# Exercise 1-2. The True Time-Delay Rotman Lens EXERCISE OBJECTIVE

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1 Exercise 1-2 The True Time-Delay Rotman Lens EXERCISE OBJECTIVE When you have completed this exercise, you will understand the operation principles of the Rotman lens. DISCUSSION Rotman lens A microwave lens is basically a phase-correction device that transforms a divergent wavefront from a point source into a plane wave and, conversely, focuses a plane wave into a single point. It is, as is the case for all antennas, a reciprocal device. The trifocal bootlace lens or Rotman lens is a device which can form simultaneous multiple beams from an antenna array. It can also be used for beam scanning if the input ports are fed in sequence according to a predetermined scheme. A phased array using a printed circuit Rotman lens has several advantages over conventional phased arrays. Table 1-3 summarizes some of the advantages and disadvantages associated with a Rotman lens based phased array. ADVANTAGES Relatively low production cost Highly repeatable Switching matrix and antenna array can be integrated with the Rotman lens on the same substrate No adjustments needed DRAWBACKS Medium to high loss Finite number of beams Large size Table 1-3. Printed circuit Rotman lens advantages and drawbacks. The Rotman lens is a quasi-optical, completely passive device, operating at RF frequencies in a way quite similar to the well-known optical lens. The size of the lens, defined by the focal length, is usually several times (typically 5 to 15 times) the guided wavelength so that the RF signals may be assumed to propagate along straight paths or rays. Standard geometrical optics theory may then be used to model and analyze the lens behavior for different sets of design parameters. The Lab-Volt Phased Array Antenna, Model 9612, has a focal length of 9 guided wavelengths (or 9 g). 1-11

2 Basic operating principles As mentioned above, the basic principles of a Rotman lens are very similar to those of a conventional optical lens. Rays coming from a distant source in a given direction (plane waves) and incident on one side of the optical lens are refracted to converge onto a single point, called the focus, on the other side of the lens as shown in Figure 1-3. Figure 1-3. Optical lens principle. If the rays were incident from a direction that is different from the one shown in Figure 1-3, the rays would converge at a different location on the other side of the lens. The particular shape of the lens is designed to alter the path (thus, the phase) followed by each ray in such a way that the transmitted wave fronts theoretically converge towards a single point on the other side of the lens. This principle, used in optical lenses, is based on the refraction phenomenon. In theory, there exists an infinite number of foci, all located on a plane called the focal plane. This plane is perpendicular to the lens axis. Inversely, if a point light source is positioned at a focus, a beam of parallel rays will emerge from the other face of the lens. Changing the location of the point source on the focal plane will orient or steer the plane wave in another direction. At radio frequencies, the parabolic antenna shares the same operating principle. The only difference is that the parabolic antenna focuses the incident waves to a single point by reflection. The basic principle of an optical lens, applied in two dimensions, may be used to design a beam-forming lens at radio frequencies, as explained in the following sections. Anatomy of a Rotman lens A Rotman lens is based on the principle that the rays transmitted by an antenna and traveling on different paths arrive at a given distance with different phases or delays. Hence, if one were able to intercept the rays with the proper delays, they could be used to feed an antenna array that would produce a beam in a direction determined 1-12

3 by the delay difference between each antenna element. Figure 1-4 shows a beam-forming lens using microstrip technology. Other technologies may be used: standard waveguide, dielectric waveguide, free space or coaxial waveguides. The lens is divided into four sections: the beam ports, the parallel plate waveguide, the array ports and the output delay lines (made with microstrip lines). Note that the part of the device that actually performs the same function as an optical lens is the section comprising the array ports and output lines, as shown on the right in Figure 1-4. However, the term Rotman lens is commonly used to describe the entire printed circuit assembly. The array ports and beam ports are transitional structures that act as both receiving and transmitting elements inside the lens. The term port indicates that the signals may enter or leave these junction points. In the following analysis, it is assumed that the lens is used as a transmitting antenna. The array and beam ports are tapered microstrip transmission lines. The length of the taper affects the input impedance of the port. The aperture's width also affects the impedance and, most importantly, the port's directivity. The width of the aperture will affect the amplitude distribution on the array ports and consequently, the amplitude of the side lobes. The beam ports are used to select the direction of the beam formed by the antenna array. They are positioned at the foci of the lens. As opposed to the optical lens, in which all the possible foci are located on a plane, these are positioned on a circular arc called the focal arc. All the beam ports point toward the center of the inner lens contour. Beam port orientation affects the amplitude and phase distribution on the lens's face. Figure 1-4. Rotman lens realized using microstrip technology. 1-13

4 The parallel plate waveguide is used to confine and to route the electromagnetic waves to the array ports. The parallel plate waveguide is etched on the same side as the microstrip transmission lines. The array ports are used to intercept the electromagnetic waves transmitted by any given beam port as shown in Figure 1-5. The signals received by the array ports are transmitted through microstrip lines to the antenna array elements where the power is radiated. Note that the paths followed by each ray in the parallel plate region are progressively longer as one moves along the array ports. Figure 1-5. Ray optics model for the Rotman lens. As shown in Figure 1-5, this means that the electromagnetic signal will arrive at array port number 1 before arriving at array port number 2, 3, etc. Thus, array element number 1 will start to radiate power before the others. Since all the radiating elements usually have a broad radiation pattern, they will radiate quasi-spherical waves. As the other elements progressively start to radiate, all the spherical waves will add-up to form a planar wave front. By changing to another beam port, the phase (or delay) distribution across the antenna array elements changes, steering the beam 1-14

5 to other directions. The phase difference required between two consecutive antenna array elements to steer the beam at an angle from the normal to the array is given by: with d being the constant distance between the elements of the array. Procedure Summary In this exercise, you will observe the operation of the Rotman lens using the oscilloscope. Then, using an absorber pen, you will locate the active beam port and you will observe the position of the beam corresponding to the active port. In the next part of this exercise, you will use the PPI display. Using an absorber pen, you will locate the beam that illuminates the target. Finally, you will move the target and repeat the procedure. PROCEDURE Set-up and calibration G 1. Before beginning this exercise, the main elements of the Radar Training System (the antenna, the target table and the training modules) must be set up as shown in Appendix A. Turn on all modules and make sure the POWER ON LEDs are lit. G 2. Make sure that the LVRTS software has been started and that the Radar Training System has been connected, adjusted and calibrated according to the instructions in Appendix B. Then set the RF POWER switch on the Radar Transmitter to the STANDBY position. Note: DO NOT connect the power cable to the MOTOR POWER INPUT of the Rotating-Antenna Pedestal. Rotman lens operation using the oscilloscope G 3. Place a half-cylinder target on the target table at about 2 m from the Phased Array Antenna, with the convex surface of the target facing the antenna. G 4. On the Radar Transmitter, turn the RF POWER on. G 5. On the Phased Array Antenna Controller, set the SCAN MODE to MANUAL, the BEAM SEQUENCE to INCREMENTAL and the DISPLAY MODE to BEAM NUMBER. Use the POSITION/SPEED buttons to select beam

6 G 6. Connect probe E to TP3 (PRF) in the Display Processor tab and connect probe 1 to TP14 (VIDEO OUTPUT) in the MTI Processor tab. Show the Oscilloscope and adjust it as follows: Channel V/div (DC coupling) Channel Off Time Base ms/div Trigger Source E Trigger Level V Trigger Slope Trigger Coupling DC Set the oscilloscope to Continuous Refresh (in the View menu, select Continuous Refresh or click in the oscilloscope toolbar.) You should see the VIDEO OUTPUT signal on the oscilloscope screen. G 7. On the Target Controller, set both SPEED controls to MIN. and set the MODE to SPEED. Set the Y SPEED control so that the target moves along the antenna axis at a speed of 5 to 10 cm/s. Once you clearly see the moving target echo on the oscilloscope display, set the MODE to POSITION to move the target to the center of the target table. Then gently turn the Phased Array Antenna from side to side by hand while observing the oscilloscope display until the maximum echo amplitude is obtained. G 8. Open the Phased Array Antenna access door, located on top of the Phased Array Antenna case, and using the absorber pen, find which beam port is active by placing the absorbing tip on every beam port in turn, as shown in Figure 1-6, while observing the echo on the oscilloscope display. When the absorber pen is placed on the active beam port, the echo on the oscilloscope will be significantly attenuated. 1-16

7 Figure 1-6. Positioning the absorber pen on a beam port. G 9. Select a different beam on the Phased Array Antenna Controller. Turn the Phased Array Antenna by hand until the target echo is visible on the oscilloscope and is maximized. Then use the absorber pen to identify the active port. Are more than one beam ports active at a time? 1-17

8 Rotman lens operation using the PPI display G 10. Show the Radar display and set the Range to 3.6 m. G 11. On the Phased Array Antenna Controller, set the SCAN MODE to CONTINUOUS, the DISPLAY MODE to SPEED and use the POSITION/SPEED buttons to set the speed at 1080 SCANS/min (at this speed, the DISPLAY alternately displays 10" and 80"). Adjust the Gain in the System Settings so that the target blip resembles a small square. Turn the Phased Array Antenna so that the target bearing is close to 0. G 12. Open the access door, located on top of the Phased Array Antenna case, and using the absorber pen, find which beam is directed toward the target by placing the absorber pen on every beam port in turn while observing the PPI display. When the absorber pen is placed on the corresponding beam port, the target blip will be significantly weakened or disappear. Is the target affected by more than one beam port? G 13. Using the Target Controller, move the target 30 cm to the left or the right and repeat the previous step. G 14. On the Radar Transmitter, make sure that the RF POWER switch is in the STANDBY position. The RF POWER STANDBY LED should be lit. If no one else will be using the system, turn off all equipment. CONCLUSION In this exercise, you learned the operation principles of the Rotman lens. With the oscilloscope, you located the active beam port and you observed the position of the beam corresponding to the selected beam port. Then you did the same using the PPI display. 1-18

9 REVIEW QUESTIONS 1. Briefly explain how phase shift is accomplished within the Rotman lens? 2. What is the purpose of building Rotman lenses that are 5 to 15 times the guided wavelength in diameter? 3. Briefly explain the basic operation principles of the Rotman lens? 1-19

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