Patent Publication Number: US-7221920-B2

Title: Voltage controlled oscillator, frequency synthesizer and communication apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application is based upon and claims the benefit of priority from prior Japanese Patent Application P2003-201199 filed on Jul. 24, 2003; the entire contents of which are incorporated by reference herein. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a voltage controlled oscillator using a film bulk acoustic resonator and, more particularly, to a voltage controlled oscillator having a variable oscillation frequency, a communication apparatus and a frequency synthesizer using the same. 
   2. Description of the Related Art 
   In recent years, the market for a wireless communication system including a mobile phone and the like, has expanded, and at the same time, mobile communications services have been increasingly sophisticated. Moreover, it is expected that a local area network (LAN) system will rapidly become widespread in coming years. In these wireless communication systems, a radio frequency (RF) band of 2 GHz, 5 GHz, or more, is generally used. 
   In the RF band wireless communication systems, frequency synthesizers are used which are capable of oscillating in frequency bands required in the respective systems. The use of a quartz oscillator makes it possible to generate a highly precise reference frequency. However, a voltage controlled oscillator (VCO) is generally used in an RF band where the quartz oscillator cannot directly oscillate. Although a VCO alone cannot generate a highly precise frequency, frequency precision of a VCO or a frequency synthesizer is provided by implementing feedback control using a phase locked loop (PLL) circuit so as to generate integer or fracture times the frequency of a quartz oscillator. However, a VCO using a quartz oscillator normally provides a frequency band around 5 to 30 MHz, and even the highest frequency band of approximately 100 MHz at most. 
   Requirements for a VCO used in a frequency synthesizer include a wide tunability of an oscillation frequency so as to cover enough frequency range, and a low phase noise characteristic, as well as compactness and low power consumption. 
   A phase noise is an index to characterize dispersion of an oscillation frequency. The lower phase noise indicates that the oscillation frequency is closer to a single frequency, that is, almost ideal. The phase noise of a VCO, through frequency conversion by a frequency mixer, adversely affects the spectrum of signals in transmitting and receiving. In an orthogonal frequency division multiplex (OFDM) system, which is used for a wireless LAN system, an asymmetrical digital subscriber line (ADSL), a digital terrestrial television and the like, the lower the phase noise of a VCO, the higher the quality of signals. Accordingly, in principle, the quantity of information for transmitting and receiving can be increased. 
   A phase noise is caused by a thermal noise, flicker noise (1/f noise) and the like, inside an oscillator circuit. The noises emerge, as a momentary shift in the oscillation frequency, at an output node of the oscillator circuit. In order to reduce a phase noise in an oscillator, it is effective to increase the quality factor (Q value) of a resonator used in an oscillator circuit. 
   As a resonator exhibiting a high Q value in an RF band of GHz frequency or more, a film bulk acoustic resonator (FBAR) has been proposed recently and has collected attention. Currently, as resonators used in RF communication systems, bulk (ceramic) dielectric resonators or surface acoustic wave (SAW) devices have been used. As compared with the currently used resonators, the FBAR is suitable for miniaturization, and also for higher frequency applications. On the basis of the above reasons, a high frequency filter using an FBAR has already been commercially manufactured. Moreover, there is a proposal to use an FBAR of an aluminum nitride (AlN) as a resonator of VCO (see A. P. S. Khanna, et al., “A 2 GHz Voltage Tunable FBAR Oscillator,” IEEE MTT Symposium Digest, pp. 717–720, 2003). 
   Moreover, there is a proposal in which, in order to achieve a wide oscillation frequency tunability, a detection circuit is added to detect the transition of an oscillating operation from an initial state into a steady state, and a load capacitance in a resonator is connected to improve tunability of the oscillation frequency. (refer to Japanese Patent Laid-Open No. 2002-344242). 
   Furthermore, there is another proposal employing a wide-band frequency synthesizer in a wireless communication system, in which a wide frequency tunability is realized by means of selecting a VCO from a plurality of VCOs having different frequency bands (refer to Japanese Patent Laid-Open No. 2002-314414). 
   The VCO disclosed in Japanese Patent Laid-Open No. 2002-344242 is a quartz oscillator and therefore inapplicable in a GHz frequency band. In addition, the VCO requires an additional detection circuit for an oscillation signal and, therefore, is not suitable for miniaturization. Moreover, according to A. P. S. Khanna, et al., a prototype of a VCO using an AlN FBAR with an oscillation frequency of 2 GHz has achieved an extremely low phase noise (C/N). However, only a value of approximately 0.1% can be achieved for a frequency tunability. Further, in Japanese Patent Laid-Open No. 2002-314414, the frequency synthesizer is constructed by using an LC oscillator having inductors and capacitors for a resonator. Therefore, the circuitry becomes large and phase noise reduction is difficult. 
   As described above, currently, a VCO using a FBAR which is suitable for miniaturization and capable to oscillate a frequency range over GHz has not yet reached a point of providing a needed frequency tunablilty. Therefore, there have been few disclosed frequency synthesizers with a VCO using a FBAR. 
   SUMMARY OF THE INVENTION 
   A first aspect of the present invention inheres in a voltage controlled oscillator, including a resonator configured to oscillate with an initial oscillation frequency during starting period of oscillation and with a steady oscillation frequency during a steady state oscillation, the resonator including a film bulk acoustic resonator having a series resonance frequency higher than the oscillation frequency; and a negative resistance circuit connected to the film bulk acoustic resonator, configured to drive the resonator, the negative resistance circuit having a positive increment for reactance in the steady state oscillation compared with reactance in the starting period. 
   A second aspect of the present invention inheres in a frequency synthesizer, including a voltage controlled oscillator including a plurality of film bulk acoustic resonators having different resonance frequencies, configured to generate an oscillation signal; a first frequency divider configured to divide the oscillation signal from the voltage controlled oscillator and to generate a divided oscillation signal; a second frequency divider configured to divide a reference signal and to generate a divided reference signal; a phase comparator configured to compare phases of the divided oscillation signal and the divided reference signal and to generate a phase error signal; a control voltage generator configured to generate a control voltage for the voltage controlled oscillator based on the phase error signal; and a control circuit configured to generate a control signal based on the control voltage so as to select the film bulk acoustic resonators, and to control an oscillation frequency of the oscillation signal. 
   A third aspect of the present invention inheres in a communication apparatus, including a frequency synthesizer configured to provide an oscillation signal, including: a voltage controlled oscillator including a plurality of film bulk acoustic resonators having different resonance frequencies, configured to generate the oscillation signal; a first frequency divider configured to divide the oscillation signal from the voltage controlled oscillator and to generate a divided oscillation signal; a second frequency divider configured to divide a reference signal and to generate a divided reference signal; a phase comparator configured to compare phases of the divided oscillation signal and the divided reference signal and to generate a phase error signal; a control voltage generator configured to generate a control voltage for the voltage controlled oscillator based on the phase error signal; and a control circuit configured to generate a control signal based on the control voltage so as to select the film bulk acoustic resonators, and to control an oscillation frequency of the oscillation signal; a receiver configured to convert a high frequency receiving signal into an intermediate frequency receiving signal by use of the oscillation signal; a baseband processor configured to demodulate the intermediate frequency receiving signal and to modulate a transmitting signal; and a transmitter configured to transmit a radio frequency transmitting signal provided by converting the modulated transmitting signal by use of the oscillation signal. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  is an example of a circuitry of a VCO according to a first embodiment of the present invention. 
       FIG. 2  is an example of a circuitry of a negative resistance circuit according to the first embodiment of the present invention. 
       FIG. 3  is a schematic diagram of an example of an equivalent circuit model relevant to a resonant characteristic of a resonator according to the first embodiment of the present invention. 
       FIG. 4  is a schematic view showing an example of a time dependence of the VCO according to the first embodiment of the present invention leading up to oscillating in a steady state. 
       FIGS. 5A and 5B  are schematic diagrams of equivalent circuits explaining operation of an example of the negative resistance circuit. 
       FIGS. 6A and 6B  are schematic views illustrating a transconductance dependence of impedance and a vector diagram for the equivalent circuit shown in  FIG. 5A . 
       FIGS. 7A and 7B  are schematic diagrams of equivalent circuits explaining operation of another example of the negative resistance circuit. 
       FIGS. 8A and 8B  are schematic views illustrating a transconductance dependence of impedance and a vector diagram for the equivalent circuit shown in  FIG. 7A . 
       FIGS. 9A and 9B  are schematic diagrams of equivalent circuits explaining operation of still another example of the negative resistance circuit. 
       FIGS. 10A and 10B  are schematic views illustrating a transconductance dependence of impedance and a vector diagram for the equivalent circuit shown in  FIG. 9A . 
       FIG. 11  is a graph showing an example of a frequency characteristic of an admittance of the stand-alone FBAR according to the first embodiment of the present invention. 
       FIG. 12  is a graph showing examples of frequency characteristics of a real part of complex impedance (resistance) of the resonator and the negative resistance circuit according to the first embodiment of the present invention. 
       FIG. 13  is a graph showing examples of frequency characteristics of an imaginary part of complex impedance (reactance) of the resonator and the negative resistance circuit according to the first embodiment of the present invention. 
       FIG. 14  is a graph showing an example of a control voltage dependence for a oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 15  is a graph showing an example of a control voltage dependence for a variation ratio of an oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 16  is a graph showing an example of a phase noise characteristic of the VCO according to the first embodiment of the present invention. 
       FIG. 17  is a graph showing an example of a frequency characteristic of a reactance component of complex impedance when the FBAR having a different electrode area according to the first embodiment of the present invention, used in the resonator. 
       FIG. 18  is a graph showing examples of a FBAR electrode area dependence for an initial oscillation frequency and a steady oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 19  is a graph showing examples of the FBAR electrode area dependence for an initial oscillation frequency and a steady oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 20  is a graph showing an example of the FBAR electrode area dependence for a variable ratio of an oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 21  is a graph showing an example of a reactance ratio X VAR0 /X FBAR0  dependence for a variable ratio of an oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 22  is a graph showing examples of a frequency dependence for a reactance component of the FBAR and the reactance controller of the VCO according to the first embodiment of the present invention. 
       FIG. 23  is a graph showing an example of a ΔX VAR /ΔX FBAR  dependence for a variable ratio of an oscillation frequency of the VCO according to the first embodiment of the present invention. 
       FIG. 24  is an example of a circuitry of a VCO according to a first modification of the first embodiment of the present invention. 
       FIG. 25  is an example of a circuitry of a reactance controller of the VCO according to the first modification of the first embodiment of the present invention. 
       FIG. 26  is an example of a circuitry of a VCO according to a second modification of the first embodiment of the present invention. 
       FIG. 27  is an example of a circuitry of a frequency synthesizer according to a second embodiment of the present invention. 
       FIG. 28  is a schematic view showing an example of a relation between a control voltage and a oscillation frequency in VCOs having different frequency bands of the frequency synthesizer according to a second embodiment of the present invention. 
       FIG. 29  is an example of a circuitry of a frequency synthesizer according to a first modification of the second embodiment of the present invention. 
       FIG. 30  is a schematic view showing an example of a relation between a control voltage and a oscillation frequency in VCOs by use of FBARs having different frequency bands of the frequency synthesizer according to the first modification of the second embodiment of the present invention. 
       FIG. 31  is an example of a circuitry of a frequency synthesizer according to a second modification of the second embodiment of the present invention. 
       FIG. 32  is a schematic view of an example of an algorithm for searching the FBAR having a desired frequency band in the frequency synthesizer according to a second modification of the second embodiment of the present invention. 
       FIG. 33  is an example of a circuitry of a frequency synthesizer according to a third modification of the second embodiment of the present invention. 
       FIG. 34  is a schematic view of an example of a timing chart for up and down signals of a phase comparator in the frequency synthesizer according to the third modification of the second embodiment of the present invention. 
       FIG. 35  is an example of a circuitry of a frequency synthesizer according to a fourth modification of the second embodiment of the present invention. 
       FIG. 36  is an example of a circuitry of a frequency synthesizer according to a fifth modification of the second embodiment of the present invention. 
       FIG. 37  is an example of a circuitry of a frequency synthesizer according to a sixth modification of the second embodiment of the present invention. 
       FIG. 38  is an example of a circuitry of a frequency synthesizer according to a seventh modification of the second embodiment of the present invention. 
       FIG. 39  is a block diagram showing an example of a wireless communication system according to an application of the second embodiment of the present invention. 
       FIG. 40  is an example of a circuitry of a VCO of a frequency synthesizer according to other embodiment of the present invention. 
       FIG. 41  is another example of a circuitry of a VCO of a frequency synthesizer according to the other embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Various embodiments of the present invention will be described with reference to the accompanying drawings. It is to be noted that the same or similar reference numerals are applied to the same or similar parts and elements throughout the drawings, and the description of the same or similar parts and elements will be omitted or simplified. 
   First Embodiment 
   As shown in  FIG. 1 , a VCO  50  according to a first embodiment of the present invention includes a resonator  70  and a negative resistance circuit  60  connected to the resonator  70  at a connection node  72 . 
   The resonator  70  includes a reactance controller  52  connected to an input node  62 , a phase adjuster  54  connected in series to the reactance controller  52 , and a FBAR  56  connected in series to the phase adjuster  54 . A control voltage source  66 , which is grounded, is connected to the input node  62 . Moreover, an output node  64  is provided at the other end of the negative resistance circuit  60  which is connected to the resonator  70  at the connection node  72 , and a load  68  is connected to the output node  64 . 
   As shown in  FIG. 2 , the negative resistance circuit  60  includes an inductor L 1  connected between a DC power supply Vcc which is grounded at a negative side, and a collector of a transistor Q 1 ; a resistance R 1  connected between the DC power supply Vcc and a base of the transistor Q 1 ; a resistance R 2  connected to the base of the transistor Q 1 ; a resistance R 4  connected between the resistance R 2  and a base of the transistor Q 2  in which a collector is connected to an emitter of the transistor Q 1 ; a grounded resistance R 3  connected to the resistance R 2  and R 4 ; a resistance R 5  connected between an emitter of the transistor Q 2  and a grounded inductor L 2 ; a capacitor C 5  connected between the collector of the transistor Q 1  and the output node  64 ; a capacitor C 1  connected between the base of the transistor Q 1  and the emitter of the transistor Q 2 ; a grounded capacitor C 2  connected to the emitter of the transistor Q 1 ; a capacitor C 3  connected between the base and emitter of the transistor Q 2 ; a grounded capacitor C 4  connected to the emitter of the transistor Q 2 ; and the connection node  72  connected to the base of the transistor Q 2 . 
   The bipolar transistors Q 1  and Q 2  construct a cascode circuit where the emitter of the transistor Q 1  and the collector of the transistor Q 2  are connected to each other. The transistor Q 1  is a buffer transistor for driving the load, and the transistor Q 2  serves as an oscillation transistor. 
   The DC power supply Vcc supplies a bias voltage to the transistors Q 1  and Q 2 . The resistances R 1  to R 5  are bias resistances for determining operating points of the transistors Q 1  and Q 2 . The inductor L 1  connected between the DC power supply Vcc and the collector of the transistor Q 1 , and the grounded inductor L 2  connected with the resistance R 5  which is connected from the emitter of the transistor Q 2 , allow only direct-current components to pass therethrough and prevent high-frequency components from escaping into the DC power supply Vcc and the ground GND, respectively. 
   The capacitor C 1  provides a high frequency wave oscillated by the transistor Q 2  to the transistor Q 1 . The capacitor C 2  grounds the collector of the transistor Q 2  in a high frequency range. The capacitors C 3  and C 4  allow a signal, which emerges at the emitter of the transistor Q 2  by amplifying a high frequency signal provided into the base of the transistor Q 2 , to feed back the signal again to the base of the transistor Q 2  through the resonator  70 . The capacitor C 5  provides a high frequency signal from the collector of the transistor Q 2  to the output node  64 . In addition, the connection node  72  is connected to the resonator  70 . 
   Note that, in the first embodiment, the bipolar transistor Q 1  and Q 2  are used in the negative resistance circuit  60 . Although a field effect transistor (FET) or the like may be used instead of a bipolar transistor, it is desirable, in terms of noise reduction, to use the bipolar transistor which has a relatively low flicker noise. Further, a negative resistance circuit using a complementary metal oxide semiconductor (CMOS) inverter may be used. 
   The resonator  70  has a circuitry where the reactance controller  52 , the phase adjuster  54  and the FBAR  56  are connected in series. The resonator  70  can be represented by an equivalent circuit model as shown in  FIG. 3 . 
   In the reactance controller  52 , which varies reactance depending on a control voltage V control  applied from the control voltage source  66 , a variable capacitance C VAR  is used. The variable capacitances C VAR  is provided by a variable capacitance diode using a pn junction of a semiconductor, a metal-oxide-semiconductor (MOS) capacitor, a high dielectric thin film capacitor which varies capacitance by using nonlinearity of a strontium titanate (SrTiO 3 ) film or the like, an electrostatic capacitor having a variable gap between electrodes by using an electrostatic force, a piezoelectric property, and the like. One end of the capacitance C VAR  is connected to an inductance L DC  for removing high-frequency components included in the control voltage V control  applied from the input node  62 . The other end of the capacitance C VAR  is grounded. 
   In the phase adjuster  54 , an inductance L ADJ , such as a microstrip line or a spiral inductor, is used. Note that it is desirable that the phase adjuster  54  has a structure which enables fine adjustment of phase characteristics of the resonator  70  by adjusting the inductance L ADJ  by laser trimming after the oscillator circuit is fabricated. 
   The FBAR  56  includes a piezoelectric thin film having a pair of electrodes on both sides and an acoustic reflector abutting on at least one of the pair of electrodes. The piezoelectric material includes an aluminum nitride (AlN), a zinc oxide (ZnO), a lead zirconate titanate (Pb(Zr,Ti)O 3 ), a barium titanate (BaTiO 3 ), and the like, or materials modified composition, for example, by adding another component thereto. The acoustic reflector is provided to enhance the Q value representing a resonance characteristic of the FBAR. The acoustic reflector may be a cavity, or may be a multilayer film for acoustic reflection. The resonance characteristic of the FBAR  56  can be appreciably precisely expressed by using the equivalent circuit shown in  FIG. 3 . A capacitance C F0  is an electrostatic capacity of the FBAR  56 . The combination of a capacitance C F1 , an inductance L F  and a resistance R F , which is connected in parallel to the capacitance C F0 , corresponds to an electrical equivalent circuit representing a mechanical oscillation generated due to the piezoelectric property of the FBAR  56 . 
   In the first embodiment, an initial oscillation angular frequency ω start  immediately after the introduction of power into the VCO  50 , is designed to be between a series resonance angular frequency ω s  and a parallel resonance angular frequency ω p  of the FBAR  56  so as to stably start the oscillation. Then, a steady oscillation angular frequency ω osc , after amplitude of the oscillation settles into a state of saturation, is designed to be lower than the series resonance angular frequency ω s  by using the nonlinearity of the negative resistance circuit  60 . If the VCO  50  is thus designed, the frequency tunability of the VCO  50  can be increased as described below. 
   The impedance characteristic of the FBAR  56  around the resonance frequency can be generally described as follows. In an angular frequency range lower than the series resonance angular frequency ω s  of the FBAR  56  and an angular frequency range higher than the parallel resonance angular frequency ω p  of the FBAR  56 , a reactance X FBAR =Im(Z FBAR ) of the FBAR  56  is a negative value and the FBAR  56  behaves like a capacitor. On the other hand, in a limited frequency range from the series resonance angular frequency ω s  to the parallel resonance angular frequency ω p , the reactance X FBAR  is a positive value and the FBAR  56  behaves like an inductor. At the series resonance angular frequency ω s , a real part R FBAR =Re(Z FBAR ) of a complex impedance of the FBAR  56  is a relatively small value. By contrast, the R FBAR  is the largest at the parallel resonance angular frequency ω p . 
   It is usual, for an oscillator circuit using piezoelectric resonator, in order to achieve stable oscillating operation, that the circuit is designed so as to oscillate in a frequency range where a piezoelectric resonator behaves like an inductor, that is, between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p . Accordingly, in the oscillator circuitry providing an oscillation in the frequency range where the piezoelectric resonator behaves like an inductor, an only narrow frequency tunability may be realized. 
   To the contrast, according to the first embodiment, as will be described below, the initial oscillation angular frequency ω start , which is 2*π*f start , immediately after the introduction of power into the VCO  50  is designed such that the initial oscillation frequency is between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p . However, the steady oscillation angular frequency ω osc , which is 2*π*f osc , after amplitude of the oscillation settles into a state of saturation, is designed to be lower than the series resonance angular frequency ω s . Thus, the frequency tunability of the VCO  50  may increase. 
   Using equivalent circuit parameters, the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p  of the FBAR  56  can be expressed by the following equations.
 
ω s =2 *π*f   s =[1/( L   F   *C   F1 )] 1/2   (1)
 
ω p =2 *π*f   p =[(1 /C   F1 +1 /C   F0 )/ L   F ] 1/2   (2)
 
   Moreover, using the equivalent circuit parameters, the complex impedance Z FBAR  of the FBAR  56  with respect to an angular frequency ω can be expressed by the following equation:
 
 Z   FBAR =1/( j*ω*C   F0 )+1/((ω* C   F0 ) 2   /{R   F   +j*[*L   F −(1 /C   F1 +1 /C   F0 )/ω]}  (3)
 
where the first term in the right-hand side of the equation (3) relates to an electrostatic capacitance C F0  of the FBAR  56 , and the second term relates to a acoustic piezoelectric vibration of the FBAR  56 .
 
   Here, an antiresonance resistance R A  and a phase angle θ are defined as follows.
 
 R   A =1/(ω 2   *C   F0   *R   F )  (4)
 
tan θ=[ω* L   F −(1 /C   F1 +1 /C   F0 )/ω]/ R   F   (5)
 
−π/2&lt;θ&lt;π/ 2   (6)
 
Using the antiresonance resistance R A  and the phase angle θ, the complex impedance Z FBAR  can be expressed as follows.
 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   The VCO  50  shown in  FIG. 1  is divided at the connection node  72  into two parts which are the negative resistance circuit  60  and the resonator  70 . The complex impedance when viewing the negative resistance circuit  60  from the connection node  72  is denoted by Z NEG , and the complex impedance when viewing the resonator  70  from the connection node  72  is denoted by Z RES . Strictly speaking, the complex impedances are both functions relating to an oscillation frequency and an oscillation amplitude. If the frequency is limited around the resonance frequency of the FBAR  56 , the complex impedance Z NEG  can be substantially approximated to a constant value with respect to the frequency, while the complex impedance Z RES  is a function varying sharply with the frequency because the complex impedance Z RES  includes the complex impedance of the FBAR  56 . 
   Referring to  FIG. 3 , the complex impedance Z RES  of the resonator  70  can be expressed as follows.
 
 Z   RES   =Z   FBAR   +j*[L   ADJ −1/(ω* C   VAR )]  (8)
 
Accordingly, it is understood that the variable capacitance C VAR  and the inductance L ADJ  are circuit elements for adding or subtracting to the imaginary component, that is, the reactance component X FBAR , of the complex impedance of the FBAR  56 . Strictly speaking, ω*L ADJ  or 1/(ω*C VAR ) is also a function relating to the frequency. However, each of ω*L ADJ  and 1/(ω*C VAR ) can be thought to be an approximately constant value in the narrow resonance frequency range in comparison with the reactance component X FBAR  of the FBAR  56  sharply increasing or decreasing around the resonance frequency.
 
   Moreover, as shown in  FIG. 1 , the variable capacitance C VAR  of the reactance controller  52  is a function relating to the control voltage V control  of the control voltage source  66 . Consequently, as the equation (8) shows, the value of 1/(ω*C VAR ) is varied depending on the control voltage V control , and the reactance component X RES  of the resonator  70  is accordingly varied. Note that the value of the inductance L ADJ  of the phase adjuster  54  is not varied by the control voltage V control . 
   As for a variation of the complex impedance with respect to the oscillation amplitude, since the complex impedance Z RES  of the resonator  70  is provided by impedances of passive elements, the complex impedance Z RES  can be thought to be approximately constant even if the oscillation amplitude varies. On the other hand, since the complex impedance Z NEG  of the negative resistance circuit  60  includes the transistors which are active elements, the complex impedance Z NEG , reflecting the nonlinearity of the transistors, is a function varying values according to the magnitude of the oscillation amplitude. 
   The complex impedance Z NEG  of the negative resistance circuit  60  cannot be expressed by a simple expression like the equation (8) because the negative resistance circuit  60  is a nonlinear circuit including the transistors. However, by use of a large signal nonlinear transistor model, such as a Gummel-Poon model, and model parameters having experimentally sufficient precision, it is possible to precisely predict the complex impedance Z NEG  by circuit simulation. Note that, for designing the negative resistance circuit  60  which operates at a high frequency, it is necessary to sufficiently consider parasitic components of individual parts other than the parameters including parasitic components concerning the above-discussed transistors so that the impedance characteristics correspond in the oscillation frequency band. Moreover, it is necessary to use a circuit where consideration has been previously provided to parasitic components of circuit wirings connecting one part to another. 
   As shown in  FIG. 4 , after the elapse of an activation duration from a time of turning on power of the VCO  50  by controlling the reactance controller  52  with control voltage of the control voltage source  66  shown in  FIG. 1 , the VCO  50  according to the first embodiment first starts to oscillate at a frequency that satisfies a oscillation condition at small amplitude. Thereafter, the oscillation amplitude gradually increases and, after the elapse of an amplification duration, the VCO  50  oscillates in a steady state. Even if the loop gain of the negative resistance circuit  60  in the VCO  50  is one or more, the VCO  50  cannot start to oscillate immediately after turning on, as long as there is no signal to amplify. In practice, the oscillation is started by selectively amplifying a frequency component that satisfies an oscillation condition among fluctuations FL existing in the negative resistance circuit  60  of the VCO  50 , such as weak noise voltage/current, and minute harmonic components caused by transient phenomena at the time of turning on power. Generally, the higher Q value of a resonator used in an oscillator circuit exhibits, the longer the activation duration tends to be until the start of oscillation. 
   Since the oscillation amplitude is extremely small immediately after the oscillation has started, a condition for small signal operation of a transistor applies. In general, in order to decrease the duration from the time of turning on the power until steady state oscillating, it is desirable to set a loop gain of the negative resistance circuit  60  for the small signal operation to 3 or more. Here, the frequency ω start  that satisfies a phase condition during the small signal operation, during the activation duration of the oscillation, is to be in the frequency range between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p  of the FBAR  56 . Once the oscillation starts, due to a loop gain of greater than one of the negative resistance circuit  60 , the oscillation is amplified during the amplification duration and the oscillation amplitude accordingly increases. When the oscillation amplitude increases, due to the nonlinearity of the transistors, the loop gain gradually decreases to one. Consequently, the oscillation is close to steady state. Thus, intentionally using the nonlinearity of the transistors in the negative resistance circuit  60 , the frequency that satisfies the phase condition in the steady state may be lower than the series resonance angular frequency ω s  of the FBAR  56 . 
   First, the activation duration when the VCO  50  starts to oscillate is considered. During the activation duration, a small signal source, such as a weak noise voltage/current existing in the circuit, and a minute harmonic component caused by the transient phenomena at the time of turning on power, is selectively amplified. Therefore, an oscillation condition to be determined can be analyzed, using parameters of a small signal linear circuit. The oscillation start conditions of an oscillation circuit can be represented by the following expressions, respectively relating to resistance components R in the complex impedances of the resonator  70  and the negative resistance circuit  60 , and the reactance components X thereof.
 
 R   RES   ≦−R   NEG ( A   small )  (9)
 
 X   RES   =−X   NEG ( A   small )  (10)
 
Here, A small  is a small signal oscillation amplitude.
 
   As for the oscillation start condition, that is a gain condition, relating to the resistance components R in the complex impedances in the expression (9), the impedance of the FBAR  56  may decrease by increasing the area of the FBAR  56  to a certain level or more so that the transistors included in the negative resistance circuit  60  can be driven. Therefore, for the oscillation start condition, it is sufficient to mainly consider the phase condition relating to the reactance components X in the equation (10). 
   The equation (10), which represents the phase condition of the resonator  70 , can be transformed into the following equation:
 
 X   FBAR ((ω start )+ X   VAR (ω start )+ X   ADJ ((ω start )= −X   NEG ( A   small , ω start )  (11)
 
where X VAR (ω start ) is the reactance of the reactance controller  52 , and X ADJ (ω start ) is the reactance of the phase adjuster  54 . Accordingly, the reactance X FBAR (ω start ) of the FBAR  56  can be expressed as follows.
 
 X   FBAR (ω start )= −X   NEG ( A   small , ω start )− X   VAR (ω start )− X   ADJ (ω start )  (12)
 
   The value of the reactance X FBAR (ω start ) is a positive value between the series resonance and parallel resonance of the FBAR  56 , and the FBAR  56  behaves as an inductor. Consequently, a condition which makes the value of {−X NEG (A small , ω start )−X VAR (ω start )−X ADJ (ω start )} a positive value, as expressed by the following inequality, provides the oscillation to start between the series resonance and the parallel resonance.
 
 X   NEG ( A   small , ω start )+ X   VAR (ω start )+ X   ADJ (ω start )&lt;0  (13)
 
   Next, the case where the oscillation amplitude has been gradually increased and settles in the steady state as shown in  FIG. 4  will be considered. 
   The active elements, such as the transistors, included in the negative resistance circuit  60  linearly operate during the small signal operation. However, the active elements may nonlinearly operate when the signals become large. During the large signal operation, an average complex impedance Z NEG (A osc ) generally exhibits a different value from the complex impedance Z NEG (A small ) during the small signal operation. A difference between the reactance component X NEG (A osc ) of the negative resistance circuit  60  around the resonance frequency during the large signal operation and the reactance component X NEG (A small ) during the small signal operation is denoted by ΔX NEG . Note that the term “A osc ” is a large signal oscillation amplitude. In other words, the difference ΔX NEG  means a difference between the reactances of the negative resistance circuit  60  during the large signal operation and during the small signal operation. 
   If the VCO  50  can be designed such that the value of {X NEG (A small , ω start )+X VAR (ω start )+X ADJ (ω start )} during the small signal operation is negative and the value of {X NEG (A osc , ω osc )+ΔX NEG +X VAR (ω osc )+X ADJ (ω osc )} during the large signal operation in the steady state is positive, the VCO  50  may start to oscillate at a frequency f start  between a series resonance frequency f s  and a parallel resonance frequency f p  of the FBAR  56 . Further, the oscillation frequency is gradually reduced as the oscillation amplitude is increased, and the VCO  50  may steadily oscillate at a frequency f osc  that is lower than the series resonance frequency f s . 
   Next, a description will be given of how a reactance component in a circuit can be varied between at starting of oscillation and during a steady state oscillation. Note that a difference between oscillation frequencies at the staring of oscillation and during the steady state is small in comparison with a value of the oscillation frequency of a negative resistance circuit. Therefore, the difference between the oscillation frequencies will be ignored in the following description. 
     FIG. 5A  shows an equivalent circuit of a negative resistance circuit simplified from a Colpitts oscillator circuit. In  FIG. 5A , C 3  and C 4  correspond to C 3  and C 4  in the negative resistance circuit shown in  FIG. 2 . Moreover, in  FIG. 5A , the transistor Q 2  for oscillation in  FIG. 2 , is modeled by a voltage dependent current source. This is the simplest model where an emitter current g m *ν flows in response to a base voltage ν. Here, the “g m ” represents a transconductance of the transistor Q 2  for oscillation. Impedance Z neg  is an impedance of the negative resistance circuit viewed from an input side of the transistor Q 2 . The equivalent circuit shown in  FIG. 5A  can be further replaced by a series connection model of a negative resistance (−g m /(ω 2 *C 3 *C 4 )) and a capacitance (C 3 *C 4 /(C 3 +C 4 )) shown in  FIG. 5B . 
   Here, it is assumed that only the transconductance g m  is varied depending on voltage amplitude. That is, it is assumed that the large transconductance g m  is determined when the amplitude of an input voltage ν is sufficiently small, but the transconductance g m  gradually decreases as the voltage amplitude increases because the transistor may be saturated. An examination will be made of what influence such a variation of the transconductance g m  has on the impedance Z neg  of the negative resistance circuit in  FIG. 5A . 
     FIG. 6A  shows how the impedance Z neg  of the negative resistance circuit varies with g m . Since the impedance Z neg  is represented by the series connection of the capacitance and the negative resistance, an imaginary part Im(Z neg ) of Z neg  does not depend on the transconductance g m . On the other hand, a real part Re(Z neg ) of Z neg  is a negative value and varies in proportion to the transconductance g m . In the simplest model shown in  FIG. 5A , only the real part Re(Z neg ) varies depending on the amplitude of the input voltage, while the imaginary part Im(Z neg ), i.e., the reactance component does not vary due to the saturation of the transistor. For example, as shown in  FIG. 6B , during the small signal operation at the start of oscillation, the transconductance g m (A start ) is large and the absolute value of Re(Z neg (A start )) is also large. During the large signal operation in steady state oscillation, the transconductance g m (A osc ) is small and the absolute value of Re(Z neg (A osc )) is also small. In contrast, Im(Z neg (A start )) and Im(Z neg (A osc )) are the same value of ((C 3 +C 4 )/((ω*C 3 *C 4 )), 
   Next, an examination will be made of a case where, as shown in  FIG. 7A , a base-collector parasitic capacitance C bc  is introduced into the transistor model.  FIG. 7B  shows a further simplified equivalent circuit. As shown in  FIGS. 8A and 8B , the impedance Z neg  of a negative resistance circuit in  FIG. 7A  exhibits not only a dependence of the real part Re(Z neg ) on the transconductance g m  but also a dependence of the imaginary part Im(Z neg ) on the transconductance g m . The influence of the parasitic capacitance C cb  will be described qualitatively. As shown in  FIG. 7B , the parasitic capacitance C cb  is connected in parallel to a negative resistance (−g m /(ω 2 *C 3 *C 4 )) and a capacitance (C 3 *C 4 /(C 3 +C 4 )) attributable to capacitances C 3  and C 4 . It can be assumed that the parasitic capacitance C cb  connected in parallel has an effect of causing the vector of the impedance to rotate counterclockwise by a phase φ in a manner of the first approximation. As a result, as shown in the vector diagram of  FIG. 8B , when the transconductance varies from g m (A start ) to g m (A osc ), not only the real part of the impedance of the negative resistance but also the imaginary part thereof, that is, the reactance component can be varied. In addition, in a variation of the reactance, the reactance component exhibits a positive increase ΔX NEG  when g m (A osc ) is small in steady state oscillation as compared with when g m (A start ) is large during activation of oscillation. 
   Next, an examination will be made of a case where, as shown in  FIG. 9A , an inductor L adj  is connected as a phase adjusting means to the above-discussed negative resistance circuit. Since the inductor L adj  is simply connected in series to the negative resistance circuit, as shown in  FIG. 9B , the overall impedance can be provided simply by adding an impedance Z adj  attributable to the phase adjusting means to the impedance Z neg  of the negative resistance circuit. As a result, as shown in  FIGS. 10A and 10B , when the transconductance g m  is large, an imaginary part of the overall impedance (Z neg +Z adj ) provides a negative value, that is, an capacitive reactance, and when the transconductance g m  is small, the imaginary part provides a positive value, that is, an inductive reactance. In other words, when the transconductance g m  of the transistor varies with amplitude of a signal, the sign of the reactance is varied from negative to positive with the transition of oscillation from a starting state to the steady state. 
   Assuming that a piezoelectric resonator is connected to the negative resistance circuit and the above-discussed phase adjusting means, when the transconductance g m  is large at the start of oscillation, the negative resistance circuit oscillates with a positive reactance component of the piezoelectric resonator, that is, in a frequency range between the series resonance frequency and the parallel resonance frequency. Moreover, when the transconductance g m  is small in steady state oscillation, the negative resistance circuit oscillates with a negative reactance component of the piezoelectric resonator, that is, below the series resonance frequency. 
   Note that the variable capacitance C var  of the reactance controller  52  has been ignored for simplification in the foregoing description. However, even when the variable capacitance C var  is present, the variable capacitance C var  only has an influence of relatively varying the value of the reactance. Therefore, the case where the variable capacitance C var  is present also conforms to the foregoing description qualitatively. 
   The foregoing description has been given using the simplest model where only the minimum parasitic component of transistors is considered in the negative resistance circuit. Therefore, it is necessary in practice to consider other various parasitic components. Accordingly, when designing the VCO  50 , it is necessary to adjust circuit parameters using a more precise transistor model and a circuit simulator so as to satisfy the following equation relating to steady state oscillation at an angular frequency lower than the series resonance angular frequency ω s  of the FBAR  56  alone.
 
 Z   NEG ( A   osc , ω osc )+ Z   RES (ω osc )=0.  (14)
 
   At a frequency equal to a series resonance frequency f s  or lower, the reactance X FBAR (ω osc ) of the FBAR  56  provides a negative value. However, the reactance X FBAR (ω osc ) is greater than a value of reactance {−1/(ω s ·C F0 )} attributable to the electrostatic capacity C F0 . Therefore, in order to achieve steady state oscillation, by focusing attention on large signal reactance of circuitry elements other than the FBAR  56 , a circuit of the resonator may be constructed such that the following inequality is satisfied for the series resonance angular frequency ω 0 , of the FBAR  56 .
 
0 &lt;X   VAR(ω   s )+ X   ADJ (ω s )+ X   NEG ( A   osc , ω s )&lt;1/(ω s   ·C   F0 )  (15)
 
Here, for the value of each of the reactance components X VAR (ω s ) X ADJ (ω s ), and X NEG (A osc , ω s ), it is necessary to consider parasitic components involved in packaging of respective circuitry elements and circuit wirings. For the negative resistance circuit  60 , in particular, it is necessary to predict the parasitic components with high precision simulation of a high frequency circuit, using a large amplitude model capable of precisely representing the value of the reactance X NEG (A osc , ω s ) as well as the nonlinearity of the transistor.
 
   Moreover, in the inequality (15), the reactance X VAR (ω s ) of the reactance controller  52  always presents a negative value. In addition, the reactance X NEG (A osc , ω s ) of the negative resistance circuit  60  also often presents a negative value. In such case, in order to satisfy the inequality (15), reactance of the resonator  70  is adjusted using a reactance X ADJ (ω s ) of a positive value of the phase adjuster  54 . 
   In the resonator  70 , it is assumed that, the reactance X VAR (ω s ) of the reactance controller  52  on the series resonance angular frequency ω s  of the FBAR  56 , varies with a maximum of ΔX VAR  within a voltage variable range of the control voltage V control  of the control voltage source  66 . It is also assumed that the reactance X RES (ω s ) of the resonator  70  is accordingly varied with a maximum of ΔX VAR , which causes a variation in the phase condition for oscillation and thus causes a variation of Δf osc  in the oscillation frequency. Assuming that, around the series resonance frequency f s  of the FBAR  56 , each of the reactances X NEG (A osc , ω s ) and X ADJ (ω s ) of the negative resistance circuit  60  and the phase adjuster  54 , respectively, can be approximated to a substantially constant value. Then, the variation Δf osc  in the oscillation frequency can be approximately expressed by the following equation.
 
Δ f   sc =(∂ f/∂X   RES )*Δ X   RES ≈(∂ X   FBAR /∂f) −1   *ΔX   VAR   (16)
 
   When focusing attention on a frequency around the series resonance frequency f s  which allows the resistance components R FBAR  of the complex impedance of the FBAR  56  to provide a small value, the gradient of the reactance X FBAR  of the FBAR  56  with respect to the frequency is high when the frequency is higher than the series resonance frequency f s . Accordingly, the value of (∂X FBAR /∂f) −1  in the right hand side of the equation (16) is small. More specifically, only a small variation Δf osc  in the oscillation frequency can be determined for a reactance difference ΔX VAR  of the reactance controller  52 . 
   On the other hand, when the oscillation frequency is lower than the series resonance frequency f s , the gradient of the reactance X FBAR  of the FBAR  56  with respect to the frequency is low. Accordingly, the value (∂X FBAR /∂f) −1  in the right hand side of the equation (16) provides a relatively large value. Therefore, a large variation Δf osc  in the oscillation frequency can be determined for the reactance difference ΔX VAR  of the reactance controller  52 . 
   In principle, the operation of the VCO  50  has a characteristic that only a frequency that satisfies the oscillation condition at small signals is selectively amplified. The first embodiment is characterized in that the oscillation start condition is limited to an extremely narrow frequency range between the series resonance and parallel resonance of the FBAR  56 . Such characteristic has the effect of suppressing abnormal oscillation at an undesired frequency. Accordingly, stable oscillation can be achieved. Moreover, in the steady state where the oscillation amplitude is sufficiently amplified, the oscillation frequency f osc  may vary in a wide frequency range by varying the oscillation frequency f osc  to a frequency lower than the series resonance frequency f s . 
   When a reactance attributable to the electrostatic capacity C F0  of the FBAR  56  at the series resonance angular frequency ω s  is defined as X FBAR0 , the X FBAR0  can be represented as follows.
 
 X   FBAR0 =−1/(ω s   *C   F0 )  (17)
 
In addition, a reactance at a center value of the control voltage V control  for the reactance controller  52  at the series resonance angular frequency ω s  is defined as X VAR0 . For example, it has been confirmed that a wide frequency tunability of approximately 1% or more can be assured by designing an area S of the FBAR  56  such that a value of a reactance ratio X VAR0 /X FBAR0  is 0.30 or larger. When the value of the reactance ratio X VAR0 /X FBAR0  is 1.50 or larger, the VCO  50  cannot oscillate in the entire control voltage range. Therefore, it is desirable that the value of the reactance ratio X VAR0 /X FBAR0  is in a range of not less than 0.30 and not more than 1.50.
 
   Furthermore, a difference between a maximum value X FBARMax  and a minimum value X FBARMin  of the reactance around the resonance frequency of the FBAR  56  is defined as follows.
 
Δ X   FBAR   =X   FBARMax   −X   FBARMin   (18)
 
For example, around the resonance frequency of the FBAR  56 , by converting a scattering (S) parameter measured by a network analyzer into a complex impedance, the difference ΔX FBAR  can be provided. When the complex impedance Z FBAR  around the series resonance frequency f s  of the FBAR  56  is plotted on a complex plane (R FBAR , jX FBAR ), an impedance circle can be drawn. Approximately, the difference ΔX FBAR  corresponds to the diameter of the impedance circle. The diameter of the impedance circle is reduced in substantially inverse proportion to an area S of opposing electrodes of the FBAR  56 .
 
   Similarly, when the high frequency characteristic around the resonance frequency of the FBAR  56  is measured by varying the control voltage V control  applied to the reactance controller  52 , it is possible to measure a maximum reactance difference ΔX VAR  within the control voltage variable range around the oscillation frequency of the reactance controller  52 . For example, when the reactance controller  52  is a variable capacitance diode, the maximum reactance difference can be approximately expressed by the following expression,
 
Δ X   VAR &gt;&gt;|1 /C   VARMax −1 /C   VARMin |(2 *π* f   s )  (19)
 
Here, C VARMax  is a maximum capacitance and C VARMin  is a minimum capacitance in the control voltage range.
 
   In the VCO  50  using the FBAR  56 , the value of the ratio ΔX VAR /ΔX FBAR  between the maximum reactance difference ΔX VAR  of the reactance controller  52  and the reactance difference ΔX FBAR  of the FBAR  56  is important. The larger the value of the ratio ΔX VAR /ΔX FBAR , the wider the frequency tunability. For example, since the variable capacitance diode as the reactance controller  52  uses a variation of pn junction capacitance, it is difficult to obtain more than a certain fixed value of a reactance difference ΔX VAR  within the limited control voltage range. In such case, it is possible to obtain the value of the ratio ΔX VAR /ΔX FBAR  by enlarging the area S of the FBAR  56 . 
   Specifically, it has been confirmed that a wide frequency tunability of approximately 1% or more can be assured by designing the area S of the FBAR  56  such that the value of the ratio ΔX VAR /ΔX FBAR  is 0.05 or larger. When the value of the ratio ΔX VAR /ΔX FBAR  is 0.30 or larger, the VCO  50  cannot oscillate in the entire control voltage range. Therefore, it is desirable that the value of the ratio ≢X VAR /ΔX FBAR  is in a range of not less than 0.05 and not more than 0.30. 
   As described above, according to the first embodiment, the initial oscillation angular frequency ω start  immediately after turning on power to the VCO  50  enables oscillation to start stably between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p  of the FBAR  56 . Moreover, the oscillation angular frequency ω osc  after the oscillation settles into the steady state may be lower than the series resonance angular frequency ω s  by using the nonlinearity of the negative resistance circuit  60 , which makes it possible to increase the frequency tunability of the VCO  50 . 
   Next, an example of the VCO  50  according to the first embodiment will be described. For a piezoelectric thin film of the FBAR  56 , for example, AlN is used. An opposing electrode area of the FBAR  56  is 10000 μm 2 . Values of equivalent circuit parameters of the FBAR  56  are calculated by fitting so that the values are best matched with a measurement result of the resonance characteristic of the FBAR  56 .  FIG. 11  is a graph obtained by plotting a real part Re(Y FBAR ) and an imaginary part Im(Y FBAR ) of an admittance Y FBAR  of the FBAR  56 , that is, conductance and susceptance, with respect to the frequency. In  FIG. 11 , the measured values are indicated by white circles, and the results of the fitting are indicated by a solid line. The equivalent circuit parameters used in the fitting are as follows: C F0 =2.25 pF; C F1 =0.098 pF; L F =17.0 nH; R F =3.0. Based on the results, it can be calculated that an effective value of an electromechanical coupling coefficient k eff   2  of the FBAR  56  is approximately 5.1%, and a mechanical Q value is approximately 140. Moreover, from  FIG. 11 , the series resonance frequency f s . of the FBAR  56  is approximately 3.90 GHz, and the parallel resonance frequency f p  thereof is approximately 3.98 GHz. 
   As shown in  FIGS. 12 and 13 , the frequency characteristics of the resistance component R RES  and the reactance component X RES  of the resonator  70  around the resonance frequency of the FBAR  56 , respectively, sharply vary between the series resonance frequency f s  and the parallel resonance frequency f p . The resistance component R RES  exhibits a frequency characteristic having a steep peak with the maximum value around the parallel resonance frequency f p  of the FBAR  56 . The reactance component X RES  has a positive value, which indicates inductivity, around the series resonance frequency fs, and has a negative peak around the parallel resonance frequency fp. 
   Moreover, the frequency characteristics of the resistance component (−R NEG ) and the reactance component (−X NEG ) of the negative resistance circuit  60  also shown in  FIGS. 12 and 13 , respectively, shows gradual decreases as the frequency increases. Note that, for the negative resistance circuit  60 , the components of the negative complex impedance (−Z NEG ) are used for convenience.  FIG. 13  shows a reactance {X NEG (A small )} of the negative resistance circuit  60  in relation to the amplitude A small  during the small signal oscillation, and a reactance {−X NEG (A osc )} of the negative resistance circuit  60  in relation to the large amplitude A osc  during the oscillation in the steady state. Note that the control voltage V control  for the resonator  70  applied from the control voltage source  66  and the DC voltage for the negative resistance circuit  60  are set to, for example, 1.35 V and 2.7 V, respectively. 
   From  FIG. 13 , it can be perceived based on intersections f start  and f ns  of the reactance X RES  of the resonator  70  and the small signal operation reactance {−X NEG (A small )} of the negative resistance circuit  60 , whether the oscillation start condition of the equation (10) is satisfied. The values of f start  and f ns  are 3.92 GHz and 3.97 GHz, respectively, each of which is higher than the series resonance frequency f s  of approximately 3.90 GHz of the FBAR  56  and lower than the parallel resonance frequency f p  of approximately 3.98 GHz thereof. Accordingly, it is understood that both intersections f start  and f ns  satisfy the oscillation start condition of the equation (10). 
   Moreover, from  FIG. 12 , the value that satisfies the oscillation start condition expressed by the inequality (9) is 3.92 GHz, which is the frequency f start  shown in  FIGS. 12 and 13 . On the other hand, the frequency f ns  of 3.97 GHz, does not satisfy the oscillation start condition, and it is therefore understood that the frequency f ns  does not serve as the oscillation start point. 
   Next, after the oscillation has started, the VCO  50  settles into the steady state. As shown in  FIG. 13 , the VCO  50  stably oscillates at the oscillation frequency f osc  of approximately 3.84 GHz which is an intersection of the reactance X RES  of the resonator  70  and the large signal operation reactance {−X NEG (A osc )} of the negative resistance circuit  60 . In the steady state, current consumption Icc of the DC power supply Vcc is approximately 9.5 mA, and output power Pout for a load of 50, is approximately −4 dBm. It is understood that the oscillation frequency f osc  in the steady state is lower than the series resonance frequency f s  of approximately 3.90 GHz of the FBAR  56 . 
   The reason why the oscillation frequency varies from the initial oscillation frequency f start  to the steady oscillation frequency f osc  is that, as stated above, the values of the small signal operation reactance {−X NEG (A small )} and the large signal operation reactance {−X NEG (A osc )} vary due to the nonlinearity of the transistors included in the negative resistance circuit  60 . An example can be found in which the phenomenon that the initial oscillation frequency f start  and the steady oscillation frequency f osc , vary as described above has been observed in an oscillator other than the VCO  50  using the FBAR  56  (refer to Kazuhiko Honjo, “Microwave semiconductor circuit—fundamentals and developments,” published by Nikkan Kogyo Shimbun, p. 170 (1993)). However, there have been no reported examples concerning a VCO using an FBAR. Further, in the VCO  50  using the FBAR  56 , oscillation is normally implemented in a frequency range where the reactance X FBAR  of the FBAR  56  is a positive value to be assumed as an inductance. In other words, oscillation is implemented in a frequency range from the series resonance frequency f s  to the parallel resonance frequency f p  of the FBAR  56 . No example is found in which oscillation is stably implemented in a frequency outside the frequency range between the series resonance frequency f s  and the parallel resonance frequency f p . 
   As a comparative example, in order to provide steady oscillation in the frequency range between the series resonance frequency f s  and the parallel resonance frequency f p  of the FBAR  56 , a VCO circuit is designed with a similar circuitry of the VCO  50  so that large signal reactances of circuitry elements other than the FBAR  56  satisfy the following inequality,
 
 Xa   VAR (ω s )+ Xa   ADJ (ω s )+ Xa   NEG ( A   osc , ω s )&lt;0.  (20)
 
Here, Xa VAR (ω s ) is a reactance of a reactance controller, Xa ADJ (ω s ) is a reactance of a phase adjuster, and Xa NEG (A osc , ω s ) is a reactance of the negative resistance circuit  60  during the steady oscillation.
 
   In the first embodiment, as shown in  FIG. 14 , the steady oscillation frequency f osc  of the VCO  50  exhibits great dependency on the control voltage V control  in comparison with that in the comparative example. Here, assuming that 1.35 V is a center value of the control voltage V control , the steady oscillation frequency f osc  when the control voltage is 1.35V is defined as a center frequency f 0 . In the first embodiment, the center frequency f 0  is in a frequency range lower than the series resonance frequency f s  of the FBAR  56 . When the control voltage V control  is in a range from 0.6 V to 2.1 V, the steady oscillation frequency f osc  varies from approximately 3.802 GHz to 3.867 GHz. On the other hand, in the comparative example, the center frequency f 0  is in a frequency range between the series resonance frequency f s  and the parallel resonance frequency f p  of the FBAR  56 . When the control voltage V control  is in the range from 0.6 V to 2.1 V, the steady oscillation frequency f osc  varies very little, from approximately 3.932 GHz to 3.945 GHz. 
     FIG. 15  shows the dependence of the steady oscillation frequency f osc  shown in  FIG. 14  on the control voltage V control , as a variation ratio of oscillation frequency. Here, the variation ratio of oscillation frequency is defined as (f osc −f 0 )/f 0 . The VCO  50  according to the first embodiment can yield a variation ratio of oscillation frequency of approximately 1.6% when varying the control voltage V control  from 0.6 V to 2.1 V. On the other hand, the VCO according to the comparative example yields a variation ratio of oscillation frequency of approximately 0.3% when varying the control voltage V control  from 0.6 V to 2.1 V. Therefore, it is understood that the VCO according to the comparative example can yield only one fifth or less the variation ratio of oscillation frequency yielded by the VCO  50  according to the first embodiment. 
   As shown in  FIG. 16 , the VCO  50  according to the first embodiment provides a low phase noise characteristic, specifically, a phase noise of approximately −140 dBc/Hz in a frequency offset of 1 MHz. The reason why the phase noise is suppressed to a low level is that the FBAR  56  having a high Q value is used as the resonator  70 . 
   As described above, the VCO  50  using the FBAR  56  according to the first embodiment can provide low phase noise and assures a sufficiently wide frequency tunability because of the high Q value of the FBAR  56  at resonance. Accordingly, a communication apparatus having the VCO  50  using the FBAR  56  as a local oscillator can transmit high quality information in bulk. 
     FIG. 17  shows frequency dependences of the reactance X RES  of the resonator  70 , and the reactances {−X NEG (A small )} and {−X NEG (A osc )} of the negative resistance circuit  60 , which are measured by varying the electrode area S of the FBAR  56  while the other circuitry is not changed. The FBAR  56  is fabricated using AlN as the piezoelectric thin film. Here, a bias voltage applied by the DC power supply Vcc of the negative resistance circuit  60  is set to 2.7 V, and the control voltage V control  is set to 1.35 V (the center voltage). When the electrode area S of the FBAR  56  is increased from 6400 μm 2  to 27500 μm 2 , the initial oscillation frequency f start  in the small signal operation is shifted to higher frequencies between the series resonance frequency f s  and the parallel resonance frequency f p  of the FBAR  56 . Moreover, the stable oscillation frequency f osc  in the steady state is further shifted to lower frequencies than the series resonance frequency f s  of the FBAR  56 . That is, a VCO using the FBAR  56  with an electrode area S of 6400 μm 2  to 27500 μm 2  satisfies the conditions for oscillation start and for steady oscillation in the first embodiment. 
     FIG. 18  is a graph obtained by plotting the initial oscillation frequency f start  and the stable oscillation frequency f osc  in relation to the electrode area S of the FBAR  56  shown in  FIG. 17  when changing the area S of the FBAR  56  from 6400 μm 2  to 27500 μm 2 . The initial oscillation frequency f start  in the small signal operation is between the series resonance frequency f s  and the parallel resonance frequency f p  of the FBAR  56 , and the stable oscillation frequency f osc , is lower than the series resonance frequency f s  of the FBAR  56 . When the FBAR  56  is extrapolated up to the electrode area S=0, the values of the initial oscillation frequency f start  and the stable oscillation frequency f osc  both substantially correspond to the series resonance frequency f s  of the FBAR  56 . 
     FIG. 19  shows the control voltage dependence of the stable oscillation frequency f osc  when the electrode area S of the FBAR  56  is 6400 μm 2 , 10000 μm 2  and 18200 μm 2 . It is understood from  FIG. 19  that the oscillation frequency f osc  in the steady state is lower than the series resonance frequency f s  of the FBAR  56  in a range of entire control voltages from 0 V to 2.7 V. Moreover, a larger electrode area S of the FBAR  56  can provide a VCO having a greater variation in frequency with respect to the control voltage V control . 
     FIG. 20  shows frequency variable ratios plotted in relation to the electrode area S of the FBAR  56  when the control voltage V control  for the reactance controller  52  is controlled within a range from 0 V to 2.7 V and a range from 0.6 V to 2.1 V. The frequency variable ratio is defined as (f max −f min )/f 0  where the f max  and f min  indicate the highest and lowest oscillation frequencies, respectively, in each control voltage range, and the center frequency f 0  is an oscillation frequency when the control voltage V control  is the center voltage of 1.35V. It is understood from  FIG. 20  that the frequency tunability increases substantially in direct proportion to the electrode area S of the FBAR  56 . However, in a region where the electrode area S of the FBAR  56  is larger than 18200 μm 2 , although oscillation occurs in part of the range of the control voltage V control , oscillation cannot be provided in the entire range of the control voltage V control . 
     FIG. 21  shows frequency variable ratios (f max −f min )/f 0  plotted in relation to the reactance ratio X VAR0 /X FBAR0  of the reactance controller  52  to the FBAR  56  when the control voltage V control  for the reactance controller  52  is controlled within a range from 0 V to 2.7 V and a range from 0.6 V to 2.1 V. It is understood from  FIG. 21  that a larger value of the reactance ratio X VAR0 /X FBAR0  can yield a wider frequency tunability. For example, when the voltage tunability of the control voltage V control  is set from 0.6 V to 2.1 V, a frequency tunability of 1% or more can be obtained if the value of the reactance ratio X VAR0 /X FBAR0  is 0.30 or larger. However, when the value of the reactance ratio X VAR0 /X FBAR0  is larger than 1, oscillation is stopped at some control voltages V control . Therefore, in order to oscillate in the entire range of the control voltage V control , it is desirable that the value of the reactance ratio X VAR0 /X FBAR0  is less than 1.50. 
   Note that, in the first embodiment, a variable capacitance diode or the like, is used for the reactance controller  52 . Since the variable capacitance diode and the FBAR  56  are both capacitive elements, the reactance is inversely proportional to the electrostatic capacity CFO. Therefore,  FIG. 21  shows the fact that the greater the ratio of the electrostatic capacity C F0  of the FBAR  56  to the electrostatic capacity C VAR  of the variable capacitance diode, the larger the frequency variable ratio. 
     FIG. 22  shows the definition of values of a maximum reactance difference ΔX VAR  of the reactance controller  52  and of a reactance difference ΔX FBAR  of the FBAR  56 , around the resonance frequency. 
   The reactance X VAR  of the reactance controller  52  varies with the control voltage V control . When the voltage variable range of the control voltage V control  is set from 0.6 V to 2.1 V, as shown in  FIG. 22 , the value of the reactance X VAR  of the reactance controller  52  at the series resonance frequency f s  is varied from −5.6 Ω to −14.2 Ω. Accordingly, the maximum reactance difference ΔX VAR  is 8.6 Ω. Similarly, when the control voltage V control  is varied from 0 V to 2.7 V, the maximum reactance difference ΔX VAR  is 15.7 Ω. Therefore, when the voltage variable range of the control voltage V control  is set from 0.6 V to 2.1 V, the value of the reactance variation ratio ΔX VAR /ΔX VAR0  is approximately 0.85. The value of the reactance variation ratio ΔX VAR /ΔX VAR0  reflects the capacitance variation ratio of the used variable capacitance diode for the reactance controller  52 . In order to obtain a large frequency variable ratio, it is desirable that the reactance variation ratio ΔX VAR /ΔX VAR0  is a large value of larger than 0.50. 
   The value of the reactance difference ΔX FBAR  of the FBAR  56  shown in  FIG. 22  is a value obtained by subtracting the minimum value X FBARMin  from the maximum value X FBARMax  of X FBAR  around the resonance frequency, as already shown in the equation (18). The value of ΔX FBAR  varies with the electrode area S of the FBAR  56 . When the electrode area S of the FBAR  56  shown in  FIG. 22  is 10000 μm 2 , the value of the ΔX FBAR  is approximately 98 Ω. The larger the electrode area S of the FBAR  56 , the smaller the value ΔX FBAR  tends to be. For example, when the electrode area S of the FBAR  56  is 18200 μm 2 , the value of ΔX FBAR  is approximately 55 Ω. 
     FIG. 23  shows frequency variable ratios (f max −f min )/f 0  plotted in relation to ΔX VAR /ΔX FBAR  when the control voltage V control  for the reactance controller  52  is controlled within a range from 0 V to 2.7 V and a range from 0.6 V to 2.1 V. It is understood that the frequency variable ratio (f max −f min )/f 0  increases with an increase in the value of the reactance ratio ΔX VAR /ΔX FBAR . It is found that a frequency tunability of 1% or more can be obtained by setting the value of the reactance ratio ΔX VAR /ΔX FBAR  to 0.05 or larger. When the value of the reactance ratio ΔX VAR /ΔX FBAR  is too large, however, oscillation is stopped at some control voltages V control . Therefore, in order to oscillate in the entire range of the control voltage V control , it is desirable that the value of the reactance ratio ΔX VAR /ΔX FBAR  be 0.30 or smaller. 
   In  FIG. 21 , the dependences of the frequency variable ratio (f max −f min )/f 0  on the reactance ratio X VAR0 /X FBAR0  when the control voltage variable range is from 0.6 V to 2.1 V and from 0 V to 2.7 V are represented by different straight lines. By comparison, in  FIG. 23 , the dependences of the frequency variable ratio (f max −f min )/f 0  on the reactance ratio ΔX VAR /ΔX FBAR  when the control voltage variable range is from 0.6 V to 2.1 V and from 0 V to 2.7 V are represented by substantially identical straight lines. Accordingly, the expression using the reactance ratio ΔX VAR /ΔX FBAR  has more general meaning than the expression using the reactance ratio X VAR0 /X FBAR0 . 
   As described above, it is possible to vary the oscillation frequency band of the VCO by varying the electrode area S of the FBAR  56 . However, the oscillation frequency band of the VCO can be also varied by varying thickness of the piezoelectric thin film of the FBAR  56 . The series resonance frequency f s  and the parallel resonance frequency f p  of the FBAR  56  are determined depending on a time period taken for a sound to travel in the piezoelectric thin film between the electrodes of the FBAR  56 . When the thickness of the piezoelectric thin film is increased by, for example, 10%, both the series resonance frequency f s  and the parallel resonance frequency of the FBAR  56  decrease by approximately 10%. On the contrary, when the thickness of the piezoelectric thin film decreases, the series resonance frequency f s  and the parallel resonance frequency of the FBAR  56  increase substantially in direct proportion to the thickness of the piezoelectric thin film. Accordingly, it is possible to vary the oscillation frequency band of the VCO by varying the thickness of the piezoelectric thin film of the FBAR  56  and thereby varying the series resonance frequency f s  of the FBAR  56 . 
   First Modification of the First Embodiment 
   As shown in  FIG. 24 , a VCO  50   a  according to a first modification of the first embodiment of the present invention includes a resonator  70   a  in which a reactance controller  52   a , a phase adjuster  54  and an FBAR  56  are coupled, and a negative resistance circuit  60   a  connected to the resonator  70   a.    
   The negative resistance circuit  60   a  includes a CMOS inverter  80 , a feedback resistance R fb  connected to an input and an output of the CMOS inverter  80 , a load capacitance C L1  connected to the input side of the CMOS inverter  80 , and a load capacitance C L2  connected to the output thereof. The load capacities C L1  and C L2  are grounded. The output of the CMOS inverter  80  is connected to the output node  64  of the VCO  50   a.    
   The FBAR  56  in the resonator  70   a  is connected to a node  74  between the load capacity C L2  on the output of the CMOS inverter  80  and the output node  64 . The phase adjuster  54 , connected to the FBAR  56 , is connected to the reactance controller  52   a  with a node  78  interposed therebetween. The reactance controller  52   a  is connected to the input node  62  to which a control voltage for reactance control is applied. Moreover, the reactance controller  52   a  is connected to the input of the CMOS inverter  80 , to which the feedback resistance R fb  and the load capacity C L1  are connected, with a node  76  interposed therebetween. 
   The VCO  50   a  according to the first modification of the first embodiment is different from the VCO according to the first embodiment in that the CMOS inverter  80  is used as the negative resistance circuit  60   a . The other configurations are similar to the first embodiment. Therefore, redundant descriptions will be omitted. 
   As shown in  FIG. 25 , in the reactance controller  52   a  in the resonator  70   a , a variable capacitance C VAR  such as a variable capacitance diode is used. An inductance L DC  for removing high frequency components included in control voltage applied from the input node  62  is connected between the variable capacitance C VAR  and the node  78 . A DC cut capacitance C CUT  is connected between the variable capacitance C VAR  and the node  76 . Moreover, a high frequency signal blocking inductance L C , which is grounded, is connected between the variable capacitance C VAR  and the DC cut capacitance C CUT . 
   The DC cut capacitance C CUT  and the high frequency signal blocking inductance L C , both connected to the variable capacitance C VAR , are unnecessary components in the resonator  70   a . Therefore, in order not to affect the oscillation conditions of VCO  50   a , the values of the DC cut capacitance C CUT  and the high frequency signal blocking inductance L C  are designed larger so that the DC cut capacitance C CUT  and the high frequency signal blocking inductance L C  can be ignored with respect to the reactance of the series connection of the FBAR  56 , the phase adjuster  54  and the reactance controller  52   a . For example, it is sufficient that the value of the DC cut capacitance C CUT  is at least one order of magnitude greater than the value of the variable capacitance C VAR , and that the high frequency signal blocking inductance L C  is at least one order of magnitude greater than the inductance L ADJ  in the phase adjuster  54 . 
   Accordingly, a circuit equivalent to the resonator  70   a  may be substantially the same as that shown in  FIG. 3 , and therefore the complex impedance Z RES  of the resonator  70   a  can be expressed similarly by the equation (8). 
   The CMOS inverter  80  in the negative resistance circuit  60   a  provides nonlinearity in the large amplitude steady state. Therefore, circuit parameters for the CMOS inverter  80  and the resonator  70   a  are determined by simulation. Thus, it is possible to determine the complex impedances Z RES  and Z NEG  of the resonator  70   a  and the negative resistance circuit  60   a , respectively, which satisfy the oscillation start conditions at small signals represented by the expressions (9) and (10) and the steady oscillation condition represented by the equation (14). 
   As described above, according to the first modification of the first embodiment, it is possible to stably start oscillation by satisfying the inequality (13) immediately after turning on power to the VCO  50   a  and thereby allowing the initial oscillation angular frequency ω start  between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p  of the FBAR  56 . In the steady state after the oscillation has started, it is possible to achieve the steady oscillation angular frequency ω osc  lower than the series resonance angular frequency ω s  by satisfying the inequality (15) utilizing the nonlinearity of the negative resistance circuit  60   a . Thus, it is possible to increase the frequency tunability of the VCO  50   a.    
   In addition, the CMOS inverter  80  in the negative resistance circuit  60   a  is desirable for integration and manufacturing in comparison with a bipolar transistor and therefore advantageous in reducing the size and costs of the VCO  50   a . Further, the development of a high frequency CMOS analog circuit is in progress, and thus merged installation of a high frequency analog circuit and a digital circuit will be facilitated. 
   Second Modification of the First Embodiment 
   As shown in  FIG. 26 , a VCO  50   b  according to a second modification of the first embodiment of the present invention includes a resonator  70   b  in which a reactance controller  52   b , a phase adjuster  54  and an FBAR  56  are coupled, and a negative resistance circuit  60   b  connected to the resonator  70   b.    
   The negative resistance circuit  60   b  includes a CMOS inverter  80  and a feedback resistance R fb  connected to an input and an output of the CMOS inverter  80 . The output of the CMOS inverter  80  is connected to an output node  64  of the VCO  50   b.    
   The FBAR  56  in the resonator  70   b  is connected between the output of the CMOS inverter  80  and the output node  64 . The phase adjuster  54 , connected to the FBAR  56 , is connected between the input of the CMOS inverter  80  and the feedback resistance R fb . The reactance controller  52   b  includes first and second variable capacitances C VAR1  and C VAR2  which are variable capacitance diodes or the like. The first variable capacitance C VAR1  is connected between the output of the CMOS inverter  80  and the output node  64  to the FBAR  56 , with a DC cut capacitance C CUT1  interposed therebetween. An input node  62   a , to which control voltage for reactance control is applied and is connected between the first variable capacitance C VAR1  and the DC cut capacitance C CUT1 , with an inductance L DC1  removing a high frequency component interposed therebetween. Moreover, the second variable capacitance C VAR2  is connected between the input of the CMOS inverter  80  and the feedback resistance R fb  to the phase adjuster  54 , with a DC cut capacitance C CUT2  interposed therebetween. An input node  62   b , to which control voltage for reactance control is applied, is connected between the second variable capacitance C VAR2  and the DC cut capacitance C CUT2 , with an inductance L DC2  removing a high frequency component interposed therebetween. 
   Although the first and second variable capacitances C VAR1  and C VAR2  of the reactance controller  52   b  are provided in the resonator  70   b , the first and second variable capacitances C VAR1  and C VAR2  also serve as load capacitances of the CMOS inverter  80  in the negative resistance circuit  60   b . Thus, the circuitry of the negative resistance circuit  60   b  can be simplified. Note that values of the DC cut capacitances C CUT1  and C CUT2  are at least one order of magnitude greater than the first and second variable capacitance C VAR 1  and C VAR2 , and therefore can be ignored as reactance. 
   The second modification of the first embodiment is different from the first modification of the first embodiment in that the first and second variable capacitances C VAR1  and C VAR2  are provided for the reactance controller  52   b  in the resonator  70   b  and also serve as the load capacitances of the CMOS inverter  80  in the negative resistance circuit  60   b . The other configurations are substantially the same as the first modification of the first embodiment. Therefore, redundant descriptions will be omitted. 
   Unlike the complex impedances in the first embodiment and the first modification of the first embodiment, the complex impedance of the resonator  70   b  shown in  FIG. 26  is expressed by a complicated expression. Therefore, for convenience, allowing the first and second variable capacitances C VAR1  and C VAR2  in the resonator  70   b  to be included in the negative resistance circuit  60   b , complex impedances Zb RES  and Zb NEG  of the resonator  70   b  and the negative resistance circuit  60   b , respectively, are expressed as follows.
 
 Zb   RES   =Z   FBAR   +Z   ADJ   (21)
 
 Zb   NEG =1/{1 /Z   NEG +1/(2 *Z   VAR )}= Rb   NEG   +j*Xb   NEG   (22)
 
Here, the complex impedance Zb NEG  of the negative resistance circuit  60   b  is equivalent to a parallel connection of a component Z NEG  attributable to the CMOS inverter  80  and a composite component of (2*Z VAR ) in a series connection of the first and second variable capacitances C VAR1  and C VAR2 , which results in the complicated expression. However, by mathematically arranging the expression, the expression can be finally expressed using a resistance Rb NEG  and a reactance Xb NEG .
 
   In such case, corresponding to the inequality (13), an expression to satisfy the oscillation start condition of the VCO  50   b  can be expressed as follows.
 
 Xb   NEG ( A   small , ω osc )+ X   ADJ (ω osc )&lt;0  (23)
 
Moreover, corresponding to the expressions (14) and (15) expressions to satisfy the steady oscillation condition are expressed as follow.
 
 Zb   NEG ( A   osc , ω osc )+ Zb   RES (ω osc) =0  (24)
 
0 &lt;X   ADJ (ω s )+ Xb   NEG ( A   osc , ω s )&lt;1/(  7   s *C F0 )  (25)
 
   As described above, according to the second modification of the first embodiment, it is possible to stably start oscillation by satisfying the inequality (23) immediately after turning on power to the VCO  50   b  and thereby allowing the initial oscillation angular frequency ω start  between the series resonance angular frequency ω s  and the parallel resonance angular frequency ω p  of the FBAR  56 . In the steady state after the oscillation has started, it is possible to allow the steady oscillation angular frequency ω osc  lower than the series resonance angular frequency by satisfying the inequality (25) utilizing the nonlinearity of the negative resistance circuit  60   b . Thus, it is possible to increase the frequency tunability of the VCO  50   b.    
   In addition, the CMOS inverter  80  in the negative resistance circuit  60   b  is desirable for integration and manufacturing in comparison with a bipolar transistor. Further, the CMOS inverter  80  is advantageous in reducing the size and cost of the VCO  50   b . Furthermore, since the first and second variable capacitances C VAR1  and C VAR2  in the reactance controller  52   b  are used as the load capacities of the CMOS inverter  80 , it is possible to simplify the circuitry of the negative resistance circuit  60   b.    
   Second Embodiment 
   As shown in  FIG. 27 , a frequency synthesizer according to a second embodiment of the present invention includes a PLL circuit  99  which generates a high frequency oscillation signal S HF ; first and second voltage comparators  96  and  98  which monitor a control voltage V control  generated by the PLL circuit  99  so as to compare with first and second comparison potentials V comp1  and V comp2 , respectively; and a control circuit  100  which generates any one of control signals SG C1  to SG C4  to the PLL circuit  99  based on an output signal V C1  or V C2  from the first or second voltage comparator  96  or  98 . 
   The PLL circuit  99  includes first to fourth VCOs  51   a  to  51   d  having inputs connecting with each other, to which the control voltage V control  for resonators in the respective VCOs is applied. The first to fourth VCOs  51   a  to  51   d  are connected to an output node  64  and to an input of a first frequency divider  82  via switches SW 1  to SW 4 , respectively, which are connected to outputs of the respective VCOs. Outputs of the first frequency divider  82  and a second frequency divider  84  connected to a reference signal source  86  are connected to an input of a phase comparator  88 . Moreover, a lock detector  90  is connected to the phase comparator  88 . An input and an output of a control voltage generator  91  are respectively connected to the output of the phase comparator  88 , and to the inputs of the first and second voltage comparators  96  and  98 . The output of the control voltage generator  91  is also connected to the inputs of the first to fourth VCOs  51   a  to  51   d . The control voltage generator  91  has a charge pump  92  on the input portion and a loop filter  94  on the output portion. 
   The first and second comparison potentials V comp1  and V comp2  are applied to the first and second voltage comparators  96  and  98 , respectively, to which the output of the control voltage generator  91  is connected. Here, the first and second comparison potentials V comp1  and V comp2  correspond to the lower and upper limit potentials of the control voltage generated by the control voltage generator  91 , respectively. The outputs of the first and second voltage comparators  96  and  98  are connected to the control circuit  100 . Moreover, outputs of the control circuit  100  generating the control signals SG C1  to SG C4  are respectively connected to the switches SW 1  to SW 4  of the first to fourth VCOs  51   a  to  51   d.    
   The first to fourth VCOs  51   a  to  51   d  are designed such that the respective oscillation frequencies are variable in different frequency bands from one another, using FBARs having different film thicknesses. A circuitry inside the first to fourth VCOs  51   a  to  51   d  is similar to that of the VCO  50  in the first embodiment. Therefore, redundant descriptions will be omitted. 
   As shown in  FIG. 28 , the first to fourth VCOs  51   a  to  51   d  have oscillation frequency bands different from one another and are controlled by the control voltage V control  having a value between the first and second comparison potentials V comp1  and V comp2  The range of the lower limit to upper limit of the oscillation frequency bands for the first to fourth VCOs  51   a  to  51   d  are f 1Min  to f 1Max , f 2Min  to f 2Max , f 3Min  to f 3Max , and f 4Min  to f 4Max , respectively. The upper limit oscillation frequency f 1Max  of the first VCO  51   a  is set higher than the lower limit oscillation frequency f 2Min  of the second VCO  51   b . The upper limit oscillation frequency f 2Max  of the second VCO  51   b  is set higher than the lower limit oscillation frequency f 3  Min of the third VCO  51   c . The upper limit oscillation frequency f 3Max  of the third VCO  51   c  is set to be higher than the lower limit oscillation frequency f 4Min  of the fourth VCO  51   d . Therefore, an overlap is provided between the oscillation frequency bands of the first and second VCOs  51   a  and  51   b , between the oscillation frequency bands of the second and third VCOs  51   b  and  51   c , and between the oscillation frequency bands of the third and fourth VCOs  51   d  and  51   d . Accordingly, the first to fourth VCOs  51   a  to  51   d  collectively have a frequency band from the lower limit oscillation frequency f 1Min  of the first VCO  51   a  to the upper limit oscillation frequency f 4Max  of the fourth VCO  51   d.    
   The first to fourth VCOs  51   a  to  51   d  are switched in order from the first VCO  51   a  to the fourth VCO  51   d , or reversely in order from the fourth VCO  51   d  to the first VCO  51   a , using the switches SW 1  to SW 4  which are switched by the control signals SG C1  to SG C4  from the control circuit  100  to be described later. Thus, it is possible for the frequency synthesizer to operate in a wide oscillation frequency band from f 1Min  to f 4Max . 
   The first frequency divider  82  in the PLL circuit  99  divides an oscillation signal S HF  which is oscillated by the first to fourth VCOs  51   a  to  51   d  and selected using the switches SW 1  to SW 4 . The second frequency divider  84  sets a dividing ratio based on frequency data provided by an external circuit (not shown) and divides a reference signal S REF  from the reference signal source  86 . For example, the oscillation signal S HF  provided by one of the first to fourth VCOs  51   a  to  51   d  is in a GHz band. On the other hand, the reference signal S REF  provided by the oscillation of, for example, a quartz oscillator or the like is in a band from approximately 5 MHz to 40 MHz. Particularly, a band from 16 MHz to 32 MHz is used for communication. Therefore, the dividing ratio used in the first frequency divider  82  is set to a magnitude of a single digit greater than that used in the second frequency divider  84 . Moreover, the first frequency divider  82  is set such that the dividing ratio thereof is altered depending on the frequency data of the reference signal source  86  when the frequency data are altered. 
   The phase comparator  88  compares a phase of a divided oscillation signal D F1 , which is divided by the first frequency divider  82 , with a phase of a divided reference signal D F2 , which is divided by the second frequency divider  84 . The charge pump  92  in the control voltage generator  91  implements time integration for a phase error signal ΔD F  which is generated as a result of the comparison of the phases of the divided oscillation signal D F1  and the divided reference signal D F2  by the phase comparator  88 . The charge pump  92  then generates a phase error integrated signal S DF  having a magnitude corresponding to the phase error signal ΔDF. The loop filter  94  in the control voltage generator  91  converts the phase error integrated signal S DF  into a DC voltage and thus generates the control voltage V control . The charge pump  92  and the loop filter  94  are designed based on a phase lock technology and enable the reference signal S REF  and the oscillation signal S HF  to synchronize with each other within a predetermined period of time. Based on the phase error signal ΔD F  from the phase comparator  88 , the lock detector  90  detects whether the PLL circuit  99  is in an unlock condition or in a lock condition. When detecting the lock condition, the lock detector  90  locks the PLL circuit  99 . 
   The first and second voltage comparators  96  and  98  have the first and second comparison potentials V comp1  and V comp2 , respectively, which are lower and upper limit potentials, respectively. The first and second voltage comparators  96  and  98  monitor whether the control voltage V control  is within a range between the first and second comparison potentials V comp1  and V comp2  Specifically, when the control voltage V control  is lower than the first comparison potential V comp1 , the first voltage comparator  96  generates an output signal VC 1 . When the control voltage V control  is higher than the second comparison potential V comp2 , the second voltage comparator  98  generates an output signal VC 2 . 
   The control circuit  100  generates any one of the control signals SG C1  to SG C4  in response to the output signal VC 1  or VC 2  from the first or second voltage comparator  96  or  98 , so as to turn on any one of the switches SW 1  to SW 4 . When neither of the output signals VC 1  nor VC 2  is received, the control circuit  100  retains any one of the control signals SG C1  to SG C4  which is last generated. 
   Next, a description will be given of the operation of the frequency synthesizer according to the second embodiment. When turning on power, the control circuit  100  generates as an initial value, for example, a control signal SG C1  to select the first VCO  51   a . The control signal SG C1  turns on the switch SW 1 . The other control signals SG C2  to SG C4  are not provided, and therefore the switches SW 2  to SW 4  are off. Accordingly, the oscillation signal S HF  having the oscillation frequency of the first VCO  51   a  is divided by the first frequency divider  82 , and a divided oscillation signal D F1  is sent to the phase comparator  88 . 
   The reference signal S REF  is divided by the second frequency divider  84 , and the divided reference signal D F2  is added to the phase comparator  88 . 
   In the phase comparator  88 , the phases of the divided oscillation signal D F1  and the divided reference signal D F2  are compared with each other. When the oscillation frequency of the first VCO  51   a  is higher than a desired frequency, the phase error signal ΔD F  is generated in the phase comparator  88 . The phase error signal ΔD F  is added to the charge pump  92  in the control voltage generator  91  and then implemented time integration. A phase error integrated signal SD F  provided by the time integration is smoothed by the loop filter  94 , and the control voltage V control  is thus provided. The control voltage V control  is sent to the first and second voltage comparators  96  and  98  and then compared with the first and second comparison potentials V comp1  and V comp2 , respectively. 
   For example, it is assumed that a signal which allows a desired oscillation signal S HF  provided within the oscillation frequency band of the third VCO  51   c  is provided from an external circuit to the first frequency divider  82 . In such case, the control voltage V control  provided from the control voltage generator  91  is so high as to exceed the second comparison potential V comp2 , which is the upper limit potential. Accordingly, the second voltage comparator  98  sends the output signal VC 2  to the control circuit  100  so as to provide an instruction to switch to the second VCO  51   b  having the higher oscillation frequency band. 
   The control circuit  100  stores the fact that the first VCO  51   a  has been selected. When the output signal VC 2  is sent from the second voltage comparator  98 , the control circuit  100  generates the control signal SG C2  to turn on the switch SW 2  in order to switch to the higher frequency band. Control signals SG C1 , SG C3  and SG C4  are not provided, and the switches SW 1 , SW 3  and SW 4  are turned or remain off. 
   The oscillation signal S HF  having the oscillation frequency of the second VCO  51   b  is processed by the above-described PLL circuit  99 , and the control voltage V control  is re-generated. The control voltage V control  is sent into the first and second voltage comparators  96  and  98  and then compared with the first and second comparison potentials V comp1  and V comp2 . However, the control voltage V control  is still higher than the second comparison potential V comp2 , which is the upper limit potential, and therefore the output signal VC 2  providing the instruction to switch to the third VCO  51   c  having the higher oscillation frequency band is sent from the second voltage comparator  98  to the control circuit  100 . The control circuit  100  generates the control signal SG C3  instead of the control signal SG C2  and thereby turns on the switch SW 3 . 
   The oscillation signal S HF  having the oscillation frequency of the third VCO  51   c  is similarly processed by the above-described PLL circuit  99 . Since the oscillation signal S HF  from the third VCO  51   c  is in the desired frequency band, a phase difference between the divided oscillation signal D F1  and the divided reference signal D F2  is small. Therefore, the small phase error signal ΔD F  is generated by the phase comparator  88 . Then, the control voltage V control  newly smoothed by the charge pump  92  and loop filter  94  in the control voltage generator  91  is within a voltage range between the first and second comparison potentials V comp1  and V comp2 . Accordingly, the output signals VC 1 , and VC 2  are not generated by the first and second voltage comparators  96  and  98 . As a result, the control circuit  100  holds the switch SW 3  in an on-state. 
   Subsequently, in the phase comparator  88 , the phases of the divided oscillation signal D F1  and the divided reference signal D F2  are compared with each other, and the phase error signal ΔD F  is generated. When no phase difference exist between the divided oscillation signal D F1  and the divided reference signal D F2  as a result of the feedback control by the PLL circuit  99 , the lock detector  90  operates to lock the PLL circuit  99 . Once the PLL circuit  99  is locked, the control circuit  100  stops the operation of switching the VCOs  51   a  to  51   d  thereafter and holds the locked state even if the unlock condition is temporarily detected due to a disturbance. More specifically, as long as the unlock condition is not continuously detected for a predetermined period of time by the lock detector  90 , the oscillation signal S HF  from the currently selected third VCO  51   c  is provided from the output node  64 . 
   Next, it is assumed that frequency alteration data are provided to the PLL circuit  99  from the reference signal source  86  to oscillate in a different frequency band. In such case, since the VCOs  51   a  to  51   d  having a suitable frequency band are not selected, the phases of a divided oscillation signal D F1  and the divided reference signal D F2  are compared with each other by the phase comparator  88 , and the phase error signal ΔD F  is detected by the lock detector  90 . Since the phase error signal ΔD F  is not temporarily detected due to a disturbance, the phase error signal ΔD F  is continuously detected over the predetermined period of time. In such case, the PLL circuit  99  is unlocked by the lock detector  90 . The control circuit  100  is reset similarly when turning on power, and a control signal SG C1 , which is generated in the initial condition, is provided. The control signal SG C1  turns on the switch SW 1  to again select the first VCO  51   a  and controls the other switches SW 2  to SW 4  to be off. In such way, another search for a suitable VCO having a desired frequency band is performed again. 
   Note that, when the frequency alteration data is sent from the reference signal source  86  to the PLL circuit  99  to oscillate in a different frequency band, it is possible to achieve an operation similar to the foregoing with a circuitry which resets the control circuit  100  to the initial condition by using a frequency alteration signal of the frequency alteration data. 
   In the frequency synthesizer according to the second embodiment of the present invention, a plurality of VCOs having different frequency bands can be used for switching the VCOs. Therefore, it is possible to provide a frequency synthesizer which has a small phase noise and a wide variable frequency range. 
   First Modification of the Second Embodiment 
   As shown in  FIG. 29 , a frequency synthesizer according to a first modification of the second embodiment of the present invention includes a PLL circuit  99   a  which generates a high frequency oscillation signal S HF ; first and second voltage comparators  96  and  98  which monitor a control voltage V control  generated by the PLL circuit  99   a  by comparing with first and second comparison potentials V comp1  and V comp2 , respectively; and a control circuit  100  which generates any one of control signals SG C1  to SG C4  to a VCO  51 , based on an output signal V C1  or V C2  from the first or second voltage comparator  96  or  98 . 
   In the second embodiment, as shown in  FIG. 27 , the first to fourth VCOs  51   a  to  51   d  are used in the PLL circuit  99 . The first modification of the second embodiment is different from the second embodiment in that a single VCO  51  including first to fourth FBARs  56   a  to  56   d  is used in the PLL circuit  99   a . The other configurations are similar to each other. Therefore, redundant descriptions will be omitted. 
   The VCO  51  includes a resonator  70   c  connected to an output of a control voltage generator  91 ; and a negative resistance circuit  60  having an input connected to the resonator  70   c , and an output connected between an input of a first frequency divider  82  and an output node  64 . In the resonator  70   c , a phase adjuster  54  is connected in series to a reactance controller  52  to which the control voltage V control  is sent, and is connected to a plurality of switches SW 1  to SW 4  connected in parallel to one another. The switches SW 1  to SW 4  are connected to first to fourth FBARs  56   a  to  56   d , respectively, and output ends of the first to fourth FBARs  56   a  to  56   d  are connected to the input of the negative resistance circuit  60 . Outputs of the control circuit  100  generating the control signals SG C1  to SG C4  are respectively connected to the switches SW 1  to SW 4  for the first to fourth FBARs  56   a  to  56   d.    
   Using FBARs having different film thicknesses, the first to fourth FBARs  56   a  to  56   d  are designed such that the respective oscillation frequencies are variable in frequency bands different from one another. As shown in  FIG. 30 , in the VCO  51 , any one of the first to fourth FBARs  56   a  to  56   d  is incorporated by means of the switches SW 1  to SW 4 . The VCO  51  has oscillation frequency bands different from one another, depending on the incorporated FBAR, controlled by the control voltage V control  having a value between the first and second comparison potentials V comp1    and V   comp2 . The range of the lower limit to upper limit of the oscillation frequency bands for the first to fourth VCOs  51   a  to  51   d  are f 1Min  to f 1Max , f 2Min  to f 2Max , f 3Min  to f 3Max , and f 4Min  to f 4Max , respectively. The upper limit oscillation frequency f 1Max  of the VCO  51  incorporating the first FBAR  56   a  is set higher than the lower limit oscillation frequency f 2Min  of the VCO  51  incorporating the second FBAR  56   b . The upper limit oscillation frequency f 2Max  of the VCO  51  incorporating the second FBAR  56   b  is set higher than the lower limit oscillation frequency f 3Min  of the VCO  51  incorporating the third FBAR  56   c . The higher limit oscillation frequency f 3Max  of the VCO  51  incorporating the third FBAR  56   c  is set higher than the lower limit oscillation frequency f 4Min  of the VCO  51  incorporating the fourth FBAR  56   d . Therefore, an overlap is provided between the oscillation frequency bands provided by the first and second FBARs  56   a  and  56   b , between the oscillation frequency bands provided by the second and third FBARs  56   b  and  56   c , and between the oscillation frequency bands provided by the third and fourth FBARs  56   c  and  56   d . Accordingly, the VCO  51  incorporating the first to fourth FBAR  56   a  to  56   d  has a frequency band from the lower limit oscillation frequency f 1Min  provided by the first FBAR  56   a  to the upper limit oscillation frequency f 4Max  provided by the fourth FBAR  56   d.    
   Moreover, the first to fourth FBARs  56   a  to  56   d  are switched in order from the first FBAR  56   a  to the fourth FBAR  56   d , or reversely in order from the fourth FBAR  56   d  to the first FBAR  56   a , using the switches SW 1  to SW 4  which are switched by the control signals SG C1  to SG C4  from the control circuit  100 . Thus, it is possible for the frequency synthesizer to operate in the wide oscillation frequency band from f 1Min  to f 4Max . 
   In the above description, FBARs having different film thicknesses are used as the first to fourth FBARs  56   a  to  56   d . However, similar effects may be provided by using FBARs having different electrode areas. 
   As described above, according to the first modification of the second embodiment, since the single VCO  51  is used, it is possible to reduce the size and cost of resonator circuitry. In addition, low power consumption operation can be achieved. Moreover, the VCO  51  may be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100  sending the control signals SG C1  to SG C4  to the switches SW 1  to SW 4 . Thus, it is possible to provide a frequency synthesizer which has a small phase noise and a wide frequency tunability. 
   Second Modification of the Second Embodiment 
   As shown in  FIG. 31 , a frequency synthesizer according to a second modification of the second embodiment of the present invention includes a PLL circuit  99   b  which generates a high frequency oscillation signal S HF ; a voltage comparator  102  which monitors a control voltage V control  generated by the PLL circuit  99   b  so as to compare with a standard potential V STD ; and a control circuit  100   a  which generates any one of control signals SG C1  to SG C5  to a VCO  51 , based on an output signal VC L  or VC H  from the voltage comparator  102 . 
   The second modification of the second embodiment of the present invention is different from the first modification of the second embodiment in that a switch SW 5  for switching the control voltage V control , connected to an input of the VCO  51  in the PLL circuit  99   b , is used. The switch SW 5  switches between an output of a control voltage generator  91  and a standard potential V STD  of the voltage comparator  102  by a control signal SG C5  which is provided from the control circuit  100   a  based on the output signals VC H  and VC L  from the voltage comparator  102 . The other configurations are similar to the first modification of the second embodiment. Therefore, redundant descriptions will be omitted. 
   In an initial condition, the switch SW 5  connected to the input of the VCO  51 , is connected to the standard potential V STD . The standard potential V STD  for the voltage comparator  102  is set to the upper limit of the control voltage V control  for the reactance controller  52  in the resonator  70   c . The voltage comparator  102  compares the control voltage V control  with the standard potential V STD . The voltage comparator  102  sends the output signal VC H  to the control circuit  100   a  when the control voltage V control  is higher than the standard potential V STD  and sends the output signal VC L  when the control voltage V control  is lower than the standard potential V STD . 
   The control circuit  100   a  sends any one of the control signals SG C1  to SG C4  to the switches SW 1  to SW 4  for switching the first to fourth FBARs  56   a  to  56   d  in the resonator  70   c  depending on the output signal VC H  or VC L  from the voltage comparator  102 , in accordance with a predetermined algorithm. Moreover, when the voltage comparator  102  sends the output signal VC L , the control circuit  100   a  switches the switch SW 5  from the standard potential V STD  of the initial condition, to the output of the control voltage generator  91 . Therefore, when the oscillation signal S HF  from the VCO  51  is set in a desired frequency band, a feedback loop of the PLL circuit  99   b  is established. The feedback control by the PLL circuit  99   b  eliminates a phase difference between a divided oscillation signal D F1  and a divided reference signal D F2 . Accordingly, the PLL circuit  99   b  is locked. 
   Next, a description will be given of the operation of the frequency synthesizer according to the second modification of the second embodiment. The control circuit  100   a  in the frequency synthesizer uses the algorithm shown in  FIG. 32  in order to search an FBAR having a desired frequency band among the first to fourth FBARs  56   a  to  56   d  using the voltage comparator  102 . In the second modification of the second embodiment, searching is implemented in accordance with the algorithm shown in  FIG. 32 , initially using the second FBAR  56   b  having an intermediate frequency band. Here, for example, it is assumed that the reference signal source  86  sends such frequency data as to lock a phase in a frequency band including an oscillation signal S HF  of a desired high frequency when the fourth FBAR  56   d  is connected. 
   When turning on power of the frequency synthesizer, the control circuit  10   a  is reset, and a control signal SG C2  to select the second FBAR  56   b  as an initial value is generated to turn on only the switch SW 2 . The switch SW 5  is connected to the standard potential V STD , and the standard potential V STD  is provided to the reactance controller  52  of the resonator  70   c  in the VCO  51  shown in  FIG. 31 . The loop of the PLL circuit  99   b  is opened. The standard potential V STD  is set beforehand to the upper limit of the control voltage V control . Accordingly, the VCO  51  oscillates at a frequency determined by the resonance characteristics of the second FBAR  56   b  depending on the standard potential V STD . The oscillation signal S HF  is divided by the first frequency divider  82 , and the generated divided oscillation signal D F1  is sent to the phase comparator  88 . The divided reference signal D F2  provided by the second frequency divider  84  dividing the reference signal S REF  is also added to the phase comparator  88 . 
   In the phase comparator  88 , a phase error signal ΔD F  is generated. The phase error signal ΔD F  is added to the charge pump  92  in the control voltage generator  91  to implement time integration. A phase error integrated signal SD F  provided by the time integration is smoothed by the loop filter  94 , and thus the control voltage V control  is generated. Since the oscillation frequency using the second FBAR  56   b  is lower than the desired frequency, the control voltage V control  is higher than the standard potential V STD  for the voltage comparator  102 . Accordingly, the output signal VC H  is sent from the voltage comparator  102  to the control circuit  100   a.    
   In accordance with the algorithm shown in  FIG. 32 , the control circuit  100   a  sends, to the switch SW 3 , the control signal SG C3  to switch from the currently selected second FBAR  56   b  to the third FBAR  56   c  having a higher frequency band. Moreover, the control circuit  100   a  holds the switch SW 5  in connection with the standard potential V STD . 
   Since the oscillation frequency of the oscillation signal SH F  generated by using the third FBAR  56   c  is lower than the desired frequency, the generated control voltage V control  is higher than the standard potential V STD . Accordingly, the output signal VC H  is sent from the voltage comparator  102  to the control circuit  100   a . In accordance with the algorithm shown in  FIG. 32 , the control circuit  100   a  sends, to the switch SW 4 , the control signal SG C4  to switch from the currently selected third FBAR  56   c  to the fourth FBAR  56   d  having a higher frequency band. Moreover, the control circuit  100   a  holds the switch SW 5  in connection with the standard potential V STD . 
   The oscillation frequency of the oscillation signal SH F  generated by using the fourth FBAR  56   d  is close to the desired frequency. Then, the generated control voltage V control  is lower than the standard potential V STD . Accordingly, the output signal VC L  is sent from the voltage comparator  102  to the control circuit  100   a . Therefore, the control circuit  100   a  holds the switch SW 4  in an on-state. At the same time, the control circuit  100   a  turns the switch SW 5  from the connection to the standard potential V STD  to the connection to the output of the control voltage generator  91 . As a result, the control voltage V control  provided from the loop filter  94  is applied to the resonator  70   c  in the VCO  51 , and thus the feedback loop of the PLL circuit  99   b  is established. The feedback control by the PLL circuit  99   b  eliminates a phase difference between the divided oscillation signal D F1  and the divided reference signal D F2 . Accordingly, the PLL circuit  99   b  is locked. Thus, the search for the FBAR having a frequency band including a frequency of the reference signal S REF  from the reference signal source  86  is implemented following a path indicated by the dashed line in  FIG. 32 . 
   As described above, according to the second modification of the second embodiment, since the single VCO  51  is used, it is possible to reduce the size and cost of a resonator circuit. In addition, low power consumption operation can be achieved. Moreover, since the single voltage comparator  102  is used to monitor the control voltage V control  so as to compare with the standard potential V STD , it is possible to simplify the circuitry. Furthermore, the VCO  51  may be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100  sending the control signals SG C1  to SG C4  to the switches SW 1  to SW 4  for switching the FBARs. Thus, it is possible to provide a frequency synthesizer which has a small phase noise and a wide frequency tunability. 
   Third Modification of the Second Embodiment 
   As shown in  FIG. 33 , a frequency synthesizer according to a third modification of the second embodiment of the present invention includes: a PLL circuit  99   c  which generates a high frequency oscillation signal S HF ; a control circuit  100   b  which sends any one of control signals SG C1  to SG C5  to the PLL circuit  99   c , based on an output signal corresponding to a phase difference generated by a phase comparator  88   a  in the PLL circuit  99   c ; and a reset signal generator  104  which sends a dividing reset signal DS RST  to first and second frequency dividers  82  and  84 , triggered by a reset command signal SG RST  from the control circuit  100   b.    
   The third modification of the second embodiment is different from the second modification of the second embodiment in that the control circuit  100   b  sends any one of the control signals SG C1  to SG C4  to the switches SW 1  to SW 4  for switching the first to fourth FBARs  56   a  to  56   d  provided in the VCO  51 , based on an up signal DS UP  or a down signal DS DOWN  according to a phase difference between a divided oscillation signal D F1  and a divided reference signal D F2  from the phase comparator  88   a  in the PLL circuit  99   c . The other configurations are similar to the second modification of the second embodiment. Therefore, redundant descriptions will be omitted. 
   The operation of the phase comparator  88   a  will be described using a timing chart shown in  FIG. 34 . The phase comparator  88   a  generates the up signal DS UP  or down signal DS DOWN  depending on a phase difference between the falling edges of the divided oscillation signal D F1  sent from the first frequency divider  82 , and the divided reference signal D F2  sent from the second frequency divider  84 . When the phase of the divided oscillation signal D F1  is delayed with respect to that of the divided reference signal D F2 , the phase comparator  88   a  generates the up signal DS UP , so as to electrically charge the loop filter  94  through a charge pump  92   a  in a control voltage generator  91 . As a result, the control voltage V control  is higher, so as to make the oscillation frequency of the VCO  51  higher. Contrary, when the phase of the divided oscillation signal D F1  is advanced with respect to the divided reference signal D F2 , the phase comparator  88   a  generates the down signal DS DOWN , so as to discharge the loop filter  94  through the charge pump  92   a . As a result, the control voltage V control  is lower, so as to decrease the oscillation frequency of the VCO  51 . The PLL circuit  99   c  in the frequency synthesizer has a feedback loop and detects a phase lock when the phases of the divided oscillation signal D F1  and the divided reference signal D F2  finally agree. Thus, the output frequency of the VCO  51  is stabilized. A process for altering the dividing ratio of the first frequency divider  82  in order to alter the frequency of the oscillation signal S HF  of the VCO  51 , until locking the phase is called a “pull-in” process, and a period of time required for the pull-in process is called a “lock up time”. 
   In addition, when the control circuit  100   b  switches the first to fourth FBARs  56   a  to  56   d  by generating any one of the control signals SG C1  to SG C4 , the reset signal generator  104  generates the reset signal DS RST  so as to simultaneously reset the first and second frequency dividers  82  and  84 . Furthermore, the switch SW 5  connects an input of the resonator  70   c  in the VCO  51  with any one of the standard potential V STD  and the control voltage V control  which is the output of the control voltage generator  91 , based on the control voltage control signal SG C5  from the control circuit  100   b . Note that the standard potential V STD  is set to the upper limit of the control voltage V control . 
   Next, a description will be given of the operation of the frequency synthesizer according to the third modification of the second embodiment. The control circuit  100   b  in the frequency synthesizer uses the algorithm shown in  FIG. 32 , discussed in the second modification of the second embodiment, in order to search for an FBAR having a desired frequency band among the first to fourth FBARs  56   a  to  56   d  using the up and down signals DS UP  and DS DOWN  from the phase comparator  88   a . Here, it is assumed that the reference signal source  86  sends the reference signal S REF  of such frequency data so as to lock the PLL circuit  99   c  when the fourth FBAR  56   d  is connected. 
   In the third modification of the second embodiment as well, searching is started with the second FBAR  56   b  having an intermediate band. When turning on power, the PLL circuit  99   c  is forced to reset to an initial condition by the control circuit  100   b . The control signal SG C2  to select the second FBAR  56   b  as an initial value is generated to turn on only the switch SW 2 . In the initial condition, the switch SW 5  is connected to the standard potential V STD . Thus, the standard potential V STD  is provided to the reactance controller  52  of the resonator  70   c  in the VCO  51 . Accordingly, the loop of the PLL circuit  99   c  is opened in the initial condition. In addition, the standard potential V STD  is set beforehand to the upper limit of the control voltage V control . 
   The VCO  51  starts oscillation at a frequency determined by the resonance characteristics of the second FBAR  56   b  depending on the standard potential V STD . The first frequency divider  82  divides the oscillation signal S HF  of the oscillation frequency to generate a divided oscillation signal D F1 . The divided oscillation signal D F1  is sent to the phase comparator  88   a . The second frequency divider  84  divides the reference signal S REF  to generate a divided reference signal D F2 . The divided reference signal D F2  is also added to the phase comparator  88   a . In the phase comparator  88   a , the phases of the divided oscillation signal D F1  and the divided reference signal D F2  are compared. 
   The control circuit  100   b  sends the reset command signal SG RST  to the reset signal generator  104 . The reset signal generator  104  sends the reset signal DS RST  to the first and second frequency dividers  82  and  84 . When the reset signal DS RST  is received, the first and second frequency dividers  82  and  84  simultaneously start dividing. Since the oscillation frequency of the VCO  51  using the second FBAR  56   b  is lower than the desired frequency, the falling edge of the divided oscillation signal D F1  provided to the phase comparator  88   a  is delayed with respect to the falling edge of the divided reference signal D F2 . Accordingly, the phase delay of the divided oscillation signal D F1  is detected by the phase comparator  88   a . Thus, the generated up signal DS UP  is provided to the control circuit  100   b.    
   When the up signal DS UP  is provided to the control circuit  100   b , the control circuit  100   b , in accordance with the algorithm shown in  FIG. 32 , generates the control signal SG C3  to turn on the switch SW 3  so as to select the third FBAR  56   c  in place of the currently selected second FBAR  56   b . Moreover, the control circuit  100   b  holds the switch SW 5  in connection with the standard potential V STD  and thus holds the loop of the PLL circuit  99   c  open. Furthermore, the reset command signal SG RST  is sent from the control circuit  100   b  to the reset signal generator  104 . The reset signal DS RST  sent from the reset signal generator  104  causes the first and second frequency dividers  82  and  84  to simultaneously start dividing again. 
   The oscillation signal S HF  provided by the VCO  51  using the third FBAR  56   c  is added to the first frequency divider  82 , and divided into the divided oscillation signal D F1 . The divided oscillation signal D F1  is provided to the phase comparator  88   a . However, since the third FBAR  56   c  is selected, oscillation at the desired frequency cannot be provided. Therefore, again, a phase delay of the divided oscillation signal D F1  is detected by the phase comparator  88   a . Thus, the up signal DS UP  is provided to the control circuit  100   b.    
   When the up signal DS UP  is provided to the control circuit  100   b , in accordance with the algorithm shown in  FIG. 32 , the control circuit  100   b  generates the control signal SG C4  to turn on the switch SW 4  so as to select the fourth FBAR  56   d . The switch SW 5 , which is held in connection with the reference potential V STD  side, holds the loop of the PLL circuit  99   c  open. Moreover, the reset command signal SG RST  is sent from the control circuit  100   b  to the reset signal generator  104 . The reset signal DS RST  sent from the reset signal generator  104  causes the first and second frequency dividers  82  and  84  to simultaneously start dividing again. 
   The oscillation signal S HF  provided by the VCO  51  using the fourth FBAR  56   d  is added to the first frequency divider  82 , and divided into the divided oscillation signal D F1 . The divided oscillation signal D F1  is provided to the phase comparator  88   a . Since the frequency of the divided oscillation signal D F1  provided by the first frequency divider  82  is higher than that of the divided reference signal D F2 , the falling edge of the divided oscillation signal D F1  is advanced with respect to the falling edge of the divided reference signal D F2 . Accordingly, the phase advance of the divided oscillation signal D F1  is detected by the phase comparator  88   a . Thus, the generated down signal DS DOWN  is provided to the control circuit  10   b.    
   As a result, the control signal SG C4  from the control circuit  100   b  holds the switch SW 4  in the on-state. Moreover, at the same time, the control signal SG C5  is sent from the control circuit  100   b  to turn the switch SW 5  from the standard potential V STD  to the output of the control voltage generator  91 . Thus, the feedback loop of the PLL circuit  99   c  is established. 
   With closing of the PLL circuit  99   c , the up signal DS UP  or down signal DS DOWN  sent from the phase comparator  88   a  is detected in the control circuit  100   b . The reset command signal SG RST  is sent from the control circuit  100   b  to the reset signal generator  104 . When the reset signal DS RST  are sent from the reset signal generator  104  to the first and second frequency dividers  82  and  84 , the first and second frequency dividers  82  and  84  simultaneously start dividing. Therefore, one of the falling edges of the divided oscillation signal D F1  and the divided reference signal D F2  to be provided to the phase comparator  88   a , which has a lower frequency, is delayed with respect to the other. In the pull-in processes thereafter, since the operation start times of the first and second frequency dividers  82  and  84  are always synchronized, the phase comparator  88   a  will compare phases and frequencies at the same time. Therefore, when the frequencies of the outputs of the first and second frequency dividers  82  and  84  are the same, the phases thereof are always the same as well. 
   Fine adjustment of the oscillation frequency of the VCO  51  is implemented with the feedback control by the PLL circuit  99   c . When no phase difference is detected between the divided oscillation signal D F1  and the divided reference signal D F2  in the end as a result of the feedback control, the lock detector  90  operates to lock the phase of the PLL circuit  99   c . At the same time, the control circuit  100   b  stops providing the reset command signal SG RST . Thus, the output frequency of the VCO  51  is stabilized. 
   In addition, once the PLL circuit  99   c  is locked, the operation of switching the FBARs is stopped. Even when an unlocking condition is temporarily detected due to a disturbance, the lock condition is held. 
   As described above, according to the third modification of the second embodiment, since a single VCO  51  is used, it is possible to reduce the size and cost of a resonator circuit. In addition, low power consumption operation can be achieved. Moreover, instead of the control voltage V control  generated by the loop filter  94  in the control voltage generator  91 , the up and down signals DS UP  and DS DOWN  generated by the phase comparator  88   a , which is provided in the preceding stage of the control voltage generator  91 , are used to search for an FBAR having a suitable frequency band. Therefore, it is possible to reduce the time required for searching for an FBAR. Furthermore, the VCO  51  can be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100   b  generating the control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the FBARs. Thus, it is possible to provide a frequency synthesizer which has a small noise and a wide frequency tunability. 
   Fourth Modification of the Second Embodiment 
   As shown in  FIG. 35 , a frequency synthesizer according to a fourth modification of the second embodiment of the present invention includes a PLL circuit  99   d  which generates a high frequency oscillation signal S HF ; a phase discriminator  106  which determines a phase difference between a divided oscillation signal D F1  and a divided reference signal D F2  generated by first and second frequency dividers  82  and  84  in the PLL circuit  99   d , respectively; a control circuit  100   c  which generates any one of control signals SG C1  to SG C5  to a VCO  51 , based on a phase discrimination signal DS PH ; and a reset signal generator  104  which provides a dividing reset signal DS RST  to the first and second frequency dividers  82  and  84 , triggered by a reset command signal SG RST  from the control circuit  100   b.    
   The fourth modification of the second embodiment is different from the third modification of the second embodiment in that any one of the control signals SG C1  to SG C4  for the switches SW 1  to SW 4  for switching the first to fourth FBARs  56   a  to  56   d  provided in the VCO  51  is generated based on the phase discrimination signal DS PH  generated by the phase discriminator  106 . The other configurations are similar to the third modification of the second embodiment. Therefore, redundant descriptions will be omitted. 
   The divided oscillation signal D F1  and the divided reference signal D F2  sent from the first and second frequency dividers  82  and  84  respectively, are not only provided to the phase comparator  88  but also provided to the phase discriminator  106 . The phase discriminator  106  compares the phases of the divided oscillation signal D F1  and the divided reference signal D F2  and thereby determines whether the phase of the divided oscillation signal D F1  delays or advances with respect to that of the divided reference signal D F2 . Then, the phase discriminator  106  provides the result of the determination as the phase discrimination signal DS PH  to the control circuit  100   c . As for the comparison of the phases of the divided oscillation signal D F1  and the divided reference signal D F2 , in a similar way to that shown in  FIG. 34  for example, the determination may be provided based on the falling edges of the divided oscillation signal D F1  and the divided reference signal D F2  by the phase discriminator  106  after the reset signals DS RST  are sent from the reset signal generator  104  to the first and second frequency dividers  82  and  84 . 
   In the fourth modification of the second embodiment as well, searching for an FBAR having a suitable frequency band is started with the second FBAR  56   b  having an intermediate frequency band. When turning on power, the PLL circuit  99   d  is forced to reset to an initial condition by the control circuit  100   c . The control signal SG C2  to select the second FBAR  56   b  as an initial value is generated to turn on only the switch SW 2 . In the initial condition, the switch SW 5  is connected to the standard potential V STD . Thus, the standard potential V STD  is provided to the reactance controller  52  of the resonator  70   c  in the VCO  51 . Accordingly, the loop of the PLL circuit  99   d  is opened in the initial condition. In addition, the standard potential V STD  is set beforehand to the upper limit of the control voltage V control . 
   When the reset command signal SG RST  is sent from the control circuit  100   c  to the reset signal generator  104 , the reset signal DS RST  is sent from the reset signal generator  104  to the first and second frequency dividers  82  and  84 . Due to the reset signal DS SRT , the oscillation signal S HF  and the reference signal S REF  are simultaneously divided by the first and second frequency dividers  82  and  84 , respectively. As a result, the divided oscillation signal D F1  and the divided reference signal D F2  are provided to the phase comparator  88  and the phase discriminator  106 . When it is determined by the phase discriminator  106  that the phase of the divided oscillation signal D F1  is delayed with respect to that of the divided reference signal D F2 , the phase discrimination signal DS PH  indicating a phase delay is provided to the control circuit  100   c . In the control circuit  100   c , based on the phase discrimination signal DS PH , the control signal SG C3  to turn on the switch SW 3  is generated to select the third FBAR  56   c  in place of the currently selected second FBAR  56   b . The switch SW 5  is held in connection with the standard potential V STD . Thus, the loop of the PLL circuit  99   c  is held open. Further, the reset command signal SG RST  is sent from the control circuit  100   c  to the reset signal generator  104 , and the above-described search for the FBAR is continued. 
   When the fourth FBAR  56   d  is selected and it is determined by the phase discriminator  106  that the phase of the divided oscillation signal D F1  is advanced with respect to that of a divided reference signal D F2 , the phase discrimination signal DS PH  indicating a phase delay is provided to the control circuit  100   c . As a result, the control signal SG C4  from the control circuit  100   c  holds the switch SW 4  in the on-state. At the same time, the control signal SG C5  is sent from the control circuit  100   c  and turns the switch SW 5  from the standard potential V STD  to the output of the control voltage generator  91 . Thus, the feedback loop of the PLL circuit  99   c  is established. The feedback control by the PLL circuit  99   c  eliminates a phase difference between the divided oscillation signal D F1  and the divided reference signal D F2 . Thus, the PLL circuit  99   c  is locked. 
   As described above, according to the fourth modification of the second embodiment, since the single VCO  51  is used, it is possible to reduce the size and cost of a resonator circuit. In addition, low power consumption operation can be achieved. Moreover, since the phases of the divided oscillation signal D F1  and the divided reference signal D F2  are compared by the phase discriminator  106  in order to search for an FBAR having a suitable frequency band, it is possible to reduce the time required for searching for an FBAR. Furthermore, the VCO  51  can be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100   c  generating the control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the FBARs. Thus, it is possible to provide a frequency synthesizer which has a small noise and a wide frequency tunability. 
   Fifth Modification of the Second Embodiment 
   As shown in  FIG. 36 , a frequency synthesizer according to a fifth modification of the second embodiment of the present invention includes a PLL circuit  99   e  which generates a high frequency oscillation signal S HF ; first and second counters  107  and  108  which count the number of pulses in a divided oscillation signal D F1  and a divided reference signal D F2  generated by the first and second frequency dividers  82  and  84  in the PLL circuit  99   e , respectively; a time difference detector  110  which measures a time difference based on first and second counting end signals SC E1  and SC E2  sent from the first and second counters  107  and  108 , respectively; a control circuit  100   d  which provides any one of control signals SG C1  to SG C5  to the VCO  51 , based on a time difference signal SC TD  sent from the time difference detector  110 ; and a reset signal generator  104   a  which provides a dividing reset signal DS RST  to the first and second frequency dividers  82  and  84  and provides a count reset signal SC RST  to the first and second counters  107  and  108 , triggered by a reset command signal SG RST  from the control circuit  100   d.    
   The first and second counters  107  and  108  are connected to outputs of the first and second frequency dividers  82  and  84 , respectively. The output of the reset signal generator  104   a  connected to the control circuit  100   d , is connected to the first and second frequency dividers  82  and  84  and to the first and second counters  107  and  108 . An output of the time difference detector  110 , to which the outputs of the first and second counters  107  and  108  and of the reference signal source  86  are connected, is connected to the control circuit  100   d . The control circuit  100   d  is connected to the switches SW 1  to SW 4  for switching the FBARs in the VCO  51  and to the switch SW 5 . 
   In the fifth modification of the second embodiment, the first and second counters  107  and  108  count a predetermined number of the pulses in the divided oscillation signal D F1  and the divided reference signals D F2 , which are sent from the first and second frequency dividers  82  and  84 , respectively. Thereafter, the first and second counters  107  and  108  provided the first and second counting end signals SC E1  and SC E2 , respectively, to the time difference detector  110 . The time difference detector  110  calculates a number of reference signals S REF  within a time difference between the first and second counting end signals SC E1  and SC E2  and provides the calculated number, as the time difference signal SC TD , to the control circuit  100   d . Based on the time difference signal SC TD , the control circuit  100   d  generates any one of the control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the first to fourth FBARs  56   a  to  56   d  provided in the VCO  51 . The fifth modification of the second embodiment is different from the third modification of the second embodiment in the above-discussed points. The other configurations of the fifth modifications of the second embodiment are similar to the third modifications of the second embodiment. Therefore, redundant descriptions will be omitted. 
   In the fifth modification of the second embodiment as well, searching for an FBAR having a suitable frequency band is started with the second FBAR  56   b  having an intermediate frequency band. When turning on power, the PLL circuit  99   e  is forced to reset to an initial condition by the control circuit  100   d . The control signal SG C2  to select the second FBAR  56   b  as an initial value is sent from the control circuit  100   d  to turn on only the switch SW 2 . In the initial condition, the switch SW 5  is connected to the standard potential V STD . Thus, the standard potential V STD  is provided to the reactance controller  52  of the resonator  70   c  in the VCO  51 . Accordingly, the loop of the PLL circuit  99   e  is opened in the initial condition. In the fifth modification of the second embodiment, the standard potential V STD  is set beforehand to an intermediate potential between the upper limit and lower limit of the control voltage V control . 
   The reset command signal SG RST  is sent to the reset signal generator  104   a  from the control circuit  10   d . The reset signal generator  104   a  provides the reset signal DS RST  to the first and second frequency dividers  82  and  84 , and the count reset signal SC RST  to the first and second counters  107  and  108 . The first and second frequency dividers  82  and  84  simultaneously start dividing so as to generate the divided oscillation signals D F1  and the divided reference signals D F2 , respectively. The first and second counters  107  and  108  simultaneously start counting the divided oscillation signals D F1  and the divided reference signals D F2  sent from the first and second frequency dividers  82  and  84 , respectively. 
   When the first and second counters  107  and  108  finish counting the predetermined number of pulses, the first and second counters  107  and  108  send the first and second counting end signal SC E1  and SC E2 , respectively, to the time difference detector  110 . When the time difference detector  110  detects the earlier one of the first and second counting end signals SC E1  and SC E2 , the time difference detector  110  starts counting reference signals S REF . The counting is continued until the later one of the first and second counting end signals SC E1  and SC E2  is detected. When the first counting end signal SC E1  is earlier, a positive sign is provided to a resulting value. When the second counting end signal SC E2  is earlier, a negative sign is provided to a resulting value. The counting result is sent to the control circuit  100   d  as the time difference signal SC TD . 
   In the control circuit  10   d , a frequency difference having the positive or negative sign is calculated from the time difference signal SC TD . Then, it is determined whether or not an FBAR in the VCO  51  needs switching. Moreover, the control circuit  100   d  stores information of the currently selected second FBAR  56   b . When an FBAR needs switching, the FBAR having a suitable frequency band is selected from among the first to fourth FBAR  56   a  to  56   d , based on the calculated frequency difference. For example, when the time difference signal SC TD  has a positive sign, the FBAR  56   b  is switched to an FBAR having a lower frequency band. When the time difference signal SC TD  has a negative sign, the FBAR  56   b  is switched to an FBAR having a higher frequency band. 
   In the fifth modification of the second embodiment, for example, it is assumed that it is determined that an FBAR having a suitable frequency band is the fourth FBAR  56   d  which has a two-level higher frequency band than the second FBAR  56   b . In such case, the control signal SG C4  is sent from the control circuit  100   d  so as to turn on the switch SW 4 . Accordingly, in the resonator  70   c , the fourth FBAR  56   d  having the suitable oscillation frequency band is selected instead of the currently selected second FBAR  56   b . In addition, the switch SW 5  is held in connection with the standard potential V STD . 
   Subsequently, the reset command signal SG RST  is sent again to the reset signal generator  104   a  from the control circuit  10   d . Thus, the first and second counters  107  and  108  simultaneously start counting again. When the first and second counters  107  and  108  finish counting the predetermined number of respective pulses the first and second counters  107  and  108  provide the first and second counting end signals SC E1  and SC E2 , respectively, to the time difference detector  110 . The time difference detector  110  calculates the number of reference signals S REF  within a time difference between the first and second counting end signals SC E1  and SC E2 . The calculating result is sent to the control circuit  100   d  as the time difference signal SC TD . 
   The control circuit  100   d  calculates a frequency difference from the time difference signal SC TD . Since the fourth FBAR  56   d  having a suitable frequency band has already been selected, a magnitude of the time difference signal SC TD  is in a predetermined tolerance level. Accordingly, it is determined that the FBAR does not need switching. As a result, the control signal SG C5  is sent from the control circuit  100   d  to turn the switch SW 5  from the standard potential V STD  to the output of the loop filter  94  in the control voltage generator  91 . Thus, the feedback loop of the PLL circuit  99   e  is closed. 
   The control circuit  100   d  continues monitoring the oscillation frequency of the VCO  51  for a period of time after the feedback loop of the PLL circuit  99   e  is closed until the phase lock is detected by the lock detector  90 , using the first and second counters  107  and  108  and the time difference detector  110 . In the meantime, the control circuit  100   d  continues monitoring the oscillation frequency by using time difference signals SC TD  sent from the time difference detector  110 . Additionally, the control circuit  100   d  sends the reset command signal SG RST  to the reset signal generator  104   a  when the time difference signal SC TD  is greater than a reference value for the phase lock of the feedback loop of the PLL circuit  99   e . The reset signal generator  104   a  provides the reset signal DS RST  to the first and second frequency dividers  82  and  84  respectively, and the count reset signal SC RST  to the first and second counters  107  and  108  respectively. For every reception of the reset signal DS RST  and the count reset signal SC RST , the first and second frequency dividers  82  and  84  simultaneously start dividing, and the first and second counters  107  and  108  simultaneously start counting. In such way, the dividing start time for the first and second frequency dividers  82  and  84  are always synchronized in the pull-in process. Further, when the divided oscillation signal D F1  and the divided reference signal D F2  respectively sent from the first and second frequency dividers  82  and  84  is the same, the phases of these signals is always the same as well. Thus, when the phase lock is finally detected by the lock detector  90 , the control circuit  100   d  stops providing the reset command signal SG RST  to the reset signal generator  104   a.    
   As described above, according to the fifth modification of the second embodiment, since the single VCO  51  is used, it is possible to reduce the size and cost of a resonator circuit. In addition, low power consumption operation can be achieved. Moreover, in order to search for an FBAR having a suitable frequency band, the suitable frequency band is determined based on the frequency difference between the divided oscillation signal D F1  and the divided reference signal D F2 , using the first and second counters  107  and  108  and the time difference detector  110 . Accordingly, it is possible to reduce the time required for searching for an FBAR. Furthermore, the VCO  51  can be operate by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100   d  generating the control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the FBAR. Thus, it is possible to provide a frequency synthesizer which has a small noise and a wide frequency tunability. 
   Sixth Modification of the Second Embodiment 
   As shown in  FIG. 37 , a frequency synthesizer according to a sixth modification of the second embodiment of the present invention includes a PLL circuit  99   f  which generates a high frequency oscillation signal S HF ; a counter  112  which counts the number of pulses in the oscillation signals S HF  generated by the VCO  51  in the PLL circuit  99   f , using a divided reference signal D F2  as a reset signal; a control circuit  100   e  which compares a count signal SC CNT  sent from the counter  112  with a standard count value SC STD  and generates control signals SG C1  to SG C5  to the VCO  51 ; and a reset signal generator  104  which provides a dividing reset signal DS RST  to the first and second frequency dividers  82  and  84 , triggered by a reset command signal SG RST  from the control circuit  100   e.    
   The counter  112  is connected to an output node  64  of the VCO  51  and an output of the second frequency divider  84 . An output of the counter  112  is connected to the control circuit  100   e . Moreover, the control circuit  100   e  is connected to the reset signal generator  104   a , and an output of the reset signal generator  104   a  is connected to the first and second frequency dividers  82  and  84 . The control circuit  100   e  is also connected to the switches SW 1  to SW 4  for switching first to fourth FBARs  56   a  to  56   d  in the VCO  51  and to the switch SW 5 . 
   By receiving an input of a divided reference signal DF 2  to be used as the count reset signal, the counter  112  counts the number of pulses in the oscillation signal S HF  from the VCO  51  until the next divided reference signal D F2  is received. The control circuit  10   e  calculates a frequency difference between the oscillation signal S HF  and a desired frequency, based on the count signal SC CNT  sent from the counter  112  and on the count standard value SC STD . The control circuit  10   e  determines whether to switch the first to fourth FBARs  56   a  to  56   d  depending on the frequency difference calculation based on the count signal SC CNT  and the count standard value SC STD . The standard count value SC STD  is altered based on frequency data provided to the reference signal source  86  so as to respond to a suitable frequency. The control circuit  10   e  generates any one of control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the first to fourth FBARs  56   a  to  56   d  in the VCO  51 , based on the frequency difference calculated using the count signal SC CNT  and the standard count value SC STD . The sixth modification of the second embodiment is different from the fifth modification of the second embodiment in the above-discussed points. The other configurations of the sixth modifications of the second embodiment are similar to the fifth modifications of the second embodiment. Therefore, redundant descriptions will be omitted. 
   In the sixth modification of the second embodiment, searching for the FBAR having a suitable frequency band is started with the second FBAR  56   b  having an intermediate band. When turning on power, the PLL circuit  99   f  is forced to reset to an initial condition by the control circuit  100   e . The control signal SG C2  to select the second FBAR  56   b  as an initial value is sent from the control circuit  100   e  to turn on only the switch SW 2 . In the initial condition, the switch SW 5  is connected to the standard potential V STD . Thus, the standard potential V STD  is provided to the reactance controller  52  of the resonator  70   c  in the VCO  51 . Accordingly, the loop of the PLL circuit  99   f  is opened in the initial condition. In the sixth modification of the second embodiment, the standard potential V STD  is set beforehand to an intermediate potential between the upper and lower limits of the control voltage V control . 
   The oscillation signal S HF  generated by the VCO  51  using the second FBAR  56   b  and the divided reference signal D F2  are provided to the counter  112 . When the divided reference signal D F2  is received, the count in the counter  12  is reset. The counter  12  counts the number of pulses in the oscillation signal S HF  until the next divided reference signal D F2  is received, and sends the count value, as the count signal SC CNT , to the control circuit  100   e.    
   The control circuit  100   e  calculates a frequency difference by comparing the count signal SC CNT  with the count standard value SC STD  and determines whether or not the FBAR in the VCO  51  needs switching. Moreover, the control circuit  100   e  stores information of the currently selected second FBAR  56   b . When the FBAR needs switching, an FBAR having a suitable frequency band is selected based on the calculated frequency difference. For example, when the count signal SC CNT  is greater than the standard count value SC STD , an FBAR having a lower frequency band is selected, instead of the second FBAR  56   b . When the count signal SC CNT  is smaller than the standard count value SC STD , an FBAR having a higher frequency band is selected. 
   In the sixth modification of the second embodiment, for example, it is assumed that it is determined that an FBAR having a suitable frequency band is the fourth FBAR  56   d  which has a two-level higher frequency band than the second FBAR  56   b . In such case, the control signal SG C4  is sent from the control circuit  10   e  so as to turn on the switch SW 4 . Accordingly, in the resonator  70   c , the fourth FBAR  56   d  having a suitable oscillation frequency band is selected instead of the currently selected second FBAR  56   b . In addition, the switch SW 5  is held in connection with the standard potential V STD . 
   Subsequently, the reset command signal SG RST  is sent to the reset signal generator  104   a  from the control circuit  10   e . The reset signals DS RST  are sent to the first and second frequency dividers  82  and  84  from the reset signal generator  104   a . Triggered by these signals, the first and second frequency dividers  82  and  84  start dividing again. The oscillation signals S HF  generated by oscillation by the VCO  51  using the fourth FBAR  56   d  and the divided reference signal D F2  are provided to the counter  112 . When the divided reference signal D F2  is received, the count in the counter  112  is reset, and the number of pulses in the oscillation signals S HF  are counted until the next divided reference signal D F2  is received. The count value is sent to the control circuit  10   e  as a count signal SC CNT . 
   The control circuit  10   e  calculates a frequency difference by comparing the count signal SC CNT  and the standard count value SC STD . Since the fourth FBAR  56   d  having a suitable frequency band has already been selected, the frequency difference is within a predetermined tolerance level. Accordingly, it is determined that the FBAR does not need switching. As a result, the control signal SG C5  is sent from the control circuit  10   e  to turn the switch SW 5  from the standard potential V STD  to the output of the loop filter  94  in the control voltage generator  91 . Thus, the feedback loop of the PLL circuit  99   f  is closed. 
   As described above, according to the sixth modification of the second embodiment, since a single VCO  51  is used, it is possible to reduce the size and cost of a resonator circuit. In addition, low power consumption operation can be achieved. Moreover, in order to search for an FBAR having a suitable frequency band, the suitable frequency band is determined by monitoring the oscillation signals S HF  using the counter  112 . Accordingly, it is possible to reduce the time required for searching for an FBAR. Furthermore, the VCO  51  can be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  10   e  generating the control signals SG C1  to SG C4  of the switches SW 1  to SW 4  for switching the FBAR. Thus, it is possible to provide a frequency synthesizer which has a small noise and a wide frequency tunability. 
   Seventh Modification of the Second Embodiment 
   As shown in  FIG. 38 , a frequency synthesizer according to a seventh modification of the second embodiment includes first and second VCOs  51   e  and  51   f  in a PLL circuit  99   g  which generates a high frequency oscillation signal S HF . A first resonator  70   d  in the first VCO  51   e , connected to an output of the loop filter  94  in a control voltage generator  91 , includes first and third FBARs  56   a  and  56   c . A second resonator  70   e  in the second VCO  51   f , connected to the output of the loop filter  94 , includes the second and fourth FBARs  56   b  and  56   d.    
   The control circuit  100   f  generates control signals SG C1  to SG C4  to select switches SW 1  to SW 4  for switching the FBARs in the first and second VCOs  51   e  and  51   f . Moreover, the control circuit  100   f  provides a control signal SG CC  to a switch SW VCO  for the first and second VCOs  51   e  and  51   f.    
   In the seventh modification of the second embodiment, in order to search for a suitable VCO and a suitable FBAR, any one set of control signals SG C1 and SG   C2  for the first and second FBARs  56   a  and  56   b  respectively, control signals SG C2  and SG C3  for the second and third FBARs  56   b  and  56   c  respectively, and control signals SG C3  and SG C4  for the third and fourth FBARs  56   c  and  56   d  respectively, are simultaneously generated. As described using  FIG. 4 , the larger the Q value of a FBAR, the longer the oscillation start time of a VCO. In the first modification of the second embodiment, the control circuit  100  in  FIG. 29  generates one of the control signals SG C1  to SG C4  of the first to fourth FBARs  56   a  to  56   d , and the oscillation start time of the VCO  51  tends to be long when the first to fourth FBARs  56   a  to  56   d  are switched from one to another. The seventh modification of the second embodiment is different from the first modification of the second embodiment in that the control circuit  100   f  sequentially generates two of the control signals SG C1  to SG C4 , and that the first and second VCOs  51   e  and  51   f  are always oscillated in steady states. The other configurations are similar to the first modification of the second embodiment. Therefore, redundant descriptions will be omitted. 
   In the seventh modification of the second embodiment, for example, as an initial condition, the control signals SG C1  and SG C2  of the switches SW 1  and SW 2  are sent from the control circuit  100   f  to turn on the first and second FBARs  56   a  and  56   b  in the first and second resonators  70   d  and  70   e  respectively. Then, the first and second VCOs  51   e  and  51   f  are oscillated. In addition, the switch SW VCO  is connected to the first VCO  51   e.    
   When the oscillation signal S HF  generated by the first VCO  51   e  using the first FBAR  56   a  is not in a desired oscillation frequency band, the control signal SG CC  is sent from the control circuit  10   f , and the switch SW VCO  is connected to the second VCO  51   f . At the same time, the control signal SG C1  of the switch SW 1  is turned off, and a control signal SG C3  of the switch SW 3  is sent from the control circuit  100   f  to turn on the third FBAR  56   c  in the first resonator  70   d . As a result, if the oscillation signal S HF  generated by the second VCO  51   f  using the second FBAR  56   b  is determined to be the desired oscillation frequency band, the first VCO  51   e  starts oscillation using the third FBAR  56   c.    
   In the seventh modification of the second embodiment, while the oscillation signal S HF  generated by one of the VCOs  51   e  and  51   f , which is connected to the PLL circuit  99   g  by the switch SWVCO, is determined to be a desired oscillation frequency band, the FBARs are switched in the other VCO, and the other VCO oscillates in a steady state by using the newly selected FBAR. Further, when it is determined by the control circuit  100   f  that the oscillation signal S HF  is in the desired oscillation frequency band, the control circuit  100   f  stops generating the control signals of the FBARs in the VCO which is not connected to the PLL circuit  99   g  by the Switch SW VCO . Accordingly, once searching for an FBAR is finished, only one of the VCOs  51   e  and  51   f  remains in operation. Thus, it is possible to reduce power consumption. 
   As described above, according to the seventh modification of the second embodiment, since the two VCOs  51   e  and  51   f  which are simultaneously operated are switched by the switch SW VCO , it is possible to search for an FBAR having a suitable frequency band in a shorter period of time. Moreover, since only one VCO is used after searching for an FBAR, low power consumption operation can be achieved. Furthermore, the VCOs  51   e  and  51   f  can be operated by switching the first to fourth FBARs  56   a  to  56   d  having different resonance frequencies by the control circuit  100   f  generating the control signals SG C1  to SG C4  of the switches SW 1  to SW 4 . Thus, it is possible to provide a frequency synthesizer which has a small phase noise and a wide frequency tunability. 
   Application of the Second Embodiment 
   As shown in  FIG. 39 , a communication apparatus according to an application of the second embodiment of the present invention includes an antenna  122  which receives and transmits RF signals; a frequency synthesizer  120  connected to the reference signal source  86  for supplying a standard frequency, which generates an oscillation signal by using a VCO having a plurality of FBARs having different resonance frequencies; a receiving unit  142  which converts an RF receiving signal from the antenna  122  into an intermediate frequency (IF) receiving signal, by using the oscillation signal; a baseband processor  140  which demodulates the IF receiving signal and modulates a transmitting signal; and a transmitting unit  144  which converts the modulated transmitting signal into an RF transmitting signal, by using the oscillation signal and provides the RF transmitting signal to the antenna  122 . Here, as the frequency synthesizer  120 , anyone of the frequency synthesizers according to the second embodiment and the first to seventh modifications of the second embodiment may be used. 
   The receiving unit  142  includes an RF receiver  126  connected to the antenna  122  via a duplexer  124 ; a down converter (D/C)  128  connected to the RF receiver  126  and to the frequency synthesizer  120 ; and an IF receiver  130  connected to the D/C  128 . The IF receiver  130  is connected to the baseband processor  140 . 
   The transmitting unit  144  includes an IF transmitter  132  connected to the baseband processor  140 ; an up converter (U/C)  134  connected to the IF transmitter  132  and to the frequency synthesizer  120 ; and an RF transmitter  136  connected to the U/C  134 . The RF transmitter  136  is connected to the antenna  122  via the duplexer  124 . 
   When the communication apparatus according to the application of the second embodiment of the present invention receives an RF receiving signal for communication, the duplexer  124  for the antenna  122  is switched to a connection with the receiving unit  142 . In the RF receiver  126  of the receiving unit  142 , the RF receiving signal, which has passed through a desired receiving frequency band by using, such as, a band-pass filter, is amplified by a low noise amplifier. In the D/C  128 , the amplified RF receiving signal is converted into an IF receiving signal with an intermediate frequency by using an oscillation signal sent from the frequency synthesizer  120 . In the IF receiver  130 , the IF receiving signal, converted to a frequency in an intermediate frequency band, is subjected to signal processing, such as waveform shaping. The IF receiving signal processed in the IF receiver  130  is provided to the baseband processor  140 . In the baseband processor  140 , a demodulated signal is generated which is provided by demodulating the IF receiving signal. 
   Moreover, when a transmitting signal for communication is provided to the baseband processor  140 , the transmitting signal is modulated in the baseband processor  140 . The modulated transmitting signal is subjected to signal processing in the IF transmitter  132  of the transmitting unit  144 . In the U/C  134 , the signal-processed transmitting signal is converted into an RF transmitting signal by using an oscillation signal sent from the frequency synthesizer  120 . In the RF transmitter  136 , the RF transmitting signal provided by converting the signal-processed transmitting signal, is passed through a desired frequency band by using, such as, a band-pass filter and is also power-amplified by a power amplifier. The power-amplified RF transmitting signal is transmitted from the antenna  122  via the duplexer  124  which has been switched to connect to the transmitting unit  144 . 
   In the application of the second embodiment, a frequency synthesizer including a VCO having FBARs is used, which has a small phase noise and a wide frequency tunability. Accordingly, it is possible to achieve a wireless communication apparatus capable of stability transmitting and receiving high quality bulk information. 
   OTHER EMBODIMENTS  
   The present invention has been described as discussed above. However the descriptions and drawings that constitute a portion of this disclosure should not be perceived as limiting this invention. Various alternative embodiments and operational techniques will become clear to persons skilled in the art from this disclosure. 
   In the second embodiment, the description has been given using the negative resistance circuit  60  in the VCO. However, as shown in  FIG. 40 , the negative resistance circuit  60   a  using the CMOS inverter  80  shown in  FIG. 24  may be used in a VCO  51   g . For example, when the VCO  51   g  is used in place of the VCO  51  in  FIG. 29 , each of the ends of the switches SW 1  to SW 4  used to switch the first to fourth FBARs  56   a  to  56   d , is connected to an output node  64 , that is, to the first frequency divider  82 . The first to fourth FBARs  56   a  to  56   d , connected to other ends of the respective switches SW 1  to SW 4 , are connected to the phase adjuster  54 . An input node  62  of the reactance controller  52   a  connected to the phase adjuster  54 , is connected to the output of the control voltage generator  91 . 
   Moreover, as shown in  FIG. 41 , the negative resistance circuit  60   b  using the CMOS inverter  80  shown in  FIG. 26  may be used in a VCO  51   h . For example, when the VCO  51   h  is used in place of the VCO  51  in  FIG. 29 , each of the ends of the switches SW 1  to SW 4  used to switch the first to fourth FBARs  56   a  to  56   d , is connected to an output node  64 , that is, to the first frequency divider  82 . The first to fourth FBARs  56   a  to  56   d , connected to other ends of the respective switches SW 1  to SW 4 , are connected to the phase adjuster  54 . Input terminals  62   a  and  62   b  of a reactance controller  52   b , which is connected to the phase adjuster  54  and the ends of the switches SW 1  to SW 4 , are connected to the output of the control voltage generator  91 . 
   Since the CMOS inverter  80  used in the negative resistance circuit  60   a  or  60   b  is superior to a bipolar transistor in terms of integration and manufacturing, the CMOS inverter is advantageous in reducing the size and cost of the VCO  51   h  or  51   g . Moreover, development of a high-frequency CMOS analog circuit is advanced, which may facilitate merged installation of a high frequency analog circuit and a digital circuit.