Abstract:
A phase shifter circuit includes a plurality of first series circuits each comprised of a series connection of one capacitor and one resistor, a first circuit element including at least inductance connecting between a first end and a second end of a chain structure made by connecting the plurality of first series circuits in series, the first circuit element and the chain structure together constituting a first loop circuit, a plurality of second series circuits each comprised of a series connection of one capacitor and one resistor, a second circuit element including at least inductance connecting between a first end and a second end of a chain structure made by connecting the plurality of second series circuits in series, the second circuit element and the chain structure together constituting a second loop circuit, and a plurality of connection lines connecting between the first loop circuit and the second loop circuit.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2006-191874 filed on Jul. 12, 2006, with the Japanese Patent Office, the entire contents of which are incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention generally relates to circuits for converting the characteristics of a signal, and particularly relates to a phase shifter for changing the phase of a signal. 
         [0004]    2. Description of the Related Art 
         [0005]    Phase shifters for changing the phase of a signal are widely used as a component for a system such as a wired/wireless communication apparatus or measurement apparatus utilizing microwave bands or milliwave bands. In the orthogonal modulation which is widely used in the wireless communication system of today, for example, a 90-degree phase shifter is used as an indispensable component in order to generate an orthogonal signal having a 90-degree phase displacement. A variable phase shifter that is capable of changing the amount of phase shift is used for various purposes such as for the phased array operation that controls the direction of transmission by supplying signals having different phases to a plurality of antenna transmitters, for the spatial synthesis operation that synthesizes in the same phase a plurality of signals received by a plurality of antennas, or for the accuracy maintaining function that electrically adjusts phases inside measurement apparatus. 
         [0006]    Performance required of such phase shifters conventionally includes high precision, low loss, controllability, low cost, etc. As progress toward the use of higher frequencies and broader bands has been made in wireless systems in recent years, there is also a demand for increased bandwidths. As a 90-degree phase shifter required in the orthogonal modulation/demodulation system, a polyphase filter or hybrid coupler has conventionally been used. 
         [0007]      FIGS. 1A and 1B  are drawings showing a typical configuration of a polyphase filter. A polyphase filter  10  shown in  FIG. 1A  includes four resistors R and four capacitors C. A series connection of one resistor R and one capacitor C forms one series circuit, and four series circuits are connected in series, with the head end and the tail end being coupled to form a loop. Input terminals I 1  through I 4  are coupled to the connection points between every two adjacent series circuits, and output terminals O 1  through O 4  are coupled to the connection points between the resistor R and the capacitor C of each series circuit. 
         [0008]    A positive-phase signal (i.e., signal having a 0-degree phase) is supplied to the input terminals I 1  and I 4 , for example, and a negative-phase signal (i.e., signal having a 180-degree phase) is supplied to the input terminals I 2  and I 3 . With the input signals supplied in this manner, signals having a 0-degree phase, a 90-degree phase, a 180-degree phase, and a 270-degree phase appear at the output terminals O 1  through O 4 , respectively. Polyphase filters  10  having the same configuration as shown in  FIG. 1A  may be connected in cascade with the output of a given filter connected to the input of a next filter as shown in  FIG. 1B . Such configuration can generate the individual phase signals in a relatively stable manner over a broad band of frequencies. 
         [0009]      FIG. 2  is a drawing showing a typical configuration of a hybrid coupler. A hybrid coupler  11  shown in  FIG. 2  is implemented by connecting transmission lines  12 ,  13 ,  14 , and  15  in series to form a loop. The transmission lines  12  and  13  have a characteristic impedance of Z 0 , and have a length that is equal to ¼ of signal wavelength λ. The transmission lines  14  and  15  have a characteristic impedance of 0.707×Z 0  (i.e., Z 0 /√2), and have a length that is equal to ¼ of signal wavelength λ. With an input terminal IN positioned between the transmission line  12  and the transmission line  14 , for example, two signals Q 0  and Q 90  having a 90-degree phase difference appear at the opposite ends of the transmission line  13 . 
         [0010]    In the case of the polyphase filter as shown in  FIG. 1 , three to five units need to be connected in cascade in order to obtain a 90-degree phase difference over a broad band of frequencies. This results in increased circuit size. An increase in circuit size means an increase in the time required for signal propagation inside the filter, which gives rise to a problem in that a phase deviation (i.e., absolute phase deviation responsive to frequency) within the band increases. There are also an increase in loss and cost increase. In the case of the hybrid coupler shown in  FIG. 2 , the loss is relatively small, but this coupler is not suitable for broadband operations because of the use of ¼ wavelength transmission lines. Phase deviation (i.e., absolute phase deviation responsive to frequency) within the band is larger than in the case of the polyphase filter. 
         [0011]    In this manner, related-art 90-degree phase shifters have a problem of poor broadband performance, i.e., a problem of a large phase deviation within the band. 
         [0012]    Accordingly, there is a need for a phase shifter that has a small phase deviation over a broad band of frequencies. 
         [0013]    [Patent Document 1] Japanese Patent Application Publication No. 6-69753 
       SUMMARY OF THE INVENTION 
       [0014]    It is a general object of the present invention to provide a phase shifter circuit that substantially obviates one or more problems caused by the limitations and disadvantages of the related art. 
         [0015]    Features and advantages of the present invention will be presented in the description which follows, and in part will become apparent from the description and the accompanying drawings, or may be learned by practice of the invention according to the teachings provided in the description. Objects as well as other features and advantages of the present invention will be realized and attained by a phase shifter circuit particularly pointed out in the specification in such full, clear, concise, and exact terms as to enable a person having ordinary skill in the art to practice the invention. 
         [0016]    To achieve these and other advantages in accordance with the purpose of the invention, the invention provides a phase shifter circuit, which includes a plurality of first series circuits each comprised of a series connection of one capacitor and one resistor, a first circuit element including at least inductance connecting between a first end and a second end of a chain structure made by connecting the plurality of first series circuits in series, the first circuit element and the chain structure together constituting a first loop circuit, a plurality of second series circuits each comprised of a series connection of one capacitor and one resistor, a second circuit element including at least inductance connecting between a first end and a second end of a chain structure made by connecting the plurality of second series circuits in series, the second circuit element and the chain structure together constituting a second loop circuit, a plurality of connection lines connecting between the first loop circuit and the second loop circuit, a signal input terminal connected to a node in the first loop circuit, and a signal output terminal connected to a node in the second loop circuit. 
         [0017]    According to at least one embodiment of the present invention, a phase shifter circuit is provided that is superior in terms of broadband performance, i.e., has a smaller phase deviation over the intended frequency band, compared with related-art circuits. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    Other objects and further features of the present invention will be apparent from the following detailed description when read in conjunction with the accompanying drawings, in which: 
           [0019]      FIGS. 1A and 1B  are drawings showing a typical configuration of a polyphase filter; 
           [0020]      FIG. 2  is a drawing showing a typical configuration of a hybrid coupler; 
           [0021]      FIGS. 3A and 3B  are drawings showing an example of the circuit configuration of a 90-degree phase shifter according to the present invention; 
           [0022]      FIGS. 4A and 4B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter; 
           [0023]      FIGS. 5A and 5B  are drawings showing an example of the operation characteristics of the +45 degree phase shifter; 
           [0024]      FIGS. 6A and 6B  are drawings showing an example of the operation characteristics of a polyphase filter for the purpose of comparison with the present invention; 
           [0025]      FIGS. 7A and 7B  are drawings showing an example of the operation characteristics of a hybrid coupler for the purpose of comparison with the present invention; 
           [0026]      FIG. 8  is a drawing showing a variation of the phase shifter according to the present invention; 
           [0027]      FIGS. 9A and 9B  are drawings showing the comparison of operations between the variable phase shifter according to the present invention and a variable phase shifter using the related-art polyphase filter; 
           [0028]      FIG. 10  is a drawing showing a first variation of the −45 degree phase shifter according to the present invention; 
           [0029]      FIGS. 11A and 11B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter of  FIG. 10 ; 
           [0030]      FIG. 12  is a drawing showing a second variation of the −45 degree phase shifter according to the present invention; 
           [0031]      FIGS. 13A and 13B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter of  FIG. 12 ; 
           [0032]      FIG. 14  is a drawing showing a third variation of the −45 degree phase shifter according to the present invention; 
           [0033]      FIGS. 15A and 15B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter of  FIG. 14 ; 
           [0034]      FIG. 16  is a drawing showing a fourth variation of the −45 degree phase shifter; 
           [0035]      FIG. 17  is a drawing showing a fifth variation of the −45 degree phase shifter according to the present invention; and 
           [0036]      FIGS. 18A and 18B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter of  FIG. 17 . 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0037]    In the following, embodiments of the present invention will be described with reference to the accompanying drawings. 
         [0038]      FIGS. 3A and 3B  are drawings showing an example of the circuit configuration of a 90-degree phase shifter according to the present invention. The 90-degree phase shifter of the present invention includes a −45 degree phase shifter  21  configured to receive a positive-phase signal IN of differential input signals as an input thereof to delay its phase by 45 degrees and a +45 degree phase shifter  22  configured to receive a negative-phase signal /IN as an input thereof to advance its phase by 45 degrees. An output signal Q−45 having a 45-degree phase delay generated by the −45 degree phase shifter  21  and an output signal Q+45 having a 45-degree phase advance generated by the +45 degree phase shifter  22  are different in phase by 90 degrees. In this manner, signals having a 90-degree phase difference are generated. 
         [0039]    The −45 degree phase shifter  21  shown in  FIG. 3A  and the +45 degree phase shifter  22  shown in  FIG. 3B  have the same circuit configuration, except for differences in the circuit parameters. Each of the −45 degree phase shifter  21  and the +45 degree phase shifter  22  is a novel phase shifter according to the present invention, and has a different configuration than the related-art phase shifters. 
         [0040]    As shown in  FIG. 3A , the −45 degree phase shifter  21  includes capacitors  31  through  36 , resistors  41  through  46 , and transmission lines  51  and  52 . As shown in  FIG. 3B , the +45 degree phase shifter  22  includes capacitors  61  through  66 , resistors  71  through  76 , and transmission lines  81  and  82 . In the following, the configuration and operation of the −45 degree phase shifter  21  will be described. What will be described also applies to the +45 degree phase shifter  22 . 
         [0041]    In the −45 degree phase shifter  21 , one of the capacitors  31  through  36  and a corresponding one of the resistors  41  through  46  together constitute a series circuit comprised of a series connection of one capacitor and one resistor. Three such series circuits are connected in series to form a chain, and the head end and tail end of the chain are coupled via the transmission line  51  to form a first loop circuit. Three series circuits each comprised of a series connection of one capacitor and one resistor are connected in series to form a chain, and the head end and tail end of this chain are coupled via the transmission line  52  to form a second loop circuit. In an example shown in  FIG. 3A , it is preferable to provide three series circuits in each of the first loop circuit and the second loop circuit. The number of the series circuits, however, is not limited to three. If the loss of the output signal is small, any number of series circuits may be provided As will later be described, the transmission lines  51  and  52  may alternatively be inductors. The transmission lines  51  and  52  may be implemented as microstrip lines, for example. 
         [0042]    Each of the three series circuits (i.e., a first series circuit  31  and  41 , a second series circuit  32  and  42 , and a third series circuit  33  and  43 ) included in the first loop circuit has one end thereof on the same side serving as a connection point to the second loop circuit. Each of the three series circuits (i.e., a first series circuit  34  and  44 , a second series circuit  35  and  45 , and a third series circuit  36  and  46 ) included in the second loop circuit has a connection point between the capacitor and the resistor thereof serving as a connection point to the first loop circuit. The connection points of the first loop circuit are connected in one-to-one correspondence to the connection points of the second loop circuits according to the order of their spatial arrangement. 
         [0043]    An input terminal IN is connected to the connection point between the capacitor and the resistor of one of the series circuits included in the first loop circuit. An output terminal Q−45 is connected to the connection point between two adjacent series circuits included in the second loop circuit. 
         [0044]    In the first loop circuit, the capacitors  31  through  33  have the same capacitance C 1p , and the resistors  41  through  43  have the same resistance R 1p . In the second loop circuit, the capacitors  34  through  36  have the same capacitance C 2p , and the resistors  44  through  46  have the same resistance R 2p . The transmission line  51  has a characteristic impedance Z 0  and a line length L 1p , and the transmission line  52  has a characteristic impedance Z 0  and a line length L 2p . The capacitance C 1p  and the capacitance C 2p  are different from each other, and the resistance R 1p  and the resistance R 2p  are different from each other. Further, the line length L 1p  and the line length L 2p  are different from each other. The characteristic impedance are the same between the transmission lines  51  and  52 . 
         [0045]    The adjustment of the capacitances, resistances, line lengths, and characteristic impedance makes it possible to control the amount of phase deviation. These parameters are set to different values between the −45 degree phase shifter  21  shown in  FIG. 3A  and the +45 degree phase shifter  22  shown in  FIG. 3B , thereby achieving a −45 degree phase shift in one of the phase sifters and a +45 degree phase shift in the other one of the phase shifters. Namely, when a sinusoidal wave is input into the input terminal IN of the −45 degree phase shifter  21 , a sinusoidal wave having a 45-degree phase delay relative to the input sinusoidal wave is output from the output terminal Q−45. Further, when a sinusoidal wave having a predetermined phase is input into the input terminal /IN of the +45 degree phase shifter  22 , a sinusoidal wave having a 45-degree phase advance relative to the input sinusoidal wave is output from the output terminal Q+45. 
         [0046]      FIGS. 4A and 4B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter  21 .  FIG. 4A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 4B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the −45 degree phase shifter  21  shown in  FIGS. 4A and 4B , the capacitance C 1p  of the capacitors  31  through  33  is 640 fF, the resistance R 1p  of the resistors  41  through  43  being 25 Ω, the characteristic impedance Z 0  of the transmission line  51  being 50 Ω, the line length L 1p  of the transmission line  51  being 500 μm, the capacitance C 2p  of the capacitors  34  through  36  being 220 fF, the resistance R 2p  of the resistors  44  through  46  being 40 Ω, the characteristic impedance Z 0  of the transmission line  52  being 50 Ω, and the line length L 2p  of the transmission line  52  being 1600 μm. 
         [0047]    With the parameter settings as specified above, the phase of the output of the −45 degree phase shifter  21  is maintained substantially at −45 degrees as shown in  FIG. 4A , and exhibits a phase deviation as small as about 0.6 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 4B , further, the loss ranges between −11 decibel and −12 decibel in the frequency range of 59 GHz to 66 GHz. 
         [0048]      FIGS. 5A and 5B  are drawings showing an example of the operation characteristics of the +45 degree phase shifter  22 .  FIG. 5A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 5B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the +45 degree phase shifter  22  shown in  FIGS. 5A and 5B , the capacitance C 1n  of the capacitors  61  through  63  is 70 fF, the resistance R 1n  of the resistors  71  through  73  being 90 Ω, the characteristic impedance Z 0  of the transmission line  81  being 50 Ω, the line length L 1n  of the transmission line  81  being 700 μm, the capacitance C 2n  of the capacitors  64  through  66  being 65 fF, the resistance R 2 , of the resistors  74  through  76  being 30 Ω, the characteristic impedance Z 0  of the transmission line  82  being 50 Ω, and the line length L 2n  of the transmission line  82  being 400 μm. 
         [0049]    With the parameter settings as specified above, the phase of the output of the +45 degree phase shifter  22  is maintained substantially at +45 degrees as shown in  FIG. 5A , and exhibits a phase deviation as small as about 0.5 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 5B , further, the loss ranges between −10 decibel and −12 decibel in the frequency range of 59 GHz to 66 GHz. 
         [0050]    As can be seen from comparison between the phase shown in  FIG. 4A  and the phase shown in  FIG. 5A , the phase of the output signal of the −45 degree phase shifter  21  and the phase of the output signal of the +45 degree phase shifter  22  exhibit similar characteristics, such that these phases become maximum at the middle of the frequency range between 59 GHz and 66 GHz, with the lowering of phases towards the opposite ends thereof. Accordingly, when attention is focused on a 90-degree phase difference between these phase signals, such a phase difference exhibits little changes. 
         [0051]      FIGS. 6A and 6B  are drawings showing an example of the operation characteristics of a polyphase filter for the purpose of comparison with the present invention.  FIG. 6A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 6B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. The polyphase filter whose operation characteristics are shown in  FIGS. 6A and 6B  has a circuit configuration as shown in  FIGS. 1A and 1B . 
         [0052]    As can be seen from  FIG. 6A , the output of the polyphase filter exhibits a phase deviation greater than 20 degrees (close to 30 degrees) as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 6B , further, the loss ranges between −20 decibels and −25 decibels in the frequency range of 59 GHz to 66 GHz. Namely, the 90-degree phase shifter of the present invention whose characteristics are shown in  FIGS. 4A and 4B  and  FIGS. 5A and 5B  has a far smaller phase deviation and smaller signal loss over a broad range of frequencies than does the polyphase filter. 
         [0053]      FIGS. 7A and 7B  are drawings showing an example of the operation characteristics of a hybrid coupler for the purpose of comparison with the present invention.  FIG. 7A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 7B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. The hybrid coupler whose operation characteristics are shown in  FIGS. 7A and 7B  has a circuit configuration as shown in  FIG. 2 . 
         [0054]    As can be seen from  FIG. 7A , the output of the hybrid coupler exhibits a phase deviation greater than 20 degrees (close to 30 degrees) as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 7B , further, the loss ranges between 0 decibel and −5 decibels in the frequency range of 59 GHz to 66 GHz. Namely, the 90-degree phase shifter of the present invention whose characteristics are shown in  FIGS. 4A and 4B  and  FIGS. 5A and 5B  has a far smaller phase deviation over a broad range of frequencies than does the hybrid coupler. 
         [0055]      FIG. 8  is a drawing showing a variation of the phase shifter according to the present invention. In the case of the −45 degree phase shifter  21  and the +45 degree phase shifter  22  shown in  FIGS. 3A and 3B , respectively, the values of the capacitors and resistors are fixed. IN the case of a variable phase shifter  23  shown in  FIG. 8 , the values of the capacitors and resistors are adjustable by use of variable capacitors and variable resistors. 
         [0056]    The variable phase shifter  23  shown in  FIG. 8  includes variable capacitors  111  through  116 , variable resistors  121  through  126 , and transmission lines  131  and  132 . In this example, both the capacitances and the resistances are made adjustable. Alternatively, only one of the capacitances and the resistances may be made adjustable. 
         [0057]    In the first loop circuit, the capacitors  111  through  113  have the same capacitance C 1 , and the resistors  121  through  123  have the same resistance R 1 . In the second loop circuit, the capacitors  114  through  116  have the same capacitance C 2 , and the resistors  124  through  126  have the same resistance R 2 . The transmission line  131  has a characteristic impedance Z 0  and a line length L 1 , and the transmission line  132  has a characteristic impedance Z 0  and a line length L 2 . The capacitance C 1  and the capacitance C 2  are different from each other, and the resistance R 1  and the resistance R 2  are different from each other. Further, the line length L 1  and the line length L 2  are different from each other. The characteristic impedance are the same between the transmission lines  131  and  132 . 
         [0058]    The adjustment of capacitances and resistances by use of the variable capacitors and the variable resistors makes it possible to control the amount of phase deviation. Namely, a −45 degree phase shifter may be implemented by use of the variable phase shifter  23 , or a +45 degree phase shifter may be implemented by use of the variable phase shifter  23 . 
         [0059]      FIGS. 9A and 9B  are drawings showing the comparison of operations between the variable phase shifter according to the present invention and a variable phase shifter using the related-art polyphase filter.  FIG. 9A  shows changes in an output Q 270  when the value of capacitance is changed in the polyphase filter shown in  FIGS. 1A and 1B  in which variable capacitors are used as capacitor devices.  FIG. 9B  shows changes in the output signal of the variable phase shifter  23  shown in  FIG. 8  in which the values of the capacitances are changed.  FIGS. 9A and 9B  show frequency along the horizontal axis and phase along the vertical axis, and illustrate phase deviation responsive to changes in frequency. 
         [0060]    In the case of the variable polyphase filter shown in  FIG. 9A , phase deviation is relatively large in the frequency range of 59 GHz to 66 GHz, and a phase deviation of 20 degrees at minimum is observed. In the case of the variable phase shifter  23  of the present invention shown in  FIG. 9B , on the other hand, phase deviation is relatively small in the frequency range of 59 GHz to 66 GHz, and a phase deviation of 15 degrees at the maximum is observed. 
         [0061]    In the following, variations of the −45 degree phase shifter  21  according to the present invention will be described. These variations are also applicable to the +45 degree phase shifter  22 . 
         [0062]      FIG. 10  is a drawing showing a first variation of the −45 degree phase shifter according to the present invention. In  FIG. 10 , the same elements as those of  FIG. 3A  are referred to by the same numerals, and a description thereof will be omitted. 
         [0063]    A −45 degree phase shifter  21 A shown in  FIG. 10  includes capacitors  31  through  36 , resistors  41  through  46 , and transmission lines  51  and  52 . In the −45 degree phase shifter  21 A, compared with the configuration shown in  FIG. 3A , the positions of capacitors and the positions of resistors are swapped in the first loop circuit, and the positions of capacitors and the positions of resistors are swapped in the second loop circuit. Except for the swapping of the positions of capacitors and the positions of resistors, this configuration is the same as that of the −45 degree phase shifter  21  shown in  FIG. 3A . 
         [0064]    In the first loop circuit, the capacitors  31  through  33  have the same capacitance C 1 , and the resistors  41  through  43  have the same resistance R 1 . In the second loop circuit, the capacitors  34  through  36  have the same capacitance C 2 , and the resistors  44  through  46  have the same resistance R 2 . The transmission line  51  has a characteristic impedance Z 0  and a line length L 1 , and the transmission line  52  has a characteristic impedance Z 0  and a line length L 2 . The capacitance C 1  and the capacitance C 2  are different from each other, and the resistance R 1  and the resistance R 2  are different from each other. Further, the line length L 1  and the line length L 2  are different from each other. The characteristic impedance are the same between the transmission lines  51  and  52 . 
         [0065]      FIGS. 11A and 11B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter  21 A.  FIG. 11A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 11B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the −45 degree phase shifter  21 A whose operation characteristics are shown in  FIGS. 11A and 11B , the capacitance C 1  of the capacitors  31  through  33  is 4 pF, the resistance R 1  of the resistors  41  through  43  being 25 Ω, the characteristic impedance Z 0  of the transmission line  51  being 50 Ω, the line length L 1  of the transmission line  51  being 120 μm, the capacitance C 2  of the capacitors  34  through  36  being 4 pF, the resistance R 2  of the resistors  44  through  46  being 1000 Ω, the characteristic impedance Z 0  of the transmission line  52  being 50 Ω, and the line length L 2  of the transmission line  52  being 360 μm. 
         [0066]    With the parameter settings as specified above, the phase of the output of the −45 degree phase shifter  21 A is maintained substantially at −45 degrees as shown in  FIG. 11A , and exhibits a phase deviation as small as about 1.4 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 11B , further, the loss ranges between −8 decibels and −11 decibels in the frequency range of 59 GHz to 66 GHz. 
         [0067]      FIG. 12  is a drawing showing a second variation of the −45 degree phase shifter according to the present invention. In  FIG. 12 , the same elements as those of  FIG. 10  are referred to by the same numerals, and a description thereof will be omitted. 
         [0068]    A −45 degree phase shifter  21 B shown in  FIG. 12  includes capacitors  31  through  36 , resistors  41  through  46 , and transmission lines  51  and  52 . In the −45 degree phase shifter  21 B, compared with the −45 degree phase shifter  21 A shown in  FIG. 10 , the position of the output terminal Q−45 is moved. Except for the change in the position of the output terminal Q−45, this configuration is the same as that of the −45 degree phase shifter  21 A shown in  FIG. 10 . 
         [0069]      FIGS. 13A and 13B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter  21 B.  FIG. 13A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 13B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the −45 degree phase shifter  21 B whose operation characteristics are shown in  FIGS. 13A and 13B , the capacitance C 1  of the capacitors  31  through  33  is 0.15 pF, the resistance R 1  of the resistors  41  through  43  being 720 Ω, the characteristic impedance Z 0  of the transmission line  51  being 50 Ω, the line length L 1  of the transmission line  51  being 60 μm, the capacitance C 2  of the capacitors  34  through  36  being 0.12 pF, the resistance R 2  of the resistors  44  through  46  being 1950 Ω, the characteristic impedance Z 0  of the transmission line  52  being 50 Ω, and the line length L 2  of the transmission line  52  being 820 μm. 
         [0070]    With the parameter settings as specified above, the phase of the output of the −45 degree phase shifter  21 B is maintained substantially at −45 degrees as shown in  FIG. 13A , and exhibits a phase deviation as small as about 0.5 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 13B , further, the loss is about −18 decibels in the frequency range of 59 GHz to 66 GHz. 
         [0071]    The position of the output terminal may be moved as described above. It should be noted, however, that the position of the output terminal is preferably at a connection point between two adjacent series circuits (wherein one series circuit is comprised of a series connection of one resistor and one capacitor) included in the second loop circuit. If the output terminal Q−45 is positioned at a point A or point B shown in  FIG. 12 , which is a connection point between a series circuit and the transmission line  52 , and is different from a connection point between two adjacent series circuits, the signal loss is undesirably too large. 
         [0072]      FIG. 14  is a drawing showing a third variation of the −45 degree phase shifter according to the present invention. In  FIG. 14 , the same elements as those of  FIG. 10  are referred to by the same numerals, and a description thereof will be omitted. 
         [0073]    A −45 degree phase shifter  21 C shown in  FIG. 14  includes capacitors  31  through  36 , resistors  41  through  46 , and transmission lines  51  and  52 . In the −45 degree phase shifter  21 C, compared with the −45 degree phase shifter  21 A shown in  FIG. 10 , the connections between the first loop circuit and the second loop circuit are changed. Except for the change in connections between the first loop circuit and the second loop circuit, this configuration is the same as that of the −45 degree phase shifter  21 A shown in  FIG. 10 . 
         [0074]      FIGS. 15A and 15B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter  21 C.  FIG. 15A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 15B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the −45 degree phase shifter  21 C whose operation characteristics are shown in  FIGS. 15A and 15B , the capacitance C 1  of the capacitors  31  through  33  is 0.25 pF, the resistance R 1  of the resistors  41  through  43  being 10 Ω, the characteristic impedance Z 0  of the transmission line  51  being 50 Ω, the line length L 1  of the transmission line  51  being 70 μm, the capacitance C 2  of the capacitors  34  through  36  being 0.87 pF, the resistance R 2  of the resistors  44  through  46  being 100 Ω, the characteristic impedance Z 0  of the transmission line  52  being 50 Ω, and the line length L 2  of the transmission line  52  being 75 μm. 
         [0075]    With the parameter settings as specified above, the phase of the output of the −45 degree phase shifter  21 C is maintained substantially at −45 degrees as shown in  FIG. 13A , and exhibits a phase deviation as small as about 0.2 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 15B , further, the loss is about −8 decibels in the frequency range of 59 GHz to 66 GHz. 
         [0076]    When the first loop circuit is connected to the second loop circuit, as previously described, each of the three series circuits included in the first loop circuit has one end thereof on the same side serving as a connection point to the second loop circuit, and each of the three series circuits included in the second loop circuit has a connection point between the capacitor and the resistor thereof serving as a connection point to the first loop circuit. The connection points of the first loop circuit are then connected in one-to-one correspondence to the connection points of the second loop circuits according to the order of their spatial arrangement. 
         [0077]    In so doing, connections between the one ends of the first through third series circuits included in the first loop circuit and the internal connection points of the first through third series circuits included in the second loop circuit are required to keep the order of the first, the second, and the third while allowing a cyclic shift. Namely, as shown in  FIG. 10 , the first, second, and third series circuits provided in the first loop circuit may be connected to the first, second, and third series circuits provided in the second loop circuit, respectively, or, as shown in  FIG. 14 , the first, second, and third series circuits provided in the first loop circuit may be connected to the second, third, and first series circuits provided in the second loop circuit, respectively. 
         [0078]    By the same token, the first, second, and third series circuits provided in the first loop circuit may be connected to the third, first, and second series circuits provided in the second loop circuit, respectively.  FIG. 16  is a drawing showing a fourth variation of the −45 degree phase shifter. In a −45 degree phase shifter  21 D shown in  FIG. 16 , the first, second, and third series circuits provided in the first loop circuit are connected to the third, first, and second series circuits provided in the second loop circuit, respectively. 
         [0079]      FIG. 17  is a drawing showing a fifth variation of the −45 degree phase shifter according to the present invention. In  FIG. 17 , the same elements as those of  FIG. 3A  are referred to by the same numerals, and a description thereof will be omitted. 
         [0080]    A −45 degree phase shifter  21 E shown in  FIG. 17  includes capacitors  31  through  36 , resistors  41  through  46 , and inductors  55  and  56 . In the −45 degree phase shifter  21 E, compared with the configuration shown in  FIG. 3A , the inductors  55  and  56  are provided in place of the transmission lines  51  and  52 . Except for the provision of the inductors  55  and  56  in place of the transmission lines  51  and  52 , this configuration is the same as that of the −45 degree phase shifter  21  shown in  FIG. 3A . 
         [0081]    In the first loop circuit, the capacitors  31  through  33  have the same capacitance C 1 , and the resistors  41  through  43  have the same resistance R 1 . In the second loop circuit, the capacitors  34  through  36  have the same capacitance C 2 , and the resistors  44  through  46  have the same resistance R 2 . The inductors  55  and  56  have inductances L 1  and L 2 , respectively. The capacitance C 1  and the capacitance C 2  are different from each other, and the resistance R 1  and the resistance R 2  are different from each other. Further, the inductance L 1  and the inductance L 2  are different from each other. 
         [0082]      FIGS. 18A and 18B  are drawings showing an example of the operation characteristics of the −45 degree phase shifter  21 E.  FIG. 18A  shows frequency along the horizontal axis and phase along the vertical axis, and illustrates phase deviation responsive to changes in frequency.  FIG. 18B  shows frequency along the horizontal axis and loss (decibel) along the vertical axis, and illustrates changes in loss responsive to changes in frequency. In the −45 degree phase shifter  21 E whose operation characteristics are shown in  FIGS. 18A and 18B , the capacitance C 1  of the capacitors  31  through  33  is 3.3 pF, the resistance R 1  of the resistors  41  through  43  being 215 Ω, the inductance L 1  of the inductor  55  being 0.45 nH, the capacitance C 2  of the capacitors  34  through  36  being 1.9 pF, the resistance R 2  of the resistors  44  through  46  being 1250 Ω, and the inductance L 2  of the inductor  56  being 0.76 nH. 
         [0083]    With the parameter settings as specified above, the phase of the output of the −45 degree phase shifter  21 E is maintained substantially at −45 degrees as shown in  FIG. 18A , and exhibits a phase deviation as small as about 0.6 degrees as the frequency changes from 59 GHz to 66 GHz. As shown in  FIG. 18B , further, the loss ranges between −6 decibels and −7 decibels in the frequency range of 59 GHz to 66 GHz. 
         [0084]    In the phase shifter of the present invention as described above, the advantage that a phase deviation is kept small over a broad range of frequencies is achieved even if inductors are used in place of transmission lines. 
         [0085]    In this manner, the phase shifter of the present invention may be modified in various fashions while maintaining the advantage that a small phase deviation is achieved over a broad range of frequencies, and is not limited to the particular configurations described in the above embodiments. It should be noted that the values of circuit parameters suitable to the individual circuit configurations as shown in the various embodiments and variations described above are not uniquely determined through a calculation method that is mathematically proven. The values of circuit parameters suitable to a phase shifter of the present invention may properly be determined through numerical computation based on the numerical analysis of the circuit conducted by use of a computer. 
         [0086]    Further, the present invention is not limited to these embodiments, but various variations and modifications may be made without departing from the scope of the present invention.