Abstract:
A design and physical configuration for multi-frequency, low-profile, capacitively loaded magnetic dipole (CLMD) antennas to be used in wireless communications. One component of the CLMD antenna having one to three metal plates, and one component having one to n elements. The range of frequencies covered to be determined by the shape, size, and number of elements in the physical configuration of the components.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application relates to co-pending application Ser. No. 09/892,928, filed on Jun. 26, 2001, entitled “Multi Frequency Magnetic Dipole Antenna Structure and Methods Reusing the Volume of an Antenna” by L. Desclos et al., owned by the assignee of this application and incorporated herein by reference.  
         [0002]    This application relates to co-pending application Ser. No. 10/076922, entitled “Multi Frequency Magnetic Dipole Antenna Structures with a New E-Field Distribution for Very Low-Profile Antenna Applications” by G. Poilasne et al., owned by the assignee of this application and incorporated herein by reference. 
     
    
     
       BACKGROUND INFORMATION  
         [0003]    1. Field of the Invention  
           [0004]    The present invention relates generally to the field of wireless communications, and particularly to multi-band antennas used in wireless communications.  
           [0005]    2. Background  
           [0006]    Certain wireless communication applications such as the Global System for Mobile Communications (GSM) and Personal Communications Service (PCS) require that multiple bands be accessible, depending upon the local frequency coverage available from a service provider. Because applications such as GSM and PCS are used in the context of wireless communications devices that have relatively small form-factors, a low profile is also required.  
           [0007]    The present invention addresses the requirements of certain wireless communications applications by providing configurations for low profile, multi-frequency, multi-band, capacitively loaded magnetic dipole (CLMDs) antennas.  
         SUMMARY OF THE INVENTION  
         [0008]    The present invention discloses a myriad physical arrangements of multiple antenna elements configured to cover one to n number of frequencies or bands of frequencies.  
           [0009]    In the present invention, the antenna elements include both inductive and capacitive parts. Each element can provide a single frequency or band of frequency. The physical design of each element can vary, but the design allows for multiple frequencies by using a plurality of single elements to provide a multi-frequency antenna.  
           [0010]    In one embodiment, a single element has two top plates and a bottom plate. In another embodiment a single element has one u-shaped top plate and one bottom plate. Each element produces a specific frequency or band of frequencies based on its relative size and shape. Different physical configurations can be considered to adapt the antenna and its elements to the physical environment specific to a particular application. In each case, each plate is connected to the ground and only one plate is connected to a feeding point.  
           [0011]    Once the plates have been cut and folded into the desired form for the purpose of matching a frequency or frequency band, the elements can be arranged to target multiple bands. In one embodiment, the elements can be placed one next to the other. In another embodiment, the elements can be stacked, one on top of another. In yet another embodiment, the elements can be inserted one inside the other. A multi-frequency, multiband, capacitively loaded magnetic dipole (CLMD) antenna is configured by arranging the multiple elements to both meet the frequency and space requirements of the specific application.  
           [0012]    Further features and advantages of this invention as well as the structure and operation of various embodiments are described in detail below with reference to the accompanying drawings.  
           [0013]    This summary does not purport to define the invention. The invention is defined by the claims. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]    The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated by reference to the following detailed description, when taken in connection with the accompanying drawings, wherein:  
         [0015]    [0015]FIG. 1A is perspective view of an antenna which can be used as a component in accordance with the present invention;  
         [0016]    [0016]FIG. 1B is a side view of the antenna component of FIG. 1A;  
         [0017]    [0017]FIG. 1C is a top view of the antenna component of FIG. 1A;  
         [0018]    [0018]FIG. 2A is a top view one embodiment of an antenna in accordance with the present invention;  
         [0019]    [0019]FIG. 2B is a top view of one alternative embodiment of the antenna of FIG. 2A;  
         [0020]    [0020]FIG. 3A is a top view of another embodiment of an antenna in accordance with the present invention;  
         [0021]    [0021]FIG. 3B is a frequency graph corresponding to the coverage of the antenna shown in FIG. 3A;  
         [0022]    [0022]FIG. 4A is a top view of another embodiment of an antenna in accordance with the present invention;  
         [0023]    [0023]FIG. 4B is a top view of an alternative embodiment of the antenna of FIG. 4A;  
         [0024]    [0024]FIG. 4C is a top view of an alternative embodiment of the antenna of FIG. 4A;  
         [0025]    [0025]FIG. 4D is a top view of an alternative embodiment of the antenna of FIG. 4A;  
         [0026]    [0026]FIG. 5A is a top-view an alternative embodiment of an antenna in accordance with the present invention;  
         [0027]    [0027]FIG. 5B is a side view of the antenna of FIG. 5A;  
         [0028]    [0028]FIG. 5C is an alternative embodiment of the antenna of FIG. 5A;  
         [0029]    [0029]FIG. 5D is a side view of the antenna of FIG. 5C;  
         [0030]    [0030]FIG. 6A is a perspective view of an alternative embodiment of a CLMD antenna component according to the present invention;  
         [0031]    [0031]FIG. 6B is a side view of the CLMD antenna component of FIG. 6A;  
         [0032]    [0032]FIG. 6C is a top view of the CLMD antenna component of FIG. 6 a:    
         [0033]    [0033]FIG. 7A is a top view of an alternative embodiment of a CLMD antenna according to the present invention;  
         [0034]    [0034]FIG. 7B is a top view of an alternative embodiment of the CLMD antenna of FIG. 7B;  
         [0035]    [0035]FIG. 8A is a top view of an alternative embodiment of a CLMD antenna according to the present invention;  
         [0036]    FIGS.  8 B-D are top views of alternative embodiments of the antenna of FIG. 8A;  
         [0037]    [0037]FIG. 9A is a top view of an alternative embodiment of a CLMD antenna component according to the present invention:  
         [0038]    [0038]FIG. 9B is a side view of the antenna component of FIG. 9A;  
         [0039]    [0039]FIG. 9C is a side view of an alternative embodiment of the antenna component of FIG. 9A;  
         [0040]    [0040]FIG. 10A is a top view of an alternative embodiment of a CLMD antenna component according to the present invention;  
         [0041]    [0041]FIG. 10B is a side view of the antenna component of FIG. 10A;  
         [0042]    [0042]FIGS. 10C and 10D are side views of alternative embodiments of the antenna component of FIG. 10A;  
         [0043]    [0043]FIG. 11A is a top view of an alternative embodiment of a CLMD antenna component according to the present invention;  
         [0044]    [0044]FIGS. 11B and 11C are top views of alternative embodiments of the antenna component of FIG. 11A;  
         [0045]    [0045]FIG. 12A is a top view of an alternative embodiment of a CLMD antenna component according to the present invention;  
         [0046]    [0046]FIGS. 12B and 12C are top views of alternative embodiments of the antenna component of FIG. 12A;  
         [0047]    [0047]FIG. 13 is a top view of various antenna components and configures according to the present invention;  
         [0048]    [0048]FIGS. 14A and 14B are top views of alternative embodiment of CLMD antennas according to the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0049]    In the following description, for purposes of explanation and not limitation, specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known methods and devices are omitted so as to not obscure the description of the present invention with unnecessary detail.  
         [0050]    A CLMD antenna produces a specific frequency, band of frequency, or combination therein for a targeted applications like Global System for Mobile Communications (GSM) and Personal Communications Service (PCS). The resonant frequency is a result of the inductance and capacitance. CLMD antennas present various advantages, chief among them is excellent isolation. Different configurations of the CLMD antennas are available which have varying degrees of isolation and different bandwidths.  
         [0051]    [0051]FIG. 1A illustrates one embodiment of a single-element CLMD antenna  10  that can be used in accordance with the present invention. The CLMD antenna  10  comprises two top plates  12  and  14 , a bottom plate  16 , and an antenna feed line  18 . The two top plates  12  and  14  create the capacitive part  20  of antenna  10  and the loop between the two top plates  12  and  14  and the bottom plate  16  creates the inductive part  22  of antenna  10 . The electric field is confined in the capacitive part  16  of antenna  10  and the magnetic field is expelled in the inductive part  22  of antenna  10 . Power is supplied to the antenna  10  through the feed line  18 . In FIG. 1A, the feed line  18  is a coaxial cable with the inner conductor connected to one top plate  14  and the outer conductor connected to the bottom plate  16 , which serves as ground.  
         [0052]    [0052]FIG. 1B illustrates a side-view of antenna  10 . As can be seen the two top plates  12  and  14  create the capacitive part  20  of the antenna  10  while the loop between the two top plates  12  and  14 , and the bottom plate  16  creates the inductive part  22 . The far field of such an antenna is actually due to the expelled field, mainly magnetic, in the area closely surrounding the antenna  10 .  
         [0053]    [0053]FIG. 1C illustrates a top-view of antenna  10  with a horizontal electric field  24  shown between the two top plates  12  and  14  in accordance with the present invention. The horizontal electric field  24  allows for a lower antenna profile, because electric field  24  is confined in a horizontal orientation as opposed to a vertical orientation. The electric field confinement can be optimized and frequency bandwidth can be tuned, at least in part, by adjusting the distance between the two top plates  12  and  14 . For example, increasing the distance between the two top plates  12  and  14 , which increases the antenna mode volume, can enlarge the frequency bandwidth. Increasing the antenna mode volume will result in more leaks around the antenna. On the other hand, as confinement increases, the isolation increases, but the bandwidth becomes narrower. Thus, isolation and bandwidth can be optimized by adjusting the distance between the two top plates  12  and  14 .  
         [0054]    Turning now to FIG. 2A, one embodiment of a multi-element, multi-frequency, either mono or dual band CLMD antenna in accordance with the present invention is shown as reference numeral  100 . Antenna  100  comprises two separate CLMD antenna components  102  and  104 , such as antenna  10  shown in FIG. 1A, placed one beside the other. The antenna components  102  and  104  each include two top plates  112  and  114 , one bottom plate  116 , and a feed line  118  connected to one top plate  114 . The antenna components  102  and  104  are configured to operate at different frequencies within a specified frequency range. In this configuration, the frequency characteristics of antenna components  102  and  104  combine to give antenna  100  a frequency range including the combined operating frequencies of both antenna components  102  and  104 .  
         [0055]    An alternative embodiment of the antenna  100  is shown in FIG. 2B. In this embodiment, only one antenna component  102  is connected to the feed line  118 . In this configuration, antenna component  104  is excited by a magnetic coupling  120  coming from antenna component  102 . As in the previous embodiment, each antenna component  102  and  104  is configured to operate at a different frequency within a specified frequency range giving the resulting antenna  100  a frequency range that includes the combined operating frequencies of both antenna components  102  and  104 . In this configuration, 1 to n parasitic components can be coupled to the component connected to the feed line  118 .  
         [0056]    The antenna components  102  and  104  presented in FIGS. 2A and 2B can be sized for very different frequency ranges making it possible to obtain the multi-frequency, multi-band CLMD antenna  125  shown in FIG. 3A. Reference numerals  122  and  124 , of FIG. 3B, are the graphical representations of the frequencies covered by two larger components  126  and  128 , of FIG. 3A, and reference numerals  130  and  132  are the graphical representations of the frequencies covered by two smaller components  134  and  136 . Larger components  126  and  128  generally provide coverage for lower frequencies, for example in the 800 MHz range , while smaller components  134  and  136  provide coverage for higher frequencies, for example in the 1900 MHz range. Thus, the frequency coverage for antenna  125  is shown in FIG. 3B is the combined coverage of components  126 ,  128 ,  134 , and  136 .  
         [0057]    For purposes of this specification and the claims that follow, it can be said that antenna components  102  and  104  in FIGS. 2A and 2B are vertically aligned with respect to each other. Further, it can be said that antenna components  134  and  136  are horizontally aligned with respect to antenna elements  126  and  128  in FIG. 3A.  
         [0058]    Multiple configurations of feeding the components  126 ,  128 ,  134  and  136  are contemplated. For example, one component can be connected to a feed line and the others can be excited by magnetic coupling. Alternatively one component in each band (i.e. 800 MHz, 1900 MHz) can be connected to a feed line and the other component in each band is excited by magnetic coupling to its counter part in the frequency band. Another possible arrangement would be to connect each component to a feed line.  
         [0059]    [0059]FIGS. 4A, 4B,  4 C and  4 D illustrate the aforementioned feeding solutions plus different component placement. Components corresponding to similar frequency ranges can be placed side-by-side or inserted between the other components. These different configurations can be applied not only to two components of each frequency range but also at n components within m frequency ranges.  
         [0060]    [0060]FIG. 4A illustrates one embodiment of a multi-element, multi-band CLMD antenna  138 , in accordance with the present invention. In this configuration, there are four antenna components  140 ,  142 ,  144 , and  146 , placed parallel to one-another. Components  140  and  146  are the larger components, each covering different frequencies within a relatively lower frequency range. Components  142  and  144 , as the smaller of the four components, each cover different frequencies within a relatively higher frequency range. In this embodiment, power is supplied to each component  140 ,  142 ,  144 , and  146  through separate feed lines  118 . The invention can include 1 to n components and one to n feed lines.  
         [0061]    [0061]FIG. 4B illustrates an alternative embodiment of the antenna  138  of FIG. 4A. In this configuration, the four separate components  140 ,  142 ,  144 , and  146  again are placed parallel to one-another. However, in this arrangement, the larger components  140  and  146  and smaller components  142  and  144  are interspersed in the following order:  140 ;  142 ;  146 ; and  144 . In this embodiment, power is supplied to each component through a separate feed line  118 . Again, there can be 1 to n components and one to n feed lines.  
         [0062]    [0062]FIG. 4C illustrates another alternative embodiment of the antenna  138  of FIG. 4A. In this configuration, the two larger components  140  and  146  are grouped next to each other and the two smaller components  142  and  144  are grouped next to each other, with the larger grouping next to the smaller grouping. In this embodiment, power is supplied to the two larger components  140  and  146  through a single feed line  118  attached to component  140 . Power is supplied to parasitic component  156  through magnetic coupling  120 . Similarly, the two smaller components  142  and  144  are also feed with a single feed line  118  attached to component  142 . Power is supplied to parasitic component  144  through magnetic coupling  120 .  
         [0063]    [0063]FIG. 4D illustrates alternative embodiment of the antenna  138  of FIG. 4B. In this configuration, the larger components  140  and  146  are again interspersed with the smaller components  142  and  144 . However, in this embodiment, power is supplied to only one component, in this example larger component  140 , through feed line  118 . All other components  142 ,  144 , and  146  are powered through magnetic coupling  120 , which can supply 1 to n elements.  
         [0064]    Up to this point, the different embodiments of CLMD antennas have been presented having parallel components. As shown in FIG. 5, alternative embodiments of the invention can include stacking the components. The relative direction of one component with regard to the other is on factor in the strength of magnetic coupling between the components. When the components are arranged parallel to each other, the coupling is generally maximized and when they are orthogonal, the coupling is minimized. The two components can also be inserted one into the other for those different directions. If the larger component is placed on top, the smaller component can fit inside. Alternatively, the smaller component can be placed standing over the larger component as presented respectively in FIGS.  5 A- 5 B and  5 C- 5 D.  
         [0065]    [0065]FIGS. 5A and 5B illustrate one embodiment of a multi-element, multi-band CLMD antenna  148  in which the components  150  and  152  are orthogonal to each other, in accordance with the present invention. FIG. 5A is a top view, while FIG. 5B is a side view. In this embodiment, the components  150  and  152  are arranged one inside the other, with the larger component  150  on the outside and the smaller component  152  on the inside. On the horizontal plane, either component  150  or  152  can be arranged to any angle relative to the other from 0 to 360°.  
         [0066]    [0066]FIGS. 5C and 5D illustrate an alternative embodiment of the antenna  148  of FIGS. 5A and 5B. Again, FIG. 5C is a top view and FIG. 5D is a side view. In this embodiment, the components  150  and  152  are arranged one on top of the other. In this case, the smaller component  152  is positioned above the larger component  150 . Again, on the horizontal plane, either component can be arranged to any angle relative to the other from 0 to 360°.  
         [0067]    The aforementioned embodiments of the CLMD antenna  148  of the present invention have excellent isolation due to the high confinement of the electric field. Unfortunately, their bandwidth is relatively narrow. For some applications, the required bandwidth is too wide to use these CLMD antenna components. In order to increase the bandwidth, it is possible to relax the confinement. This relaxation can be obtained using various alternative relaxed component embodiments described below.  
         [0068]    [0068]FIG. 6A illustrates one embodiment of a relaxed single-element CLMD antenna  154  comprising top section antenna element  155 , a ground plate  164  and a feed line  118 . In this embodiment, the top section antenna element  155  is cut to include two top plates  158  and  160  and a connection section  162  connecting the two top plates  158  and  160  which creates a distributed capacitance  166  in a horizontal electric field as well as an inductance  168 .  
         [0069]    One way to relax the confinement antenna  154  is to increase the gap  156  between the two top plates  158  and  160 . At some point, the capacitance  166  of the antenna  154  becomes too small to keep a low frequency due to the increased gap  156  size between the two top plates  158  and  160 . The capacitance  166  reduction can be compensated for by increasing the inductance  168  of the antenna  154 . This can be achieved by connecting the two top plates  158  and  160  with a connection section  162 . In operation, the two top plates  158  and  160  and connection section  162  form a magnetic dipole field loop  170  shown in FIG. 6B.  
         [0070]    Similar to the embodiments described above, multiple configurations of multi-element, multi-frequency relaxed CLMD antennas can be assembled using relaxed single element CLMD antennas similar to the one shown in FIGS.  6 A-C. FIG. 7A illustrates one embodiment of such a multi-element, either mono or dual band CLMD antenna  170 , in accordance with the present invention. Antenna  170  comprises two top section antenna elements  172  and  174 , similar to top section antenna element  155  shown in FIGS.  6 A-C, mounted on a ground plane  164 . Alternatively, a separate ground plane can be attached to each top section antenna element. Each top section antenna element  172  and  174  is powered by a feed line  118 . The top section antenna elements  172  and  174  are placed parallel to one another and each is configured for covering a specific frequency range.  
         [0071]    [0071]FIG. 7B illustrates an alternative embodiment of the antenna of FIG. 7A in which only top section antenna element  172  is powered by a feed line  118 . In this embodiment, top section antenna element  174  is powered through magnetic coupling  176  with top section antenna element  172 . Magnetic coupling can be used to supply power to 1 to n elements.  
         [0072]    [0072]FIGS. 8A, 8B,  8 C and  8 D illustrate different alternative embodiments of a multi-element, multi-band CLMD antenna  178  in accordance with the present invention. The embodiments shown in FIGS. 8A and 8B each include four top section antenna elements  180 ,  182 ,  184  and  186  positioned on a common ground plate  170 . FIGS. 8C and 8D include four top section antenna elements  180 ,  182 ,  184  and  186  each positioned on a separate ground plate  188 . It should be noted that each of the configurations illustrated in FIGS. 8C and 8D can include a single ground plane  170  or multiple ground planes  188 . In fact, this is true for all of the embodiments disclosed herein. Further, it is possible for some top sections to share a common ground plane, while the other top sections either share a separate ground plane or are associated each with their own. For example, in FIG. 8A top sections  180  and  182  can share a common ground plane, while top sections  184  and  186  either share a ground plane or have their own ground planes. In general, the ground plane configuration for all of the antenna embodiments disclosed herein will depend on the particular implementation.  
         [0073]    In FIGS.  8 A- 8 D, two top section antenna elements are configured for each frequency range (e.g. elements  180  and  186  are configured for one frequency range and elements  182  and  184  are configured for another frequency range) and the different embodiment illustrated in the figures show exemplary physical and powering configurations. Further, in FIGS. 8A and 8B each top section antenna element  180 ,  182 ,  184  and  186  is powered by a feed line  118 . In FIG. 8C elements  180  and  186  are powered by a feeding line  118 , while elements  182  and  184  are powered by magnetic coupling  187  with elements  180  and  186  respectively. In FIG. 8D, only element  180  is powered using a feed line  118 , while elements  182 ,  184  and  186  are powered by magnetic coupling  187  with adjacent elements. Elements corresponding to the same frequency range can be placed side-by-side or inserted between elements corresponding to a different frequency range. These different configurations can be applied not only to two elements of each frequency range but also at n elements within m frequency ranges.  
         [0074]    A relaxed CLMD antenna  190  can also be arranged vertically similar to the CLMD antenna shown in FIG. 5. Again, the relative direction of one antenna element related to the other will control the strength of magnetic coupling between the elements. When the elements are parallel, the coupling is maximum and when they are orthogonal, the coupling is minimum. Multiple elements can also be stacked one on top of the other to produce addition embodiment of the invention. In configurations where the top element is larger  192 , other elements  194  can fit inside. In configurations where the top element is smaller  194 , it can stand over the other elements  192  as presented respectively in FIGS.  9 A- 9 B and  9 C.  
         [0075]    The bandwidth obtained with the relaxed CLMD antenna of the type illustrated in FIG. 6 may have to be increased for certain applications. In this case, the bandwidth can then be improved further by adding a bridge  157  over the slot of the top plate antenna element  155  as illustrated by the relaxed CLMD antenna  196  presented in FIG. 10A.  
         [0076]    Various bridge configurations can be applied to the present invention each creating unique ways to control the interaction between the antenna and its surrounding. Several exemplary embodiments are illustrated in FIGS. 10A, 10B,  10 C and  10 D. The bridge  157  can be electrically connected on both top plates  158  and  160  as shown in FIG. 10B; it can be connected on one top plate  158  and capacitively loaded  198  on the other top plate  160 , as shown in FIG. 10C; or it can be capacitively loaded  198  on both top plates  158  and  160  as shown in FIG. 10D.  
         [0077]    Volume and surface area are critical issues for handheld devices. Therefore it can be advantageous to have a dual band antenna component with a low volume and surface area. A relaxed CLMD antenna component can make this because the part of the top plate that is the farthest from the feeding point has very low sensitivity. Therefore, it is possible to inscribe a second, higher frequency in this part of the first element.  
         [0078]    [0078]FIG. 11A illustrates a top-view of one embodiment of a single-element, dual-band CLMD antenna component  2000  where one antenna element  202  is inserted into another antenna element  204 , in accordance with the present invention. In this embodiment areas  206  and  208  comprise the capacitive parts respectively for each band while areas  210  and  212  comprise the complementary inductive parts of the antenna  200  to keep a low frequency. Power is supplied to the antenna through a feed line  118 .. In this case, the antenna element  202  corresponding to the higher frequency is inserted into the lower frequency antenna element  204  and is oriented toward the same direction.  
         [0079]    [0079]FIG. 11B illustrates an alternative embodiment of a single-element, dual-band CLMD antenna component  200 . In this case, the antenna element  202  corresponding to the higher frequency is inserted into the antenna element corresponding to the lower frequency and is oriented in the opposite direction with a mirror symmetry.  
         [0080]    [0080]FIG. 11C illustrates a top-view of an alternative embodiment of a single-element, dual-band CLMD component  200 . In this case, the antenna element  204  corresponding to the higher frequency is inserted into the lower frequency antenna element  202  and is oriented in the opposite direction.  
         [0081]    [0081]FIGS. 12A, 12B, and  12 C illustrate the alternative embodiments of the antenna component  200  of FIGS. 11A, 11B and  11 C respectively, in which bridges  157  are added to improve bandwidth.  
         [0082]    [0082]FIG. 13 summarizes the various antenna embodiments illustrated in the previous figures. The important point is that the different presented solutions can actually be mixed in order to obtain multi-bands. For example, a dual-band relaxed CLMD component can be stacked with a mono-band, relaxed, bridged CLMD component in order to obtain a tri-band antenna.  
         [0083]    [0083]FIG. 14 shows an example of a quad-band, relaxed CLMD antenna component  220 . It is comprised of a top plate, tri-band inserted CLMG antenna element  222 , stacked with a mono-band regular CLMD antenna element  224  FIG. 14B illustrates an alternative embodiment of the antenna component  220  in which the top plate, tri-band inserted CLMG antenna element  222  is bridged  157 .  
         [0084]    It should also be noted that active or passive components can be placed on the under side of the ground plane of any of the antennas described herein in order to save circuit board real estate within whatever device the antenna is ultimately installed.  
         [0085]    While embodiments and implementations of the invention have been shown and described, it should be apparent that many more embodiments and implementations are within the scope of the invention. Accordingly, the invention is not to be restricted, except in light of the claims and their equivalents.