Abstract:
A resonator circuit is shown that is fabricated with substantially identical elements disposed symmetrically along an axis such that the circuit has a linear response to bias current. The alignment of the circuit permits multiple characteristics of the circuit to be calibrated.

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS 
     This patent application claims the benefit of U.S. Provisional Patent Application No. 60/606,037, filed Aug. 31, 2004. 
    
    
     FIELD OF THE INVENTION 
     This invention pertains to poly-phase filters and, more particularly, a tunable poly-phase filter and a method for calibration thereof. 
     BACKGROUND OF THE INVENTION 
     Gyrator type resonators are widely used to implement poly-phase filters on integrated circuits. For example, see Integration of Analog Filters in a Bipolar process. J. O. Voorman, W. H. A. Brüils and P. J. Barth, IEEE Journal of Solid-State Circuits, Vol. SC-17, No. 4, August, 1982. Their symmetrical construction makes them well suited to filtering low intermediate frequency filtering in receivers using both in-phase and quadrature-phase signals that provide low signal distortion due to the advantages of the well known image rejection and the symmetrical (around the resonance frequency) frequency responses of both the amplitude and group-delay. For example, see U.S. Pat. No. 4,193,033. 
     Some conventional filter implementations of the gyrator type resonator use a combination of resistors and transconductors to tune the damping and hence the bandwidth. For examples, see U.S. Pat. No. 5,220,686 or patent application WO 02/087071 A3. Tolerances and temperature dependencies of the integrated resistors, capacitors and transconductors biasing circuitry all have their effect on the filter parameters, such as center frequency, bandwidth, shape and gain. Several solutions exist to counter this alignment problem. In one example (see Datasheet TEA6850, Philips Semiconductors, July, 1994), two potentiometers need hand alignment to set the center frequency and the bandwidth. It will be evident that hand tuning is not acceptable for high volume products due to cost considerations. 
     A second known solution is to add separate control loops on the receiver integrated circuit. In A wideband tunable CMOS channel-select filter for a low-IF wireless receiver. F. Behbahani, W. Tan, A. Karimi, A. Roithmeier, and A. A. Abidi. Custom IC Conf., San Diego, pp. 501-504, May 1999, a channel-select filter is described. A complex mixed analog-digital automatic frequency control loop is used to tune the center frequencies of the resonators in the filter. On top of that, a second mixed analog-digital loop is required to tune the Q of the filters. 
     The multiple loop calibration requirement is also apparent in some products currently on the market. S. Sandee and G. van Werven (Application Note, AN 00001, version 1.2. Philips Semiconductors, Jun. 26, 2000), for example, describe a radio with circumstantial controlled selectivity wherein a 7 bit digital to analog converter (DAC) is used to calibrate the center frequency, the bandwidth is dynamically controlled using an analog loop and the gain is calibrated using a 4 bit DAC. In another current product, the TEAS5767HL (see Datasheet TEA5767HL, Philips Semiconductors, Sep. 13, 2002) shows a low intermediate frequency filter that requires two separate alignment loops, one for the center frequency and one for the gain. In addition, both loops of the TEAS5767HL require a pin and an external component. Each of these calibration loops requires a supply current, which requires additional chip area and, in some cases, requires additional interface pins and external components. 
     A third solution is to correct the process spread by using an external micro-controller. This approach is demonstrated in A Digitally Programmable Zero External Components FM Radio Receiver with luV Sensitivity, H. van Rumpt, D. Kasperkovitz, J. van der Tang. IEEE—ISSCC 2003 and in a part currently available on the market, see Datasheet TDA7513T, ST Microelectronics, June 2004. [10, 11]. In most products, micro-controllers have a specific function, such as polling interrupts, updating the display, controlling the modes of functions, or scanning a keypad. The introduction of micro-controlled calibration may place an undesirable load on the micro-controller along with the system bus that may impair the micro-controller&#39;s ability to perform its primary functions. 
     It is an objective of the invention to obviate these drawbacks so that poly phase type filters can be produced with a high production yield, using less chip area, less current consumption and no additional pins nor external components. 
     BRIEF SUMMARY OF THE INVENTION 
     In one embodiment, a resonator circuit has a first phase stage that includes a first inverting transconductor having an input and an output, a first non-inverting transconductor having an input coupled to the output of the first inverting transconductor to form a first circuit node and an output coupled to the input of the first inverting transconductor to form a second circuit node. A second inverting transconductor has an input and an output, where both the input and output are coupled to the first circuit node. A first capacitor is coupled to the first circuit node. A third inverting transconductor has an input and an output, where both the input and output are coupled to the second circuit node. A second capacitor is coupled to the second circuit node. In a further refinement of this embodiment, the first inverting transconductor, the first capacitor and the second inverting transconductor are fabricated on a die symmetrically to the first non-inverting transconductor, the second capacitor and the third inverting transconductor along an axis of the die. 
     In yet a further refinement, the first phase stage also includes a second non-inverting transconductor with an input for receiving a first input voltage signal and an output coupled to the first circuit node and a third non-inverting transconductor with an input for receiving a second input voltage signal and an output coupled to the second circuit node, where the second and third non-inverting transconductors are fabricated symmetrically to one another along the axis of the die. 
     In still another refinement, the resonator circuit includes a second phase stage that is substantially identical to the first stage, where the input of the second non-inverting transconductor of the second phase stage is coupled to the first circuit node of the first phase stage, the input of the third non-inverting transconductor of the second phase stage is coupled to the second circuit node of the first phase stage, and the resonator circuit further includes a first feedback inverting transconductor with an input coupled to the first circuit node of the second phase stage and an output coupled to the first circuit node of the first phase stage and a second feedback inverting transconductor with an input coupled to the second circuit node of the second phase stage and an output coupled to the second circuit node of the first phase stage. 
     In one additional refinement, the resonator circuit further includes a first current circuit configured to receive a calibration voltage signal and produce a first bias current that is proportional to the calibration voltage. A calibration circuit includes a replica of the first phase stage of the resonator circuit, where the replica is coupled to the first current circuit and is biased by the first bias current and the calibration circuit is configured to generate the calibration voltage signal. The calibration circuit is further configured to receive a reference frequency and adjust the calibration voltage signal until a resonance of the replica matches the reference frequency. A second current circuit is configured to receive the calibration voltage signal and produce a second bias current that is proportional to the calibration voltage for biasing the first inverting transconductor and the first non-inverting transconductor. A third current circuit is configured to receive the calibration voltage signal and produce a third bias current that is proportional to the calibration voltage for biasing the second inverting transconductor and the third non-inverting transconductor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Certain embodiments will be described with reference to the following drawings, wherein: 
         FIG. 1  is a functional block diagram illustrating an exemplary embodiment of a basic resonator circuit; 
         FIG. 2  is a functional block diagram of an exemplary embodiment of a first order poly-phase resonator filter; 
         FIG. 3  is a functional block diagram of an exemplary embodiment of a poly-phase band-pass filter; and 
         FIG. 4  is a functional block diagram of an exemplary embodiment of a circuit for implementing a calibration method. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the present invention, by using a certain arrangement of transconductors (described in the preferred embodiments), a gyrator type poly-phase filter can be realized that has the same dependencies for both bandwidth and resonance frequency determination. Furthermore, this arrangement, in accordance to the present invention, simplifies calibration significantly: calibrating the resonance frequency or the bandwidth implicitly calibrates the remaining parameters. For example, when the resonance frequency is calibrated, then the bandwidth, forward-gain and feedback-gain are calibrated implicitly. Consequently, multiple calibration loops are not necessary. 
     An embodiment of a basic resonator circuit, having a single phase stage, is shown in  FIG. 1 . Two transconductors  110  and  120 , having transconductance values G 1  and G 2 , respectively, together with two capacitors  114  and  124 , having capacitance values C 1  and C 2 , respectively, form a gyrator resonator  100 . The resonator  100  is damped by transconductors  112  and  114 , having having transconductance values G 3  and G 4 , respectively, to create the desired bandwidth. Note that transconductors  110 ,  112  and  122  each have an inverting transconductance. 
     At node I, capacitor  124  (C 2 ) behaves as an inductor due to the gyrator principle, hence an LC-like parallel resonator is formed. The same is valid at node Q, where capacitor  114  (C 1 ) behaves as an inductor in parallel with capacitor  124 . The resonance frequency is determined by the values of G 1 , G 2 , C 1  and C 2 . 
     In a preferred embodiment, the resonator components, including its values and layout, are substantially symmetrical with respect to the axis A depicted in  FIG. 1 . Furthermore, the transconductors have substantially the same dependencies, which means that their transconductances, as a function of such factors as biasing, temperature, process spread, operating voltage, are essentially the same. An optional property of the preferred embodiment is that the transconductance of each transconductor is essentially linearly controlled as a function of the biasing current or voltage. By fabricating the resonator components on a die in a symmetrical layout and fabricating the components to have the same dependencies, the resonant frequency of the resulting resonator can be linearly controlled by the biasing current or voltage. The following values are used to demonstrate the properties of the resonator according to the embodiment of  FIG. 1 : 
     transconductance G 1 =transconductance G 2 =g f    
     capacitance C 1 =capacitance C 2 =C 
     transconductance G 3 =transconductance G 4 =g bw    
     With this arrangement, the resonance frequency (F res ) and the −3 dB bandwidth (BW) of the resonator are calculated as follows: 
     
       
         
           
             
               
                 
                   
                     F 
                     res 
                   
                   = 
                   
                     
                       g 
                       f 
                     
                     
                       2 
                       ⁢ 
                       
                         π 
                         · 
                         C 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   BW 
                   = 
                   
                     
                       g 
                       bw 
                     
                     
                       π 
                       · 
                       C 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Equations (1) and (2) above show that when g f  and g bw  have the same dependencies, and both are biased from a common calibration source, as is discussed in further detail below with respect to  FIG. 3 , then the relative error in resonance frequency is substantially equal to the relative error in the bandwidth. In other words, when one is calibrated to cancel this error, then the other is calibrated implicitly with the high accuracy of integrated component matching. 
     With the optional property of the preferred embodiment, e.g. all transconductances are linearly controlled as a function of the biasing current or voltage, the desired g f  to g bw  relation can be realized by a simple linear scaling of the biasing signal. 
     The resonator  100  of  FIG. 1  can be used to implement a first order poly-phase resonator filter  200 , as shown in  FIG. 2 . To the circuit of  FIG. 1  is added transconductor  230 , which has transconductance value G 5  and drives node I in response to input voltage signal Vi-in. Also added is transconductor  240 , which has transconductance value G 6  and drives node Q in response to input voltage signal Vq-in. The input signals Vi-in and Vq-in have a phase quadrature relation, which can be realized, for example, by a quadrature transposition stage, an example of which is illustrated in U.S. Pat. No. 4,193,033. Output voltages Vi-out and Vq-out appear at circuit nodes I and Q, respectively. 
     In a preferred embodiment of a poly-phase resonator filter  200 , the components, including values and layout, are substantially symmetrical around axis A depicted in  FIG. 2 . Furthermore, the transconductor devices have substantially the same dependencies, which means that their transconductances, as a function of biasing, temperature, process spread, and operating voltage, for example, are essentially the same. An optional property of the preferred embodiment is that the transconductance of each transconductor is essentially linearly controlled as a function of the biasing current or voltage. The following values are used to demonstrate the properties of the poly-phase resonator filter according to the invention: 
     transconductance G 1 =transconductance G 2 =g f    
     capacitance C 1 =capacitance C 2 =C 
     transconductance G 3 =transconductance G 4 =g bw    
     transconductance G 5 =transconductance G 6 =g g    
     The resonance frequency and the bandwidth is as calculated in equations (1) and (2). The gain for sinusoidal inputs (cosine and sine) at the resonant frequency is expressed as follows: 
     
       
         
           
             
               
                 
                   GAIN 
                   = 
                   
                     
                       
                         Vi 
                         - 
                         out 
                       
                       
                         Vi 
                         - 
                         in 
                       
                     
                     = 
                     
                       
                         
                           Vq 
                           - 
                           out 
                         
                         
                           Vq 
                           - 
                           in 
                         
                       
                       = 
                       
                         
                           g 
                           g 
                         
                         
                           g 
                           bw 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Equations (2) and (3) show that when g bw  and g g  have the same dependencies, like temperature coefficient and operating voltage dependency, and all transconductors are biased from a common calibration source, then the gain is determined by a substantially constant transconductance ratio. For example, when the frequency is calibrated to cancel the resonant frequency error, then the bandwidth and gain are implicitly calibrated with the high accuracy of integrated component matching. 
     With the optional property of the preferred embodiment (e.g. all transconductances are linearly controlled as a function of the biasing current or voltage) the desired g f  to g bw  to g g  relation can be realized by a simple linear scaling of the biasing signal. 
     The poly-phase resonator filter  200  of  FIG. 2  can be further expanded through the addition of a second phase stage to create a poly-phase band-pass filter  300 , as is shown in  FIG. 3 . To the first phase filter stage of poly-phase filter  200  is added a second phase stage that is substantially similar to the first phase stage. The second phase stage includes transconductor  330 , having transconductance G 5 ′, coupled between circuit node I and circuit node I′ and transconductor  340 , having transconductance G 6 ′, coupled between circuit node Q and circuit node Q′. Transconductor  310 , having transconductance G 1 ′, and transconductor  320 , having transconductance G 2 ′, are coupled between circuit node I′ and circuit node Q′ in reverse directions. Note that transconductor  310 , like transconductor  110 , has an inverting transconductance, while transconductors  120  and  320  have non-inverting transconductances G 2  and G 2 ′, respectively. 
     Capacitor  314 , with capacitance C 1 ′, is coupled to circuit node I′ while capacitor  324 , having capacitance C 2 ′, is coupled to circuit node Q′. The input and output of transconductor  312 , having transconductance G 3 ′, are coupled to circuit node I′ just as transconductor  112  is coupled to circuit node I. Likewise, the input and output of transconductor  322 , having transconductance G 4 ′, are coupled to circuit node Q′ just as transconductor  122  is coupled to circuit node Q. Transconductor  350 , having transconductance G 7 , has its input coupled to circuit node I′ and its output coupled to circuit node I. Similarly, transconductor  360 , having transconductance G 8 , has its input coupled to circuit node Q′ and its output coupled to circuit node Q. 
     In a preferred embodiment of a poly-phase band-pass filter  300 , the components including its values and layout are substantially symmetrical around the dashed line C depicted in  FIG. 3 . Furthermore, the transconductors have substantially the same dependencies, which means that their transconductances as a function of biasing, temperature, process spread, and operating voltage, for example, are essentially the same. An optional property of the preferred embodiment is that the transconductance of each transconductor is essentially linearly controlled as a function of the biasing current or voltage. The following values are used to demonstrate the properties of the poly-phase band-pass filter  300  of  FIG. 3 : 
     G 1 =G 2 =G 1 ′=G 2 ′=g f    
     C 1 =C 2 =C 1 ′=C 2 ′=C 
     G 3 =G 4 =G 3 ′=G 4 ′=g bw    
     G 5 =G 6 =G 5 ′=G 6 ′=g g    
     G 7 =G 8 =g fb    
     The band-pass center frequency is calculated as in equation (1). The shape of the filter is determined by the feedback factor (FB): 
     
       
         
           
             
               
                 
                   FB 
                   = 
                   
                     
                       
                         g 
                         s 
                       
                       · 
                       
                         g 
                         fb 
                       
                     
                     
                       g 
                       bw 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Equation (4) shows that when g bw , g g  and g fb  have the same dependencies, such as temperature coefficient and operating voltage dependency, and the transconductors are biased from a common calibration source, then the shape of the response is determined by a substantially constant transconductance ratio. For example, when the frequency is calibrated to cancel the resonance frequency error, then the bandwidth, the gain and the shape are implicitly calibrated with the high accuracy of integrated component matching. With the optional property of the preferred embodiment (e.g. all transconductances are linearly controlled as a function of the biasing current or voltage) the desired g f  to g bw  to g g  to g fb  relation can be realized by a simple linear scaling of the biasing signal. 
     An embodiment of a circuit  400  for application of a biasing method is shown in  FIG. 4 . Only one calibration circuit  410  is used in this embodiment. Calibration circuit  410  uses a resonator that is an accurate replica (or a scaled replica) of the resonator or resonators utilized in a filter, such as filter  300  in  FIG. 3 , that needs calibration. The replica  412  is aligned along the same axis C as the filter  300  and is composed of circuit components that are the same geometry or a scaled geometry of the components of filter  300  so that the replica  412  has the same linear response as the filter  300 . 
     The replica is automatically aligned by calibration circuit  410  to resonate on a desired frequency by using, for example, a Phase Locked Loop (PLL) or a Frequency Locked Loop (FLL) and a reference frequency (F ref ) derived from an accurate quartz crystal. The calibration circuit  410  adjusts calibration voltage V cal  until replica  412  resonates at the desired frequency. In this embodiment, the calibration voltage V cal  controls a current source circuit  414  that converts the voltage into a bias current bias current (I f ) by multiplying the calibration current by the transistor gain (g) of the transistors of current circuit  414 . 
     The bias current I f  that is generated to provide this resonance frequency is copied to the filter  300  that needs calibration through the use of current circuits  420 ,  422 ,  424  and  426 . These current circuits, in one example, are implemented as current mirrors that multiply the bias current I f  generated by current circuit  414 . In this embodiment, current scaling circuit  420  provides the biasing current for transconductors  110  and  120  (for the circuits of  FIGS. 1 and 2 ), as well as transconductors  310  and  320  (for the circuit of  FIG. 3 ) and, therefore, can be used to control the resonant frequency of the circuit  100 ,  200  or  300  that is being calibrated. Current scaling circuit  422  provides the biasing current for transconductors  112  and  122  (for the circuits of  FIGS. 1 and 2 ), as well as transconductors  312  and  322  (for the circuit of  FIG. 3 ) and, therefore, can be used to control the bandwidth of the circuit  100 ,  200  or  300  that is being calibrated. Current scaling circuit  424  provides the biasing current for transconductors  230  and  240  (for the circuit of  FIG. 2 ), as well as transconductors  330  and  340  (for the circuit of  FIG. 3 ) and, therefore, can be used to control the gain of the circuit  200  or  300  that is being calibrated. Current scaling circuit  426  provides the biasing current for transconductors  350  and  360  for the circuit of  FIG. 3  and, therefore, can be used to control the feedback of the circuit  300  that is being calibrated. 
     In this example, the scaling factors k f , k bw , k g , and k fb  can, therefore, be implemented through the sizing of the resistors and the transistor emitter areas of the components of current scaler circuits  420 ,  422 ,  424  and  426 . By way of further example, if the scaling factor k f  is chosen to be 1 and the replica  412  is a 1:1 copy, then the resonators used in the filter  300  will have the same resonant frequency as the resonator replica  412  in the calibration circuit  410  with the high accuracy of the integrated component matching. The other biasing currents are derived by simply scaling the generated biasing current I f . No additional calibration loops are necessary. 
     Depending on the complexity of the filter, several currents need to be copied into the filter, as indicated by the factor N. For example, when the filter of  FIG. 3  is used, then N f =4, N bw =4, N g =4 and N fb =2. Note that different characteristics for the performance of the filter can be obtained by utilizing different ratios than those set forth for this example. 
     The following example calculations demonstrate the calibration method shown in  FIG. 4 . Some assumptions are made that are achievable through the use of integrated circuit techniques:
         In this calculation example, the poly phase filter of  FIG. 3  is used including the values that are listed above.   The transconductors and the capacitors used in the poly phase filters are substantially exact copies.   The resonator in the calibration circuit is substantially a replica of the resonator used in the poly phase filter.   The transconductance of each transconductor is I bias /V T , where V T  is kT/q, k=Boltzmann&#39;s constant (1.38·10 −23  Joule/Kelvin), T=absolute temperature in Kelvin, and q is the elementary charge of an electron (1.6·10 −19  Coulombs).   Note that the optional property of the preferred embodiment is fulfilled with this assumption: e.g. the transconductance is a linear function of the biasing current (I bias ).       All integrated components have the same operating temperature.   

     The resonant frequency of the resonator in the calibration circuit is: 
                     F   res     =         g   f       2   ⁢     π   ·   C         =     F   ref               (   5   )               
Consequently:
   g   f =2π· F   ref   (6) 
The resonant frequency and hence the center frequency of the poly-phase filter is:
 
                     F   filter     =           k   f     ·     g   f         2   ⁢     π   ·   C         =       k   f     ·     F   ref                 (   7   )               
The bandwidth of the poly phase filter is proportional to:
 
                   BW   =           k   bw     ·     g   f         π   ⁣     ·   C         =     2   ·     k   bw     ·     F   ref                 (   8   )               
The gain at the center frequency is equal to:
 
                         GAIN   =       g   g         g   bw     +         g   g     ·     g   fb         g   bw                       =         k   g     ·     g   f             k   bw     ·     g   f       +         k   g     ·     g   f     ·     k   fb     ·     g   f           k   bw     ·     g   f                         =       k   g         k   bw     +         k   g     ·     k   fb         k   bw                         (   9   )               
The feedback factor (FB) that determines the shape of the filter is formed by:
 
     
       
         
           
             
               
                 
                   FB 
                   = 
                   
                     
                       
                         
                           g 
                           g 
                         
                         · 
                         
                           g 
                           fb 
                         
                       
                       
                         g 
                         bw 
                         2 
                       
                     
                     = 
                     
                       
                         
                           
                             k 
                             g 
                           
                           · 
                           
                             g 
                             f 
                           
                           · 
                           
                             k 
                             fb 
                           
                           · 
                           
                             g 
                             f 
                           
                         
                         
                           
                             ( 
                             
                               
                                 k 
                                 bw 
                               
                               · 
                               
                                 g 
                                 f 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       = 
                       
                         
                           
                             k 
                             g 
                           
                           · 
                           
                             k 
                             fb 
                           
                         
                         
                           k 
                           bw 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     From equations 6 to 10, it can be seen that the filter parameters are well defined and coupled to either the product of a scaling factor and the reference frequency or by a ratio of current scaling factors. 
     From equations 6 to 10, the tuning capabilities of the present invention also become apparent:
         The center frequency can be accurately shifted by changing the k f  scaling factor.   The gain, bandwidth and feedback factor (and hence the filter shape) are independent from the k f  scaling factor. In other words, the filter center frequency can be tuned without affecting the remaining filter parameters.   The bandwidth can be accurately tuned by changing k bw . When k g  and k fb  are changed proportionally then the filter gain and shape are not affected.   The gain can be changed independently when transconductors  230  and  240  (with transconductance values G 5  and G 6 , respectively) shown in  FIG. 3  are biased using a separate current scaler circuit  424 .       

     Note that the transconductors discussed above and illustrated in the drawings are shown as single ended devices, but may be implemented as differential devices, as well, without departing from the teachings of the present invention. 
     All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein. 
     The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention. 
     Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. It should be understood that the illustrated embodiments are exemplary only, and should not be taken as limiting the scope of the invention.