# Patent

## Title
Capacitive-degeneration double cross-coupled voltage-controlled oscillator

## Abstract

A capacitive-degeneration double cross-coupled voltage-controlled oscillator is provided. The capacitive-degeneration double cross-coupled voltage-controlled oscillator includes a main cross-coupled oscillating unit including an oscillation transistor pair cross-coupled to first and second output nodes of a resonating unit to perform an oscillation operation; and an auxiliary cross-coupled oscillating unit including a positive-feedback transistor pair cross-coupled to the first and second output nodes and the transistor pair of the main cross-coupled oscillating unit and a degeneration capacitance connected between emitters of the positive-feedback transistor pair so as to increase a negative resistance of the main cross-coupled oscillating unit. Accordingly, it is possible to increase a maximum attainable oscillation frequency and to decrease an input capacitance.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the priority of Korean Patent Application No. 10-2007-121639 filed on Nov. 27, 2007, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a voltage-controlled oscillator, and more particularly, to a capacitive-degeneration double cross-coupled voltage-controlled oscillator capable of increasing a MAOF (maximum attainable oscillation frequency) and decreasing an input capacitance.
2. Description of the Related Art
Recently, as demands for millimeter-wave band frequency resources increase, associated wire/wireless communication devices have been actively developed.
Particularly, due to an increase in processing speeds of silicon devices, conventional expensive millimeter-wave compound semiconductor monolithic microwave integrated circuit (MMIC) devices are gradually replaced with inexpensive silicon millimeter-wave MMIC devices.
However, only the development of the silicon millimeter-wave MMIC is reported, but performance of the silicon is lower than that of the compound semiconductor MMIC in terms of noise and gain characteristics.
In addition, unlike the compound semiconductor, since the silicon substrate has large loss, the silicon substrate causes serious problems such signal leakage and interference in millimeter-wave band.
Therefore, various circuit design technique for solving the problems of the silicon semiconductor in millimeter-wave band have been researched.
A low noise/low power consumption voltage-controlled oscillator is one of the important components of millimeter-wave band wire/wireless communication system. A voltage-controlled oscillator widely used for a silicon integrated circuit includes an LC resonator and negative resistance cells that are constructed as a simple cross-coupled pair. A negative resistance generated by the cross-coupled pair compensates for a loss of the LC resonator, so that oscillation can be generated and sustained.
However, since the simple cross-coupled pair has a small MAOF and a large input capacitance, the simple cross-coupled pair cannot be easily applied to the millimeter-wave voltage-controlled oscillator.
The MAOF is defined as a frequency at which a negative resistance becomes zero when the negative resistance is increased from a negative region to a positive region. That is, the MAOF is a maximum frequency among frequencies at which the negative resistance occurs. As a result, the voltage-controlled oscillator having an oscillation frequency higher than the MAOF cannot be designed.
In addition, as the input capacitance of the cross-coupled pair is increased, a capacitance, coupling with LC resonator and determining a resonance frequency, is also increased. Therefore, the oscillation frequency is lowered.
Furthermore, since modeling accuracy of active and passive devices including inductor, varactor, and transistor becomes lowered in millimeter-wave band, a voltage-controlled oscillator designed and manufactured by using the simple cross-coupled pair may neither obtain a desired oscillation frequency nor oscillate.
In order to increase the MAOF and decrease the input capacitance of the simple cross-coupled pair, a capacitive-degeneration cross-coupled pair has been developed.
In the capacitive-degeneration cross-coupled pair structure, emitters of cross-coupled pair transistors are connected to each other through a capacitance, or the emitters of the cross-coupled pair transistors are connected to ground through a capacitance. As a result, it is possible to increase the MAOF and decrease the input capacitance of the cross-coupled pair.
Although the capacitive-degeneration cross-coupled pair voltage-controlled oscillator uses the cross-coupled pair structure, the MAOF or input capacitance cannot be satisfactorily improved in comparison with the simple cross-coupled pair.
FIGS. 1A and 1B are circuit diagrams illustrating a conventional simple cross-coupled voltage-controlled oscillator 100.
Referring to FIG. 1A, the conventional voltage-controlled oscillator 100 includes a resonating unit 110 and an oscillating unit 120.
The resonating unit 110 includes a supply voltage Vcc, first and second inductors Lr1 and Lr2 commonly connected to the supply voltage Vcc, and a varactor capacitance Cr and a parasitic resistance Rr which are connected in parallel to the first and second inductors Lr1 and Lr2.
The oscillating unit 120 includes first and second transistors Q1 and Q2 which are connected to respective ends of the parasitic resistance Rr and of which collectors and bases are cross-coupled to each other and a current source Is connected to emitters of the first and second transistors Q1 and Q2.
FIG. 1B is a circuit diagram illustrating a small-signal equivalent circuit of the simple cross-coupled oscillating unit 120 of FIG. 1A.
In FIG. 1B,




  
    β
    ⁡
    
      (
      ω
      )
    
  
  =
  
    -
    
      j
      ⁡
      
        (
        
          
            ω
            T
          
          ω
        
        )
      
    
  




denotes a high-frequency small-signal current gain, and gm, re, rb, and ib denote a transconductance, an emitter resistance, an intrinsic base resistance, and a base current of a transistor, respectively.

Input admittances Yin, that is, an input resistance Rin and an input capacitance Cin of the circuit of FIG. 1B can be represented by Equations 1 and 2, respectively.




  
    
      
        
          R
          
            i
            ⁢
            
              
            
            ⁢
            n
          
        
        =
        
          
            
              2
              ⁢
              
                
                  (
                  
                    
                      r
                      b
                    
                    +
                    
                      r
                      e
                    
                  
                  )
                
                2
              
            
            +
            
              2
              ⁢
              
                
                  (
                  
                    
                      ω
                      T
                    
                    ω
                  
                  )
                
                2
              
              ⁢
              
                
                  (
                  
                    
                      1
                      
                        g
                        m
                      
                    
                    +
                    
                      r
                      e
                    
                  
                  )
                
                2
              
            
          
          
            
              (
              
                
                  r
                  b
                
                +
                
                  r
                  e
                
              
              )
            
            -
            
              
                
                  (
                  
                    
                      ω
                      T
                    
                    ω
                  
                  )
                
                2
              
              ⁢
              
                (
                
                  
                    1
                    
                      g
                      m
                    
                  
                  +
                  
                    r
                    e
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          1
        
        ]
      
    
  








  
    
      
        
          C
          
            i
            ⁢
            
              
            
            ⁢
            n
          
        
        =
        
          
            
              (
              
                
                  ω
                  T
                
                
                  ω
                  2
                
              
              )
            
            ⁢
            
              (
              
                
                  1
                  
                    g
                    m
                  
                
                +
                
                  r
                  b
                
                +
                
                  2
                  ⁢
                  
                    r
                    e
                  
                
              
              )
            
          
          
            
              2
              ⁢
              
                
                  (
                  
                    
                      r
                      b
                    
                    +
                    
                      r
                      e
                    
                  
                  )
                
                2
              
            
            +
            
              2
              ⁢
              
                
                  (
                  
                    
                      ω
                      T
                    
                    ω
                  
                  )
                
                2
              
              ⁢
              
                
                  (
                  
                    
                      1
                      
                        g
                        m
                      
                    
                    +
                    
                      r
                      e
                    
                  
                  )
                
                2
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          2
        
        ]
      
    
  




Here,




  
    
      ω
      T
    
    =
    
      
        2
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          f
          T
        
      
      =
      
        
          g
          m
        
        
          
            C
            π
          
          +
          
            C
            μ
          
        
      
    
  
  ,




and fT, gm, rb, and re denote a maximum transition frequency, a transconductance, an intrinsic base resistance, and an emitter resistance of a transistor, respectively.

Since the MAOF ftrans is a frequency at which a negative resistance becomes zero when an input negative resistance is increased from a negative region to a positive region, the MAOF ftrans represented by Equation 3 can be calculated from Equation 1.




  
    
      
        
          f
          T
        
        ⁢
        
          
            
              
                r
                e
              
              +
              
                1
                
                  g
                  m
                
              
            
            
              
                r
                b
              
              +
              
                r
                e
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          3
        
        ]
      
    
  




Since the simple cross-coupled oscillating unit 120 has a simple structure and easily generates a differential signal, the simple cross-coupled oscillating unit 120 is widely used for an integrated circuit. However, as seen in Equation 3, the simple cross-coupled oscillating unit 120 has a problem in that the MAOF ftrans is limited due to the intrinsic base resistance rb of the transistor.
In addition, due to a base-emitter capacitance, a base-collector capacitance, and a base-substrate capacitance of each transistor, the voltage-controlled oscillator of FIG. 1 has such problems as a large input capacitance and a lower oscillation frequency.
In order to solve the above-mentioned problems, a new-type capacitive-degeneration cross-coupled voltage-controlled oscillator capable of increasing the MAOF ftrans and decreasing the input capacitance by using a degeneration capacitance has been proposed.
FIG. 2A is a circuit diagram illustrating a conventional capacitive-degeneration cross-coupled voltage-controlled oscillator.
Referring to FIG. 2A, the capacitive-degeneration cross-coupled voltage-controlled oscillator 200 includes a resonating unit 210 and an oscillating unit 220.
The resonating unit 210 includes a supply voltage Vcc, first and second inductors Lr1 and Lr2 commonly connected to the supply voltage Vcc, and a varactor capacitance Cr and respective ends of the parasitic resistance Rr and of which are connected in parallel to the first and second inductors Lr1 and Lr2.
The oscillating unit 220 includes first and second transistors Q1 and Q2 which are connected to respective ends of the parasitic resistance Rr and of which collectors and bases are cross-coupled to each other, a degeneration capacitance Cd connected between emitters of the first and second transistors Q1 and Q2, and a current source Is connected to emitters of the first and second transistors Q1 and Q2.
Unlike the simple cross-coupled voltage-controlled oscillator 100 of FIG. 1A, in the capacitive-degeneration cross-coupled voltage-controlled oscillator 200 of FIG. 2A, the degeneration capacitance Cd is connected between the emitters of the first and second transistors Q1 and Q2, so that a negative resistance of the oscillating unit 220 can be increased.
Accordingly, in the capacitive-degeneration cross-coupled voltage-controlled oscillator, since the negative resistance of the oscillating unit 220 can be increased, the increased negative resistance compensates for a loss of the resonating unit 210, so that oscillation can be generated and sustained.
In addition, due to the newly added component, that is, the degeneration capacitance Cd, in the oscillating unit 220, the first transistor Q1, the degeneration capacitance Cd, and the second transistor Q2 constitutes a positive feedback loop.
Therefore, the input capacitance Cin of the oscillating unit 220 can be intuitively represented by Equation 4.




  
    
      
        
          1
          
            
              1
              
                
                  C
                  
                    be
                    2
                  
                
                ⁢
                
                  
                
              
            
            +
            
              1
              
                2
                ⁢
                
                  C
                  d
                
              
            
          
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          1
          
            
              1
              
                
                  C
                  
                    be
                    1
                  
                
                ⁢
                
                  
                
              
            
            +
            
              1
              
                2
                ⁢
                
                  C
                  d
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          4
        
        ]
      
    
  




Here, Cbe1 denotes a base-emitter capacitance of the first transistor Q1, and Cbe2 denotes a base-emitter capacitance of the second transistor Q2.
That is, the input capacitance Cin of the oscillating unit 220 of FIG. 2 is inverse proportion to 1/(2Cd) due to the degeneration capacitance Cd.
More specifically, input admittances Yin, that is, an input resistance Rin and an input capacitance Cin can be exactly represented by Equations 5 and 6, respectively.




  
    
      
        
          R
          
            i
            ⁢
            
              
            
            ⁢
            n
          
        
        =
        
          
            
              
                
                  
                    
                      2
                      ⁡
                      
                        [
                        
                          
                            (
                            
                              
                                r
                                b
                              
                              +
                              
                                r
                                e
                              
                            
                            )
                          
                          -
                          
                            
                              (
                              
                                
                                  ω
                                  T
                                
                                ω
                              
                              )
                            
                            ⁢
                            
                              1
                              
                                2
                                ⁢
                                ω
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  C
                                  d
                                
                              
                            
                          
                        
                        ]
                      
                    
                    2
                  
                  +
                
              
            
            
              
                
                  
                    2
                    ⁡
                    
                      [
                      
                        
                          
                            (
                            
                              
                                ω
                                T
                              
                              ω
                            
                            )
                          
                          ⁢
                          
                            (
                            
                              
                                1
                                
                                  g
                                  m
                                
                              
                              +
                              r
                            
                            )
                          
                        
                        +
                        
                          1
                          
                            2
                            ⁢
                            ω
                            ⁢
                            
                              
                            
                            ⁢
                            
                              C
                              d
                            
                          
                        
                      
                      ]
                    
                  
                  2
                
              
            
          
          
            
              (
              
                
                  r
                  b
                
                +
                
                  r
                  e
                
              
              )
            
            -
            
              
                
                  (
                  
                    
                      ω
                      T
                    
                    ω
                  
                  )
                
                2
              
              ⁢
              
                (
                
                  
                    1
                    
                      g
                      m
                    
                  
                  +
                  
                    r
                    e
                  
                  +
                  
                    1
                    
                      
                        ω
                        T
                      
                      ⁢
                      
                        C
                        d
                      
                    
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          5
        
        ]
      
    
  








  
    
      
        
          C
          
            i
            ⁢
            
              
            
            ⁢
            n
          
        
        =
        
          
            
              (
              
                
                  ω
                  T
                
                
                  ω
                  2
                
              
              )
            
            ⁡
            
              [
              
                
                  (
                  
                    
                      r
                      b
                    
                    +
                    
                      2
                      ⁢
                      
                        r
                        e
                      
                    
                    +
                    
                      1
                      
                        g
                        m
                      
                    
                  
                  )
                
                +
                
                  1
                  
                    2
                    ⁢
                    
                      ω
                      T
                    
                    ⁢
                    
                      C
                      d
                    
                  
                
                -
                
                  
                    (
                    
                      
                        ω
                        T
                      
                      ω
                    
                    )
                  
                  ⁢
                  
                    1
                    
                      2
                      ⁢
                      ω
                      ⁢
                      
                        
                      
                      ⁢
                      
                        C
                        d
                      
                    
                  
                
              
              ]
            
          
          
            
              
                
                  
                    
                      2
                      ⁡
                      
                        [
                        
                          
                            (
                            
                              
                                r
                                b
                              
                              +
                              
                                r
                                e
                              
                            
                            )
                          
                          -
                          
                            
                              (
                              
                                
                                  ω
                                  T
                                
                                ω
                              
                              )
                            
                            ⁢
                            
                              1
                              
                                2
                                ⁢
                                ω
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  C
                                  d
                                
                              
                            
                          
                        
                        ]
                      
                    
                    2
                  
                  +
                
              
            
            
              
                
                  
                    2
                    ⁡
                    
                      [
                      
                        
                          1
                          
                            2
                            ⁢
                            ω
                            ⁢
                            
                              
                            
                            ⁢
                            
                              C
                              d
                            
                          
                        
                        +
                        
                          
                            (
                            
                              
                                ω
                                T
                              
                              ω
                            
                            )
                          
                          ⁢
                          
                            (
                            
                              
                                1
                                
                                  g
                                  m
                                
                              
                              +
                              
                                r
                                e
                              
                            
                            )
                          
                        
                      
                      ]
                    
                  
                  2
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          6
        
        ]
      
    
  




The MAOF ftrans of the capacitive-degeneration cross-coupled oscillating unit 220 represented by Equation 7 can be calculated from Equation 5. As seen in Equation 7, the MAOF ftrans is in proportion to a square root of 1/(Cd).




  
    
      
        
          f
          trans
        
        =
        
          
            f
            T
          
          ⁢
          
            
              
                
                  r
                  e
                
                +
                
                  1
                  
                    g
                    m
                  
                
                +
                
                  1
                  
                    
                      ω
                      T
                    
                    ⁢
                    
                      C
                      d
                    
                  
                
              
              
                (
                
                  
                    r
                    b
                  
                  +
                  
                    r
                    e
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
  




Here,




  
    
      ω
      T
    
    =
    
      
        2
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          f
          T
        
      
      =
      
        
          g
          m
        
        
          
            C
            π
          
          +
          
            C
            μ
          
        
      
    
  
  ,




and fT, gm, rb, and re denote a maximum transition frequency, a transconductance, an intrinsic base resistance, and an emitter resistance of a transistor.

However, the capacitive-degeneration voltage-controlled oscillator 200 has a problem in that the negative resistance disappears when the degeneration capacitance Cd is too small or 0.
In addition, since the capacitive-degeneration voltage-controlled oscillator 200 can adjust the MAOF ftrans or the input capacitance Cin by using only the degeneration capacitance Cd, a satisfactory performance cannot be obtained in comparison with a simple cross-coupled pair voltage-controlled oscillator.
SUMMARY OF THE INVENTION
The present invention provides a voltage-controlled oscillator capable of more effectively increasing a MAOF and decreasing an input capacitance.
The present invention also provides a voltage-controlled oscillator capable of stably operating with overcoming influence of a parasitic resistance and a parasitic capacitance at terahertz band as well as millimeter-wave band.
According to an aspect of the present invention, there is provided a voltage-controlled oscillator comprising: a main cross-coupled oscillating unit including an oscillation transistor pair cross-coupled to first and second output nodes of a resonating unit to perform an oscillation operation; and an auxiliary cross-coupled oscillating unit including a positive-feedback transistor pair cross-coupled to the first and second output nodes and the oscillation transistor pair and a degeneration capacitance connected between emitters of the positive-feedback transistor pair so as to increase a negative resistance of the main cross-coupled oscillating unit.
In the above aspect of the present invention, the main cross-coupled oscillating unit may comprises: first and second transistors of which bases are connected to the respective first and second output nodes of the resonating unit and of which collectors and bases are cross-coupled to each other; and a second current source connected to emitters of the first and second transistors.
In addition, the auxiliary cross-coupled oscillating unit may comprises: a third transistor having a collector connected to the base of the first transistor and a base connected to the emitter of the second transistor; a fourth transistor having a collector connected to the base of the second transistor and a base connected to the emitter of the first transistor; a degeneration capacitance connected between emitters of the third and fourth transistors; and a first current source connected to emitters of the third and fourth transistors. In addition, the resonating unit may comprises: first and second inductors commonly connected to a supply voltage; and first and second NMOS varactors of which sources and drains are commonly connected to a tuning voltage and of which gates are connected to the respective first and second inductors.
In addition, the main cross-coupled oscillating unit may comprises: first and second coupling capacitances connected to the respective first and second output nodes; a first transistor having a base connected to the second output node of the resonating unit and a collector connected to a supply voltage; a second transistor having a base connected to the first output node of the resonating unit and a collector connected to the supply voltage; and a second current source connected to emitters of the first and second transistors.
In addition, the auxiliary cross-coupled oscillating unit may comprise: a third transistor having a collector commonly connected to the base of the first transistor and the first output node and a base connected to the emitter of the second transistor; a fourth transistor having a collector commonly connected to the base of the second transistor and the second output node and a base connected to the emitter of the first transistor; a degeneration capacitance connected between emitters of the third and fourth transistors; and a first current source connected to emitters of the third and fourth transistors. In addition, the resonating unit may comprise: a base bias resistance connected to a base voltage; a center-tapped inductor connected to the base bias resistance; and a varactor capacitance connected in parallel to the center-tapped inductor.
According to another aspect of the present invention, there is provided a voltage-controlled oscillator comprising: a main cross-coupled oscillating unit including an oscillation transistor pair cross-coupled to first and second output nodes of a resonating unit to perform an oscillation operation; and an auxiliary cross-coupled oscillating unit including a positive-feedback transistor pair cross-coupled to the first and second output nodes and the transistor pair of the main cross-coupled oscillating unit so as to increase a negative resistance of the main cross-coupled oscillating unit.
In the above aspect of the present invention, the main cross-coupled oscillating unit may comprise: first and second transistors of which bases are connected to the respective first and second output nodes, and of which collectors and bases are cross-coupled to each other; and a second current source connected to emitters of the first and second transistors.
In addition, the auxiliary cross-coupled oscillating unit may comprise: a third transistor having a collector connected to the base of the first transistor and a base connected to the emitter of the second transistor; a fourth transistor having a collector connected to the base of the second transistor and a base connected to the emitter of the first transistor; and a first current source commonly connected to emitters of the third and fourth transistors. In addition, the auxiliary cross-coupled oscillating unit may comprise: a third transistor having a collector connected to the base of the first transistor and a base connected to the emitter of the second transistor; a fourth transistor having a collector connected to the base of the second transistor and a base connected to the emitter of the first transistor; and first current sources connected to the emitters of the third and fourth transistors, respectively.



BRIEF DESCRIPTION OF THE DRAWINGS
The above and other features and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings in which:
FIG. 1A is a circuit diagram illustrating a conventional simple cross-coupled voltage-controlled oscillator;
FIG. 1B is a circuit diagram illustrating a small-signal equivalent circuit of a simple cross-coupled oscillating unit of FIG. 1A;
FIG. 2A is a circuit diagram illustrating a conventional capacitive-degeneration cross-coupled voltage-controlled oscillator;
FIG. 2B is a circuit diagram illustrating a capacitive-degeneration cross-coupled oscillating unit of FIG. 2A;
FIG. 3A is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator according to a first embodiment of the present invention;
FIG. 3B is a circuit diagram illustrating another expression of the capacitive-degeneration double cross-coupled oscillating unit of FIG. 3A;
FIG. 4A is a circuit diagram illustrating a small-signal equivalent circuit of a main cross-coupled oscillating unit of FIG. 3A;
FIG. 4B is a circuit diagram illustrating a small-signal equivalent circuit of an auxiliary cross-coupled oscillating unit of FIG. 3A;
FIG. 5A is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator according to a second embodiment of the present invention;
FIG. 5B is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator according to a third embodiment of the present invention;
FIG. 6 is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator according to a fourth embodiment of the present invention;
FIGS. 7A and 7B are graphs for explaining operational performance of the capacitive-degeneration double cross-coupled voltage-controlled oscillator according to the fourth embodiment of the present invention;
FIG. 8 is a graph illustrating a simulation result of a change in MAOF of a double cross-coupled oscillating unit when a current of a first current source of the auxiliary cross-coupled oscillating unit according to the first embodiment of the present invention is changed from 0 A to 1 mA;
FIG. 9 is a view illustrating an implementation example of the capacitive-degeneration double cross-coupled voltage-controlled oscillator according to the first embodiment of the present invention; and
FIG. 10 is a graph illustrating a phase noise characteristic of the capacitive-degeneration double cross-coupled voltage-controlled oscillator of FIG. 9.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. For clarifying the present invention, detailed description of well-known functions and constructions will be omitted.
In the accompanying drawing, elements having similar functions and operations are denoted by the same reference numerals.
FIG. 3A is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator 300 according to a first embodiment of the present invention.
As shown in FIG. 3A, the capacitive-degeneration double cross-coupled voltage-controlled oscillator 300 includes a resonating unit 310, a main cross-coupled oscillating unit 321, and an auxiliary cross-coupled oscillating unit 322.
The resonating unit 310 determines an oscillation frequency and filters noises. The main cross-coupled oscillating unit 321 performs an oscillation operation including an oscillation transistor pair Q1 and Q2 cross-coupled to first and second output nodes n1 and n2 of the resonating unit 310. And the auxiliary cross-coupled oscillating unit 322 increases a negative resistance of the main cross-coupled oscillating unit 321 including a positive-feedback transistor pair Q3 and Q4 cross-coupled to the transistor pair Q1 and Q2 of the main cross-coupled oscillating unit 321 and the first and second output nodes n1 and n2 of the resonating unit 310 and a degeneration capacitance Cd connected between emitters of the positive-feedback transistor pair Q3 and Q4 to
Here, the main cross-coupled oscillating unit 321 and the auxiliary cross-coupled oscillating unit 322 operate as one oscillating unit 320.
More specifically, the resonating unit 310 includes a supply voltage Vcc, first and second inductors L1 and L2 commonly connected to the supply voltage Vcc, and two identical first and second NMOS varactors NMV1 and NMV2 of which sources and drains are commonly connected to a tuning voltage Vtu and of which gates are connected to the first and second inductors L1 and L2, respectively.
The main cross-coupled oscillating unit 321 includes first and second transistors Q1 and Q2 of which bases are connected to the respective gates of the first and second NMOS varactors NMV1 and NMV2, that is, the respective first and second output nodes n1 and n2 of the resonating unit 310 and of which collectors and bases are cross-coupled to each other and a second current source Is2 connected to emitters of the first and second transistors Q1 and Q2.
The auxiliary cross-coupled oscillating unit 322 includes a third transistor Q3 having a collector connected to the base of the first transistor Q1 and a base connected to the emitter of the second transistor Q2, a fourth transistor Q4 having a collector connected to the base of the second transistor Q2 and a base connected to the emitter of the first transistor Q1, a degeneration capacitance Cd connected between emitters of the third and fourth transistors Q3 and Q4, and a first current source Is1 connected to emitters of the third and fourth transistors Q3 and Q4.
The oscillating unit 320 of FIG. 3A can be illustrated by an equivalent circuit of FIG. 3B.
Referring FIG. 3B, the main cross-coupled oscillating unit 321 includes first and second transistors Q1 and Q2 of which collectors and bases are cross-coupled to each other, a degeneration capacitance Ct connected between emitters of the first and second transistors Q1 and Q2, and a second current source Is2 connected the emitters of the first and second transistors Q1 and Q2.
The degeneration capacitance (hereinafter, referred to as main degeneration capacitance) Ct of the main cross-coupled oscillating unit 321 is constructed with a base-emitter capacitance Cbe3 connected in series to the emitters of the first and second transistors Q1 and Q2, a degeneration capacitance (hereinafter, referred to as an auxiliary degeneration capacitance) Cd connected between the emitters of the third and fourth transistors Q3 and Q4, and a base-emitter capacitance Cbe4 of the fourth transistor Q4.
Therefore, the main degeneration capacitance Ct can be represented by Equation 8.




  
    
      
        
          
            C
            π
          
          ⁢
          
            C
            d
          
        
        
          
            C
            π
          
          +
          
            2
            ⁢
            
              C
              d
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
  




Here, Cπ=Cbe3=Cbe4.
The auxiliary cross-coupled oscillating unit 322 includes third and fourth transistors Q3 and Q4 of which collectors and bases are cross-coupled to each other via a base-emitter capacitance Cbe1 of the first transistor Q1 and a base-emitter capacitance Cbe2 of the second transistor Q2, and an auxiliary degeneration capacitance Cd connected between emitters of the third and fourth transistors Q3 and Q4, and a first current source Is1 connected to emitters of the third and fourth transistors Q3 and Q4.
In this manner, according to the present invention, the oscillating unit 320 of the capacitive-degeneration double cross-coupled voltage-controlled oscillator 300 has double cross-coupled pairs of transistors.
Therefore, in the oscillating unit 320, the first transistor Q1, the fourth transistor Q4, the auxiliary degeneration capacitance Cd, the third transistor Q3, and the second transistor Q2 constitute a positive feedback loop.
As a result, due to the third and fourth transistors Q3 and Q4 and the auxiliary degeneration capacitance Cd of the auxiliary cross-coupled oscillating unit 322, the negative resistance of the main cross-coupled oscillating unit 321 can be further increased, and the input capacitance Cin of the oscillating unit 320 can be decreased.
The input capacitance Cin of the oscillating unit 320 can be simply represented by Equation 9.




  
    
      
        
          1
          
            
              1
              
                C
                
                  be
                  1
                
              
            
            +
            
              1
              
                C
                
                  be
                  4
                
              
            
            +
            
              1
              
                2
                ⁢
                
                  C
                  d
                
              
            
          
        
        ⁢
        
          
        
        ⁢
        or
        ⁢
        
          
        
        ⁢
        
          1
          
            
              1
              
                C
                
                  be
                  2
                
              
            
            +
            
              1
              
                C
                
                  be
                  3
                
              
            
            +
            
              1
              
                2
                ⁢
                
                  C
                  d
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          9
        
        ]
      
    
  




That is, the input capacitance Cin of the oscillating unit 320 is in inverse proportion to




  
    1
    
      C
      
        be
        2
      
    
  
  +
  
    1
    
      C
      
        be
        3
      
    
  
  +
  
    
      1
      
        2
        ⁢
        
          C
          d
        
      
    
    .
  




As a result, the capacitive-degeneration double cross-coupled voltage-controlled oscillator 300 according to the present invention can increase the negative resistance up to a high frequency band and decrease the input capacitance Cin.
Therefore, in given power consumption, the negative resistance can be obtained in a higher frequency band. In addition, since the input capacitance Cin is lowered, a frequency adjustable range can be widened, or signal amplitude can be increased. Accordingly, phase noise can be reduced.
More specifically, the input resistance Rin and the input capacitance Cin of the double cross-coupled pair oscillating unit 320 can be calculated by using a small-signal equivalent circuit of the main cross-coupled oscillating unit 321 of FIG. 4A and a small-signal equivalent circuit of the auxiliary cross-coupled oscillating unit 322 of FIG. 4B.
The input admittance Yin of the double cross-coupled pair oscillating unit 320 can be calculated by using the input admittance Yin1 of main cross-coupled oscillating unit 321 and the input admittance Yin2 of the auxiliary cross-coupled oscillating unit 322. As a result, the input admittance Yin, that is input resistance Rin and the input capacitance Cin of the double cross-coupled pair oscillating unit 320 can be represented by Equations 10 and 11, respectively.




  
    
      
        
          R
          in
        
        =
        
          1
          
            
              
                
                  
                    
                      [
                      
                        
                          (
                          
                            
                              r
                              b
                            
                            +
                            
                              r
                              e
                            
                          
                          )
                        
                        -
                        
                          
                            
                              (
                              
                                
                                  ω
                                  T
                                
                                ω
                              
                              )
                            
                            2
                          
                          ⁢
                          
                            (
                            
                              
                                1
                                
                                  g
                                  m
                                
                              
                              +
                              
                                r
                                e
                              
                              +
                              
                                1
                                
                                  
                                    ω
                                    T
                                  
                                  ⁢
                                  
                                    C
                                    T
                                  
                                
                              
                            
                            )
                          
                        
                      
                      ]
                    
                    
                      
                        
                          
                            
                              
                                2
                                ⁡
                                
                                  [
                                  
                                    
                                      (
                                      
                                        
                                          r
                                          b
                                        
                                        +
                                        
                                          r
                                          e
                                        
                                      
                                      )
                                    
                                    -
                                    
                                      
                                        (
                                        
                                          
                                            ω
                                            T
                                          
                                          ω
                                        
                                        )
                                      
                                      ⁢
                                      
                                        1
                                        
                                          2
                                          ⁢
                                          ω
                                          ⁢
                                          
                                            
                                          
                                          ⁢
                                          
                                            C
                                            T
                                          
                                        
                                      
                                    
                                  
                                  ]
                                
                              
                              2
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              2
                              ⁡
                              
                                [
                                
                                  
                                    1
                                    
                                      2
                                      ⁢
                                      ω
                                      ⁢
                                      
                                        
                                      
                                      ⁢
                                      
                                        C
                                        T
                                      
                                    
                                  
                                  +
                                  
                                    
                                      (
                                      
                                        
                                          ω
                                          T
                                        
                                        ω
                                      
                                      )
                                    
                                    ⁢
                                    
                                      (
                                      
                                        
                                          1
                                          
                                            g
                                            m
                                          
                                        
                                        +
                                        
                                          r
                                          e
                                        
                                      
                                      )
                                    
                                  
                                
                                ]
                              
                            
                            2
                          
                        
                      
                    
                  
                  +
                
              
            
            
              
                
                  
                    [
                    
                      
                        (
                        
                          
                            r
                            b
                          
                          +
                          
                            r
                            e
                          
                        
                        )
                      
                      -
                      
                        
                          
                            (
                            
                              
                                ω
                                T
                              
                              ω
                            
                            )
                          
                          2
                        
                        ⁢
                        
                          (
                          
                            
                              1
                              
                                g
                                m
                              
                            
                            +
                            
                              r
                              e
                            
                            +
                            
                              1
                              
                                
                                  ω
                                  T
                                
                                ⁢
                                
                                  C
                                  d
                                
                              
                            
                            +
                            
                              1
                              
                                
                                  ω
                                  T
                                
                                ⁢
                                
                                  C
                                  π
                                
                              
                            
                          
                          )
                        
                      
                    
                    ]
                  
                  
                    
                      
                        
                          
                            
                              2
                              ⁡
                              
                                [
                                
                                  
                                    (
                                    
                                      
                                        r
                                        b
                                      
                                      +
                                      
                                        r
                                        e
                                      
                                    
                                    )
                                  
                                  -
                                  
                                    
                                      (
                                      
                                        
                                          ω
                                          T
                                        
                                        ω
                                      
                                      )
                                    
                                    ⁢
                                    
                                      1
                                      
                                        2
                                        ⁢
                                        ω
                                        ⁢
                                        
                                          
                                        
                                        ⁢
                                        
                                          C
                                          d
                                        
                                      
                                    
                                  
                                
                                ]
                              
                            
                            2
                          
                          +
                        
                      
                    
                    
                      
                        
                          
                            2
                            ⁡
                            
                              [
                              
                                
                                  1
                                  
                                    ω
                                    ⁢
                                    
                                      
                                    
                                    ⁢
                                    
                                      C
                                      π
                                    
                                  
                                
                                +
                                
                                  1
                                  
                                    2
                                    ⁢
                                    ω
                                    ⁢
                                    
                                      
                                    
                                    ⁢
                                    
                                      C
                                      d
                                    
                                  
                                
                                +
                                
                                  
                                    (
                                    
                                      
                                        ω
                                        T
                                      
                                      ω
                                    
                                    )
                                  
                                  ⁢
                                  
                                    (
                                    
                                      
                                        1
                                        
                                          g
                                          m
                                        
                                      
                                      +
                                      
                                        r
                                        e
                                      
                                    
                                    )
                                  
                                
                              
                              ]
                            
                          
                          2
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          10
        
        ]
      
    
  








  
    
      
        
          C
          
            i
            ⁢
            
              
            
            ⁢
            n
          
        
        =
        
          
            
              
                (
                
                  
                    ω
                    T
                  
                  
                    ω
                    2
                  
                
                )
              
              ⁡
              
                [
                
                  
                    (
                    
                      
                        r
                        b
                      
                      +
                      
                        2
                        ⁢
                        
                          r
                          e
                        
                      
                      +
                      
                        1
                        
                          g
                          m
                        
                      
                    
                    )
                  
                  +
                  
                    1
                    
                      2
                      ⁢
                      
                        ω
                        T
                      
                      ⁢
                      
                        C
                        T
                      
                    
                  
                  -
                  
                    
                      (
                      
                        
                          ω
                          T
                        
                        ω
                      
                      )
                    
                    ⁢
                    
                      1
                      
                        2
                        ⁢
                        ω
                        ⁢
                        
                          
                        
                        ⁢
                        
                          C
                          T
                        
                      
                    
                  
                
                ]
              
            
            
              
                
                  
                    
                      
                        2
                        ⁡
                        
                          [
                          
                            
                              (
                              
                                
                                  r
                                  b
                                
                                +
                                
                                  r
                                  s
                                
                              
                              )
                            
                            -
                            
                              
                                (
                                
                                  
                                    ω
                                    T
                                  
                                  ω
                                
                                )
                              
                              ⁢
                              
                                1
                                
                                  2
                                  ⁢
                                  ω
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  
                                    C
                                    T
                                  
                                
                              
                            
                          
                          ]
                        
                      
                      2
                    
                    +
                  
                
              
              
                
                  
                    
                      2
                      ⁡
                      
                        [
                        
                          
                            1
                            
                              2
                              ⁢
                              ω
                              ⁢
                              
                                
                              
                              ⁢
                              
                                C
                                T
                              
                            
                          
                          +
                          
                            
                              (
                              
                                
                                  ω
                                  T
                                
                                ω
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                
                                  1
                                  
                                    g
                                    m
                                  
                                
                                +
                                
                                  r
                                  e
                                
                              
                              )
                            
                          
                        
                        ]
                      
                    
                    2
                  
                
              
            
          
          +
          
            
              
                (
                
                  
                    ω
                    T
                  
                  ω
                
                )
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          (
                          
                            
                              r
                              b
                            
                            +
                            
                              2
                              ⁢
                              
                                r
                                e
                              
                            
                            +
                            
                              1
                              
                                g
                                m
                              
                            
                          
                          )
                        
                        +
                      
                    
                  
                  
                    
                      
                        
                          1
                          
                            2
                            ⁢
                            
                              ω
                              T
                            
                            ⁢
                            
                              C
                              d
                            
                          
                        
                        +
                        
                          1
                          
                            
                              ω
                              T
                            
                            ⁢
                            
                              C
                              π
                            
                          
                        
                        -
                        
                          
                            (
                            
                              
                                ω
                                T
                              
                              ω
                            
                            )
                          
                          ⁢
                          
                            1
                            
                              2
                              ⁢
                              ω
                              ⁢
                              
                                
                              
                              ⁢
                              
                                C
                                d
                              
                            
                          
                        
                      
                    
                  
                
                ]
              
            
            
              
                
                  
                    
                      
                        2
                        ⁡
                        
                          [
                          
                            
                              (
                              
                                
                                  r
                                  b
                                
                                +
                                
                                  r
                                  e
                                
                              
                              )
                            
                            -
                            
                              
                                (
                                
                                  
                                    ω
                                    T
                                  
                                  ω
                                
                                )
                              
                              ⁢
                              
                                1
                                
                                  2
                                  ⁢
                                  ω
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  
                                    C
                                    d
                                  
                                
                              
                            
                          
                          ]
                        
                      
                      2
                    
                    -
                  
                
              
              
                
                  
                    
                      2
                      ⁡
                      
                        [
                        
                          
                            1
                            
                              ω
                              ⁢
                              
                                
                              
                              ⁢
                              
                                C
                                π
                              
                            
                          
                          +
                          
                            1
                            
                              2
                              ⁢
                              ω
                              ⁢
                              
                                
                              
                              ⁢
                              
                                C
                                d
                              
                            
                          
                          +
                          
                            
                              (
                              
                                
                                  ω
                                  T
                                
                                ω
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                
                                  1
                                  
                                    g
                                    m
                                  
                                
                                +
                                
                                  r
                                  e
                                
                              
                              )
                            
                          
                        
                        ]
                      
                    
                    2
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          11
        
        ]
      
    
  




The MAOF ftrans of the capacitive-degeneration double cross-coupled voltage-controlled oscillator 300 according to the present invention can be approximately derived from Equation 10, as represented by Equation 12.




  
    
      
        
          f
          trans
        
        ⁢
        
          
            =
            .
          
          .
        
        ⁢
        
          
            f
            T
          
          ⁢
          
            
              
                
                  r
                  e
                
                +
                
                  1
                  
                    g
                    m
                  
                
                +
                
                  1
                  
                    
                      ω
                      T
                    
                    ⁢
                    
                      C
                      t
                    
                  
                
              
              
                (
                
                  
                    r
                    b
                  
                  +
                  
                    r
                    e
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          12
        
        ]
      
    
  




Here,




  
    
      ω
      T
    
    =
    
      
        2
        ⁢
        π
        ⁢
        
          
        
        ⁢
        
          f
          T
        
      
      =
      
        
          g
          m
        
        
          
            C
            π
          
          +
          
            C
            μ
          
        
      
    
  
  ,




and fT, gm, rb, and re denote a maximum transition frequency, a transconductance, an intrinsic base resistance, and an emitter resistance of a transistor.

Therefore, according to the present invention, although the MAOF ftrans is limited due to the intrinsic base resistance rb of the transistor, the MAOF ftrans is increased in proportion to a square root of 1/(Ct).
As a result, as the main degeneration capacitance Ct is decreased, the MAOF ftrans is increased.
However, the MAOF ftrans is not almost changed according to a change in the auxiliary degeneration capacitance Cd included in the main degeneration capacitance Ct.
Since the auxiliary degeneration capacitance Cd is serial connection to the base-emitter capacitances Cbe3 and Cbe4 of the third and forth transistor Q3, Q4, the auxiliary degeneration capacitance Cd does not almost influence the main degeneration capacitance Ct.
However, if the auxiliary degeneration capacitance Cd is smaller than the base-emitter capacitance Cbe of the transistor, the auxiliary degeneration capacitance Cd can influence the main degeneration capacitance Ct.
FIG. 5A and FIG. 5B are circuit diagrams illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator according to a second and third embodiment of the present invention.
As shown in FIG. 5A, the auxiliary degeneration capacitance Cd is not provided, and the emitters of the third and fourth transistors Q3 and Q4 are short-circuited.
However, emitters of the first and second transistors Q1 and Q2 of the main cross-coupled oscillating unit 321′ can be degenerated due to serial connection of each of the base-emitter capacitances of the third and fourth transistors Q3 and Q4.
Similarity, as shown in FIG. 5B, the auxiliary degeneration capacitance Cd is not provided, and emitters of the third and fourth transistors Q3 and Q4 of the auxiliary cross-coupled oscillating unit 322′′ is open-circuited as shown in FIG. 5B.
However, emitters of the first and second transistors Q1 and Q2 of the main cross-coupled oscillating unit 321′′ can be degenerated due to serial connection of each of the base-emitter capacitances of the third and fourth transistors Q3 and Q4 and the input capacitance of the current source Is1. According to a simulation result, the MAOF has the highest value.
Therefore, even in a case where the auxiliary degeneration capacitance Cd becomes small or zero, the voltage-controlled oscillator can be stably operated.
In this manner, according to the capacitive-degeneration double cross-coupled voltage-controlled oscillator of the present invention, it is possible to increase the MAOF ftrans and decrease the input capacitance. In addition, the voltage-controlled oscillator can be stably operated even in a case where the degeneration capacitance Cd becomes small or zero.
If needed, the structure of the capacitive-degeneration double cross-coupled voltage-controlled oscillator may be modified so as to directly obtain an output of the oscillator through the first and second transistors Q1 and Q2 of the main cross-coupled oscillating unit.
FIG. 6 is a circuit diagram illustrating a capacitive-degeneration double cross-coupled voltage-controlled oscillator 400 according to a fourth embodiment of the present invention.
Referring to FIG. 6, similarly to the voltage-controlled oscillator 300 of FIG. 5, the voltage-controlled oscillator 400 includes a resonating unit 410, a main cross-coupled oscillating unit 421, and an auxiliary cross-coupled oscillating unit 422. However, detailed constructions of those are different from the voltage-controlled oscillator 300.
More specifically, the resonating unit 410 includes a base bias resistance Rb connected to a base voltage Vb, a center-tapped inductor Lr connected to the base bias resistance Rb, and a varactor capacitance Cv connected parallel to the center-tapped inductor Lr.
The main cross-coupled oscillating unit 421 includes two coupling capacitances Cc1 and Cc2 connected to respective ends of the varactor capacitance Cv (that is, the respective first and second output nodes n1 and n2 of the resonating unit 410), a first transistor Q1 having abase connected to the second output node n2 and a collector connected through a first load impedance ZL1 to a supply voltage Vcc, a second transistor Q2 having a base connected to the first output node n1 and a collector connected through a second load impedance ZL2 to the supply voltage Vcc, and a second current source Is2 connected to emitters of the first and second transistors Q1 and Q2. The auxiliary cross-coupled oscillating unit 422 includes a third transistor Q3 having a collector commonly connected to the base of the first transistor Q1 and the second output node n2 and a base connected to the emitter of the second transistor Q2, a fourth transistor Q4 having a collector commonly connected to the base of the second transistor Q2 and the first output node n1 and a base connected to the emitter of the first transistor Q1, a degeneration capacitance Cd connected between emitters of the third and fourth transistors Q3 and Q4, and a first current source Is1 connected to emitters of the third and fourth transistors Q3 and Q4.
In this manner, the oscillating unit 420 of FIG. 6 comprises the main cross-coupled oscillating unit 421 and the auxiliary cross-coupled oscillating unit 422, and has double cross-coupled pairs of transistors.
Therefore, in the oscillating unit 420, the first transistor Q1, the third transistor Q3, the degeneration capacitance Cd, the fourth transistor Q4, and the second transistor Q2 constitute a positive feedback loop.
As a result, due to the third and fourth transistors Q3 and Q4 of the auxiliary cross-coupled oscillating unit 422 and the degeneration capacitance Cd connected between the emitters of the third and fourth transistors Q3 and Q4, the negative resistance of the main cross-coupled oscillating unit 421 can be further increased, and the input capacitance Cin of the oscillating unit 420 can be decreased.
In the main cross-coupled oscillating unit 421 of the oscillating unit 420, the bases and the collectors of the first and second transistors Q1 and Q2 are electrically separated from each other by the coupling capacitances Cc1 and Cc2, respectively, so that output signals can be directly extracted from each of the collectors of the first and second transistors Q1 and Q2.
FIGS. 7A and 7B are graphs for explaining operational performance of the capacitive-degeneration double cross-coupled voltage-controlled oscillator according to the fourth embodiment of the present invention. FIG. 7A is a graph of modeling of Equations 1, 5, and 10 of the input resistances Rin of the input admittance Yin (=1/Rin+jωCin) of the aforementioned oscillating units. FIG. 7B is a graph of modeling of Equations 2, 6, and 11 of the input capacitances Cin thereof.
Referring to FIG. 7A, it can be seen that the MAOF of the capacitive-degeneration double cross-coupled voltage-controlled oscillator according to the present invention is 197 GHz, but the maximum attainable oscillation frequencies of the simple cross-coupled voltage-controlled oscillator and the capacitive-degeneration voltage-controlled oscillator are 90 GHz and 110 GHz, respectively, in the same conditions and parameters of equivalent circuits.
That is, it can be understood from Equations 1, 5, and 10 that the capacitive-degeneration double cross-coupled voltage-controlled oscillator can provide the MAOF that is almost twice the maximum attainable oscillation frequencies of the conventional voltage-controlled oscillators.
Referring to FIG. 7B, the capacitive-degeneration double cross-coupled voltage-controlled oscillator has the lowest input capacitance in a range of 34 GHz to 135 GHz, that is, in millimeter-wave band.
As described above, this is because the input capacitance of the oscillating unit 320 is decreased due to the serial connection of the base-emitter capacitance Cbe2 of the second transistor Q2, the base-emitter capacitance Cbe3 of the third transistor Q3, and the degeneration capacitance Cd or due to the serial connection of the base-emitter capacitance Cbe1 of the first transistor Q1, the base-emitter capacitance Cbe4 of the fourth transistor Q4, and the degeneration capacitance Cd.
FIG. 8 is a graph illustrating a simulation result of a change in MAOF of a double cross-coupled oscillating unit when a current of a first current source of the auxiliary cross-coupled oscillating unit according to the first embodiment of the present invention is changed from 0 A to 1 mA.
Referring to FIG. 8, it can be seen that the MAOF ftrans has the highest value when the first current source Is1 has a value of 0. That is, the auxiliary cross-coupled oscillating unit 322 according to the present invention can increase the MAOF ftrans without power consumption.
According to the present invention, since the positive feedback loop including the auxiliary cross-coupled oscillating unit 322 additionally provides the negative resistance to the main cross-coupled oscillating unit 321 without additional power consumption, the MAOF can be increased, and the input capacitance can be decreased, so that the phase noise can be reduced.
FIG. 9 is a view illustrating an implementation example of the capacitive-degeneration double cross-coupled voltage-controlled oscillator of FIG. 3A.
Referring to FIG. 9, it can be seen that the capacitive-degeneration double cross-coupled voltage-controlled oscillator according to the present invention can be implemented with a size of 0.5×0.5 mm2 by using a 0.25 μm SiGe BiCMOS process.
The implemented capacitive-degeneration double cross-coupled voltage-controlled oscillator consumes 6 mA at 2.5V and generates an oscillation frequency of 60 GHz.
In addition, referring to FIG. 10, it can be seen that the phase noise of −91 dBc/Hz can be obtained at an offset frequency of 1 MHz.
According to the present invention, a capacitive-degeneration double cross-coupled voltage-controlled oscillator can more effectively increase a MAOF and decrease an input capacitance in millimeter-wave band. In addition, the capacitive-degeneration double cross-coupled voltage-controlled oscillator can be stably operated with overcoming influence of a parasitic resistance and a parasitic capacitance in a terahertz band as well as millimeter-wave band.
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the following claims.

## Claims

1. A voltage-controlled oscillator comprising:
a main cross-coupled oscillating unit including first and second transistors cross-coupled to first and second output nodes of a resonating unit to perform an oscillation operation; and
an auxiliary cross-coupled oscillating unit including third and fourth transistors cross-coupled to the first and second output nodes and the first and second transistors and a degeneration capacitor connected between emitters of the first and second transistors so as to form a positive-feedback loop capable of increasing a negative resistance and decreasing an input capacitance by the positive-feedback loop,
wherein the positive-feedback loop is contributed to by the first transistor, the fourth transistor, the degeneration capacitor, the third transistor and the second transistor,
wherein the auxiliary cross-coupled oscillating unit comprises:
the third transistor having a collector connected to the base of the first transistor and a base connected to the emitter of the second transistor;
the fourth transistor having a collector connected to the base of the second transistor and a base connected to the emitter of the first transistor;
the degeneration capacitor connected between emitters of the third and fourth transistors; and
a first current source connected to emitters of the third and fourth transistors.

2. The voltage-controlled oscillator of claim 1, wherein the main cross-coupled oscillating unit comprises:
the first and second transistors of which bases are connected to the respective first and second output nodes of the resonating unit and of which collectors and bases are cross-coupled to each other; and
a second current source connected to emitters of the first and second transistors.

3. The voltage-controlled oscillator of claim 2, wherein the resonating unit comprises:
first and second inductors commonly connected to a supply voltage; and
first and second NMOS varactors of which sources and drains are commonly connected to a tuning voltage and of which gates are connected to the respective first and second inductors.

4. The voltage-controlled oscillator of claim 1, wherein the main cross-coupled oscillating unit comprises:
first and second coupling capacitances connected to the respective first and second output nodes;
the first transistor having a base connected to the second output node of the resonating unit and a collector connected to a supply voltage;
the second transistor having a base connected to the first output node of the resonating unit and a collector connected to the supply voltage; and
a second current source connected to emitters of the first and second transistors.

5. The voltage-controlled oscillator of claim 4, further comprising first and second load impedances connected between the supply voltage and the collector of the first transistor and between the supply voltage and the collector of the second transistor, respectively.

6. The voltage-controlled oscillator of claim 4, wherein the resonating unit comprises:
a bias resistance connected to a bias voltage;
a center-tapped inductor connected to the bias resistance; and
a varactor capacitance connected in parallel to the center-tapped inductor.

7. A voltage-controlled oscillator comprising:
a main cross-coupled oscillating unit including first and second transistors cross-coupled to first and second output nodes of a resonating unit to perform an oscillation operation; and
an auxiliary cross-coupled oscillating unit including third and fourth transistors cross-coupled to the first and second output nodes and the first and second transistors and a degeneration capacitor connected between emitters of the first and second transistors so as to form a positive-feedback loop capable of increasing a negative resistance and decreasing an input capacitance by the positive-feedback loop,
wherein the positive-feedback loop is contributed to by the first transistor, the fourth transistor, the degeneration capacitor, the third transistor and the second transistor, and
wherein the auxiliary cross-coupled oscillating unit comprises:
the third transistor having a collector commonly connected to the base of the first transistor and the second output node and a base connected to the emitter of the second transistor;
the fourth transistor having a collector commonly connected to the base of the second transistor and the first output node and a base connected to the emitter of the first transistor;
a first current source connected to emitters of the third and fourth transistors; and
wherein the degeneration capacitor is connected between emitters of the third and fourth transistors.

8. A voltage-controlled oscillator comprising:
a resonating unit having first and second output nodes;
a main cross-coupled oscillating unit configured to cooperate with the resonating unit and perform an oscillation operation, the main cross-coupled oscillating unit including:
a first transistor having a first base coupled to the first output node and a first collector coupled to the second output node, and
a second transistor having a second base coupled to the second output node and a second collector coupled to the first output node; and

an auxiliary cross-coupled oscillating unit configured to form a positive-feedback loop with the main cross-coupled oscillating unit in order to increase a negative resistance of the main cross-coupled oscillating unit, the auxiliary cross-coupled oscillating unit including:
a third transistor having a third collector coupled to the first base of the first transistor and a third base coupled to a second emitter of the second transistor, wherein the third base is configured to receive a signal from the second emitter, and
a fourth transistor having a fourth collector coupled to the second base of the second transistor and a fourth base coupled to a first emitter of the first transistor, wherein the fourth base is configured to receive a signal from the first emitter.

9. The voltage-controlled oscillator of claim 8, wherein the main cross-coupled oscillating unit further comprises:
a second current source connected to the emitters of the first and second transistors.

10. The voltage-controlled oscillator of claim 9, wherein the auxiliary cross-coupled oscillating unit further comprises:
a first current source commonly connected to the emitters of the third and fourth transistors.

11. The voltage-controlled oscillator of claim 9, wherein the auxiliary cross-coupled oscillating unit further comprises:
a first current source connected to the emitters of the third and fourth transistors, respectively.

12. The voltage-controlled oscillator of claim 8, further comprising:
a degeneration capacitor provided between the third emitter and the fourth emitter.

13. The voltage-controlled oscillator of claim 8, wherein the third base and the second emitter are connected to a common node, and wherein the fourth base and the first emitter are connected to a common node.