Patent Publication Number: US-11641061-B2

Title: Millimeter wave patch antennas

Description:
This application is a division of U.S. patent application Ser. No. 15/650,689, filed Jul. 14, 2017, which is hereby incorporated by reference herein in its entirety. 
    
    
     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 antennas and transceiver circuitry such as millimeter wave transceiver circuitry. The millimeter wave transceiver circuitry may convey millimeter wave signals within a millimeter wave communications band of interest using the antenna. The antenna may include an antenna ground plane, a patch antenna resonating element, an antenna feed, and a parasitic antenna resonating element. The antenna feed may include a first feed terminal coupled to the antenna resonating element and a second feed terminal coupled to the ground plane. If care is not taken, the parasitic antenna resonating element and the antenna resonating element may define a volume having a corresponding cavity resonance that serves to trap millimeter wave signals within the volume. 
     If desired, the antenna resonating element may be formed from conductive traces on multiple dielectric layers. For example, the antenna may be embedded on a stacked dielectric substrate having at least first, second, and third layers stacked over the antenna ground plane. The antenna resonating element may include first traces on the first layer, second traces on the second layer, and third traces on the third layer that are shorted together using vertical conductive interconnects such as sets of conductive vias. The second traces may be interposed between the first and third traces and the third traces may be interposed between the second traces and the parasitic antenna resonating element. The third traces may have a width that is less than the widths of the second and third traces. The third traces and the parasitic antenna resonating element may define a volume having an associated cavity resonance. Constraining the cavity resonance to the volume between the third traces and the parasitic element may serve to shift the cavity resonance to frequencies that are outside of the millimeter wave communications band of interest, thereby preventing the trapping of millimeter wave signals between the parasitic element and the antenna resonating element within the millimeter wave communications band of interest. 
     If desired, the antenna resonating element may be formed from conductive traces on a single dielectric layer. The volume between the single layer of conductive traces and the parasitic element may exhibit a corresponding cavity resonance. In this scenario, a grid of openings may be formed in the conductive traces. The openings may be sufficiently narrow so as to allow antenna currents to flow across the lateral area of the antenna resonating element. At the same time, the openings may serve to disrupt antenna impedance in a transverse direction between the parasitic element and the antenna resonating element, thereby reducing the magnitude of the cavity resonance and the corresponding trapping of millimeter wave signals between the parasitic element and the antenna resonating element. By mitigating the trapping of millimeter wave signals within the volume between the parasitic element and the antenna resonating element, the antenna may exhibit satisfactory antenna efficiency over the entire millimeter wave communications band of interest. 
    
    
     
       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 cross-sectional side view of an illustrative patch antenna having a multi-layer antenna resonating element and a parasitic element in accordance with an embodiment. 
         FIG.  10    is a top-down view of an illustrative patch antenna having a multi-layer antenna resonating element and a parasitic element in accordance with an embodiment. 
         FIG.  11    is a perspective view of an illustrative patch antenna having a multi-layer antenna resonating element and a parasitic element in accordance with an embodiment. 
         FIG.  12    is a cross-sectional side view of an illustrative patch antenna having a single layer antenna resonating element and a parasitic element with dielectric-filled openings in accordance with an embodiment. 
         FIG.  13    is a bottom-up view of an illustrative patch antenna having a single layer antenna resonating element and a parasitic element with dielectric-filled openings in accordance with an embodiment. 
         FIG.  14    is a top-down view of an illustrative patch antenna having a single layer antenna resonating element and a parasitic element with dielectric-filled openings in accordance with an embodiment. 
         FIG.  15    is perspective view of an illustrative patch antenna having a single layer antenna resonating element and a parasitic element with dielectric-filled openings in accordance with an embodiment. 
         FIG.  16    is a graph of antenna efficiency for illustrative patch antennas of the types shown in  FIGS.  7 - 15    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 a 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, in one suitable arrangement, the antenna resonating element may be formed from multiple layers of conductive traces that are shorted together. This may serve to alter the volume between the antenna resonating element and 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. In another suitable arrangement, slots may be formed in the antenna resonating element and the parasitic antenna resonating element to divide the antenna resonating element into a first set of coplanar segments and to divide the parasitic antenna resonating element into a second set of coplanar segments. This may serve to alter the electromagnetic boundary conditions defined by the parasitic antenna resonating element and the 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 these 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. 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. 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 element  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 element  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. 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 antenna resonating element  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 resonating element  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 to resonating element  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 resonating element  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 antenna resonating element  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 antenna resonating element  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 antenna resonating element  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 antenna resonating element  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 antenna resonating element  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 antenna resonating element  104  may have a width M. As examples, patch element  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 ε R , 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 ε R . As examples, dielectric constant ε R  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 antenna resonating element  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  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  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 element  104  and/or parasitic  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 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 antenna resonating 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 -P 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 antenna resonating element  104  at a first location. The second antenna feed may have a second ground feed terminal coupled to ground  92  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 resonating element  106  may be formed over patch  104 . At least some or an entirety of parasitic resonating element  106  may overlap patch  104 . In the example of  FIG.  8   , parasitic resonating 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  106  may have a rectangular (e.g., square) outline or footprint. The width N of cross-shaped parasitic element  106  may be defined by the length of a side of the rectangular footprint of element  106 , for example. 
     Cross-shaped parasitic resonating 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 element  106 . First arm  110  may oppose 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 element  106  and arms  112  and  116  may extend in parallel and from opposing sides of the point at the center of 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  120 . Longitudinal axis  118  may be oriented at an angle of approximately 90 degrees with respect to axis  120 . 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 resonating 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 - 1  and  96 - 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 - 1  or  96 - 2 . In other words, each of antenna feed terminals  96 - 1  and  96 - 2  may overlap with a respective arm of the cross-shaped parasitic antenna resonating 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 . In an example where width N is between 1.0 mm and 1.2 mm, length N′ may be between 0.3 mm and 0.4 mm. 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 antenna resonating element  106  may have additional notches  107 , fewer 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  120  and  118  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 antenna resonating element  104  may define boundaries of volume  130  between patch antenna resonating element  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, in one suitable arrangement, antenna  40  may be provided with a multi-layer patch antenna resonating element.  FIG.  9    is cross-sectional side view showing how antenna  40  may include a multi-layer patch antenna resonating element  104 . 
     As shown in  FIG.  9   , patch antenna resonating element  104  may be formed from multiple layers of conductive traces located at different distances with respect to ground plane  92  (e.g., on different dielectric layers  122  in substrate  120 ). For example, patch antenna resonating element  104  may include a first portion  104 A formed at a distance H 2  with respect to ground plane  92 , a second portion  104 B formed at distance H 3  with respect to portion  104 A (e.g., distance H 3 +H 2  with respect to ground plane  92 ), and a third portion  104 C formed at distance H 4  with respect to portion  104 B (e.g., distance H 4 +H 3 +H 2  with respect to ground plane  92 ). Portion  104 C may be formed at distance H 0  with respect to parasitic antenna resonating element  106 . First portion  104 A may be formed on a corresponding dielectric layer  122  such as dielectric layer  122 - 4 , second portion  104 B may be formed on a corresponding dielectric layer  122  such as dielectric layer  122 - 5 , and third portion  104 C may be formed on a corresponding dielectric layer  122  such as dielectric layer  122 - 6 , for example. Distance H 2 , H 3 , H 4 , and H 0  may all be equal or two or more of distances H 2 , H 3 , H 4 , and H 0  may be different. In the example of  FIG.  9   , distance H 3  is equal to distance H 4  and less than distance H 2 , whereas distance H 2  is less than distance H 0 . Distances H 0 , H 2 , H 3 , and H 4  may, for example, each be between 1 μm and 1 mm. As one example, distance H 2  may be between 100 μm and 250 μm, distance H 3  may be between 50 μm and 150 μm, distance H 4  may be between 50 μm and 150 μm, and distance H 0  may be between 100 μm and 250 μm. Optional solder mask layer  123  may, for example, have a thickness between 10 μm and 50 μm. Portions  104 A,  104 B, and  104 C of multi-layer patch antenna resonating element  104  may sometimes each be referred to herein as patch antenna resonating element portions, antenna resonating element portions, resonating element portions, conductive traces, resonating element traces, conductive layers, antenna resonating element layers, or patches. 
     Antenna feed terminal  96  may be coupled to portion  104 A of multi-layer patch antenna resonating element  104 . Antenna resonating element portion  104 A may have any desired lateral shape (e.g., in the X-Y plane of  FIG.  9   ). For example, resonating element portion  104 A may be a rectangular conductive patch, a square conductive patch, a circular conductive patch, an elliptical conductive patch, a polygonal conductive patch, a conductive patch having curved and/or straight sides, etc. Vertical conductor  124  of transmission line  64  may extend from transmission line conductor  126  through layer  122 - 2 , opening  128  in ground layer  92 , layer  122 - 3 , and layer  122 - 4  to feed terminal  96  on patch antenna resonating element portion  104 A. This example is merely illustrative and, if desired, other transmission line structures may be used. 
     An opening  140  is formed in patch antenna resonating element portion  104 A (sometimes referred to herein as notch  140 , gap  140 , or slot  140 ). Opening  140  may, for example, be completely surrounded by the conductive material in antenna resonating element portion  104 A on layer  122 - 4 . Opening  140  may, for example, be formed by removing or etching material away from traces  104 A or may be formed upon deposition of traces  104 A on layer  122 - 4 . Traces  104 A may, for example, follow a continuous lateral conductive path that runs around opening  140  (e.g., in the X-Y plane of  FIG.  9   ). 
     Antenna resonating element portion  104 A may be shorted to second antenna resonating element  104 B using a set of vertical conductive structures  136 . For example, antenna resonating element portion  104 A may be coupled to antenna resonating element portion  104 B on layer  122 - 5  by a first vertical conductive structure  136 - 1  closest to feed terminal  96  and a second vertical conductive structure  136 - 2  coupled to an opposing side of antenna resonating element portion  104 A. Vertical conductive structures  136  may, for example, include conductive through-vias extending through dielectric layer  122 - 5 , conductive pins, solder bumps, metal pillars, combinations of these, or any other desired vertical conductive interconnect structures. Antenna feed terminal  96  may be laterally separated from vertical conductive structure  136 - 1  in layer  122 - 5  by distance D 1 . Vertical conductive structure  136 - 2  may be laterally separated from an outer edge of antenna resonating element portion  104 A by distance D 5 . Vertical conductive structures  136  may each have a length equal to height H 3 , for example. 
     Antenna resonating element portion  104 B may have any desired lateral shape (e.g., in the X-Y plane). For example, resonating element portion  104 B may be a rectangular conductive patch, a square conductive patch, a circular conductive patch, an elliptical conductive patch, a polygonal conductive patch, a conductive patch having curved and/or straight sides, etc. An opening  142  may be formed in patch antenna resonating element portion  104 B (sometimes referred to herein as notch  142 , gap  142 , or slot  142 ). Opening  142  may, for example, be completely surrounded by the conductive material in antenna resonating element portion  104 B on layer  122 - 5 . Opening  142  may, for example, be formed by removing or etching material away from traces  104 B or may be formed upon deposition of traces  104 B on layer  122 - 4 . Traces  104 B may, for example, follow a continuous conductive path that runs around opening  142  (in the X-Y plane). 
     Antenna resonating element portion  104 B may be shorted to second antenna resonating element  104 C using a set of vertical conductive structures  138 . For example, antenna resonating element portion  104 B may be coupled to antenna resonating element portion  104 C on layer  122 - 6  by a first vertical conductive structure  138 - 1  located closest to vertical conductive structure  136 - 1  and a second vertical conductive structure  138 - 2  located closest to vertical conductive structure  136 - 2 . Vertical conductive structures  138  may, for example, include conductive through-vias extending through dielectric layer  122 - 6 , conductive pins, solder bumps, metal pillars, combinations of these, or any other desired vertical conductive interconnect structures. Vertical conductive structure  136 - 1  may be laterally separated from vertical conductive structure  138 - 1  by distance D 2 . Vertical conductive structure  138 - 2  may be laterally separated from vertical conductive structure  136 - 2  by distance D 4 . Vertical conductive structures  138  may each have a length equal to height H 4 , for example. 
     Antenna resonating element portion  104 C may have any desired lateral shape. For example, resonating element portion  104 C may be a rectangular conductive patch, a square conductive patch, a circular conductive patch, an elliptical conductive patch, a polygonal conductive patch, a conductive patch having curved and/or straight sides, etc. In the example of  FIG.  9   , resonating element portion  104 C is a continuous conductor (e.g., without openings or slots within the conductor). 
     Vertical conductive structure  138 - 1  may be coupled to a first location on resonating element portion  104 C. Vertical conductive structure  138 - 2  may be coupled to a second location on resonating element portion  104 C that is laterally separated from the first location by distance D 3 . The electrical path length from antenna feed terminal  96  to the opposing side of resonating element portion  104 A (e.g., through resonating element portions  104 B and  104 C and the corresponding vertical conductive structures) may be selected so that antenna  40  resonates at a desired operating frequency. The electrical path length may, for example, be approximately equal to the sum of distance D 1 , distance D 2 , distance D 3 , distance D 4 , distance D 5 , two times distance H 3  (e.g., the length of both conductors  136 - 1  and  136 - 2 ), and two times distance H 4  (e.g., the length of both conductors  138 - 1  and  138 - 2 ), this sum in turn being approximately equal to (e.g., within 15% of) the wavelength of operation of antenna  40  divided by twice the square root of dielectric constant ε R  of substrate  120 , for example. In the scenario where antenna  40  covers a millimeter wave communications band from 57 GHz to 71 GHz and dielectric constant ε R  is approximately equal to 3.45, this path length may be between 1.0 mm and 1.2 mm, for example. 
     Patch antenna resonating element portion  104 C and parasitic element  106  may define boundaries of a constrained volume  131 . Constrained volume  131  may be less than the volume  130  associated with a single layer patch antenna resonating element (e.g., as shown in  FIGS.  7  and  8   ) and parasitic element  106 . Distributing patch antenna resonating element  104  across multiple layers (e.g., by forming resonating element portions  104 A and  104 B at greater distances than distance H 0  with respect to parasitic element  106 ) may thereby serve to restrict the cavity resonance between parasitic element  106  and patch antenna resonating element  104  to constrained volume  131 . Constraining the cavity resonance to volume  131  may shift the cavity resonance to higher frequencies that are farther away from the millimeter wave communications band of interest than the cavity resonance associated with volume  130 . This may serve to minimize the amount of energy within the millimeter wave communications band of interest that is trapped between parasitic element  106  and patch antenna resonating element  104 , thereby optimizing the overall antenna efficiency of antenna  40 . 
     The example of  FIG.  9    is merely illustrative. If desired, fewer or additional layers  122  may be interposed between trace  126  and ground  92 , between ground  92  and resonating element portion  104 A, between resonating element portion  104 A and resonating element portion  104 B, between resonating element portion  104 B and resonating element portion  104 C, and/or between resonating element portion  104 C 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, resonating element portions  104 A,  104 B, and  104 C, and/or parasitic element  106  may be formed from any other desired conductive structures within device  10 . If desired, patch antenna resonating element  104  may be formed from only two different layers (e.g., conductive traces  104 A and vertical conductors  136  may be omitted and feed terminal  96  may be coupled to conductive traces  104 B) or from more than three different layers. In the example of  FIG.  9   , 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. 
       FIG.  10    is a top-down view of an antenna of the type shown in  FIG.  9    having a multi-layer patch antenna resonating element  104  and two feeds for covering two orthogonal polarizations. In the example of  FIG.  10   , dielectric substrate  120 , dielectric layer  123 , and ground  92  are not shown for the sake of clarity. As shown in  FIG.  10   , antenna feed terminals  96 -P 1  and  96 -P 2  may be coupled to patch antenna resonating element portion  104 A along to two different orthogonal edges of patch antenna resonating element portion  104 A. 
     Patch antenna resonating element portion  104 B may be formed over patch antenna resonating element portion  104 A. A set of vertical conductive structures  136  may be coupled between resonating element portions  104 A and  104 B. The set of vertical conductive structures  136  may include a vertical conductive structure  136 - 1 P 1  closest to feed terminal  96 - 1 , a vertical conductive structure  136 - 1 P 2  closest to feed terminal  96 -P 2 , a vertical conductive structure  136 - 2 P 1  opposite to vertical conductive structure  136 - 1 P 1 , and a vertical conductive structure  136 - 2 P 2  opposite vertical conductive structure  136 - 1 P 2 . Each vertical conductive structure  136  may be separated from two adjacent vertical conductive structures  136  by distance  51  (sometimes referred to herein as pitch  51 ). Distance  51  may be, for example, less than or equal to one-tenth of the wavelength of operation of antenna  40 . When configured in this way, the set of structures  136  may appear to millimeter wave signals in the communications band of interest as a single continuous conductor, for example. 
     Patch antenna resonating element portion  104 C may be formed over patch antenna resonating element portion  104 B. A set of vertical conductive structures  138  may be coupled between resonating element portions  104 B and  104 C. The set of vertical conductive structures  138  may include a vertical conductive structure  138 - 1 P 1  closest to vertical conductive structure  136 - 1 P 1 , a vertical conductive structure  138 - 1 P 2  closest to vertical conductive structure  136 - 1 P 2 , a vertical conductive structure  138 - 2 P 1  opposite vertical conductive structure  138 - 1 P 1 , and a vertical conductive structure  138 - 2 P 2  opposite vertical conductive structure  138 - 1 P 2 . Each vertical conductive structure  138  may be separated from two adjacent vertical conductive structures  138  by distance  51  (sometimes referred to herein as pitch  52 ). Distance  52  may be equal to, less than, or greater than distance  51 . Distance  52  may be, for example, less than or equal to one-tenth of the wavelength of operation of antenna  40 . When configured in this way, the set of structures  138  may appear to millimeter wave signals in the communications band of interest as a single continuous conductor, for example. 
     Parasitic antenna resonating element  106  (e.g., as described above in connection with  FIGS.  7  and  8   ) may be formed over patch antenna resonating element portion  104 C. Parasitic antenna resonating element arms  114  and  110  extending along longitudinal axis  118  may be formed over (e.g., may overlap) feed terminal  96 -P 1  and conductive structures  136 - 1 P 1 ,  138 - 1 P 1 ,  136 - 2 P 1 , and  138 - 2 P 1 . Parasitic antenna resonating element arms  112  and  116  extending along longitudinal axis  120  may be formed over feed terminal  96 -P 2  and conductive structures  136 - 2 P 2 ,  138 - 2 P 2 ,  138 - 1 P 2 , and  136 - 1 P 2 . Parasitic element  106  may serve to broaden the bandwidth of antenna  40  while also ensuring that patch antenna resonating element portions  104 A,  104 B, and  104 C are impedance matched to both transmission lines  64 - 1  and  64 - 2 , for example. 
     As shown in  FIG.  10   , patch antenna resonating element portion  104 A may have a width W 1 , patch antenna resonating element portion  104 B may have a width W 2 , and patch antenna resonating element portion  104 C may have a width W 3 . Width W 3  may be less than width W 2  and width W 2  may be less than width W 1 . Width W 1  may be less than, greater than, or equal to width N of parasitic antenna resonating element  106 . Because the resonating frequency of antenna  40  is determined by the electrical path length between feed terminal  96 -P 1  and the edge of patch  104 A adjacent to structure  136 - 2 P 1  (e.g., over a first portion of patch  104 A, structure  136 - 2 P 1 , a first portion of patch  104 B, structure  138 - 2 P 1 , patch  104 C, structure  138 - 1 P 1 , a second portion of patch  104 B, structure  136 - 1 P 1 , and a second portion of patch  104 A between structure  136 - 1 P 1  and terminal  96 -P 1 ) and/or by the electrical length between feed terminal  96 -P 2  and the edge of patch  104 A adjacent to structure  136 - 2 P 2  (e.g., over a third portion of patch  104 A, structure  136 - 2 P 2 , a third portion of patch  104 B, structure  138 - 2 P 2 , patch  104 C, structure  138 - 1 P 2 , a fourth portion of patch  104 B, structure  136 - 1 P 2 , and a fourth portion of patch  104 A between structure  136 - 1 P 2  and terminal  96 -P 2 ), width W 1  may be less than width M of the single-layer patch antenna shown in  FIG.  8   . As an example, width W 1  may be between 0.9 mm and 1.1 mm, width W 2  may be between 0.8 mm and 0.9 mm, and width W 3  may be between 0.4 mm and 0.8 mm. 
     Opening  140  in resonating element portion  104 A and opening  142  in resonating element portion  104 B ( FIG.  9   ) are not shown in  FIG.  10    for the sake of clarity. However, in a suitable arrangement, openings  140  and  142  may be square-shaped openings. In other scenarios, openings  140  and  142  may, in theory, have rectangular, circular, elliptical, polygonal, may have a shape with curved and/or straight edges, may have a cross shape similar to parasitic element  106 , etc. Opening  140  may have width (e.g., a maximum lateral dimension, a length of a side of the opening, a length of a longest side of the opening, a length of a side of a rectangular footprint of the opening, etc.) that is between 10% and 80% of width W 1  of resonating element portion  104 A. Opening  142  may have width (e.g., a maximum lateral dimension, a length of a side of the opening, a length of a longest side of the opening, a length of a side of a rectangular footprint of the opening, etc.) that is between 10% and 80% of width W 2  of resonating element portion  104 B. The example of  FIG.  10    in which patch antenna resonating element portions  104 A,  104 B, and  104 C each have square shapes with aligned edges is merely illustrative. If desired, patch antenna resonating element portions  104 A,  104 B, and/or  104 C may be formed using conductive structures having any desired shapes, orientations, and corresponding polarizations. 
     In general, any desired number of conductive structures  136  may be formed between patch antenna resonating element portions  104 A and  104 B (e.g., four structures  136  such as structures  136 - 1 P 1 ,  136 - 2 P 1 ,  136 - 1 P 2 , and  136 - 2 P 2 , between four and thirty-two structures  136 , sixteen structures  136 , etc.). Any desired number of conductive structures  138  may be formed between patch antenna resonating element portions  104 B and  104 C (e.g., four structures  138  such as structures  138 - 1 P 1 ,  138 - 2 P 1 ,  138 - 1 P 2 , and  138 - 2 P 2 , between four and thirty-two structures  138 , eight structures  138 , etc.). In another suitable arrangement, structures  136  may be formed from one or more continuous conductive walls extending between resonating element portions  104 A and  104 B and/or structures  138  may be formed from one or more continuous conductive walls extending between resonating element portions  104 B and  104 C (e.g., around all sides of openings  140  and  142 , respectively). 
       FIG.  11    is a perspective view of an antenna of the type shown in  FIGS.  9  and  10    having a multi-layer patch antenna resonating element  104  and two feeds for covering two orthogonal polarizations. In the example of  FIG.  11   , dielectric substrate  120  and dielectric layer  123  are not shown for the sake of clarity. 
     As shown in  FIG.  11   , first portion  104 A of patch antenna resonating element  104  may be formed at distance H 2  above ground plane  92 . Second portion  104 B of patch antenna resonating element  104  may be formed at distance H 3  above portion  104 A. Third portion  104 C of patch antenna resonating element  104  may be formed at distance H 4  above portion  104 B. Cross-shaped parasitic antenna resonating element  106  may be formed at distance H 0  above portion  104 C of patch antenna resonating element  104 . A set or fence of vertical conductive structures  136  may couple portion  104 A to portion  104 B. A set or fence of vertical conductive structures  138  may couple portion  104 B to portion  104 C. Conductive structures  136  may collectively appear as a single continuous conductor and/or conductive structures  138  may collectively appear as a single continuous conductor to millimeter wave signals, for example. 
     Opening  140  may be surrounded by the conductive material in resonating element portion  104 A (e.g., portion  104 A may follow a loop or ring shaped conductive path around opening  140 ). Opening  142  may be surrounded by the conductive material in resonating element portion  104 B (e.g., portion  104 B may follow a loop or ring shaped conductive path around opening  142 ). Resonating element portions  104 B and  104 C may cover an entirety of opening  140 . Resonating element portion  104 C may cover an entirety of opening  142 . The example of  FIG.  11    is merely illustrative and, if desired, other arrangements may be used. 
     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 resonating element portion  104 A. 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 resonating element portion  104 A. If desired, vertical conductors  124 -P 1  and  124 -P 2  may both pass through the same hole  128  in ground plane  92 . Feed terminals  96 -P 1  and  96 -P 2  may be overlapped by (e.g., located directly beneath or within the lateral outline of) arms  114  and  116  of cross-shaped parasitic element  106 , respectively. 
     Antenna resonating element portion  104 C and parasitic antenna resonating element  106  may define constrained volume  131 . Antenna resonating element portion  104 A and parasitic antenna resonating element  106  may define a volume that is greater than volume  131 . The reduced size of constrained volume  131  may cause antenna  40  to trap millimeter wave energy within volume  131  at higher frequencies (e.g., frequencies above the millimeter wave communications band of interest) than in scenarios where a single layer antenna resonating element is used. 
     Forming patch antenna resonating element  104  from multiple conductive layers may consume more vertical space (e.g., along the Z-axis of  FIGS.  9 - 11   ) than in scenarios where antenna resonating element  104  is confined to a single plane. As space is often at a premium in devices such as device  10 , antenna resonating element  104  may, if desired, be formed from a single conductive layer that is confined to a single plane. Dielectric-filled openings may be formed in antenna resonating element  104  in these scenarios to mitigate the trapping of millimeter wave signals between antenna resonating element  104  and parasitic element  106 . 
       FIG.  12    is cross-sectional side view showing how antenna resonating element  104  may be formed from a single conductive layer including dielectric-filled openings for mitigating the trapping of millimeter wave signals. As shown in  FIG.  12   , patch antenna resonating element  104  may be formed at a distance H 5  with respect to ground plane  92 . Distance H 5  may be the same as distance H 1  of  FIG.  7   , may be less than distance H 1 , or may be greater than distance H 1 . As one example, distance H 5  may be between 50 μm and 500 μm. Patch antenna resonating element  104  may be formed from a single layer of conductive traces on a single dielectric layer  122  of substrate  120  such as dielectric layer  122 - 6 . Parasitic antenna resonating element  106  may be formed at distance H 0  above patch antenna resonating element  104  (e.g., on layer  122 - 9 ). 
     Patch antenna resonating element  104  may have a width M (e.g., as described above in connection with  FIG.  7   ). Parasitic element  106  may configure antenna  40  to cover a relatively wide millimeter wave communications band of interest such as a frequency band between 57 GHz and 71 GHz. Volume  130  may be defined between parasitic element  106  and the single-layer patch antenna resonating element  104 . As described above in connection with  FIG.  7   , if care is not taken, volume  130  may be associated with a cavity resonance that serves to trap millimeter wave signals (energy) within volume  130  at frequencies around the upper threshold frequency of the millimeter wave communications band of interest. For example, elements  106  and  104  may serve as a parallel plate resonator and may define boundary conditions for the cavity resonance between elements  106  and  104  (e.g., nodes or boundaries for standing waves of EHF energy trapped between elements  106  and  104 ). 
     If desired, patch antenna resonating element  104  may include one or more dielectric-filled openings such as openings  180  and/or parasitic resonating element  106  may include one or more dielectric-filled openings such as openings  182 . Openings  180  and/or  182  may disrupt the cavity resonance between parasitic element  106  and patch antenna resonating element  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 ). 
     Openings  180  (sometimes referred to herein as notches  180 , slots  180 , or gaps  180 ) may each have a width  184 . Openings  182  (sometimes referred to herein as notches  182 , slots  182 , or gaps  182 ) may each have a width  186 . Openings  180  may be formed in resonating element  104  by etching (e.g., laser etching), stripping, cutting, or otherwise removing conductive material in resonating element  104  from the surface of dielectric layer  122 - 6 , or may be formed upon deposition of patch antenna resonating element  104  onto the surface of dielectric layer  122 - 6 . Openings  180  may extend through the entire thickness of antenna resonating element  104 , thereby exposing dielectric layer  122 - 6  through antenna resonating element  104 . Openings  182  may be formed in parasitic element  106  by etching (e.g., laser etching), stripping, cutting, or otherwise removing conductive material in parasitic element  106  from the surface of dielectric layer  122 - 9 , or may be formed upon deposition of parasitic element  106  onto the surface of dielectric layer  122 - 9 . Openings  182  may extend through the entire thickness of parasitic element  106 , thereby exposing dielectric layer  122 - 9  through parasitic element  106 . 
     Width  184  of gaps  180  may be selected to disrupt the cavity resonance in volume  130  while still allowing antenna currents from antenna feed terminal  96  to flow across patch antenna resonating element  104 . For example, gaps  180  may introduce an increased transverse impedance (e.g., in the direction of the Z-axis) that serves to disrupt standing waves in the transverse direction between elements  104  and  106 , while also exhibiting a relatively low lateral impedance across the surface of layer  104  (e.g., in the X-Y plane) so that antenna currents may still flow freely across layer  104 . As an example, width  184  may be between 0.1% and 10% of width M, between 10 μm and 100 μm, between 20 μm and 200 μm, between 20 μm and 40 μm (e.g., approximately equal to 30 μm), between 1 μm and 10 μm, or less than 1 μm. Width  186  of gaps  182  may be selected to adjust the impedance of patch antenna resonating element  104  (e.g., to ensure that antenna  40  is suitably matched to one or more transmission lines  64 ). As an example, width  186  may be between 10 μm and 100 μm, between 20 μm and 200 μm, between 1 μm and 10 μm, or less than 1 μm. 
     The example of  FIG.  12    is merely illustrative. If desired, fewer or additional layers  122  may be interposed between trace  126  and ground  92 , between ground  92  and resonating element  104 , and/or between resonating element  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. 
     In the example of  FIG.  12   , 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.  FIG.  13    is a bottom-up view of an antenna of the type shown in  FIG.  12    (e.g., as taken in direction  190  of  FIG.  12   ) having two feeds and a single layer patch antenna resonating element with slots for mitigating the trapping of millimeter wave signals within volume  130 . In the example of  FIG.  13   , dielectric substrate  120 , layer  123 , and ground  92  are not shown for the sake of clarity. 
     As shown in  FIG.  13   , a grid of openings  180  may be formed in patch antenna resonating element  104 . If desired, openings  180  may be filled with a dielectric material such as plastic, glass, ceramic, epoxy, adhesive, integral portions of dielectric layer  122 - 6 , integral portions of dielectric layer  122 - 7 , or other dielectric materials. If desired, openings  180  may be filled with air. In yet another suitable arrangement, openings  180  may extend only partially through the thickness of patch antenna resonating element  104  (e.g., some of the conductive material in traces  104  may remain within openings  180  if desired). 
     In the example of  FIG.  13   , openings  180  are formed within antenna resonating element  104  in a rectangular grid pattern in which openings  180  divide antenna resonating element  104  into two or more rectangular conductive segments  200  (e.g., the edges of conductive segments  200  may be defined by openings  180 ). If desired, conductive segments  200  may be arranged in an array having one or more rows and one or more columns (e.g., aligned rows and columns). In another suitable arrangement, the rows and/or columns of segments  200  in the array may be misaligned (e.g., the even numbered rows or columns of segments  200  may all be aligned with each other whereas the odd numbered rows or columns of segments  200  are all aligned with each other but misaligned with respect to the even numbered rows and columns). Segments  200  may be arranged in any other desired pattern if desired. Each of the rectangular segments  200  in antenna resonating element  104  may be separated from other rectangular segments  200  by a corresponding one of openings  180 . Conductive segments  200  may sometimes be referred to herein as conductive tiles, patches, or portions of resonating element  104 . 
     Each rectangular segment  200  may have the same size and dimensions or two or more segments  200  may have different sizes or dimensions. In the example of  FIG.  13   , each rectangular segment has a width M′. As examples, width M′ may be between 0.1% and 50% of width M of resonating element  104  (e.g., between 0.1 mm and 0.6 mm, between 0.3 mm and 0.4 mm, between 0.2 mm and 0.5 mm, etc.). Resonating element  104  may include any desired number of segments  200  (e.g., between two and four segments, four or more segments, between four and nine segments, between nine and sixteen segments, more than sixteen segments, etc.). 
     Antenna feed terminal  96 -P 1  and the corresponding transmission line  64 - 1  may be coupled to a first segment  200  at a first side of resonating element  104 . Antenna feed terminal  96 -P 2  and the corresponding transmission line  64 - 2  may be coupled to a second segment  200  at a second orthogonal side of resonating element  104 . Width  184  of openings  180  may be sufficiently small so as to allow antenna currents conveyed by feed terminals  96 -P 1  and  96 -P 1  to freely flow across the lateral area of antenna resonating element  104  (e.g., openings  180  may be narrow enough so as to appear as a short circuit in the X-Y plane at millimeter wave frequencies so that the antenna currents freely pass across multiple segments  200 ). At the same time, openings  180  may sufficiently disrupt the millimeter wave impedance of antenna  40  in the transverse direction (e.g., along the Z-axis) so as to disrupt the cavity resonance associated with volume  130 . 
     The example of  FIG.  13    in which a grid of openings  180  divide antenna resonating element  104  into an array of rectangular segments  200  is merely illustrative. If desired, openings  180  may divide antenna resonating element  104  into conductive segments of any desired shape (e.g., hexagonal segments, circular segments, elliptical segments, triangular segments, segments having curved and/or straight edges, etc.). Openings  180  may follow straight and/or curved paths in resonating element  104 . Each opening  180  may have the same width  184  or two or more openings  180  may have different widths. Openings  180  may extend parallel to at least one edge of antenna resonating element  104  or may extend at non-parallel angles with respect to all of the edges of antenna resonating element  104 . Width M′ of segments  200  may be equal to the length of a side of segments  200 , to a diameter of segments  200  (e.g., in scenarios where segments  200  are circular), equal to a major axis length of segments  200  (e.g., in scenarios where segments  200  are elliptical), may be equal to a maximum lateral dimension of the segment, a length of a side of the segment such as the longest side of the segment, a length of a side of a rectangular footprint of the segment, etc. Antenna resonating element  104  may have any desired shape or dimensions (e.g., with curved and/or straight edges). Any desired number of openings  180  may be formed in antenna resonating element  104  (e.g., one opening  180 , two openings  180 , more than two openings  180 , etc.). Openings  180  in antenna resonating element  104  need not be connected to each other. 
       FIG.  14    is a top-down view of an antenna of the type shown in  FIGS.  12  and  13    (e.g., as taken in direction  192  of  FIG.  12   ). In the example of  FIG.  14   , dielectric substrate  120 , layer  123 , and ground  92  are not shown for the sake of clarity. As shown in  FIG.  14   , 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 , integral portions of dielectric layer  123  ( FIG.  12   ), 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.  14   , 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 80% 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. Openings  182  may each have a width  186  that is equal to, greater than, or less than width  184  of openings  180  in antenna resonating element  104 . Openings  180  in antenna resonating element  104  may alter the impedance of antenna resonating element  104 . Openings  182  in parasitic element  106  may serve to compensate for the change in impedance of resonating element  104  generated by the presence of openings  180  (e.g., so that resonating element  104  may be impedance matched to both transmission lines  64 - 1  and  64 - 2 ). 
     The example of  FIG.  14    is merely illustrative. If desired, openings  182  may be arranged in a grid similar to openings  180  in resonating element  104 . 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 antenna resonating element  104  (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. 
       FIG.  15    is a perspective view of an antenna of the type shown in  FIGS.  12 - 14   . In the example of  FIG.  15   , dielectric substrate  120  and layer  123  are not shown for the sake of clarity. As shown in  FIG.  15   , patch antenna resonating element  104  may be formed at distance H 2  above ground plane  92 . Cross-shaped parasitic antenna resonating element  106  may be formed at distance H 0  above patch antenna resonating element  104 . Arm  114  of parasitic element  106  may overlap first feed terminal  96 - 1  whereas arm  116  of parasitic element  106  overlaps second feed terminal  96 - 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 segment  200  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 segment  200  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  180  may be formed within patch antenna resonating element  104  for disrupting the cavity resonance associated with volume  130  (e.g., to the mitigate trapping of millimeter wave signals within volume  130 ). Openings  182  may be formed within cross-shaped parasitic element  106  (e.g., between arms  110 ,  112 ,  114 , and  116  and central portion  106 C) to compensate for adjustments in impedance introduced by openings  180  (e.g., to ensure that resonating element  104  is suitably matched to transmission lines  64 - 1  and  64 - 2 ). 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 . Because antenna resonating element  104  is formed from a single layer of conductive material in the example of  FIG.  15   , the vertical distance required to implement antenna  40  in this example may be less than required in scenarios where resonating element  104  is formed using multiple conductive layers (e.g., as shown in  FIGS.  9 - 11   ). However, forming antenna resonating element  104  using multiple conductive layers may, for example, increase the isolation between feed terminals  96 -P 1  and  96 -P 2  relative to scenarios where resonating element  104  includes only a single conductive layer (e.g., as shown in  FIGS.  12 - 15   ). 
       FIG.  16    is a graph of antenna performance (antenna efficiency) as a function of frequency for an illustrative antenna of the types shown in  FIGS.  9 - 15   . As shown in  FIG.  16   , curve  210  illustrates the efficiency of antenna  40  of the type shown in  FIGS.  7  and  8   . Curve  210  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  210  may exhibit a minimum  212  generated as a result of the trapping of millimeter wave energy at relatively high frequencies such as frequencies around upper threshold F 2  within volume  130 . Minimum  212  of curve  210  may, for example, be at a frequency of 72 GHz. Minimum  212  may cause the efficiency of antenna  40  to be reduced around upper threshold frequency F 2 , thereby introducing the potential for data errors when antenna  40  is operated near upper threshold frequency F 2 . 
     Curve  214  illustrates the efficiency of antenna  40  when formed using a single layer patch antenna resonating element with cavity resonance mitigating openings  180  (e.g., as shown in  FIGS.  12 - 15   ) or when formed using a multi-layer patch antenna resonating element (e.g., as shown in  FIGS.  9 - 11   ). Curve  214  exhibits a peak antenna efficiency within the millimeter wave communications band of interest between frequencies F 1  and F 2 . However, minimum  212  of curve  214  is shifted to a higher frequency as shown by arrow  216 . As an example, minimum  212  of curve  214  may be shifted to a frequency of 76 GHz. This shift may allow antenna  40  to exhibit satisfactory efficiency around upper threshold frequency F 2 , thereby minimizing the risk for data errors when antenna  40  is operated near upper threshold frequency F 2 . Frequency shift  216  may be generated, for example, by constraining the volume between patch antenna resonating element  104  and parasitic element  106  (e.g., as shown by volume  131  of  FIGS.  9 - 11   ). Disrupting the cavity resonance associated with volume  130  using resonance mitigating openings  180  (e.g., as shown in  FIGS.  12 - 15   ) may also serve to generate an antenna efficiency curve such as curve  214  that covers the entirety of the millimeter wave frequency band between thresholds F 1  and F 2 . 
     The example of  FIG.  16    is merely illustrative. In general, the efficiency curve associated with antenna  40  may have any desired shape. Antenna  40  may exhibit peaks in efficiency at more than one frequency (e.g., in scenarios where antenna  40  is a multi-band antenna). The millimeter wave communications band of interest may be defined by any desired millimeter wave threshold frequencies (e.g., frequencies F 1  and F 2  may be any desired frequencies between 10 GHz and 400 GHz, where F 2  is higher than F 1 ). As other examples, the communications band of interest may be between 27.5 GHz and 28.5 GHz, may be between 37 GHz and 41 GHz, may be between 27.5 GHz and 41 GHz, may be between 41 GHz and 71 GHz, may be between 57 GHz and 64 GHz, etc. If desired, cavity resonance mitigating openings such as openings  180  of  FIGS.  12 - 15    may be formed within resonating element portions  104 A,  104 B, and/or  104 C of  FIGS.  9 - 11   . Openings  182  may be formed in parasitic  106  regardless of the number of layers used to form resonating element  104 . 
     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.