Patent Publication Number: US-9893707-B2

Title: Circuits, devices and methods related to quadrant phase shifters

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims priority to U.S. Provisional Application No. 62/211,778 filed Aug. 29, 2015, entitled CIRCUITS, DEVICES AND METHODS RELATED TO QUADRANT PHASE SHIFTERS, the disclosure of which is hereby expressly incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Field 
     The present disclosure relates to circuits providing quadrant phase shifting of signals. 
     Description of the Related Art 
     In many digital communications applications, it is desirable to be able to shift the phase of a signal. For example, phase shifters are commonly used in signal cancellers and equalizers. Phase shifters are also used in beam steering, where a phased antenna array directs the antenna energy in a desired direction, which is commonly used in radar and non-line-of-sight (NLOS) operations. In dynamic gain equalizers, phase shifters are used to fit the attenuation profile of the equalizer to a desired one to compensate for non-flat gain responses across a communication band. Other applications can also utilize phase shifters. 
     SUMMARY 
     In some implementations, the present disclosure relates to a phase shifter configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. 
     In some embodiments, the first-handed quarter-wave state can be a right-handed quarter-wave state, and the second-handed quarter-wave state can be a left-handed quarter-wave state. The bypass state, the single right-handed quarter-wave state, the double right-handed quarter-wave state, or the single left-handed quarter-wave state can yield a phase shift of approximately 0°, −90°, −180°, or +90°, respectively. 
     According to a number of implementations, the present disclosure relates to a phase shifter that includes a first node and a second node, and a first switchable path having a first inductance and a second inductance arranged in series between the first and second nodes. The phase shifter further includes a capacitive grounding path implemented on each side of each of the first and second inductances, with at least one of the capacitive grounding paths being configured as a switchable capacitive grounding path. The phase shifter further includes a reconfiguring circuit assembly configured to allow the phase shifter to provide a plurality of quadrant phase shifts utilizing the first and second inductances and the at least one switchable capacitive grounding path. 
     In some embodiments, the reconfiguring circuit assembly can include a first switch between the first and second inductances, and a second switch between the second inductance and the second node. The reconfiguring circuit assembly can further include a switchable bypass path assembly having third and fourth switches implemented in series between the first and second nodes, and a connection from a node between the third and fourth switches and a node between the first inductance and the first switch. The reconfiguring circuit assembly can be configured with each of the first and second switches open, and each of the third and fourth switches closed, to yield a bypass mode in which a phase shift of approximately 0° is achieved between the first and second nodes. 
     In some embodiments, the capacitive grounding paths associated with the first inductance can include a capacitance with a value of C implemented at the node between the first inductance and the first switch, and a first switchable capacitive grounding path having a capacitance with a value of  2 C, a fifth switch, and a capacitance with a value of  2 C, arranged in series between the first node and ground. The reconfiguring circuit assembly can be configured with each of the first, second and third switches open, and each of the fourth and fifth switches closed, to yield a shift mode in which a phase shift of approximately −90° is achieved between the first and second nodes. 
     In some embodiments, the capacitive grounding paths associated with the second inductance can include a capacitance with a value of C implemented at the node between the second inductance and the first switch, and a second switchable capacitive grounding path having a capacitance with a value of  2 C, a sixth switch, and a capacitance with a value of  2 C, arranged in series from a node between the second inductance and the second switch to ground. The reconfiguring circuit assembly can be configured with each of the third and fourth switches open, and each of the first, second, fifth and sixth switches closed, to yield a shift mode in which a phase shift of approximately −180° is achieved between the first and second nodes. 
     In some embodiments, the reconfiguring circuit assembly can further include a seventh switch implemented between ground and a node between the first switch and the second inductance, and a switchable path, having an eighth switch and a capacitance with a value of  2 C in series, implemented from the node between the second inductance and the second switch to a node between the fifth switch and the  2 C-capacitance closer to the first node. The reconfiguring circuit assembly can be configured with each of the third, fourth, fifth and sixth switches open, and each of the first, second, seventh and eighth switches closed, to yield a shift mode in which a phase shift of approximately +90° is achieved between the first and second nodes. 
     In some embodiments, the first node can be an input node, and the second node can be an output node. In some embodiments, the phase shifter can further include a fine phase shifter circuit coupled to the output node. The fine phase shifter circuit can include a first transmission line element having an inductance and a variable capacitance on each side of the inductance, such that the fine phase shifter circuit provides a phase shift in an increment having a magnitude that is less than the smallest magnitude of the non-zero quadrant shifts. The fine phase shifter circuit can further include a second transmission line element in series with the first transmission line element, with the second transmission line element including an inductance and a variable capacitance on each side of the inductance. In a number of teachings, the present disclosure relates to a method for adjusting phase of a signal. The method includes providing two or less inductors, and generating a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing the two or less inductors. 
     In some teachings, the present disclosure relates to a method for adjusting phase of a signal. The method includes receiving a signal on a first node, and routing the signal to a second node through a phase shifting circuit that includes a first switchable path having a first inductance and a second inductance arranged in series between the first and second nodes. The phase shifting circuit further includes a capacitive grounding path implemented on each side of each of the first and second inductances, with at least one of the capacitive grounding paths being configured as a switchable capacitive grounding path. The phase shifting circuit further includes a reconfiguring assembly configured to allow the phase shifting circuit to provide a plurality of quadrant phase shifts utilizing the first and second inductances and the at least one switchable capacitive grounding path. 
     According to some implementations, the present disclosure relates to a semiconductor die having a semiconductor substrate and a phase shifting circuit implemented on the semiconductor die. The phase shifting circuit is configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. 
     According to a number of implementations, the present disclosure relates to a semiconductor die having a semiconductor substrate and a phase shifting circuit implemented on the semiconductor die. The phase shifting circuit includes a first node and a second node, and a first switchable path having a first inductance and a second inductance arranged in series between the first and second nodes. The phase shifting circuit further includes a capacitive grounding path implemented on each side of each of the first and second inductances, with at least one of the capacitive grounding paths being configured as a switchable capacitive grounding path. The phase shifting circuit further includes a reconfiguring circuit assembly configured to allow the phase shifting circuit to provide a plurality of quadrant phase shifts utilizing the first and second inductances and the at least one switchable capacitive grounding path. 
     In some embodiments, the semiconductor substrate can include a silicon-on-insulator (SOI) substrate. In some embodiments, the semiconductor die can further include a fine phase shifter circuit coupled to the output node. The fine phase shifter circuit can include a first transmission line element having an inductance and a variable capacitance on each side of the inductance, such that the fine phase shifter circuit provides a phase shift in an increment having a magnitude that is less than the smallest magnitude of the non-zero quadrant shifts. 
     In some implementations, the present disclosure relates to an electronic module that includes a packaging substrate configured to receive one or more components, and a die mounted on the packaging substrate. The die includes a phase shifting circuit configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. 
     In some embodiments, the two or less inductors can be implemented on the die. 
     In some implementations, the present disclosure relates to an electronic module having a packaging substrate configured to receive one or more components, and a die mounted on the packaging substrate. The die includes a phase shifting circuit having a first node and a second node, and a first switchable path having a first inductance and a second inductance arranged in series between the first and second nodes. The phase shifting circuit further includes a capacitive grounding path implemented on each side of each of the first and second inductances, with at least one of the capacitive grounding paths being configured as a switchable capacitive grounding path. The phase shifting circuit further includes a reconfiguring circuit assembly configured to allow the phase shifting circuit to provide a plurality of quadrant phase shifts utilizing the first and second inductances and the at least one switchable capacitive grounding path. 
     In some embodiments, the electronic module can further include a fine phase shifter circuit coupled to the output node. The fine phase shifter circuit can include a first transmission line element having an inductance and a variable capacitance on each side of the inductance, such that the fine phase shifter circuit provides a phase shift in an increment having a magnitude that is less than the smallest magnitude of the non-zero quadrant shifts. The fine phase shifter circuit can be implemented substantially on the same die as the phase shifting circuit. 
     According to some implementations, the present disclosure relates to an electronic device having a processor configured facilitate processing of a signal. The electronic device further includes a phase shifting circuit configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state for the signal utilizing two or less inductors. 
     In a number of implementations, the present disclosure relates to an electronic device having a processor configured facilitate processing of a signal, and a phase shifting circuit configured to provide a phase shift for the signal. The phase shifting circuit includes a first node and a second node, and a first switchable path having a first inductance and a second inductance arranged in series between the first and second nodes. The phase shifting circuit further includes a capacitive grounding path implemented on each side of each of the first and second inductances, with at least one of the capacitive grounding paths being configured as a switchable capacitive grounding path. The phase shifting circuit further includes a reconfiguring circuit assembly configured to allow the phase shifting circuit to provide a plurality of quadrant phase shifts utilizing the first and second inductances and the at least one switchable capacitive grounding path. 
     In some embodiments, the electronic device can further include a communication component configured to facilitate interaction with another electronic device and/or a user. The electronic device can include, for example, a wireless device. 
     According to a number of implementations, the present disclosure relates to a phase shifter having a first node and a second node, and a first transmission line element having an inductance and a variable capacitance on each side of the inductance. The variable capacitance is configured to provide a plurality of capacitance values to yield corresponding phase shift values based on an increment having a magnitude that is less than 90 degrees. 
     In some embodiments, the phase shifter can further include a second transmission line element in series with the first transmission line element. The second transmission line element can have an inductance and a variable capacitance on each side of the inductance configured to extend an overall phase shift range provided by the phase shifter. 
     In some embodiments, the variable capacitance can be provided by a switchable circuit having a plurality of capacitive paths arranged in parallel, with each capacitive path including at least one capacitor in series with a switch. The capacitive path can include a first capacitor and a second capacitor arranged such that the switch is between the first and second capacitors. The series arrangement of the first capacitor, the switch, and the second capacitor can be configured to provide DC blocking functionality. 
     In some embodiments, the first and second capacitors can have substantially same capacitance values. The series arrangement of the first capacitor, the switch, and the second capacitor can be configured to provide a substantially symmetric capacitance for the capacitive path. 
     In some embodiments, the switch can include a field-effect transistor (FET) such that source and drain of the FET are connected to the first and second capacitors. The FET can be biased such that its channel and gate are biased to opposite potentials. 
     In some embodiments, the phase shifter can further include a quadrant phase shifter coupled to one of the first and second nodes. The quadrant phase shifter can be configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. The quadrant phase shifter can include two inductors, such that the phase shifter includes four inductors. The four states of the quadrant phase shifter can be achieved by a 2-bit control signal over the four quadrants. The switchable circuit can include four capacitive paths to provide a 4-bit variable capacitance values over a range of at least 90 degrees. The phase shifter can have a 6-bit phase shift resolution over a range of at least 360 degrees. 
     In some implementations, the present disclosure relates to a method for adjusting phase of a signal. The method includes providing a transmission line element having an inductance and a variable capacitance on each side of the inductance. The method further includes controlling the variable capacitance to provide a plurality of capacitance values to yield corresponding phase shift values based on an increment having a magnitude that is less than 90 degrees. 
     In some implementations, the present disclosure relates to a semiconductor die having a semiconductor substrate and a phase shifting circuit implemented on the semiconductor die. The phase shifting circuit includes a first node and a second node, and a first transmission line element having an inductance and a variable capacitance on each side of the inductance. The variable capacitance is configured to provide a plurality of capacitance values to yield corresponding phase shift values based on an increment having a magnitude that is less than 90 degrees. 
     In some embodiments, the phase shifting circuit can further include a second transmission line element in series with the first transmission line element. The second transmission line element can have an inductance and a variable capacitance on each side of the inductance configured to extend an overall phase shift range provided by the phase shifter. 
     In some embodiments, the semiconductor substrate can include a silicon-on-insulator (SOI) substrate. 
     In some embodiments, the semiconductor die can further include a quadrant phase shifter coupled to one of the first and second nodes. The quadrant phase shifter can be configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. 
     According to some teachings, the present disclosure relates to an electronic module having a packaging substrate configured to receive one or more components, and a die mounted on the packaging substrate. The die includes a phase shifting circuit having a first node and a second node. The phase shifting circuit further includes a first transmission line element having an inductance and a variable capacitance on each side of the inductance. The variable capacitance is configured to provide a plurality of capacitance values to yield corresponding phase shift values based on an increment having a magnitude that is less than 90 degrees. 
     In some embodiments, the phase shifting circuit can further include a second transmission line element in series with the first transmission line element. The second transmission line element can have an inductance and a variable capacitance on each side of the inductance configured to extend an overall phase shift range provided by the phase shifter. 
     In some embodiments, the electronic module can further include a quadrant phase shifter coupled to one of the first and second nodes. The quadrant phase shifter can be configured to provide a bypass state, a single first-handed quarter-wave state, a double first-handed quarter-wave state, or a single second-handed quarter-wave state utilizing two or less inductors. 
     In some embodiments, the inductances associated with the first and second transmission lines and the two or less inductors of the quadrant phase shifter can include corresponding inductors implemented on the die. 
     In accordance with some implementations, the present disclosure relates to an electronic device having a processor configured facilitate processing of a signal. The electronic device further includes a phase shifting circuit having a first node and a second node. The phase shifting circuit further includes a first transmission line element having an inductance and a variable capacitance on each side of the inductance. The variable capacitance is configured to provide a plurality of capacitance values to yield corresponding phase shift values based on an increment having a magnitude that is less than 90 degrees. 
     In some embodiments, the electronic device can further include a communication component configured to facilitate interaction with another electronic device and/or a user. The electronic device can include, for example, a wireless device. 
     For purposes of summarizing the disclosure, certain aspects, advantages and novel features of the inventions have been described herein. It is to be understood that not necessarily all such advantages may be achieved in accordance with any particular embodiment of the invention. Thus, the invention may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other advantages as may be taught or suggested herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects of this disclosure will be described in more detail by way of example only with reference to the accompanying drawings. The components within the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating principles. 
         FIG. 1  is a circuit diagram of a lumped element transmission line. 
         FIG. 2  is a circuit diagram of phase shifter, in accordance with some implementations. 
         FIG. 3  is a circuit diagram of a first configuration of a phase shifter embodying an aspect of the present disclosure. 
         FIG. 4  is a circuit diagram of a second configuration of a phase shifter embodying an aspect of the present disclosure. 
         FIG. 5  is a circuit diagram of a third configuration of a phase shifter embodying an aspect of the present disclosure. 
         FIG. 6  is a circuit diagram of a fourth configuration of a phase shifter embodying an aspect of the present disclosure. 
         FIG. 7  is a circuit diagram of a fine tuning phase shifter, in accordance with some implementations. 
         FIG. 8  is a plot of phase shift in accordance with an aspect of the present disclosure. 
         FIG. 9  is a plot of input impedance in accordance with an aspect of the present disclosure. 
         FIG. 10A  is a schematic of a circuit embodying a switching capacitance in accordance with an aspect of the present disclosure. 
         FIG. 10B  is a schematic of a circuit embodying a switching capacitance in accordance with an aspect of the present disclosure. 
         FIG. 11  is a schematic of a 4-bit variable capacitor in accordance with an aspect of the present disclosure. 
         FIG. 12  is a schematic of a phase shifter assembly embodying an aspect of the present disclosure. 
         FIG. 13  is a top-down view of a fabricated chip embodying a phase shifter assembly in accordance with an aspect of the present disclosure. 
         FIG. 14  is a plot of phase shift performance at 2.4 GHZ in accordance with an aspect of the present disclosure. 
         FIG. 15  is a plot of insertion loss in accordance with an aspect of the present disclosure. 
         FIG. 16  is a plot of return loss performance in accordance with an aspect of the present disclosure. 
         FIG. 17  is a plot of a frequency response in accordance with an aspect of the present disclosure. 
         FIGS. 18A-18C  illustrate block diagrams of implementations of phase shifters on a semiconductor die, in accordance with one or more aspects of the present disclosure. 
         FIG. 19  illustrates a block diagram of a phase shifter implemented in a packaged module format, in accordance with one or more aspects of the present disclosure. 
         FIG. 20  illustrates a block diagram of an electronic device implementing a phase shifter in accordance with one or more aspects of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF SOME EMBODIMENTS 
     The headings provided herein, if any, are for convenience only and do not necessarily affect the scope or meaning of the claimed invention. 
     Examples related to a compact architecture for a passive 6-bit digital phase shifter are disclosed. In some embodiments, a phase shifter can have a range of 360° with 5.6° resolution at 2.4 GHz. Such an architecture can include an ambidextrous quadrant selector in series with a digital fine-tuned phase shifter which makes use of high-ratio symmetrical digitally variable capacitors loading a lumped element transmission line. The example phase shifter can achieve a 50Ω match in all 64 states. The example circuit occupies approximately 0.47 mm 2  on die, and the entire example test chip measured 0.84 mm 2  including bond pads and ESD structures. The example chip was fabricated in a commercial 0.13 μm SOI (Silicon-on-Insulator) CMOS process. 
     Introduction: 
     Phase shifting is an important operation in many RF applications. For example, phase shifters are commonly used in signal cancellers and equalizers. Phase shifters are also used in beam steering, where a phased antenna array directs the antenna energy in a desired direction, which is commonly used in radar and non-line-of-sight (NLOS) operations. In dynamic gain equalizers, phase shifters are used to fit the attenuation profile of the equalizer to a desired one to compensate for non-flat gain responses across a communication band. Other applications can also utilize phase shifters. 
     Disclosed are examples of one or more designs related to a highly compact phase shifter that can include a digitally tuned transmission line and an ambidextrous quadrant selector. While it is not desired or intended to be bound by any particular theory or model, described herein are examples related to basic theory surrounding lumped element transmission lines to facilitate description of architectures associated with a quadrant selector and/or a fine tuning phase shifter. Examples of measured results and comparison to theory and other phase shifters are also disclosed. 
     Examples Related to Basic Theory: 
     A lumped element quarter wave transmission line, shown in  FIG. 1 , has a characteristic impedance, Z 0  that can be expressed as 
                       Z   0     =       L   C         ,           (   1   )               
and a corner frequency, ω 0  that can be expressed as
 
     
       
         
           
             
               
                 
                   
                     ω 
                     o 
                   
                   = 
                   
                     
                       1 
                       
                         LC 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     A change in inductance or capacitance will change the corner frequency of the system, and thus the phase of the signal at the output will change as well. Inductance is typically not easily altered; however, capacitance can be more readily variable with an appropriate device, such as a MOS varactor. Therefore, in a lumped element transmission line, utilizing a variable capacitance can alter the phase of the signal at the output. 
     The example lumped element circuit in  FIG. 1  typically has a low pass response up to the corner frequency response indicated in Equation 2. Below this corner frequency, the gain response is typically fairly flat, but phase can be changing. As a result, the phase can be altered while the gain of the system remains relatively flat by changing the corner frequency of the system within the pass band region close to the corner frequency. 
     Using a fine tuning system by altering the corner frequency of a circuit similar to  FIG. 1  can enable fine tuning. In order to cover 360°, a coarse tuning can be utilized as well. For example, a coarse phase shifting can include one or more 90-degree shifts. With a fixed L, C and Z 0 , the electrical length of a lumped transmission line can be substantially constant at a given frequency. Using one or more fixed quarter wave (90°) transmission lines, different quadrants (e.g., 0°, 90°, 180°, 270°) can be selected using switches to obtain the example coarse phase shift. Such a technique can yield 360° total range when paired together with a variable capacitor loaded transmission line. 
     Examples of Architectures: 
     Ambidextrous Quadrant Shifter 
     In some embodiments, a quadrant shifter can be designed by utilizing fixed quarter wave transmission lines that can be switched in or out to select a quadrant desired. For example, to select the four quadrants, one can implement three quarter wave sections selectable by switches. With three sections, there would be three inductors which can be main area consumer in this example circuit. 
     An example architecture shown in  FIG. 2  can employ inductor reuse in combination with switches to accomplish substantially the same goal, but with two inductors instead of three. It can achieve such functionality by electrically reconfiguring the circuit&#39;s inductors between series and parallel connections to make use of left handed lumped transmission lines, which can provide substantially the opposite phase shift of the right handed version shown in  FIG. 1 . The architecture can be configured to select between some or all of bypass, single right handed quarter wave, double right handed quarter wave, and single left handed quarter wave states, which can provide 0°, 90°, 180° and +90° of phase shift respectively. The example architecture shown in  FIG. 2  can provide such phase shifting functionality, and examples of how each quadrant state can be achieved are described herein in greater detail. 
       FIGS. 3-6  show example configurations of the architecture of  FIG. 2  for generating the foregoing bypass, single right handed quarter wave, double right handed quarter wave, and single left handed quarter wave states. In  FIGS. 3-6 , switches S 1 , S 2 , S 3 , S 4 , S 5 , S 6 , S 7  and S 8  can be in states as shown to achieve such states. 
     Bypass, 0°: In a bypass state, both bypass switches (S 3 , S 4 ) can be closed (ON), and all other switches can be opened (OFF), as shown in  FIG. 3 . It is noted that in some embodiments, one shunt capacitor C to ground could also be removed with another switch. 
     Single Quarter Wave Transmission Line, −90°: A single right handed transmission line can be formed by creating a shunt C at the input, and activating the bypass switch at the output, as shown in  FIG. 4 . More particularly, a shunt switch S 5  can be closed, the bypass switch S 4  can be closed, and all other switches can be opened. 
     Double Quarter Wave Transmission Line, −180°: As shown in  FIG. 5 , two series quarter wave transmission lines can be formed to produce a 180° phase shift. Such a configuration can be achieved by shunt switches S 5  and S 6 , and switches S 1  and S 2  being closed as shown, and all other switches being open. 
     Left-Handed Quarter Wave Transmission Line, +90°: As shown in  FIG. 6 , both inductors can be shunted to ground from the input and output using a switch S 7  to ground in the middle of the circuit. For example, switches S 1 , S 2 , S 7  and S 8  can be closed, and all other switches can be opened. In such a configuration, a series capacitance C can be created using the series combination of the capacitance  2 C at the input and  2 C connecting to the output through the closed switch S 8 . The previously shunted capacitance  2 C to ground is disconnected by opening the shunt switch S 5  at the input. Such a configuration creates a left handed transmission line with two series capacitors of  2 C, creating C, and two shunt inductors to ground. 
     Referring to the examples of  FIGS. 2-6 , it is noted that in addition to a significant area reduction, this design can also provide a more consistent loss between states and a lower maximum loss than that of traditional three quarter wave transmission lines. For example, the architecture of  FIGS. 2-6  can have the most loss in the double transmission line state, rather than triple in the traditional configuration. 
     Fine Phase Shifter: 
     In some embodiments, a fine tuning phase shifter can include two series lumped element transmission lines similar to the example shown in  FIG. 1 , where some or all of the capacitors can be replaced with variable capacitors to enable tuning. An example of such a fine tuning phase shifter is shown in  FIG. 7 . 
     Referring to the example of  FIG. 7 , such an architecture can utilize high-ratio variable capacitors described herein in order to, for example, achieve 90° of total phase shift while maintaining, for example, a 50Ω match with two inductors. In some embodiments, each capacitor can have a 4-bit resolution, thereby enabling approximately 6° resolution (90/(2 4 )≈6) for 90° of total phase shift. 
     A theoretical phase shift vs. capacitance can be derived from the example configuration of  FIG. 7  using Kirchoff&#39;s Voltage Law. Assuming a 50Ω voltage source at V in  and 50Ωload at V 0 , a transfer function V out /V source  can be expressed in terms of impedances as: 
                       V   out       V   in       =       (         Z   C     ⁢        50           Z   L     +       Z   C     ⁢        50           )     ⁢     (           Z   C     2     ⁢          (       Z   L     +       (     Z   C          ⁢   50       )     )           Z   L     +     (         Z   C     2     ⁢          (       Z   L     +       (     Z   C          ⁢   50       )     )       )         )     ⁢       (         Z   C     ⁢          (       Z   L     +     (         Z   C     2     ⁢          (       Z   L     +       (     Z   C          ⁢   50       )     )       )       )           50   +       Z   C     ⁢          (       Z   L     +     (         Z   C     2     ⁢          (       Z   L     +       (     Z   C          ⁢   50       )     )       )                 )     .               (   3   )               
When substituting Z C =(sC) −1  and Z L =sL into Equation 3, a Laplace transfer function can be obtained as:
 
                         V   out       V   in       ⁢     (   s   )       =       25             2500   ⁢     C   3     ⁢     L   2     ⁢     s   5       +     100   ⁢     C   2     ⁢     L   2     ⁢     s   4       +       (       7500   ⁢     C   2     ⁢   L     +     CL   2       )     ⁢     s   3       +                 200   ⁢     CLs   2       +     5000   ⁢   Cs     +   Ls   +   50             .             (   4   )               
Further, substituting s=jω and factoring into Cartesian form in the denominator, following expression can be obtained for V out /V in :
 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       out 
                     
                     
                       V 
                       in 
                     
                   
                   = 
                   
                     
                       25 
                       
                         
                           
                             
                               
                                 100 
                                 ⁢ 
                                 
                                   C 
                                   2 
                                 
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                                   2 
                                 
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                                   ω 
                                   4 
                                 
                               
                               - 
                               
                                 200 
                                 ⁢ 
                                 CL 
                                 ⁢ 
                                 
                                     
                                 
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                                   ω 
                                   2 
                                 
                               
                               + 
                               50 
                               + 
                             
                           
                         
                         
                           
                             
                               j 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2500 
                                     ⁢ 
                                     
                                       C 
                                       3 
                                     
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                                       L 
                                       2 
                                     
                                     ⁢ 
                                     
                                       ω 
                                       5 
                                     
                                   
                                   - 
                                   
                                     
                                       ( 
                                       
                                         
                                           7500 
                                           ⁢ 
                                           
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                                             2 
                                           
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                                           L 
                                         
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                                           2 
                                         
                                       
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                                     ⁢ 
                                     
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                                       3 
                                     
                                   
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                                           5000 
                                           ⁢ 
                                           C 
                                         
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                                         L 
                                       
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                                     ω 
                                   
                                 
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                     . 
                   
                 
               
               
                 
                   ( 
                   5 
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     Using Equations 1 and 2, and assuming a 50Ω transmission line at 2.4 GHz, example impedance values of L=3.32 nH and C=1.32 pF can be obtained for a fixed quarter wave transmission line. Using such an inductance value at 2.4 GHz, a phase shift can be found by use of Equation 5 for the angle of V OUT /V IN  at various capacitances. An example of such an output phase as a function of capacitance is shown in  FIG. 8 . 
     In the example of  FIG. 8 , one can see that the resulting phase shift is quite linear with respect to capacitance over a large range, which can then allow for a binary weighted digital capacitor to control the phase shift in an approximately linear fashion. 
     As an example, using ideal devices in  FIG. 8 , 90° of phase occurs between 0.5 pF and 1.5 pF, for a C MAX :C MIN  of 3:1, similar to MOS varactors. For a 360° application paired with a quadrant selector, some margin can be implemented to ensure no gaps occur from using real components and due to process variation; accordingly, a target starting design of, for example, at least 100 degrees can be selected. In addition, on chip devices can deviate from ideal; therefore, a variable capacitance with a ratio larger than 3:1 can be implemented to achieve 90° with two transmission line segments. 
     An input match is typically important for RF applications. Referring to  FIG. 7 , Z IN , which can be assumed to be equal to Z OUT,  can be found as: 
                     Z   IN     =       Z   C     ⁢          (       Z   L     +     (         Z   C     2     ⁢            (       Z   L     +     (       Z   C     ⁢        50   )       )       )     )     .                         (   6   )               
When Equation 6 is simplified into a Cartesian form and solved for magnitude, the input impedance for the example 2.4 GHz phase shifter can be as shown in  FIG. 9 . For RF applications, the foregoing design can be advantageous due to a consistent 50Ω match over a large range of capacitance values.
 
High Ratio Switched Variable Capacitors:
 
     A phase shifter having one or more features as described herein can be designed to have a very low area use. Traditional MOS varactors typically have a C MAX :C MIN  near 3:1. By using real components such as MOS varactors instead of ideal components, the capacitance ratio would likely be insufficient to achieve greater than 90° of phase shift with two transmission line segments. Such a design can therefore utilize three series transmission lines to reach 90° of phase shift. However, if a variable capacitance with a higher ratio is utilized, a larger phase shift can be attainable and using two sections. Such a design can reduce the area considerably by being able to use two sections instead of three as compared to using MOS varactors. 
     Examples of circuits implementing a switchable capacitance are shown in  FIGS. 10A and 10B . More particularly,  FIG. 10A  shows an example of a cross-biased switch, where gate and channel are inversely biased.  FIG. 10B  shows an equivalent circuit when the gate is low (off). It is noted that by using switches which are DC decoupled with fixed capacitors in parallel, capacitance can be added or removed digitally. Cross biasing of the switches as shown in  FIG. 10A , where the channel and gate are biased to opposite potentials, can include a number of benefits. 
     For example, a benefit can include a feature where the switch does not turn on or turn off easily due to a high powered RF signal. Another advantage is that by splitting the desired capacitance into two series capacitors, they can also act to block DC. Accordingly, traditionally large (e.g., RF short) DC blocking capacitors are not required, which in turn can reduce area consumption. Another benefit associated with the design is that the capacitance will be generally symmetrical because the switch&#39;s source and drain are symmetrical; accordingly, the isolating capacitors can have approximately the same value if desired. 
       FIG. 11  shows an example architecture of a 4-bit variable capacitor. In  FIG. 11 , a change in capacitance, ΔC n , can be toggled using a control signal a n  at the gate of a respective switch. A desired capacitance step can be the difference between two C n  in series with the R ON  of the switch, and two C n  and two C OFF  in series as seen in  FIG. 10B . The latter assumes a large R GATE  resistor and a large R OFF  of the switch. C OFF  is the capacitance between source/drain and gate when the switch is off as shown in  FIG. 10B . The difference ΔC n  can be expressed as: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
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                       C 
                       n 
                     
                   
                   = 
                   
                     
                       
                         C 
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                       2 
                     
                     - 
                     
                       
                         
                           
                             C 
                             n 
                           
                           ⁢ 
                           
                             C 
                             OFF 
                           
                         
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               
                                 C 
                                 n 
                               
                               + 
                               
                                 C 
                                 OFF 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   7 
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     In some embodiments, C n  can be chosen to provide desired capacitance steps, and the number of bits can be expandable. Such a design can have a C MAX :C MIN  ratio dependent of the selected C n  and only be limited at the low end by C OFF . Therefore, a large highly-linear capacitance ratio can be achieved using this architecture. 
     Phase Shifter Assembly: 
     In some embodiments, a phase shifter assembly can include a fine shifter with high-ratio variable capacitors, as described herein, in series with an ambidextrous quadrant selector, also as described herein. Such a design can be implemented as a 6-bit phase shifter, for a total of 64 phases across 360°. In some embodiments, such a phase shifter assembly can be configured to be substantially entirely passive, and only draw current when changing states. An example of such a phase shifter is shown in  FIG. 12 . 
     Examples of Measured Results: 
     Measured performance of the phase shifter of  FIG. 12  was obtained with a network analyzer.  FIG. 13  shows a micrograph of a fabricated chip with the phase shifter of  FIG. 12 . The on chip area is approximately 0.47 mm 2 , and the total area of the test die including bond pads and ESD is approximately 0.84 mm 2 , with the overall dimensions being approximately 1400 μm×600 μm. 
     In the example of  FIG. 13 , the four coil traces are the four inductors in the phase shifter of  FIG. 12 . One can see that each inductor occupies a significant portion of the overall area; thus, eliminating an inductor as described herein can yield a desirable reduction in overall dimensions of related devices. 
     An example of phase shift performance at 2.4 GHz is shown in  FIG. 14 . The phase shifter of  FIG. 12  is shown to achieve linear monotonic phase shift with an average phase step of 5.84° and a total phase range of 372°. 
     An example S 21 (dB) performance is shown in  FIG. 15 . One can see that S 21  is fairly consistent, varying between −4 and −7.4 dB at its extremes, or approximately −5.7±1.7 dB. 
     An example return loss performance is shown in  FIG. 16 . One can see that the phase shifter remains well matched at 2.4 GHz over all phases at both the input and the output terminals. 
     An example frequency response for STEP=0 is shown in  FIG. 17 . More particularly, S-parameters S 12 , S 21 , S 11  and S 22  are plotted as a function of frequency from 100 MHz to 5 GHz. 
     As shown in the example of  FIG. 17 , the phase shifter is well matched (e.g., &lt;−10 dB) in a frequency range of 1.7GHz to 2.8 GHz, and displays a stop band property after this region. In some embodiments, lower loss can be achieved by, for example, higher Q inductors and/or wider RF paths in a metal layer (e.g., top metal layer) of the phase shifter chip. 
     A comparison of properties associated with the present disclosure to other works is found in Table I. 
                                     TABLE 1               Freq.   No. of   Insertion   Area           (GHz)   Bits   Loss (dB)   (mm 2 )   Technology                                                    2.4   6   5.7 ± 1.7   0.47   130 nm SOI CMOS       2.5-3.2   6   13*   3.1**   180 nm CMOS       1.4-2.4   6   3.8 ± 0.4   3.8   0.5 μm GaAs pHEMT       1.4-2.4   4   3.8 ± 0.4   2.6   400 nm GaAs       11.6-12.6   4     9 ± 0.5*   1.72   180 nm RF CMOS       1.4-1.7   9   9.3 ± 3.3   5.94   250 nm SOS       1.8-2.4   10   5.1 ± 2.2   3.4   250 nm SOS                    
In Table 1, phase shifter chip of  FIGS. 12 and 13  is listed on the top row, implemented as 130 nm SOI CMOS technology. In Table 1, the insertion loss estimate of 13 dB for the 180 nm CMOS technology example is without amplification (active), and the listed area of 3.1 mm 2  is an estimate based on a die photograph.
 
     Based on the comparison in Table 1, one can see that the phase shifter of  FIGS. 12 and 13  has an insertion loss that is competitive relative to other designs, but not the best one. However, for all of the compared digital phase shifters, the phase shifter of  FIGS. 12 and 13  is shown to occupy nearly four times less area than the next smallest device (1.72 mm 2  for the 180 nm RF CMOS technology example, with a frequency range of 11.6-12.6 GHz). 
     It is noted that such an 180 nm RF CMOS device is designed for a much higher frequency (11.6-12.6 GHz), and therefore, components can be typically smaller. When one compares the phase shifter of  FIGS. 12 and 13  to examples in similar frequency ranges, the most area-efficient example (180 nm CMOS of the second row) has an area of 3.1 mm 2 . Accordingly, the phase shifter of  FIGS. 12 and 13  can be considered to have at least a six-fold improvement in area-efficiency over other digital phase shifters in a similar frequency range. 
     As described herein, a passive digital phase shifter having one or more features as described herein can provide, among others, a significant advantage in area efficiency. In addition, and as described herein, insertion loss performance can be improved with such an area efficiency. 
     A compact yet high performance 6-bit phase shifter has been described and demonstrated. Such a phase shifter provides performance comparable to other phase shifter designs, yet occupies less than 20% of the area. 
     Examples of Devices and Products: 
     As one can appreciate, a phase shifter having one or more features as described herein can be utilized in many electronic applications, including but not limited to RF applications. Such electronic applications can include, for example, phased array systems, frequency synthesizers, various wireless applications, etc. 
       FIGS. 18-20  show non-limiting examples of how a phase shifter having one or more features as described herein can be implemented in different products. For example,  FIGS. 18A-18C  show examples where a phase shifter can be implemented in a semiconductor die format.  FIG. 18A  shows that in some embodiments, a semiconductor die  200  can include a quadrant shifter  202  having one or more features as described herein (e.g.,  FIGS. 2-6 ).  FIG. 18B  shows that in some embodiments, a semiconductor die  200  can include a fine phase shifter  204  having one or more features as described herein (e.g.,  FIGS. 7-11 ).  FIG. 18C  shows that in some embodiments, a semiconductor die  200  can include a phase shifter  206  having functionalities associated with both of the quadrant shifter and the fine phase shifter (e.g.,  FIG. 12 ). 
       FIG. 19  shows that in some embodiments, a phase shifter having one or more features as described herein can be implemented in a packaged module format. For example, a packaged module  300  can include a packaging substrate  302  configured to receive a plurality of components. Such components can include a phase shifter  200  implemented in, for example, a die format. Such a phase shifter can facilitate operation of, for example, an RF circuit device  304 . 
     In the example of  FIG. 19 , the phase shifter die  200  is depicted as being a separate device from the RF circuit device  304 . However, it will be understood that a phase shifter having one or more features as described herein can also be part of the RF circuit device  304  (e.g., in a die format), or any combination thereof. 
     In the example of  FIG. 19 , the phase shifter is depicted as facilitating the operation of the RF circuit device. It will be understood that the module  300  can include a non-RF device (that operates with the phase shifter) instead of the RD device ( 304 ), in addition to the RF device, or any combination thereof. 
       FIG. 20  depicts an electronic device  400  having a module  300  such as the example of  FIG. 19 . Such a device can also include, for example, a processor  402  and a communication component  404 . Such a communication component can include, for example, circuits and/or devices that allow the electronic device  400  to communicate with another device (e.g., wireless or wired communication), a user (e.g., a user interface), or any combination thereof. 
     In the example of  FIG. 20 , a phase shifter having one or more features as described herein is depicted as being implemented in a module format. It will be understood that such a phase shifter can also be implemented in a die format, in a circuit format, etc., or any combination thereof. 
     In some implementations, the electronic device of  FIG. 20  can be, for example, a wireless device. In some embodiments, such a wireless device can include, for example, a cellular phone, a smart-phone, a hand-held wireless device with or without phone functionality, a wireless tablet, a wireless router, a wireless modem configured to support machine type communications, a wireless access point, a wireless base station, etc. 
     Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to.” The word “coupled”, as generally used herein, refers to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Additionally, the words “herein,” “above,” “below,” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the above Detailed Description using the singular or plural number may also include the plural or singular number respectively. The word “or” in reference to a list of two or more items, that word covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. 
     The above detailed description of embodiments of the invention is not intended to be exhaustive or to limit the invention to the precise form disclosed above. While specific embodiments of, and examples for, the invention are described above for illustrative purposes, various equivalent modifications are possible within the scope of the invention, as those skilled in the relevant art will recognize. For example, while processes or blocks are presented in a given order, alternative embodiments may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, or may be performed at different times. 
     The teachings of the invention provided herein can be applied to other systems, not necessarily the system described above. The elements and acts of the various embodiments described above can be combined to provide further embodiments. 
     While some embodiments of the inventions have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel methods and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the disclosure.