EP0288497B1 - Array beam position control using compound slots - Google Patents

Abstract

A waveguide slotted array, employing compound slots in a waveguide broad wall. The phase of the voltage excited in the slot is controlled by the slot offset and angle of inclination relative to the axis. Utilization of the additional phase control provided by the compound slots allows the beam of a travelling wave slot array to be placed far from broadside, without the need to operate the array at frequencies so close to the waveguide cutoff frequency that there is unacceptable frequency sensitivity. The beam may be placed at any angle independently of which end of the array contains the input and which end the load.

Description

• The present invention relates to slotted waveguide arrays, and more particularly to an array employing compound slots to provide control of the beam position.
• Two types of slotted waveguide arrays in common use are the serpentine slot array and the shunt slot array. In both types of array, the waveguide must be operated at wavelengths close to the waveguide cutoff wavelength if the beam is to be tilted far off broadside. Thus, the beam is scanned as the exciting frequency is scanned.
• There is therefore a need to provide a slotted waveguide array which allows the beam position to be chosen independently of the waveguide size, such that it is not necessary to operate the array at wavelengths approaching the cut off wavelength of the waveguide.
• The properties of the general inclined-displaced slot (i.e., the compound slot) are described in "The Physical Principles of Waveguide Transmission and Antenna Systems," by W.H. Watson, Oxford at the Claredon Press, 1947. Watson apparently used the special properties of these slots to build a traveling wave array in which each slot could be matched with a tuning button so that the array would operate through the broadside frequency without the customary high VSWR. Insofar as is known, however, Watson did not use the phase properties of compound slots to scan the beam.
• In the paper "Resonant Slots with Independent Control of Amplitude and Phase," B.J. Maxum, IEEE Trans. Antennas and Propagation, Vol. AP-8, pp. 384-389, July, 1960, a linear array is described in which the phase properties of compound slots are employed to achieve a particular shaped beam, wherein the coupling coefficients are limited to small values because of approximations involved in the analyis.
• US-A-4371876 discloses a slot array antenna, in which the amplitude and phase of each slot is controlled by selection of the necessary spacing between the slots, and the required waveguide termination. The slots may be parallel to the longitudinal axis of the waveguide, or slanted with the centre of each slot falling on the longitudinal axis of the waveguide.
• According to the invention, there is provided a travelling wave array antenna adapted to produce an array beam in a predetermined direction inclined from the broadside normal direction, comprising a rectangular waveguide defined by first and second conductive broadwalls and first and second conductive narrow walls; means for exciting said waveguide with an excitation signal having a prescribed wavelength and propagating in a TE₁₀ mode through said waveguide in a propagation direction from a first end of said waveguide towards a second end of said waveguide; means for terminating said waveguide at said second end thereof; and a series of compound slots formed in said first broadwall generally along the longitudinal centerline of said first broadwall; wherein each of said slots is of resonant length; first intermittent ones of said slots are positioned with their lengthwise dimensions oriented at selected angles with respect to said longitudinal centerline; and the offset distance parameter from the longitudinal centerline of said first broadwall and the angle parameter of each of said slots are selected to control the phase and amplitude of the voltage in each respective slot to position the beam resulting from the excitation signal at the predetermined direction; characterised in that said series of compound slots are arranged in a generally sinusoidal configuration; and second intermittent ones of said slots are positioned with their lengthwise dimensions oriented substantially parallel to and offset a selected distance from said longitudinal centerline, but on opposite sides thereof.
• The phase of the voltage in a broadwall-waveguide-fed slot is controlled by the offset and angle of inclination of the slot relative to the longitudinal axis of the waveguide. With the phase control provided by the compound slots, the beam resulting from an excitation signal propagating through the waveguide as the TE₁₀ mode may be directed at a desired direction relative to the broadside.
• The inclination of each slot and its offset from the longitudinal axis is determined by the required voltage phase and amplitude distribution to produce the desired beam direction. Each slot is of resonant length.
• The invention allows the beam to be placed far from the broadside direction without the need to operate so close to the waveguide cutoff frequency that there is unacceptable frequency sensitivity.
• These and other features and advantages of the present invention will become more apparent from the following detailed description of an exemplary embodiment thereof, as illustrated in the accompanying drawings, in which:
• FIGS. 1A and 1B are diagrammatic illustrations of shunt, series and compound slots in the broadwall of a rectangular waveguide.
• FIGS. 2A-2C represent respective equivalent circuits of the resonant compound slot, the shunt slot and the series slot.
• FIG. 3 is a diagrammatic illustration of a waveguide section having a plurality of compound slots formed therein.
• FIGS. 4A and 4a are plots of the radiation pattern for a travelling wave array embodying the invention with nine resonant slots fed by a dielectric filled waveguide for the forward beam and backfire cases, with the solid line depicting experimental patterns and the dashed line representing the expected theoretical patterns.
• FIG. 5 is a diagrammatic view illustrating a missile body having a plurality of travelling wave arrays embodying the invention disposed along the periphery thereof.
• FIG. 6 is a diagrammatic illustration of the positions and orientations of compound slots.
DETAILED DESCRIPTION OF THE DISCLOSURE
• The presently preferred embodiment of the invention is a slotted waveguide array comprising a waveguide having a plurality of compound slots formed along one broadwall. Certain basic principles of the invention may be appreciated with respect to FIGS. 1A and 1B, showing plan views of various slots formed in waveguide 20 (FIG. 1A) and 30 (FIG. 1B).
• Compound slots, such as slots B and D in FIG. 1A, and B' and D' in FIG. 1B, are both offset and tilted or inclined with respect to the centerline 25 of the broad wall. The equivalent circuit of the resonant compound slot is a "T" network as shown in FIG. 2A. By contrast, slots A and E are aligned in parallel with, but offset from, the axis 25, and therefore may be represented by pure shunt admittance as shown in FIG. 2B. Slots C and C' are disposed on the axis 25, but inclined with respect thereto, and therefore may be represented as pure series impedance as shown in FIG. 2c.
• An attractive feature of compound slots can be appreciated by the following analysis. Suppose that all slots shown in FIGS. 1A and 1B are of a resonant length (one-half the wavelength of the exciting energy). Then if an excitation signal of a TE₁₀ mode of unit amplitude and zero phase (referenced at the cross section Z-Z') is incident on any of these slots, traveling in the direction of arrow 26 through the waveguides 20, 30, the electric field induced in slot A will have an amplitude governed by its offset X_A from axis 25 and a phase of +90°. The electric field induced in slot E will have the same amplitude as in slot A, but the phase will be -90°. The electric field induced in slot C will have an amplitude governed by its its inclination ϑc from the axis 25 and a phase of O°.
• Since compound slots B and D may be viewed as transitions from slot A to slot C and from slot C to slot E, respectively, it follows that the phase of the electric fields induced in compound slot B and D will lie in the range (90°, O°) and (O°, -90°), respectively. The amplitudes and phases of these induced fields will depend on both the respective offsets X_B, X_D and inclinations ϑ_B, ϑ_D of slots B and D.
• In a similar fashion, since the phase of the electric field in slot C' is 180°, the phases of the induced fields in compound slots B' and D' will lie in the ranges (90°, 180°) and (180°, -90°), respectively. The amplitudes and phases of these induced fields will depend on both the offsets X_B', X_D, and inclinations ϑ_B', ϑ_D' of slots B' and D'.
• From the foregoing, the important conclusion is reached that the phase of the electric field induced in a resonant compound slot by an incident TE₁₀ mode excitation signal can be adjusted through a full range of 360° by choice of the slot offset and inclination. This conclusion suggests that the compound slot can be used for total phase control in an array, i.e., not only to adjust the phase needed to scan the beam to a given angle, but also to incorporate the phase corrections needed to compensate for the effects of mutual coupling. The design of slot arrays which include the effects of mutual coupling are reported in the papers "The Design of Small Slot Arrays," IEEE Trans. Antennas and Propagation, Vol. AP-26, pages 214-219, March 1978, by L.A. Kurtz and R.S. Elliot, and "Design of Inclined Series Slot Arrays," by M. Orefice and R.S. Elliot, UCLA Department of Electrical Sciences Report, October, 1979. In those designs, equivalent dipole arrays were introduced via Babinet's principle and an aperture-excitation-weighted sum of dipole initial impedances was seen to represent the mutual coupling. The lengths of the dipoles, and thus the slots, were adjusted so that the sum of the loaded dipole self-impedance and the mutual coupling term was pure real and at a level to produce the proper excitation and input match. Thus, for shunt slot arrays, the design parameters were (X_n, 2L_n), with X_n and 2L_n representing the offset and length, respectively, of the nth slot. For series slot arrays, the design parameters were (ϑ_n, 2L_n), with ϑ_n and 2L_n representing the inclination and length, respectively, of the nth slot.
• In contrast to these earlier designs, the invention employs resonant-length compound slots, and adjusts the two design parameters X_n and ϑ_n to account for the effects of mutual coupling, as well as adjusting the phase required by the beam scan angle.
• Arrays of resonant compound slots possess a significant advantage when used in an important class of applications where shunt and series slots are unsatisfactory, i.e., traveling wave arrays. These advantages may be appreciated with reference to FIG. 3, wherein rectangular waveguide 40 has an array of non-resonantly spaced slots S₁-S_n formed in one of its broad walls 41. The waveguide 40 is terminated in a load 43. Assume that the excitation of successive slots is by a TE₁₀ mode whose amplitude is essentially the same at the successive slots, but whose phase differs by B₁₀d radians at the two slots with d the slot spacing and B₁₀ the phase velocity of the mode (2π/λ).
• The aperture excitation has a natural phase progression such that the main beam will point at an angle ϑ_o off endfire given by ${\text{kd cos ϑ}}_{\text{o}}\text{= B₁₀d}$

  

  , where ${\text{k = 2π/λ}}_{\text{o}}$

  

  (without consideration of the additional phase control which may be provided by the compound slots). Hence ${\text{ϑ}}_{\text{o}}\text{= arc}$

  

  $\text{cos (B₁₀/k)}$

  

  . The broad wall 41 dimension of the waveguide 40 could conceivably be adjusted to accommodate any B₁₀/k, and thus any beam pointing direction ϑ_o. This is not a practical possibility where size limitations and frequency sensitivity are considerations.
• The present invention provides a solution to the problem of how to provide, in a traveling wave array, an aperture excitation with a phase progression from slot to slot other than B₁₀d, so that the beam can be placed at an angular position other than the natural one. Theoretically this could be by adjusting the slot length of pure series or shunt slots to provide a phase difference which, when added to the phase progression to the aperture excitation places the beam at a desired angle ϑ. However, for arrays of practical length, there is not enough dynamic range to the self-admittance or self-impedance to permit this phase increment to be substantial. Compound slots do not suffer from this limitation, since they permit a full phase range of 360° in the excitation of individual slots. The orientation of the compound slot adds an additional phase shift α so that the beam position ϑ_o (FIG. 3) is now determined by the relationship of Eq. 1.
  
  ${\text{cosϑ}}_{\text{o}}\text{= B₁₀/k + α/kd (1)}$

  

  
  
• As a result, a traveling wave slot array employing compound slots may provide a beam at very near endfire (90° from the broadside) without requiring an excitation signal near the waveguide cutoff wavelength.
• An exemplary design procedure for designing a particular compound slot array is now described in summary fashion. It is assumed that the waveguide size, slot spacing, frequency of operation and dielectric constant of the dielectric filling of the waveguide have all been selected. In this example, there are N resonant length compound slots in the array, with a common spacing d, and with the nth slot furthest from the excitation source. It is further assumed that the desired radiation pattern has been specified so that the total voltage in each slot has been determined in relative amplitude and phase using known techniques.
• The total voltage in the nth slot is designated as V $\genfrac{}{}{0ex}{}{\text{s}}{\text{n}}$

  

  and is composed of four components,

  

  
  in which
  V $\genfrac{}{}{0ex}{}{\text{s }}{\text{n1}}$

  

  =  partial slot voltage due to wave A_n incident from left, i.e., from z < z $\genfrac{}{}{0ex}{}{\text{o}}{\text{n}}$

  

  
  V $\genfrac{}{}{0ex}{}{\text{s }}{\text{n2}}$

  

  =  partial slot voltage due to wave D_n incident from right, i.e., from z > z $\genfrac{}{}{0ex}{}{\text{o}}{\text{n}}$

  

  .
  V $\genfrac{}{}{0ex}{}{\text{s }}{\text{n3}}$

  

  =  partial slot voltage due to external mutual coupling with all other slots in the array.
  V $\genfrac{}{}{0ex}{}{\text{s }}{\text{n4}}$

  

  =  partial slot voltage due to internal TE₂₀ mode coupling with two immediate neighbor slots in the same waveguide. Similarly, the total backward-scattered and forward-scattered TE₁₀ modes off the nth slot will have amplitudes B_n and C_n which can be shown in corresponding parts, viz.,
  
  ${\text{B}}_{\text{n}}{\text{= B}}_{\text{n1}}{\text{+ B}}_{\text{n2}}{\text{+ B}}_{\text{n3}}{\text{+ B}}_{\text{n4}}\text{ (4)}$

  

  
  
  ${\text{C}}_{\text{n}}{\text{= C}}_{\text{n1}}{\text{+ C}}_{\text{n2}}{\text{+ C}}_{\text{n3}}{\text{+ C}}_{\text{n4}}\text{ (5)}$

  

  
  
  
• The relationships which connect the quantities of Eqs. 4 and 5 are given in the Appendix.
• The central design equation which leads ultimately to a relationship between the desired slot voltages and the slot offset (x_n) from the waveguide centerline and its angle of inclination (ϑ_n) thereto is as follows:

  

  
  In the above,

  

  
  with η the impedance of free space, ${\text{λ = λ}}_{\text{o}}{\text{/(ε}}_{\text{r}}{\text{)}}^{\text{½}}$

  

  and the wavelength of plane waves traveling in an unbounded region of dielectric constant ${\text{ε}}_{\text{r}}{\text{= ε/ε}}_{\text{o}}$

  

  .
• Also,

  
• The key term relating to the slot orientation is h_n(X_n, ϑ_n, 2L_n). This term is

  

  
  with 2L_n the resonant length of the nth compound slot. 2L_n is a function of the offset of the n^th slot and perhaps also its inclination. In Eq. 7, $\text{i = arcsin (λ/2a)}$

  

  and

  

  
     To solve the central design equation (Eq. 6) shown above the constants L_n, K_1,n, and K_2,n are given initial values. Also the external and internal mutual couplings,

  

  
  and

  

  
  are calculated for these initial values. The central design equation thus yields a value from h_n which leads to new values of X_n and ϑ_n. This process is repeated with each iteration drawing closer to the true values of X_n and ϑ_n.
• The compound slots employed in the preferred embodiment of the invention are of resonant length. As is known to those skilled in the art, the resonant length is a parameter which may be determined emperically by measurements or in some cases by calculation using a method of moments technique. It has been found that a reasonable approximation of the resonant length parameter is that of a pure shunt slot with the same offset as the particular compound slot.
• The central design equation (Eq. 6) has been tested against experiments performed on two S-band antennas. Each of these antennas consisted of nine compound slots, 0.55 λ_o on centers, travelling-wave fed by a TE₁₀ wave dielectric-filled waveguide. Each waveguide was terminated in a matched load which absorbed 10% of the input power. The waveguide broadwall dimension is 33.02 mm (1.3 inches), and the narrow wall dimension is 3.81 mm (.150 inches). The waveguide was filled with a dielectric material having a dielectric constant of 2.5. The waveguides are fabricated from a material sold under the registered trade mark "Duroid 5876", a stripline board material which is copper clad on both sides, with the abutting edges copper clad to form a closed waveguide. Both of these antennas had been designed by employing an earlier, less-exact design procedure. The array were designed to produce main beams at 60° and 120°, respectively, from forward endfire, defined as being in the direction from the input to the load.
• The dimensions and orientations of the nine slots S_i of the slotted array designed for producing the main beam at 60° from forward endfire are given by way of example in Table 1. TABLE I

  Slot #	Xn(mm)	Xn (ins)	ϑn (degrees)	Length (mm)	Length (ins)
  1	+0.076	+.003	-.76°	29.77	1.172
  2	+0.457	+.018	-.35°	29.82	1.174
  3	+0.559	+.022	+1.4°	29.85	1.175
  4	0	0.0	+3.8°	29.77	1.172
  5	-0.965	-.038	+3.3°	30	1.181
  6	-1.753	-.069	-1.0°	30.48	1.200
  7	-1.321	-.052	-5.5°	30.18	1.188
  8	+0.279	+.011	-5.2°	29.77	1.173
  9	+10.414	+0.41	-2.3°	30.02	1.182

• The intended aperture distributions were the Taylor -30 dB, n = 6 distribution. With the main beam ±30° off broadside, and with the element factor included, this results in a theoretical side lobe level of -26 dB. The experimental patterns for these antennas are shown in FIGS. 4A and 4B are compared with patterns calculated using the actual slot dimensions and the corrected design equation set forth above. A unique feature of arrays embodying the invention is that the beams of the two antennas are on opposite sides of broadside while the waveguide size and slot spacing are identical. Only the slot orientations are different.
• The above examples are for arrays which produce beams at ±60° and 120°, respectively, from forward endfire, or ±30° from broadside. It is to be understood that the maximum beam scan angle achievable by the invention is limited only by the shape of the radiation patterns of the slot elements and the onset of secondary beams, and not by any limitation on achievable inter-element phase shifts. As will be appreciated by those skilled in the art, the longer the array is, the narrower the beam and the closer it may be scanned to endfire.
• One application to which the invention is particularly well suited is as a missile target detection device (TDD) or fuse antenna. A simplified perspective diagrammatic view of a portion of a missile body with the slotted arrays is shown in FIG. 5. One or more of the slotted arrays 62 designed to place the beam far from broadside may be arranged longitudinally along the outer surface of the missile body 60. The beam of these antennas may be used to detect targets being approached by the missile while the missile is some distance from the target. This provides ample time to properly detonate the missile explosive charge to destroy the target, for example. The number of the arrays placed about the periphery of the missile body will depend on the particular application.
APPENDIX
• The relations which connect the quantities of equations 4 and 5 are:

  

  

  
  and lastly,

  

  
  in which

  

  
  and the real angle i' is defined by

  

Claims (7)

1. A travelling wave array antenna adapted to produce an array beam in a predetermined direction inclined from the broadside normal direction, comprising:
      a rectangular waveguide (40) defined by first (41) and second conductive broadwalls and first (42) and second conductive narrow walls;
      means for exciting said waveguide with an excitation signal having a prescribed wavelength and propagating in a TE₁₀ mode through said waveguide in a propagation direction from a first end of said waveguide towards a second end of said waveguide;
      means for terminating (43) said waveguide at said second end thereof; and
      a series of compound slots (S₁ S₂...S_n) formed in said first broadwall (41) generally along the longitudinal centerline of said first broadwall; wherein
      each of said slots is of resonant length (2L_n);
      first intermittent ones of said slots are positioned with their lengthwise dimensions oriented at selected angles with respect to said longitudinal centerline; and
      the offset distance parameter (X_n) from the longitudinal centerline of said first broadwall and the angle parameter (ϑ_n) of each of said slots are selected to control the phase and amplitude of the voltage in each respective slot to position the beam resulting from the excitation signal at the predetermined direction;
      characterised in that:
      said series of compound slots are arranged in a generally sinusoidal configuration; and
      second intermittent ones of said slots are positioned with their lengthwise dimensions oriented substantially parallel to and offset a selected distance from said longitudinal centerline, but on opposite sides thereof.
2. An array antenna according to claim 1, wherein at least two successive ones of said slots (S₂, S₃) are offset from said longitudinal centerline on the same side thereof.
3. An array antenna according to claim 1 or claim 2, wherein said resonant length (2L_n) of each of said compound slots is defined as the resonant length of a pure shunt slot disposed at the same offset from said longitudinal centerline as the respective compound slot.
4. An array antenna according to any one of claims 1 to 3, wherein said resonant length of each of said compound slots is defined as one-half of said prescribed wavelength of said excitation signal.
5. An array antenna according to any one of claims 1 to 4, wherein said offset distance parameter of said parallel oriented slots and said angle parameter of said angularly oriented slots are further preselected to provide phase and amplitude distribution corrections to compensate for the effects of mutual coupling.
6. An array antenna according to any one of claims 1 to 5, wherein said means for terminating said waveguide comprises a matched load.
7. An array antenna according to any one of claims 1 to 6, wherein said center-to-center spacing between each adjacent pair of said slots is equal.

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