Abstract:
An amplifier circuit for an oscillator in a defined oscillating frequency range includes a plurality of transconductors, wherein at least one transconductor has a positive transconductance, and wherein at least one other transconductor has a negative transconductance, wherein the transconductors together provide a positive amplification, and a passive impedance element coupled to at least one fed back transconductor, wherein the transconductance of the transconductor and the impedance element are dimensioned so that, in the oscillating frequency range, a given phase difference is present between a signal at the input and a signal at the output.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims priority from German Patent Application No. 10 2005 008 332.3, which was filed on Feb. 23, 2005, and is incorporated herein by reference in its entirety. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to amplifier circuits and particularly to amplifier circuits for oscillators that are to have a high phase difference between input and output. 
   2. Description of the Related Art 
   The BAW (bulk acoustic wave technology) allows piezoelectric resonant elements that, for example, operate in the longitudinal wave mode and whose frequency (about 1-2 GHz) depends on the mass and elasticity coefficients of the resonator. These resonant elements are applied in RF (radio frequency) filters. A further field of application of so-called FBAR (film bulk acoustic wave resonator) are mass sensors (for example for biochemical or other applications). For this purpose, quartz crystal micro balances have primarily been used in the past. However, FBAR have a substantially higher measurement sensitivity compared to quartz crystal micro balances due to their higher resonant frequency. A further advantage of the FBAR is their integrability and thus more inexpensive manufacturing and the possibility of using them in sensor matrices. 
   The output signal of such an FBAR is the resonant frequency depending on the additional mass that is bound on the surface of the resonator and is to be measured. This requires the resonators to function not only in air (as is the case for RF filters), but also in water, for example. 
   Two methods are known for measuring the frequency:
     1. Measuring the change of the S-parameters before and after the change of the surface mass. However, this approach has three major disadvantages: 1) the measurement is not accurate, 2) the expensive S-parameter measurement setup is not applicable for reading out in mass products, and 3) the measurement has to be done with the resonator in air. This requires the sensor to be dried before the measurement, which makes the whole procedure complex.   2. Use of a hybrid circuit oscillator.  FIG. 3  shows a basic solution for an amplifier circuit having an amplifier  11  and a resonator  12 , here specifically an FBAR (film bulk acoustic wave resonator). FBAR are used in biochemistry, for example as mass sensors for gases or liquids. Depending on the chemical structure of the gases or liquids, additional mass is bound on the FBAR. This results in a change of the FBAR&#39;s resonant frequency. The output voltage V out  generated by the amplifier  11  is attenuated/amplified and phase shifted by the resonator  12  and is returned to the input of the amplifier as input voltage V in  via a feedback loop.   

   The main problem for the use of FBAR in rough environments, for example water, is the poor quality, i.e. only a small phase shift and a high attenuation at resonant frequency. 
     FIG. 4  shows two curves of an FBAR. The upper curve represents the amplitude response (V in /V out ). The lower curve represents the phase response (V in /V out ). The frequency in Hertz is plotted along the x-axis of both curves. For the amplitude response, the amplification in dB is plotted along the y-axis. The phase shift in degrees is plotted along the y-axis of the phase response. The maximum phase shift between V in  and V out  is about −60°, for the resonant frequency of 1.89 GHz, the phase shift is even as low as −30°, while the attenuation is still 2 dB. To form an oscillating circuit with a total amplification of about 3 dB and a phase shift of 360°, the amplifier has to achieve an amplification of about 5 dB and a phase delay of −330°. 
   The specialist publication “Biochemical sensors based on bulk acoustic wave resonators” by R. Brederlow et al. shows an amplifier for an oscillator having an FBAR, wherein the amplifier comprises two transistors. The collector electrodes of both transistors are coupled to a supply voltage, wherein the FBAR is connected to the emitter electrode of the first transistor, wherein the base electrode of the second transistor is connected to the collector electrode of the first transistor via a decoupling capacitor and a voltage divider, and the output voltage is tapped at the emitter electrode of the second transistor. The base electrode of the first transistor is coupled to a conducting element. 
   The disadvantage of the described known circuit is the frequency dependence of the phase shift due to the invariable conducting element and the associated potential detuning of the oscillator circuit. If the amplification-phase relationship of the amplifier is not precisely tuned to the resonator, the amplifier may not oscillate or it oscillates at another frequency than the resonant frequency of the resonator, which is undesirable since the frequency then does no longer react to mass changes, i.e. no more measurements are possible. A further disadvantage is the major space requirement of a conducting element and the inflexibility with respect to the adjustment possibilities, because the operating point of both transistors is controlled by only one supply voltage. 
   SUMMARY OF THE INVENTION 
   It is the object of the present invention to take the poor quality of the resonator into account when designing and dimensioning the amplifier circuit, and that the amplifier meets the oscillation requirement exactly in the resonant frequency range of the resonator despite a small phase shift and a high attenuation of the resonator at resonant frequency. Furthermore, the amplifier or the oscillator circuit is to be flexibly adjustable with respect to the phase shift and realizable in an efficient way. 
   In accordance with a first aspect, the present invention provides an amplifier circuit having an amplifier input and an amplifier output for an oscillator having an oscillating frequency in a defined oscillating frequency range, having a plurality of at least three transconductors, wherein the transconductors are designed to map an input voltage to an output current considering the transconductance, wherein at least one transconductor has a positive transconductance, and wherein at least one other transconductor has a negative transconductance, and wherein the transconductors together provide a positive amplification; wherein a first transconductor is coupled to the amplifier input on the input side, wherein a second transconductor is coupled to an output of the first transconductor on the input side and has a feedback from an output of the same to an input of the same, wherein a third transconductor is coupled to an output of the first transconductor and an output of the second transconductor on the input side, and wherein at least one passive impedance element is provided, which is coupled to the output of the first transconductor, wherein the transconductances of the transconductors and the at least one impedance element are dimensioned so that, in the defined oscillating frequency range, a given phase difference is present between a signal at the amplifier input and a signal at the amplifier output. 
   In accordance with a second aspect, the present invention provides an oscillator circuit having the above-mentioned amplifier circuit and a resonator connected between the amplifier input and the amplifier output, wherein the resonator is an FBAR (film bulk acoustic wave resonator). 
   The present invention provides an amplifier circuit comprising: a plurality of transconductors, wherein at least one transconductor has a positive transconductance, and wherein at least one other transconductor has a negative transconductance, and wherein the transconductors together provide a positive amplification; wherein the first transconductor is coupled to the amplifier input on the input side, the second transconductor is coupled to an output of the first transconductor on the input side and comprises a feedback from an output of the same to an input of the same, wherein the third transconductor is coupled to an output of the first transconductor and an output of the second transconductor on the input side, and a passive impedance element coupled to at least one transconductor, wherein not only the amplification, but also the phase shift of the amplifier is exactly adjustable via the transconductances of the transconductors, particularly to the resonant frequency of a resonator. 
   The present invention is based on the finding that the transconductances of the transconductors do not only serve for amplifier adjustment, as is otherwise the case in transconductors, but that the phase shift of the amplifier circuit is also adjusted by means of the transconductances. In a normal chain circuit of transistor amplifiers, the transconductances, i.e. the amplifier factors of the amplifiers, hardly have any influence at all on the phase shift. 
   However, the invention achieves that the transconductances, i.e. the amplification factors of the amplifiers, also influence the phase shift of the amplifier circuit. For this purpose, a chain circuit of the first and the third transconductors, TK 1  and TK 3 , is complemented by a second transconductor TK 2  which is connected between the first and the third one and is additionally also fed back. The impedance element IE 1  is also connected to the node with which the second transconductor TK 2  is coupled. 
   By selecting the signs of the transconductances, the invention achieves that no inductances are required, and capacitive impedance elements only are sufficient. Parallel connection of the second fed back transconductor TK 2  and the at least one impedance element IE 1  further achieves that the value of the at least one impedance element may be small, because this value is always “enlarged” by the transconductance of the second transconductor TK 2 , which is fed back, due to the mutual connection. 
   For calibrating the phase shift of the amplifier circuit, for example after manufacturing or for a changed environmental condition, there may simply be done a transconductance adjustment performed externally according to the invention. If the transconductors are designed as transistors, the operating point of the transistor simply has to be adjusted for this purpose. 
   In prior art, this tuning is not possible because a conducting element or fixed concentrated elements are used as impedance element. In prior art, this results in much reject in manufacturing or in a very limited field of application, wherein the problems are not present in the invention. 
   A preferred embodiment of the present invention further allows a change of the transconductances of the transconductors by two variable current sources and thus a change of the phase shift and the amplification of the amplifier circuit. 
   An inventive amplifier circuit is thus ideally suited for the use with a resonator of low quality, for example the FBAR described by  FIG. 4 . Here, the transconductances of the transconductors and the capacitances of the impedance elements of the amplifier circuit are dimensioned so that a necessary phase shift for the term −G m2 +C 1  and hence a phase shift required as a whole by the oscillation requirement for the entire amplifier circuit results from the transconductance G m2  of the second fed back transconductor TK 2  and the capacitance C 1  of the first impedance element IE 1 . Combined with the phase shift of the resonator at the resonant frequency, this meets the oscillation requirement for the oscillator circuit. 
   The inventive amplifier circuit includes transconductors and at least one impedance element and may thus easily be integrated onto a chip, particularly with FBAR, because the transconductors may readily be realized as transistors and because even a capacitive impedance element is sufficient as impedance element, which may also be realized by a transistor. 
   The integration has two major advantages. First, the parasitic impedances of the connection lines between the resonator and the amplifier circuit in an integrated chip solution are considerably smaller as compared to prior art, a hybrid solution, which in turn further increases the performance of the measuring device. Second, the invention thus allows cost-effective manufacturing of, for example, biochemical one-way diagnosis systems, for whose mass market success low-cost manufacturing is indispensable. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Preferred embodiments of the present invention will be explained in detail in the following with respect to the accompanying drawings, in which: 
       FIG. 1  shows a block circuit diagram of an inventive circuit for an oscillator in a defined oscillating frequency range; 
       FIG. 2  shows a block circuit diagram of a preferred embodiment of the present invention; 
       FIG. 3  shows a circuit diagram of a basic hybrid amplifier circuit for FBAR; and 
       FIG. 4  shows curves of an FBAR (V in /V out : phase and amplitude response). 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  shows a block circuit diagram of an inventive amplifier circuit  21  for an oscillator in a defined oscillating frequency range coupled to a resonator, here an FBAR  22 , and a feedback of the output signal at the input of the amplifier. V in  is the input voltage of the amplifier, and V out  is the output voltage of the amplifier. The amplifier circuit has three transconductors, a first transconductor TK 1  defined by the transconductance G m1 , a second transconductor TK 2  defined by a transconductance G m2 , and a third transconductor TK 3  defined by a transconductance G m3 . Furthermore, the amplifier has a buffer B with an amplification factor A=1 and two impedance elements, a first impedance element IE 1  with the capacitance C 1 , and a second impedance element IE 2  with the capacitance C 2 . The transconductor TK 1  is coupled to the amplifier input  21 E. The transconductor TK 2  is coupled to the output of the first transconductor TK 1  on the input side, wherein the output of the transconductor TK 2  is connected to the input of the transconductor TK 2  by feedback. The transconductor TK 3  is coupled to the output of the transconductor TK 2  on the input side, and the buffer B is coupled to the output of the transconductor TK 3  on the input side and to the amplifier output  21 A on the output side. The impedance element IE 1  is connected between the output of the transconductor TK 2  and the input of the transconductor TK 3 , and impedance element IE 2  is connected between the output of the transconductor TK 3  and the input of the buffer B. The resonator  22  is connected between the amplifier output  21 A and the amplifier input  21 E. A capacitor K 1  having the capacitance C 3  is connected between the node point  25  and a ground point. 
   This allows to derive that the following applies to the amplifier:
 
 V   out   /V   in   =G   m1   *G   m3 /(− sC 2*(− G   m2   +sC   1 )
     wherein V out  is the output voltage of the amplifier  21 ,   wherein V in  is the input voltage of the amplifier  21 ,   wherein G m1  is the transconductance of the first transconductor TK 1 ,   wherein G m2  is the transconductance of the second transconductor TK 2 ,   wherein G m3  is the transconductance of the third transconductor TK 3 ,   wherein C 1  is the capacitance of the first impedance element IE 1 ,   wherein C 2  is the capacitance of the second impedance element IE 2 , and   wherein s is an angular frequency.   

   In order to realize a sufficient phase shift of −330° for the above example of an FBAR with the curves according to  FIG. 4  to meet the resonance requirement for an oscillating circuit of 0° and/or 360°, either the transconductance G m1  or the transconductance G m3  should be negative and the other one positive. In addition, the transconductance G m2  has to be negative, and the term −G m2 +sC 1  has to have a phase angle of 60° with the angular frequency s. The amplification-phase relationship for the resonant frequency is based on the tuning between the components. Further rearrangement of the above equation yields the following:
 
 V   out   /V   in   =−G   m1   /G   m2 *1/(1+( sC   1   /G   m2 ))*( G   m3   /sC   2 )
 
   When the transconductances G m1 , G m2  and G m3  are tuned and the capacitances C 1  and C 2  of the impedance elements are also tuned, the time constants t 1 =C 1 /G m2  and t 2 =C 2 /G m3  are further also tuned, the amplification-phase relationship is thus independent of process/temperature changes. In order to guarantee that the above time constants are tuned to the resonant frequency, a transconductance adaptation (g m  tuning) is possible in the oscillator circuit by adapting the bias currents of the transconductors. 
   In the following, a preferred embodiment of the inventive amplifier circuit for an oscillator in a defined oscillating frequency range is illustrated with respect to  FIG. 2 . The first transconductor TK 1  comprises three transistors M 1 , M 2  and M 3 , wherein the gate electrode of the transistor M 1  is connected to the amplifier input  21 E, and the transistors M 2  and M 3  constitute a current mirror, and wherein the drain electrodes of the transistors M 1  and M 2  are further coupled. The drain electrode of the transistor M 3  constitutes the output of the transconductor TK 1  and is connected to the node point  26 . A current source STRQ 1  is further connected to the node point  26 . The transconductor TK 2  comprises a transistor M 4  whose gate and drain electrodes are connected to node point  26  and whose source electrode is connected to a reference potential. Transconductor TK 3  comprises a transistor M 6  whose gate electrode is coupled to the node point  26 , whose source electrode is coupled to a reference potential, and whose drain electrode is coupled to the node  27 . The transistor M 4  of the transconductor TK 2  and the transistor M 6  of the transconductor TK 3  constitute a second current mirror. 
   The transistor M 5  is connected between reference node  26  and a reference potential so that the gate-channel capacitances of the transistors M 4 , M 5  and M 6  yield a predetermined impedance value. Impedance element IE 2  comprises a transistor M 7  whose gate electrode is connected to node point  27 , and whose drain and source electrodes are shorted and coupled to a reference potential. Furthermore, a second current source STRQ 2  having the current I 2  is coupled to the node point  27 . The buffer (B) comprises a transistor M 8  whose gate electrode is connected to the reference node  27 , whose drain electrode is connected to the ground point, and whose source electrode is connected to the amplifier output  21 A. Furthermore, a third current source STRQ 3  is coupled to the source electrode of the transistor M 8  and/or the amplifier output  21 A. The capacitor K 2  having the capacitance C 2  is connected between amplifier input  21 E and the gate electrode of the transistor M 1  and only serves for the direct current decoupling, wherein an additional benefit is that no further ESD protection is necessary with this capacitor. The node point  21 E′ may thus also be considered as internal amplifier input. An ohmic resistor R having a value R 1  is connected between internal amplifier input  21 E′ and the amplifier output  21 A. The capacitor K 1  connected between node point  25  and a reference potential realizes the capacitor K 1  in  FIG. 3  having the capacitance value C 3 . 
   With the current mirror of M 2  and M 3 , the transistor M 1  realizes the positive transconductance G m1  of the transconductor TK 1 , wherein the following equation applies:
 
 G   m1   =g   m ( M 1)* g   m ( M 3)/ g   m ( M 2)
 
   The transconductance G m2  of the transconductor TK 2  is defined by the transistor M 4 , wherein the following equation applies:
 
 G   m2   =−g   m ( M 4)
 
   Likewise, the transconductance G m3  of the transconductor TK 3  is defined by the transistor M 6 , wherein the following equation applies:
 
 G   m3   =−g   m ( M 6)
 
   The capacitance C 1  of the impedance element IE 1  is defined by the gate-channel capacitances of the transistors M 4 , M 5  and M 6 . Furthermore, the capacitance C 2  of the impedance element IE 2  of  FIG. 2  is defined by the gate-channel capacitance of the transistor M 7 . The transistor M 8  realizes the buffer B with the amplification A=1 in source following circuit. The loop containing transistor M 8 , current source STRQ 3 , resistor R, and transistors M 1 , M 2 , M 3 , M 4 , current source STRQ 1 , transistor M 6 , and current source STRQ 2  defines the operating points (biasing) of all transistors of this switching network. The following equations may be derived:
 
 I ( M 2)= I ( M 1)
 
 I ( M 3)= I ( M 2)* W ( M 3)/ W ( M 2)
 
 I ( M 4)= I ( M 3)− I 1
 
 I ( M 6)= I ( M 4)* W ( M 6/ W ( M 4
 
 I ( M 6)= I 2
 
 I ( M 8)= I 3
 
wherein I represents either the drain-source current of the respective transistors or the current of the respective current source, wherein W is further the gate width of the respective transistor, and wherein it is further assumed that the following applies for the gate length L: L(M 3 )=L(M 2 ) and L(M 6 )=L(M 4 ). What is derived from the above equations is that the currents I 1  and I 2  determine the currents of the transistors M 1 , M 2 , M 3 , M 4  and M 6  and thus control the transconductances of the transconductors G m1 , G m2  and G m3 . The currents I 1  and I 2  may be adapted to compensate for the change of the time constants t 1  and t 2  induced by process and temperature. For the loop to be stable, the time constant R 1 *C in  has to be larger than any other time constant within this loop, particularly the time constant Cgs(M 7 )/gds(M 6 ) resulting from the gate-source capacitance of the transistor M 7  of the second impedance element IE 2  and the drain-source conductance of the transistor M 6  of the third transconductor TK 3 . Wherein C in  is the input capacitance of the amplifier circuit.
 
   The reason for an independent current source I 1  is to be explained in the following. For the conductances G m1 , G m2  and G m3  to be on different bias current levels, the drain-source saturation voltages V dssat  of M 1 , M 4  and M 6  have to be equal. On the other hand, it is advantageous for reasons of noise when V 1 /V out &gt;1 applies to the amplification (of  FIG. 1 ), which requires that −G m1 /G m2 &gt;1. In order to be able to meet these two requirements, an additional current source is necessary. 
   While this invention has been described in terms of several preferred embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.