Patent Publication Number: US-10763589-B2

Title: Millimeter wave patch antennas with parasitic elements

Description:
BACKGROUND 
     This relates generally to electronic devices and, more particularly, to electronic devices with wireless communications circuitry. 
     Electronic devices often include wireless communications circuitry. For example, cellular telephones, computers, and other devices often contain antennas and wireless transceivers for supporting wireless communications. 
     It may be desirable to support wireless communications in millimeter wave and centimeter wave communications bands. Millimeter wave communications, which are sometimes referred to as extremely high frequency (EHF) communications, and centimeter wave communications involve communications at frequencies of about 10-300 GHz. Operation at these frequencies may support high data rates, but may raise significant challenges. For example, millimeter wave communications are often line-of-sight communications and can be characterized by substantial attenuation during signal propagation. In addition, it can be difficult to support millimeter wave communications over a sufficiently wide frequency bandwidth. 
     It would therefore be desirable to be able to provide electronic devices with improved wireless communications circuitry such as communications circuitry that supports communications at frequencies greater than 10 GHz. 
     SUMMARY 
     An electronic device may be provided with wireless circuitry. The wireless circuitry may include one or more antenna structures and transceiver circuitry such as millimeter wave transceiver circuitry. Antenna structures in the wireless circuitry may include patch antennas that are organized in a phased antenna array. 
     The antenna structures may include patch antennas formed on a dielectric substrate. The dielectric substrate may include multiple dielectric layers. A ground plane may be formed for a patch antenna. An antenna resonating element for the patch antenna may be formed from metal traces on a first dielectric layer. A parasitic element for the patch antenna may be formed from metal traces on a second dielectric layer. The patch antenna may have a first antenna feed that includes a first feed terminal coupled to the antenna resonating element and second feed terminal coupled to the antenna ground. The patch antenna may also have a second antenna feed that includes a first feed terminal coupled to the antenna resonating element and second feed terminal coupled to the antenna ground. 
     The parasitic element for the patch antenna may have dielectric-filled openings formed between coplanar parasitic conductors. The parasitic conductors may include a central parasitic conductor. Four rectangular parasitic conductors may be formed around the central parasitic conductor, with one rectangular parasitic conductor on each side of central parasitic conductor. Corner parasitic conductors may be formed at the corners of the parasitic element, with each rectangular parasitic conductor interposed between two of the corner parasitic conductors. 
     The corner parasitic conductors may be non-rectangular. For example, the corner parasitic conductors may have first and second perpendicular edges and a third edge that joins the first and second edges. The third edge may be straight or curved. The corner parasitic conductors may optimize the uniformity of the radiation pattern of the patch antenna. 
     A phased antenna array may include a plurality of patch antennas each having corner parasitic conductors. The plurality of patch antennas may be arranged in a grid defined by orthogonal grid lines and each patch antenna may have a longitudinal axis that is oriented at a non-parallel angle with respect to the orthogonal grid lines. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of an illustrative electronic device with wireless communications circuitry in accordance with an embodiment. 
         FIG. 2  is a schematic diagram of an illustrative electronic device with wireless communications circuitry in accordance with an embodiment. 
         FIG. 3  is a rear perspective view of an illustrative electronic device showing illustrative locations at which antennas for communications at frequencies greater than 10 GHz may be located in accordance with an embodiment. 
         FIG. 4  is a diagram of an illustrative transceiver circuit and antenna in accordance with an embodiment. 
         FIG. 5  is a perspective view of an illustrative patch antenna in accordance with an embodiment. 
         FIG. 6  is a perspective view of an illustrative patch antenna with dual ports in accordance with an embodiment. 
         FIG. 7  is a cross-sectional side view of an illustrative patch antenna having a parasitic element in accordance with an embodiment. 
         FIG. 8  is a perspective view of an illustrative patch antenna having a parasitic element in accordance with an embodiment. 
         FIG. 9  is a top-down view of an illustrative patch antenna having a parasitic element with dielectric-filled openings in accordance with an embodiment. 
         FIG. 10  is a top-down view of an illustrative patch antenna having a parasitic element with dielectric-filled openings and triangular shaped corner parasitic pieces in accordance with an embodiment. 
         FIG. 11  is a top-down view of an illustrative patch antenna having a parasitic element with dielectric-filled openings and corner parasitic pieces with curved edges in accordance with an embodiment. 
         FIG. 12  is a perspective view of an illustrative patch antenna having a parasitic element with dielectric-filled openings and corner parasitic pieces with curved edges in accordance with an embodiment. 
         FIG. 13  is a top-down view of an illustrative phased antenna array including antennas arranged in a grid in accordance with an embodiment. 
         FIG. 14  is a top-down view of an illustrative phased antenna array including antennas arranged in grid and rotated by 45° relative to the grid in accordance with an embodiment. 
         FIG. 15  is a graph of antenna efficiency for illustrative patch antennas of the types shown in  FIGS. 5-12  in accordance with an embodiment. 
         FIG. 16  is a graph of antenna radiation patterns for illustrative patch antennas of the types shown in  FIGS. 5-12  in accordance with an embodiment. 
         FIG. 17  is a graph of isolation for illustrative phased antenna arrays of the types shown in  FIGS. 13 and 14  in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     An electronic device such as electronic device  10  of  FIG. 1  may contain wireless circuitry. The wireless circuitry may include one or more antennas. The antennas may include phased antenna arrays that are used for handling millimeter wave and centimeter wave communications. Millimeter wave communications, which are sometimes referred to as extremely high frequency (EHF) communications, involve signals at 60 GHz or other frequencies between about 30 GHz and 300 GHz. Centimeter wave communications involve signals at frequencies between about 10 GHz and 30 GHz. If desired, device  10  may also contain wireless communications circuitry for handling satellite navigation system signals, cellular telephone signals, local wireless area network signals, near-field communications, light-based wireless communications, or other wireless communications. 
     Antennas within electronic device  10  may include stacked patch antennas for handling communications at frequencies between 10 GHz and 300 GHz. A stacked patch antenna may include an antenna resonating element and at least one parasitic antenna resonating element formed over the antenna resonating element. If care is not taken, electromagnetic energy can be trapped between the antenna resonating element and the parasitic antenna resonating element, thereby decreasing the overall antenna efficiency. In order to mitigate this trapping, slots may be formed in the parasitic antenna resonating element to divide the parasitic antenna resonating element into coplanar segments. This may serve to alter the electromagnetic boundary conditions defined by the parasitic antenna resonating element, thereby mitigating trapping of electromagnetic energy between the antenna resonating element and the parasitic antenna resonating element within a frequency band of interest. 
     Electronic device  10  may be a computing device such as a laptop computer, a computer monitor containing an embedded computer, a tablet computer, a cellular telephone, a media player, or other handheld or portable electronic device, a smaller device such as a wristwatch device, a pendant device, a headphone or earpiece device, a virtual or augmented reality headset device, a device embedded in eyeglasses or other equipment worn on a user&#39;s head, or other wearable or miniature device, a television, a computer display that does not contain an embedded computer, a gaming device, a navigation device, an embedded system such as a system in which electronic equipment with a display is mounted in a kiosk or automobile, a wireless access point or base station, a desktop computer, a keyboard, a gaming controller, a computer mouse, a mousepad, a trackpad or touchpad, equipment that implements the functionality of two or more of these devices, or other electronic equipment. In the illustrative configuration of  FIG. 1 , device  10  is a portable device such as a cellular telephone, media player, tablet computer, or other portable computing device. Other configurations may be used for device  10  if desired. The example of  FIG. 1  is merely illustrative. 
     As shown in  FIG. 1 , device  10  may include a display such as display  14 . Display  14  may be mounted in a housing such as housing  12 . Housing  12 , which may sometimes be referred to as an enclosure or case, may be formed of plastic, glass, ceramics, fiber composites, metal (e.g., stainless steel, aluminum, etc.), other suitable materials, or a combination of any two or more of these materials. Housing  12  may be formed using a unibody configuration in which some or all of housing  12  is machined or molded as a single structure or may be formed using multiple structures (e.g., an internal frame structure, one or more structures that form exterior housing surfaces, etc.). 
     Display  14  may be a touch screen display that incorporates a layer of conductive capacitive touch sensor electrodes or other touch sensor components (e.g., resistive touch sensor components, acoustic touch sensor components, force-based touch sensor components, light-based touch sensor components, etc.) or may be a display that is not touch-sensitive. Capacitive touch screen electrodes may be formed from an array of indium tin oxide pads or other transparent conductive structures. 
     Display  14  may include an array of display pixels formed from liquid crystal display (LCD) components, an array of electrophoretic display pixels, an array of plasma display pixels, an array of organic light-emitting diode display pixels, an array of electrowetting display pixels, or display pixels based on other display technologies. 
     Display  14  may be protected using a display cover layer such as a layer of transparent glass, clear plastic, sapphire, or other transparent dielectric. Openings may be formed in the display cover layer. For example, openings may be formed in the display cover layer to accommodate one or more buttons, sensor circuitry such as a fingerprint sensor or light sensor, ports such as a speaker port or microphone port, etc. Openings may be formed in housing  12  to form communications ports (e.g., an audio jack port, a digital data port, charging port, etc.). Openings in housing  12  may also be formed for audio components such as a speaker and/or a microphone. 
     Antennas may be mounted in housing  12 . If desired, some of the antennas (e.g., antenna arrays that may implement beam steering, etc.) may be mounted under an inactive border region of display  14  (see, e.g., illustrative antenna locations  50  of  FIG. 1 ). Display  14  may contain an active area with an array of pixels (e.g., a central rectangular portion). Inactive areas of display  14  are free of pixels and may form borders for the active area. If desired, antennas may also operate through dielectric-filled openings in the rear of housing  12  or elsewhere in device  10 . 
     To avoid disrupting communications when an external object such as a human hand or other body part of a user blocks one or more antennas, antennas may be mounted at multiple locations in housing  12 . Sensor data such as proximity sensor data, real-time antenna impedance measurements, signal quality measurements such as received signal strength information, and other data may be used in determining when one or more antennas is being adversely affected due to the orientation of housing  12 , blockage by a user&#39;s hand or other external object, or other environmental factors. Device  10  can then switch one or more replacement antennas into use in place of the antennas that are being adversely affected. 
     Antennas may be mounted at the corners of housing  12  (e.g., in corner locations  50  of  FIG. 1  and/or in corner locations on the rear of housing  12 ), along the peripheral edges of housing  12 , on the rear of housing  12 , under the display cover glass or other dielectric display cover layer that is used in covering and protecting display  14  on the front of device  10 , under a dielectric window on a rear face of housing  12  or the edge of housing  12 , or elsewhere in device  10 . 
     A schematic diagram showing illustrative components that may be used in device  10  is shown in  FIG. 2 . As shown in  FIG. 2 , device  10  may include storage and processing circuitry such as control circuitry  14 . Control circuitry  14  may include storage such as hard disk drive storage, nonvolatile memory (e.g., flash memory or other electrically-programmable-read-only memory configured to form a solid state drive), volatile memory (e.g., static or dynamic random-access-memory), etc. Processing circuitry in control circuitry  14  may be used to control the operation of device  10 . This processing circuitry may be based on one or more microprocessors, microcontrollers, digital signal processors, baseband processor integrated circuits, application specific integrated circuits, etc. 
     Control circuitry  14  may be used to run software on device  10 , such as internet browsing applications, voice-over-internet-protocol (VOIP) telephone call applications, email applications, media playback applications, operating system functions, etc. To support interactions with external equipment, control circuitry  14  may be used in implementing communications protocols. Communications protocols that may be implemented using control circuitry  14  include internet protocols, wireless local area network protocols (e.g., IEEE 802.11 protocols—sometimes referred to as WiFi®), protocols for other short-range wireless communications links such as the Bluetooth® protocol or other WPAN protocols, IEEE 802.11ad protocols, cellular telephone protocols, MIMO protocols, antenna diversity protocols, satellite navigation system protocols, etc. 
     Device  10  may include input-output circuitry  16 . Input-output circuitry  16  may include input-output devices  18 . Input-output devices  18  may be used to allow data to be supplied to device  10  and to allow data to be provided from device  10  to external devices. Input-output devices  18  may include user interface devices, data port devices, and other input-output components. For example, input-output devices may include touch screens, displays without touch sensor capabilities, buttons, joysticks, scrolling wheels, touch pads, key pads, keyboards, microphones, cameras, speakers, status indicators, light sources, audio jacks and other audio port components, digital data port devices, light sensors, accelerometers or other components that can detect motion and device orientation relative to the Earth, capacitance sensors, proximity sensors (e.g., a capacitive proximity sensor and/or an infrared proximity sensor), magnetic sensors, and other sensors and input-output components. 
     Input-output circuitry  16  may include wireless communications circuitry  34  for communicating wirelessly with external equipment. Wireless communications circuitry  34  may include radio-frequency (RF) transceiver circuitry formed from one or more integrated circuits, power amplifier circuitry, low-noise input amplifiers, passive RF components, one or more antennas  40 , transmission lines, and other circuitry for handling RF wireless signals. Wireless signals can also be sent using light (e.g., using infrared communications). 
     Wireless communications circuitry  34  may include transceiver circuitry  20  for handling various radio-frequency communications bands. For example, circuitry  34  may include transceiver circuitry  22 ,  24 ,  26 , and  28 . 
     Transceiver circuitry  24  may be wireless local area network (WLAN) transceiver circuitry. Transceiver circuitry  24  may handle 2.4 GHz and 5 GHz bands for WiFi® (IEEE 802.11) communications and may handle the 2.4 GHz Bluetooth® communications band. 
     Circuitry  34  may use cellular telephone transceiver circuitry  26  for handling wireless communications in frequency ranges such as a communications band from 700 to 960 MHz, a communications band from 1710 to 2170 MHz, and a communications from 2300 to 2700 MHz or other communications bands between 700 MHz and 4000 MHz or other suitable frequencies (as examples). Circuitry  26  may handle voice data and non-voice data. 
     Millimeter wave transceiver circuitry  28  (sometimes referred to as extremely high frequency (EHF) transceiver circuitry  28  or transceiver circuitry  28 ) may support communications at frequencies between about 10 GHz and 300 GHz. For example, transceiver circuitry  28  may support communications in Extremely High Frequency (EHF) or millimeter wave communications bands between about 30 GHz and 300 GHz and/or in centimeter wave communications bands between about 10 GHz and 30 GHz (sometimes referred to as Super High Frequency (SHF) bands). As examples, transceiver circuitry  28  may support communications in an IEEE K communications band between about 18 GHz and 27 GHz, a K a  communications band between about 26.5 GHz and 40 GHz, a K u  communications band between about 12 GHz and 18 GHz, a V communications band between about 40 GHz and 75 GHz, a W communications band between about 75 GHz and 110 GHz, or any other desired frequency band between approximately 10 GHz and 300 GHz. If desired, circuitry  28  may support IEEE 802.11ad communications at 60 GHz and/or 5 th  generation mobile networks or 5 th  generation wireless systems (5G) communications bands between 27 GHz and 90 GHz. If desired, circuitry  28  may support communications at multiple frequency bands between 10 GHz and 300 GHz such as a first band from 27.5 GHz to 28.5 GHz, a second band from 37 GHz to 41 GHz, and a third band from 57 GHz to 71 GHz, or other communications bands between 10 GHz and 300 GHz. Circuitry  28  may be formed from one or more integrated circuits (e.g., multiple integrated circuits mounted on a common printed circuit in a system-in-package device, one or more integrated circuits mounted on different substrates, etc.). While circuitry  28  is sometimes referred to herein as millimeter wave transceiver circuitry  28 , millimeter wave transceiver circuitry  28  may handle communications at any desired communications bands at frequencies between 10 GHz and 300 GHz (e.g., in millimeter wave communications bands, centimeter wave communications bands, etc.). 
     Wireless communications circuitry  34  may include satellite navigation system circuitry such as Global Positioning System (GPS) receiver circuitry  22  for receiving GPS signals at 1575 MHz or for handling other satellite positioning data (e.g., GLONASS signals at 1609 MHz). Satellite navigation system signals for receiver  22  are received from a constellation of satellites orbiting the earth. 
     In satellite navigation system links, cellular telephone links, and other long-range links, wireless signals are typically used to convey data over thousands of feet or miles. In WiFi® and Bluetooth® links at 2.4 and 5 GHz and other short-range wireless links, wireless signals are typically used to convey data over tens or hundreds of feet. Extremely high frequency (EHF) wireless transceiver circuitry  28  may convey signals over short distances that travel between transmitter and receiver over a line-of-sight path. To enhance signal reception for millimeter and centimeter wave communications, phased antenna arrays and beam steering techniques may be used (e.g., schemes in which antenna signal phase and/or magnitude for each antenna in an array is adjusted to perform beam steering). Antenna diversity schemes may also be used to ensure that the antennas that have become blocked or that are otherwise degraded due to the operating environment of device  10  can be switched out of use and higher-performing antennas used in their place. 
     Wireless communications circuitry  34  can include circuitry for other short-range and long-range wireless links if desired. For example, wireless communications circuitry  34  may include circuitry for receiving television and radio signals, paging system transceivers, near field communications (NFC) circuitry, etc. 
     Antennas  40  in wireless communications circuitry  34  may be formed using any suitable antenna types. For example, antennas  40  may include antennas with resonating elements that are formed from stacked patch antenna structures, loop antenna structures, patch antenna structures, inverted-F antenna structures, slot antenna structures, planar inverted-F antenna structures, monopoles, dipoles, helical antenna structures, Yagi (Yagi-Uda) antenna structures, hybrids of these designs, etc. If desired, one or more of antennas  40  may be cavity-backed antennas. Different types of antennas may be used for different bands and combinations of bands. For example, one type of antenna may be used in forming a local wireless link antenna and another type of antenna may be used in forming a remote wireless link antenna. Dedicated antennas may be used for receiving satellite navigation system signals or, if desired, antennas  40  can be configured to receive both satellite navigation system signals and signals for other communications bands (e.g., wireless local area network signals and/or cellular telephone signals). Antennas  40  can one or more antennas such as antennas arranged in one or more phased antenna arrays for handling millimeter and centimeter wave communications. 
     Transmission line paths may be used to route antenna signals within device  10 . For example, transmission line paths may be used to couple antenna structures  40  to transceiver circuitry  20 . Transmission lines in device  10  may include coaxial probes realized by metalized vias, microstrip transmission lines, stripline transmission lines, edge-coupled microstrip transmission lines, edge-coupled stripline transmission lines, waveguide structures, transmission lines formed from combinations of transmission lines of these types, etc. Transmission lines in device  10  may be integrated into rigid and/or flexible printed circuit boards. In one suitable arrangement, transmission lines in device  10  may also include transmission line conductors (e.g., signal and ground conductors) integrated within multilayer laminated structures (e.g., layers of a conductive material such as copper and a dielectric material such as a resin that are laminated together without intervening adhesive) that may be folded or bent in multiple dimensions (e.g., two or three dimensions) and that maintain a bent or folded shape after bending (e.g., the multilayer laminated structures may be folded into a particular three-dimensional shape to route around other device components and may be rigid enough to hold its shape after folding without being held in place by stiffeners or other structures). All of the multiple layers of the laminated structures may be batch laminated together (e.g., in a single pressing process) without adhesive (e.g., as opposed to performing multiple pressing processes to laminate multiple layers together with adhesive). Filter circuitry, switching circuitry, impedance matching circuitry, and other circuitry may be interposed within the transmission lines, if desired. 
     In devices such as handheld devices, the presence of an external object such as the hand of a user or a table or other surface on which a device is resting has a potential to block wireless signals such as millimeter wave signals. Accordingly, it may be desirable to incorporate multiple antennas or phased antenna arrays into device  10 , each of which is placed in a different location within device  10 . With this type of arrangement, an unblocked antenna or phased antenna array may be switched into use. In scenarios where a phased antenna array is formed in device  10 , once switched into use, the phased antenna array may use beam steering to optimize wireless performance. Configurations in which antennas from one or more different locations in device  10  are operated together may also be used. 
       FIG. 3  is a perspective view of electronic device  10  showing illustrative locations  50  on the rear of housing  12  in which antennas  40  (e.g., single antennas and/or phased antenna arrays for use with wireless circuitry  34  such as wireless transceiver circuitry  28 ) may be mounted in device  10 . Antennas  40  may be mounted at the corners of device  10 , along the edges of housing  12  such as edge  12 E, on upper and lower portions of rear housing portion (wall)  12 R, in the center of rear housing wall  12 R (e.g., under a dielectric window structure or other antenna window in the center of rear housing  12 R), at the corners of rear housing wall  12 R (e.g., on the upper left corner, upper right corner, lower left corner, and lower right corner of the rear of housing  12  and device  10 ), etc. 
     In configurations in which housing  12  is formed entirely or nearly entirely from a dielectric, antennas  40  may transmit and receive antenna signals through any suitable portion of the dielectric. In configurations in which housing  12  is formed from a conductive material such as metal, regions of the housing such as slots or other openings in the metal may be filled with plastic or other dielectric. Antennas  40  may be mounted in alignment with the dielectric in the openings. These openings, which may sometimes be referred to as dielectric antenna windows, dielectric gaps, dielectric-filled openings, dielectric-filled slots, elongated dielectric opening regions, etc., may allow antenna signals to be transmitted to external equipment from antennas  40  mounted within the interior of device  10  and may allow internal antennas  40  to receive antenna signals from external equipment. In another suitable arrangement, antennas  40  may be mounted on the exterior of conductive portions of housing  12 . 
     In devices with phased antenna arrays, circuitry  34  may include gain and phase adjustment circuitry that is used in adjusting the signals associated with each antenna  40  in an array (e.g., to perform beam steering). Switching circuitry may be used to switch desired antennas  40  into and out of use. If desired, each of locations  50  may include multiple antennas  40  (e.g., a set of three antennas or more than three or fewer than three antennas in a phased antenna array) and, if desired, one or more antennas from one of locations  50  may be used in transmitting and receiving signals while using one or more antennas from another of locations  50  in transmitting and receiving signals. 
     A schematic diagram of an antenna  40  coupled to transceiver circuitry  20  (e.g., transceiver circuitry  28 ) is shown in  FIG. 4 . As shown in  FIG. 4 , radio-frequency transceiver circuitry  20  may be coupled to antenna feed  100  of antenna  40  using transmission line  64 . Antenna feed  100  may include a positive antenna feed terminal such as positive antenna feed terminal  96  and may include a ground antenna feed terminal such as ground antenna feed terminal  98 . Transmission line  64  may be formed form metal traces on a printed circuit or other conductive structures and may have a positive transmission line signal path such as path  91  that is coupled to terminal  96  and a ground transmission line signal path such as path  94  that is coupled to terminal  98 . Transmission line paths such as path  64  may be used to route antenna signals within device  10 . For example, transmission line paths may be used to couple antenna structures such as one or more antennas in an array of antennas to transceiver circuitry  20 . Transmission lines in device  10  may include coaxial probes realized by metal vias, microstrip transmission lines, stripline transmission lines, edge-coupled microstrip transmission lines, edge-coupled stripline transmission lines, waveguide structures, transmission lines formed from combinations of transmission lines of these types, etc. Transmission lines in device  10  may be integrated into rigid and/or flexible printed circuit boards. In one suitable arrangement, transmission lines in device  10  may also include transmission line conductors (e.g., signal and ground conductors) integrated within multilayer laminated structures (e.g., layers of a conductive material such as copper and a dielectric material such as a resin that are laminated together without intervening adhesive) that may be folded or bent in multiple dimensions (e.g., two or three dimensions) and that maintain a bent or folded shape after bending (e.g., the multilayer laminated structures may be folded into a particular three-dimensional shape to route around other device components and may be rigid enough to hold its shape after folding without being held in place by stiffeners or other structures). Filter circuitry, switching circuitry, impedance matching circuitry, and other circuitry may be interposed within transmission line  64  and/or circuits such as these may be incorporated into antenna  40  if desired (e.g., to support antenna tuning, to support operation in desired frequency bands, etc.). 
     Device  10  may contain multiple antennas  40 . The antennas may be used together or one of the antennas may be switched into use while other antenna(s) are switched out of use. If desired, control circuitry  14  may be used to select an optimum antenna to use in device  10  in real time and/or to select an optimum setting for adjustable wireless circuitry associated with one or more of antennas  40 . Antenna adjustments may be made to tune antennas to perform in desired frequency ranges, to perform beam steering with a phased antenna array, and to otherwise optimize antenna performance. Sensors may be incorporated into antennas  40  to gather sensor data in real time that is used in adjusting antennas  40 . 
     In some configurations, antennas  40  may be arranged in one or more antenna arrays (e.g., phased antenna arrays to implement beam steering functions). For example, the antennas that are used in handling millimeter and centimeter wave signals wireless transceiver circuits  28  may be implemented as phased antenna arrays. The radiating elements in a phased antenna array for supporting millimeter and centimeter wave communications may be patch antennas (e.g., stacked patch antennas), dipole antennas, dipole antennas with directors and reflectors in addition to dipole antenna resonating elements (sometimes referred to as Yagi antennas or beam antennas), or other suitable antenna elements. Transceiver circuitry can be integrated with the phased antenna arrays to form integrated phased antenna array and transceiver circuit modules. 
     An illustrative patch antenna that may be used in conveying wireless signals at frequencies between 10 GHz and 300 GHz or other wireless signals is shown in  FIG. 5 . As shown in  FIG. 5 , patch antenna  40  may have a patch antenna resonating element  104  that is separated from and parallel to a ground plane such as antenna ground plane  92 . Positive antenna feed terminal  96  may be coupled to patch antenna resonating element  104 . Ground antenna feed terminal  98  may be coupled to ground plane  92 . If desired, conductive path  88  (e.g., a coaxial probe feed) may be used to couple terminal  96 ′ to terminal  96  so that antenna  40  is fed using a transmission line with a positive conductor coupled to terminal  96 ′ and thus terminal  96 . If desired, path  88  may be omitted and other types of antenna feed arrangements may be used. The illustrative feeding configuration of  FIG. 5  is merely illustrative. 
     As shown in  FIG. 5 , patch antenna resonating element  104  may lie within a plane such as the X-Y plane of  FIG. 5  (e.g., the lateral surface area of element  104  may lie in the X-Y plane). Patch antenna resonating element  104  may sometimes be referred to herein as patch  104 , patch element  104 , patch resonating element  104 , antenna resonating element  104 , or resonating element  104 . Ground  92  may lie within a plane that is parallel to the plane of patch  104 . Patch  104  and ground  92  may therefore lie in separate parallel planes that are separated by a distance H. Patch  104  and ground  92  may be formed from conductive traces patterned on a dielectric substrate such as a rigid or flexible printed circuit board substrate, metal foil, stamped sheet metal, electronic device housing structures, or any other desired conductive structures. The length of the sides of patch  104  may be selected so that antenna  40  resonates at a desired operating frequency. For example, the sides of patch  104  may each have a length L 0  that is approximately equal to half of the wavelength (e.g., within 15% of half of the wavelength) of the signals conveyed by antenna  40  (e.g., in scenarios where patch  104  is substantially square). 
     The example of  FIG. 5  is merely illustrative. Patch  104  may have a square shape in which all of the sides of patch  104  are the same length or may have a different rectangular shape (e.g., a non-square rectangular shape). If desired, patch  104  and ground  92  may have different shapes and orientations (e.g., planar shapes, curved patch shapes, patch shapes with non-rectangular outlines, shapes with straight edges such as squares, shapes with curved edges such as ovals and circles, shapes with combinations of curved and straight edges, etc.). In scenarios where patch  104  is non-rectangular, patch  104  may have a side or a maximum lateral dimension that is approximately equal to (e.g., within 15% of) half of the wavelength of operation, for example. 
     To enhance the polarizations handled by patch antenna  40 , antenna  40  may be provided with multiple feeds. An illustrative patch antenna with multiple feeds is shown in  FIG. 6 . As shown in  FIG. 6 , antenna  40  may have a first feed at antenna port P 1  that is coupled to transmission line  64 - 1  and a second feed at antenna port P 2  that is coupled to transmission line  64 - 2 . The first antenna feed may have a first ground feed terminal coupled to ground  92  and a first positive feed terminal  96 -P 1  coupled to patch  104 . The second antenna feed may have a second ground feed terminal coupled to ground  92  and a second positive feed terminal  96 -P 2  on patch  104 . 
     Patch  104  may have a rectangular shape with a first pair of edges running parallel to dimension Y and a second pair of perpendicular edges running parallel to dimension X, for example. The length of patch  104  in dimension Y is L 1  and the length of patch  104  in dimension X is L 2 . With this configuration, antenna  40  may be characterized by orthogonal polarizations. 
     When using the first antenna feed associated with port P 1 , antenna  40  may transmit and/or receive antenna signals in a first communications band at a first frequency (e.g., a frequency at which one-half of the corresponding wavelength is approximately equal to dimension L 1 ). These signals may have a first polarization (e.g., the electric field E 1  of antenna signals  102  associated with port P 1  may be oriented parallel to dimension Y). When using the antenna feed associated with port P 2 , antenna  40  may transmit and/or receive antenna signals in a second communications band at a second frequency (e.g., a frequency at which one-half of the corresponding wavelength is approximately equal to dimension L 2 ). These signals may have a second polarization (e.g., the electric field E 2  of antenna signals  102  associated with port P 2  may be oriented parallel to dimension X so that the polarizations associated with ports P 1  and P 2  are orthogonal to each other). In scenarios where patch  104  is square (e.g., length L 1  is equal to length L 2 ), ports P 1  and P 2  may cover the same communications band. In scenarios where patch  104  is rectangular, ports P 1  and P 2  may cover different communications bands if desired. During wireless communications using device  10 , device  10  may use port P 1 , port P 2 , or both port P 1  and P 2  to transmit and/or receive signals (e.g., millimeter wave signals at millimeter wave frequencies). 
     The example of  FIG. 6  is merely illustrative. Patch  104  may have a square shape in which all of the sides of patch  104  are the same length or may have a rectangular shape in which length L 1  is different from length L 2 . In general, patch  104  and ground  92  may have different shapes and orientations (e.g., planar shapes, curved patch shapes, patch element shapes with non-rectangular outlines, shapes with straight edges such as squares, shapes with curved edges such as ovals and circles, shapes with combinations of curved and straight edges, etc.). 
     If care is not taken, antennas  40  such as single-polarization patch antennas of the type shown in  FIG. 5  and/or dual-polarization patch antennas of the type shown in  FIG. 6  may have insufficient bandwidth for covering an entirety of a communications band of interest (e.g., a communications band at frequencies greater than 10 GHz). For example, in scenarios where antenna  40  is configured to cover a millimeter wave communications band between 57 GHz and 71 GHz, patch  104  as shown in  FIGS. 5 and 6  may have insufficient bandwidth to cover the entirety of the frequency range between 57 GHz and 71 GHz. If desired, antenna  40  may include one or more parasitic antenna resonating elements that serve to broaden the bandwidth of antenna  40 . 
       FIG. 7  is a cross-sectional side view showing how antenna  40  may be provided with a bandwidth widening parasitic antenna resonating element. As shown in  FIG. 7 , antenna  40  may be formed on a dielectric substrate such as substrate  120 . Substrate  120  may be, for example, a rigid or printed circuit board or other dielectric substrate. Substrate  120  may include multiple stacked dielectric layers  122  (e.g., multiple layers of printed circuit board substrate such as multiple layers of fiberglass-filled epoxy) such as a first dielectric layer  122 - 1 , a second dielectric layer  122 - 2  over the first dielectric layer, a third dielectric layer  122 - 3  over the second dielectric layer, a fourth dielectric layer  122 - 4  over the third dielectric layer, a fifth dielectric layer  122 - 5  over the fourth dielectric layer, a sixth dielectric layer  122 - 6  over the fifth dielectric layer, a seventh dielectric layer  122 - 7  over the sixth dielectric layer, an eighth dielectric layer  122 - 8  over the seventh dielectric layer, and a ninth dielectric layer  122 - 9  over the eighth dielectric layer. Each layer  122  may have the same thickness (height) or two or more layers  122  may have different thicknesses. Additional dielectric layers  122  may be stacked within substrate  120  if desired. 
     With this type of arrangement, antenna  40  may be embedded within the layers of substrate  120 . For example, ground plane  92  may be formed on a surface of second layer  122 - 2  whereas patch  104  of antenna  40  is formed on a surface of sixth layer  122 - 6 . Antenna  40  may be fed using a transmission line  64  and an antenna feed that includes positive antenna feed terminal  96  coupled patch  104  and a ground antenna feed terminal coupled to ground plane  92 . Transmission line  64  may, for example, be formed from a conductive trace such as conductive trace  126  on a surface of first layer  122 - 1  and portions of ground layer  92 . Conductive trace  126  may form the positive signal conductor for transmission line  64  (e.g., positive signal conductor  91  as shown in  FIG. 4 ). 
     A hole or opening  128  may be formed in ground layer  92 . Transmission line  64  may include a vertical conductor  124  (e.g., a conductive through-via, conductive pin, metal pillar, solder bump, combinations of these, or other vertical conductive interconnect structures) that extends from trace  126  through layer  122 - 2 , opening  128  in ground layer  92 , and layers  122 - 3  through  122 - 6  to feed terminal  96  on patch  104 . This example is merely illustrative and, if desired, other transmission line structures may be used (e.g., coaxial cable structures, stripline transmission line structures, etc.). 
     As shown in  FIG. 7 , one or more dielectric layers such as dielectric layers  122 - 7  through  122 - 9  may be formed over patch  104 . A bandwidth widening parasitic antenna resonating element such as element  106  may be formed from conductive traces on a surface of layer  122 - 9 . Parasitic antenna resonating element  106  may sometimes be referred to herein as parasitic resonating element  106 , parasitic antenna element  106 , parasitic element  106 , parasitic patch  106 , parasitic conductor  106 , parasitic structure  106 , or patch  106 . Parasitic element  106  is not directly fed, whereas patch  104  is directly fed via transmission line  64  and feed terminal  96 . Parasitic element  106  may create a constructive perturbation of the electromagnetic field generated by patch  104 , creating a new resonance for antenna  40 . This may serve to broaden the overall bandwidth of antenna  40  (e.g., to cover the entire millimeter wave frequency band from 57 GHz to 71 GHz). 
     Parasitic element  106  may be located at a distance H 0  with respect to patch  104  (e.g., distance H 0  may be equal to the sum of the thicknesses of layers  122 - 7 ,  122 - 8 , and  122 - 9 ). Patch  104  may be located at a distance H 1  with respect to ground plane  92  (e.g., distance H 1  may be equal to the sum of the thicknesses of layers  12 - 3 ,  122 - 4 , and  122 - 5 ). Distance H 1  may be equal to, less than, or greater than distance H 0 . In practice, distances H 1  and H 0  may be adjusted to adjust the overall bandwidth of antenna  40 . 
     Patch  104  may have a width M. As examples, patch  104  may be a rectangular patch (e.g., as shown in  FIGS. 5 and 6 ) having a side of length M, a square patch having four sides of length M, a circular patch having diameter M, an elliptical patch having a major axis length M, or may have any other desired shape (e.g., where length M is the maximum lateral dimension of the patch, a length of a side of the patch such as the longest side of the patch, a length of a side of a rectangular footprint of the patch, etc.). The size of width M may be selected so that antenna  40  resonates at a desired operating frequency. For example, width M may be approximately equal to half of the wavelength (e.g., within 15% of half of the wavelength) of the signals conveyed by antenna  40  or less than this by a factor determined by the dielectric constant of substrate  120  (e.g., the dielectric constant of layers  122 - 1  through  122 - 9 ). For example, in scenarios where the dielectric constant of substrate  120  is CR, width M may be approximately equal to (e.g., within 15% of) the wavelength of operation of antenna  40  divided by two times the square root of CR. As examples, dielectric constant CR may be between 1.0 and 6.0, between 2.0 and 4.0, between 2.5 and 3.5, between 3.0 and 4.0, between 3.4 and 3.7, 3.6, 3.45, 3.5, 3.4, or any other desired value (e.g., depending on the material used in forming substrate  120 ). In the scenario where antenna  40  covers a millimeter wave frequency band from 57 GHz to 71 GHz, width M may be between 1.0 mm and 1.2 mm, for example. 
     Parasitic element  106  may have a width N. As examples, parasitic element  106  may be a rectangular patch having a side of length N, a square patch having four sides of length N, a circular patch having diameter N, an elliptical patch having a major axis length N, or may have any other desired shape (e.g., where length N is the maximum lateral dimension of the patch, a length of a side of the patch such as the longest side of the patch, a length of a side of a rectangular footprint of the patch, etc.). Width N may be the same as width M of patch  104 , may be less than width M, or may be greater than width M. If desired, an optional dielectric layer  123  such as a solder mask layer may be formed over parasitic element  106  and layer  122 - 9  of substrate  120 . Layer  123  may have a dielectric constant that is different from (e.g., greater than) the dielectric constant of layers  122 . Width N may, for example, be approximately equal to the sum of the wavelength of operation of antenna  40  and a constant offset value, the sum being divided by two times the square root of the dielectric constant of layer  123 . Layer  123  may be omitted if desired. A volume  130  may be defined between parasitic element  106  and patch antenna resonating element  104 . 
     The example of  FIG. 7  is merely illustrative. If desired, fewer or additional layers  122  may be interposed between trace  126  and ground  92 , between ground  92  and patch  104 , and/or between patch  104  and parasitic element  106 . In one suitable arrangement, a single layer  122  is formed between patch  104  and ground  92  and a single layer  122  is formed between patch  104  and parasitic element  106 . In another suitable arrangement, substrate  120  may be formed from a single dielectric layer (e.g., antenna  40  may be embedded within a single dielectric layer such as a molded plastic layer). In yet another suitable arrangement, substrate  120  may be omitted and antenna  40  may be formed on other substrate structures or may be formed without substrates. If desired, patch  104  and/or parasitic element  106  may be formed from conductive traces on one or more dielectric substrates, metal foil, stamped sheet metal, conductive electronic device housing structures, or any other desired conductive structures within device  10 . 
     In  FIG. 7 , one parasitic element  106  is shown over patch  104 . This example is merely illustrative. If desired, additional parasitic elements may be coplanar with parasitic element  106  (e.g., in a first layer of parasitic elements above patch  104 ). Additionally, one or more additional parasitic elements (e.g., a second layer of parasitic elements) may be formed above parasitic element  106  in a plane that is parallel to parasitic element  106 . One or more intervening dielectric layers (e.g., additional dielectric layers  122 ) may separate parasitic element  106  from the additional parasitic elements formed over parasitic element  106 . 
     In the example of  FIG. 7 , antenna  40  is shown as having only a single polarization (feed) for the sake of clarity. Antenna  40  may, if desired, be a dual-polarized patch antenna having two feeds (e.g., as shown in  FIG. 6 ).  FIG. 8  is a perspective view of antenna  40  having parasitic element  106  and two feeds for covering two orthogonal polarizations. In the example of  FIG. 8 , dielectric substrate  120 , dielectric layer  123 , and ground plane  92  are not shown for the sake of clarity. 
     As shown in  FIG. 8 , antenna  40  may have a first feed at antenna port P 1  that is coupled to first transmission line  64 - 1  and a second feed at antenna port P 2  that is coupled to a second transmission line  64 - 2 . The first antenna feed may have a first ground feed terminal coupled to ground (e.g., ground  92  in  FIG. 7 ) and a first positive feed terminal  96 -P 1  coupled to patch antenna resonating element  104  at a first location. The second antenna feed may have a second ground feed terminal coupled to ground and a second positive feed terminal  96 -P 2  coupled to patch antenna resonating element  104  at a second location. Feed terminal  96 -P 1  may be coupled to patch  104  adjacent to a first side of patch  104  whereas feed terminal  96 -P 2  is coupled to patch  104  adjacent to a second side of patch  104  that is perpendicular to the first side of patch  104 , for example. 
     Parasitic element  106  may be formed over patch  104 . At least some or an entirety of parasitic element  106  may overlap patch  104 . In the example of  FIG. 8 , parasitic element  106  has a cross or “X” shape. In order to form the cross shape, parasitic element  106  may include notches or slots such as slots  107  (e.g., slots formed by removing conductive material from the corners of a square or rectangular metal patch). Cross-shaped parasitic element  106  may have a rectangular (e.g., square) outline or footprint. The width N of parasitic element  106  may be defined by the length of a side of the rectangular footprint of parasitic element  106 , for example. 
     Parasitic element  106  may include a first arm  110 , a second arm  112 , a third arm  114 , and a fourth arm  116  that extend from the center of parasitic element  106 . First arm  110  opposes third arm  114  whereas second arm  112  opposes fourth arm  116  (e.g., arms  110  and  114  may extend in parallel and from opposing sides of the point at the center of parasitic element  106  and arms  112  and  116  may extend in parallel and from opposing sides of the point at the center of parasitic element  106 ). Arms  110  and  114  may extend along a first longitudinal axis  118  whereas arms  112  and  116  extend along a second longitudinal axis  119 . Longitudinal axis  118  may be oriented at an angle of approximately 90° with respect to axis  119 . In the example of  FIG. 8 , the combined length of arms  110  and  114  is equal to the combined length of arms  112  and  116  (e.g., each of arms  110 ,  112 ,  114 , and  116  has the same length). This is merely illustrative and, in scenarios where two different linear polarizations are not used, arms  110 ,  112 ,  114 , and/or  116  may have different lengths. 
     In a single-polarization patch antenna, the distance between the positive antenna feed terminal  96  and the edge of patch  104  may be adjusted to ensure that there is a satisfactory impedance match between patch  104  and the corresponding transmission line  64 . However, such impedance adjustments may not be possible when the antenna is a dual-polarized patch antenna having two feeds. Removing conductive material from parasitic element  106  to form notches  107  may serve to adjust the impedance of patch  104  so that the impedance of patch  104  is matched to both transmission lines  64 - 1  and  64 - 2 , for example. Notches  107  may therefore sometimes be referred to herein as impedance matching notches, impedance matching slots, or impedance matching structures. 
     The dimensions of impedance matching notches  107  may be adjusted (e.g., during manufacture of device  10 ) to ensure that antenna  40  is sufficiently matched to both transmission lines  64 - 1  and  64 - 2  and to tweak the overall bandwidth of antenna  40 . In order for antenna  40  to be sufficiently matched to transmission lines  64 - 1  and  64 - 2 , feed terminals  96 -P 1  and  96 -P 2  need to overlap with the conductive material of parasitic element  106 . Notches  107  may therefore be sufficiently small so as not to uncover feed terminals  96 -P 1  or  96 -P 2 . In other words, each of antenna feed terminals  96 -P 1  and  96 -P 2  may overlap with a respective arm of parasitic element  106 . As an example, notches  107  may have sides with lengths N′ that are equal to between 1% and 45% of width N of parasitic  106 . During wireless communications using device  10 , device  10  may use ports P 1  and P 2  to transmit and/or receive millimeter wave signals with two orthogonal linear polarizations. 
     The example of  FIG. 8  is merely illustrative. If desired, parasitic element  106  may have additional notches  107 , fewer notches  107 , may have additional parasitic elements that fill notches  107 , may have curved edges, straight edges, combinations of straight and curved edges, or any other desired shape (e.g., in scenarios where a dual linear polarized patch is not used). Each of notches  107  may have the same shape and dimensions or two or more of notches  107  may have different shapes or dimensions. The edges of parasitic element  106  and/or longitudinal axes  118  and  119  may each be parallel to at least one edge of patch  104 . Each arm of parasitic element  106  may have the same width (e.g., as measured perpendicular to the corresponding longitudinal axis). In another scenario, two or more arms may have different widths (e.g., in scenarios where a dual linear polarized patch is not used). Parasitic element  106  may have any desired number of arms. In general, parasitic element  106  may be referred to herein as a cross-shaped parasitic element in any scenario where parasitic element  106  includes at least three arms extending from different sides of a common point on parasitic element  106 , where the arms of parasitic element  106  extend along at least two non-parallel longitudinal axes. 
     When configured in this way, antenna  40  may cover a relatively wide millimeter wave communications band of interest such as a frequency band between 57 GHz and 71 GHz. The millimeter wave communications band of interested may be defined by a lower threshold frequency (e.g., 57 GHz) and an upper threshold frequency (e.g., 71 GHz). Parasitic element  106  and patch  104  may define boundaries of volume  130  between patch  104  and parasitic element  106 . If care is not taken, antenna  40  may exhibit a cavity resonance within volume  130  at relatively high frequencies such as frequencies around the upper threshold frequency of the millimeter wave communications band of interest. This cavity resonance may serve to trap millimeter wave signals (energy) within volume  130  at these frequencies, thereby reducing the overall antenna efficiency of antenna  40  within the millimeter wave communications band of interest. This reduction in antenna efficiency may introduce errors in the wireless data conveyed by antenna  40  and/or may cause the corresponding millimeter wave communications link to be dropped. 
     In order to mitigate the trapping of millimeter wave signals within volume  130  at frequencies in the millimeter wave communications band of interest, parasitic element  106  may include one or more dielectric-filled openings. The openings may disrupt the cavity resonance between parasitic element  106  and patch  104  (e.g., by disrupting the boundary conditions of volume  130  and corresponding standing waves of EHF energy between elements  106  and  104 ). Such disruption of the cavity resonance may serve to mitigate the trapping of corresponding millimeter wave signals within volume  130  (e.g., so that the millimeter wave signals are radiated outwards and towards external communications equipment rather than remaining trapped within volume  130 ). 
       FIG. 9  is a top-down view of an antenna that has a parasitic resonating element with dielectric-filled openings to mitigate the trapping of corresponding millimeter wave signals. As shown in  FIG. 9 , openings  182  may be formed in parasitic element  106 . Openings  182  may, for example, separate arms  110 ,  112 ,  114 , and  116  from a central portion  106 C of parasitic element  106 . If desired, openings  182  may be filled with a dielectric material such as plastic, glass, ceramic, epoxy, adhesive, integral portions of dielectric layer  122 - 9  or dielectric layer  123  ( FIG. 7 ), or other dielectric materials. If desired, openings  182  may be filled with air. In yet another suitable arrangement, openings  182  may extend only partially through the thickness of parasitic element  106  (e.g., some of the conductive material in traces  106  may remain within openings  182  if desired). 
     In the example of  FIG. 9 , openings  182  each have a length that is equal to the width N″ of central portion  106 C and arms  110 ,  112 ,  114 , and  116 . Width N″ may, for example, be equal to between 20% and 90% of the width N of the rectangular footprint of parasitic element  106 . As examples, width N″ may be between 0.7 mm and 0.8 mm, between 0.6 mm and 0.9 mm, between 0.5 mm and 0.8 mm, less than 0.5 mm, etc. 
     The example of  FIG. 9  is merely illustrative. Additional openings may be formed within central portion  106 C if desired. Openings  182  may follow straight paths and/or curved paths. Openings  182  may extend parallel to at least one edge of parasitic element  106  or may extend at non-parallel angles with respect to all of the edges of parasitic element  106 . Openings  182  may extend only part way across the width N″ of arms  110 ,  112 ,  114 , and  116  if desired. Any desired number of openings  182  may be formed in parasitic antenna resonating element  106  (e.g., one opening  182 , two openings  182 , more than two openings  182 , etc.). In another suitable arrangement, openings  182  may be omitted. In general, parasitic element  106  may have any desired shape, relative orientation with respect to the sides of antenna resonating element  104 , number of arms and longitudinal axes, curved and/or straight edges, etc. When provided with openings  182 , arms  110 ,  112 ,  114 , and  116  and central portion  106 C each form parasitic elements for patch  104  and may be referred to collectively herein as parasitic element  106 . The separate conductive structures used to form arms  110 ,  112 ,  114 , and  116 , and central portion  106 C (e.g., in scenarios where parasitic element  106  includes openings  182 ) may sometimes be referred to herein as separate parasitic conductors, parasitic segments, or parasitic patches (e.g., parasitic conductors  110 ,  112 ,  114 ,  116 , and  106 C, etc.). 
     If desired (although not shown in the example of  FIG. 9 ), patch  104  may also have dielectric-filled openings to mitigate the trapping of millimeter wave signals. For example, patch  104  may be split into nine separate segments that are arranged in a 3×3 grid and separated by dielectric-filled openings (similar to openings  182  in  FIG. 9 ). Patch  104  may have any desired number and arrangement of openings to split the antenna resonating element into any desired number of segments. 
     In practice, it may be desirable for antenna  40  to have as uniform a radiation pattern (e.g., around the Z-axis of  FIG. 9 ) as possible (e.g., to ensure that antenna  40  can maintain satisfactory wireless communications with external equipment at any desired location around antenna  40 ). However, if care is not taken, discontinuities in parasitic element  106  of  FIG. 9  may undesirably limit the symmetry and uniformity of the radiation pattern for antenna  40 . If desired, antenna  40  may be provided with additional conductive structures (e.g., additional parasitics) that serve to optimize radiation pattern symmetry for antenna  40 . 
       FIG. 10  is a top-down view showing how antenna  40  may be provided with additional conductive structures for optimizing radiation pattern symmetry. As shown in  FIG. 10 , parasitic element  106  may include parasitic conductors  106 C,  110 ,  112 ,  114 , and  116  separated by openings  182 . Parasitic element  106  may also include additional parasitic conductors such as parasitic conductors  132 ,  134 ,  136 , and  138 . Parasitic conductors  132 ,  134 ,  136 , and  138  may be formed within notches  107  at the corners of parasitic element  106  of  FIG. 9 . Parasitic conductors  132 ,  134 ,  136 , and  138  may therefore sometimes be referred to herein as corner parasitic pieces, corner parasitic patches, corner parasitic segments, corner parasitic conductors, parasitic corners, parasitic corner segments, parasitic corner conductors, parasitic corner patches, or parasitic corner pieces. 
     For example, parasitic element  106  may include a first parasitic corner conductor  132  between arms  110  and  112  (to the upper-left of parasitic conductor  106 C of  FIG. 9 ). Parasitic element  106  may include a second parasitic corner conductor  134  between arms  112  and  114  (to the lower-left of parasitic conductor  106 C). Parasitic element  106  may include a third parasitic corner conductor  136  between arms  114  and  116  (to the lower-right of parasitic conductor  106 C). Parasitic element  106  may include a fourth parasitic corner conductor  138  between arms  116  and  110  (to the upper-right of parasitic conductor  106 C). Corner parasitic conductors  132 ,  134 ,  136 , and  138  are separated from adjacent portions of parasitic element  106  by openings  182 . Corner parasitic elements  132 ,  134 ,  136 , and  138  are coplanar with central portion  106 C and arms  110 ,  112 ,  114 , and  116 . 
     In the example of  FIG. 10 , each parasitic corner conductor has a triangular shape. For example, each corner parasitic element has first and second straight edges (sides)  142  and  144  that are perpendicular to each other. Edges  142  and  144  are joined by a straight edge  146  that completes the triangular shape. In other words, each parasitic corner conductor is a right triangle, with edge  146  forming the hypotenuse of the right triangle. This example is merely illustrative. In general, each parasitic corner conductor may have any desired shape (e.g., polygonal, square, rectangular, pentagonal, hexagonal, other irregular shapes, shapes with rounded corners, etc.). 
     The parasitic corner conductors  132 ,  134 ,  136 , and  138  may optionally be separated from other portions of the parasitic element by openings  182 . For example, in the embodiment of  FIG. 10 , openings  182  are formed between parasitic corner conductor  132  and arms  110  and  112 , between parasitic corner conductor  134  and arms  112  and  114 , between parasitic corner conductor  136  and arms  114  and  116 , and between parasitic corner conductor  138  and arms  116  and  110 . The example of  FIG. 10  is merely illustrative. Additional openings may be formed within central portion  106 C if desired. Openings  182  may follow straight paths and/or curved paths. Openings  182  may extend parallel to at least one edge of parasitic element  106  or may extend at non-parallel angles with respect to all of the edges of parasitic element  106 . Openings  182  may extend only part way across the width N″ of arms  110 ,  112 ,  114 , and  116  if desired. Openings  182  may extend only part way between the parasitic corner conductors and adjacent arms of the parasitic element. Any desired number of openings  182  may be formed in parasitic element  106  (e.g., one opening  182 , two openings  182 , more than two openings  182 , etc.). In another suitable arrangement, some or all of openings  182  may be omitted. 
     To further optimize the uniformity of the radiation pattern for antenna  40 , the corner parasitic elements may have curved edges if desired.  FIG. 11  is a top-down view of antenna  40  showing how the parasitic corner conductors may have curved edges. As shown in  FIG. 11 , each parasitic corner conductor again has first and second straight edges  142  and  144  that are perpendicular to each other. However, in  FIG. 11  edges  142  and  144  are coupled by a curved edge  146 . Edge  146  may have any desired degree (radius) of curvature. Providing the parasitic corner conductors with curved edges in this way may smooth out the radiation pattern for antenna  40  to provide an even more uniform radiation pattern than in scenarios where the parasitic corner conductors have straight edges, for example. 
     The shapes of the parasitic conductors shown in  FIG. 11  are merely illustrative. Each parasitic corner conductor may have any desired shape with any desired number of edges and any desired combination of straight and curved edges. Any desired number of openings  182  may be formed in parasitic element  106 . 
       FIG. 12  is a perspective view of an antenna of the type shown in  FIG. 11 . As shown in  FIG. 12 , patch  104  may be located at distance H 1  above ground plane  92 . Parasitic element  106  (e.g., parasitic conductors  106 C,  110 ,  112 ,  114 , and  116 , and parasitic corner conductors  132 ,  134 ,  136 , and  138 ) may be located at distance H 0  above patch antenna resonating element  104 . Parasitic conductor  112  of parasitic element  106  may overlap first feed terminal  96 -P 1  whereas parasitic conductor  114  of parasitic element  106  overlaps second feed terminal  96 -P 2 . 
     A first hole  128 -P 1  and a second hole  128 -P 2  may be formed in ground plane  92 . Transmission line  64 - 1  (e.g., the corresponding vertical conductor  124 -P 1 ) may extend through hole  128 -P 1  to feed terminal  96 -P 1  on a first portion of resonating element  104 . Transmission line  64 - 2  (e.g., the corresponding vertical conductor  124 -P 2 ) may extend through hole  128 -P 2  in ground plane  92  to feed terminal  96 -P 2  on a second portion of resonating element  104 . If desired, vertical conductors  124 -P 1  and  124 -P 2  may pass through the same opening  128  in ground plane  92 . 
     Volume  130  may be defined between parasitic element  106  and patch antenna resonating element  104 . Openings  182  may be formed within parasitic element  106 . For example openings  182  are formed between arms  110 ,  112 ,  114 , and  116  and central portion  106 C. Additionally, openings  182  are formed between corner parasitic piece  132  and arms  110  and  112 , between corner parasitic piece  134  and arms  112  and  114 , between corner parasitic piece  136  and arms  114  and  116 , and between corner parasitic piece  138  and arms  116  and  110 . By disrupting the cavity resonance associated with volume  130 , millimeter wave signals that would otherwise be trapped within volume  130  may be radiated away from antenna  40 . 
     Antennas of the type shown in  FIGS. 5-12  may be arranged in an array (e.g., a phased antenna array). When arranged in a phased antenna array, it may be desirable to maximize the number of antennas that fit within a unit volume of the array (to maximize the gain of the phased antenna array). However, increasing the number of antennas per unit volume can degrade isolation between adjacent antennas, which may make beam steering with the phased antenna array difficult. 
       FIGS. 13 and 14  are top views of illustrative phased antenna arrays with antennas arranged to maximize the number of antennas per unit volume while maintaining isolation between the antennas. In  FIGS. 13 and 14 , the parasitic element  106  of each antenna  40  is shown, including parasitic corner conductors (e.g., as shown in connection with  FIGS. 10 and 11 ). Patch  104  of each antenna  40  is not shown in  FIGS. 13 and 14  for the sake of clarity. However, the location of the first and second feed terminals  96 -P 1  and  96 -P 2  (on the underlying patch  104 ) are depicted in  FIGS. 13 and 14  to help show the relative orientations of each antenna  40 . The X-axis and Y-axis in  FIGS. 13 and 14  may be parallel to walls of an antenna cavity. 
     As shown in  FIGS. 13 and 14 , the antennas are arranged in phased antenna array  60  and according to a grid pattern (e.g., grid  152 ). Grid  152  includes a first set of regularly-spaced grid lines and a second set of regularly-spaced grid lines that are perpendicular to the first set of grid lines. In the example of  FIG. 13 , the first and second sets of grid lines are rotated by 45° relative to the X-axis. This example is merely illustrative and, in general, grid  152  may be rotated at any desired angle with respect to the X-Y axes of  FIG. 13 . 
     Each row of antennas  40  in phased antenna array  60  is laterally offset from the adjacent rows of antennas in phased antenna array  60 . For example, each antenna in row  2  is shifted so as to not be directly underneath an antenna in row  1  or directly above an antenna in row  3 . The longitudinal axis  119  of each antenna may be parallel to the Y-axis. The longitudinal axis  119  of each antenna may be parallel to at least some edges of parasitic element. The longitudinal axis  119  of each antenna is oriented at an angle (e.g., a 45° angle) relative to the lines of grid  152 . When using the antenna feed associated with feed terminal  96 -P 1 , antenna  40  may transmit and/or receive antenna signals having a first polarization (e.g., the electric field E 1  of antenna signals associated with feed terminal  96 -P 1  may be oriented parallel to dimension Y). When using the antenna feed associated with feed terminal  96 -P 2 , antenna  40  may transmit and/or receive antenna signals having a second polarization (e.g., the electric field E 2  of antenna signals associated with feed terminal  96 -P 2  may be oriented parallel to dimension X so that the polarizations associated with feed terminals  96 -P 1  and  96 -P 2  are orthogonal to each other). 
     Arranging the antennas as in  FIG. 13  increases isolation compared to an embodiment where the antennas have the same orientation (e.g., with E 1  parallel to the Y-axis) but are arranged in a square grid (e.g., such that each antenna is directly adjacent to antennas in adjacent rows without any lateral offset). Another arrangement having satisfactory antenna isolation is shown in  FIG. 14 . 
     As shown in  FIG. 14 , antennas  40  may be arranged in a phased antenna array  60  and according to a grid pattern (e.g., grid  154 ). In the grid of  FIG. 14 , however, the grid lines are parallel to either the X-axis or the Y-axis. Each row of antennas is formed directly above the underlying row of antennas without any lateral offset. However, to improve isolation, the antennas are rotated relative to the X-axis. For example, the longitudinal axis  119  of each antenna may be oriented at a 45° angle (or other desired angle) relative to the X-axis. Consequently, electric fields E 1  and E 2  (while still orthogonal) are orientated at 45° angles relative to the X-axis. This type of arrangement improves efficiency and isolation of the antennas in the phased antenna array compared to an embodiment where the antennas are arranged in the square grid of  FIG. 14  but are not rotated (such that E 1  is parallel to the Y-axis). 
     In the arrangement of  FIG. 13 , grid  152  is defined by grid lines that are at a 45° angle relative to the X-axis. This example is merely illustrative and if desired the grid of  FIG. 13  may be defined by grid lines that are at other angles (e.g., between 30° and 60°, less than 60°, more than 20°, etc.) relative to the X-axis. Similarly, in  FIG. 14  each antenna is rotated by 45° relative to the X-axis. This example is merely illustrative and the antennas may be rotated by any desired amount (e.g., between 30° and 60°, less than 75°, more than 15°, etc.). The arrangements of  FIGS. 13 and 14  may be applied to any type of antenna (e.g., any of the antennas shown in  FIGS. 5-12  or any other desired type of antenna). 
       FIG. 15  is a graph of antenna performance (antenna efficiency) as a function of frequency for illustrative antennas of the types shown in  FIGS. 5-12 . As shown in  FIG. 15 , curve  202  illustrates the efficiency of an antenna of the type shown in  FIG. 6  (e.g., without a parasitic element). Curve  202  exhibits a peak antenna efficiency within a millimeter wave communications band of interest defined by lower threshold frequency F 1  (e.g., 57 GHz) and upper threshold frequency F 2  (e.g., 71 GHz). Curve  204  illustrates the efficiency of antenna  40  when formed using a parasitic antenna resonating element (e.g., as shown in  FIGS. 7 and 8 ). Curve  204  exhibits a peak antenna efficiency within the millimeter wave communications band of interest between frequencies F 1  and F 2 . However, curve  204  is shifted to a higher efficiency than curve  202  across the communications band of interest, showing the improved performance of the antenna when the parasitic antenna resonating element is included. These curves are merely illustrative. The efficiency of antennas with or without parasitic elements may have any other desired shapes. 
       FIG. 16  shows a diagram of illustrative radiation patterns for patch antennas with different parasitic element arrangements. In the perspective of  FIG. 16 , the antenna may lie in the X-Y plane and may radiate in the positive Z-direction. Curve  212  shows the radiation pattern of a patch antenna without a parasitic element (e.g., the antenna of  FIG. 6 ). When a parasitic element is added to the antenna (e.g., as in the antenna of  FIG. 9 ) the radiation pattern widens from curve  212  to curve  214 . In other words, the presence of the parasitic element may increase the coverage area of the antenna. When parasitic corner conductors are added to the antenna (e.g., as in the antenna of  FIG. 11 ), the radiation pattern again widens from curve  214  to curve  216 . The presence of the parasitic corner conductors may increase the coverage area of the antenna and may optimize the uniformity of the radiation pattern. In particular, the parasitic corner conductors reduce angular variation in the radiation pattern. These curves are merely illustrative. The radiation pattern of antennas with or without parasitic elements and parasitic corner conductors may have any other desired shapes. 
     Optimizing the uniformity of the radiation pattern for the antenna (e.g., using the parasitic corner conductors of  FIG. 11 ) may also optimize uniformity of the radiation envelope of a corresponding phased antenna array. In other words, forming a phased antenna array from antennas of the type shown in  FIG. 11  optimizes uniformity of the radiation envelope. Additionally, a phased antenna array with an antenna arrangement of the type shown in  FIG. 13  or  FIG. 14  will have optimized isolation and therefore maximized gain. 
       FIG. 17  is a graph of isolation (S 21 ) for antennas in an array. For example, curve  222  corresponds to an antenna in an array of antennas arranged in a grid without any lateral offset between adjacent rows and without any rotational adjustment of the antennas. Curve  224  corresponds to an antenna in an array of antennas in a grid with the antennas rotated by 45° relative to the grid lines (as shown in  FIGS. 13 and 14 , for example). As shown in  FIG. 17 , the arrangement of  FIG. 14  improves isolation (with curve  224  having improved isolation relative to curve  222 ). These curves are merely illustrative. The isolation pattern of antennas with or without the isolating arrangements of  FIGS. 13 and 14  may have any other desired shapes. 
     The foregoing is merely illustrative and various modifications can be made by those skilled in the art without departing from the scope and spirit of the described embodiments. The foregoing embodiments may be implemented individually or in any combination.