the beat frequency due to doppler effect only is, f d = 2v rf c = = Hz. (3.23) From Fig 3.9 the beat frequency during the increasing and decreasing portions of the transmitted frequency are f b (up) = f r + f d = = 400 Hz. f b (down) = f r - f d = = Hz. 53

11 PROBLEMS AND EXERCISES 1. Derive Eqn (3.7) from Eqn (3.6) under suitable assumptions and obtain the doppler frequency shift as given in Eqn (3.4). 2. A target is being tracked by two radars as shown below. If Radar 1 registers a doppler shift of -100 Hz and Radar 2 a doppler shift of +60 Hz, then what is the velocity of the target? Is there a direction of flight which the target can employ so that it escapes detection by both the radars at the instant shown in the figure? 3. Let a stationary CW radar, transmitting at 300 MHz, be at point A 54

12 Figure 3.10: sample figures example and a moving target at point B as shown in the figure given below. Plot θ vs. f d on a graph sheet as θ varies from, 0 to in steps of (b) Let the initial value of θ be Plot f d vs. time in seconds as time varies from 0 to 10 seconds in steps of 2 seconds. 4. What are the simplifying assumptions made to solve Example 3.2? Suppose in this problem the average transmission frequency is 400 MHz, then find f b (up) and f b (down) and show how one can obtain f r and show how one can obtain f r and f d from these two values. 5. Sketch the beat frequency curve of a sinusoidal frequency modulated CW radar for an approaching target. Find the equation for the beat frequency as a function of time. 6. In a FM-CW radar the shape of the frequency modulation is as shown 55

13 in the figure. Sketch the echo waveform from a stationary target and from a receding target. Sketch the beat frequency waveform for both cases. 56