Patent Publication Number: US-7218179-B2

Title: Methods and apparatus for calibrating gm-Z

Description:
FIELD OF THE INVENTION 
   The present invention relates to calibration of a control circuit, and more particularly to calibration of a circuit having a transconductance and impedance (gm-Z). 
   BACKGROUND 
   Numerous circuits used in radio (high) frequency (RF) electrical devices, such as low noise amplifiers (LNAs), mixers, synthesizers, resistance capacitance (RC) filters and transconductance capacitance (gm-C) filters, require calibration. Specifically, calibration of open loop gain for such circuits is needed, because of the inability at high frequencies to use feedback techniques that normally work in conjunction with readily available matched passive components to set the gain. Gain is thus usually set by matching active transistor components to passive elements such as inductors, resistors and capacitors. Active components on an integrated circuit (IC) do not typically match very well to the passive components. As a result, a method of calibrating the gain to ensure that a design is manufacturable is needed. 
   Accordingly, separate control circuitry, namely calibration circuitry, is used to provide calibration of the gain of these RF components. Such calibration circuits typically include circuitry similar to or matched to that within the target circuit so that the target circuit may be calibrated for power supply variations, temperature variations, integrated circuit process parameter variations, parasitic capacitance, transconductance and the like. Such calibration circuits typically use the large signal characteristics of the devices in the target circuit. However, such calibration circuits can suffer from inaccuracies due to poor matching of large signal parameters to the small signal parameters, and it is the small signal parameters that determine the gain of the devices. As process geometries get finer, the large signal models for the devices no longer match simple textbook models for the transistors. This makes the task of building these circuits harder. As a result, a method for directly measuring and calibrating the small-signal parameters of transistors is increasingly necessary. 
   SUMMARY OF THE INVENTION 
   In certain embodiments, the present invention may include a plurality of gain stages each having a gain greater than one, and which are coupled to create a positive feedback at an oscillation frequency. In certain embodiments, the gain stages may be formed of transconductance gain stages which may be coupled together as a ring oscillator. Alternately, gain stages in accordance with one embodiment of the present invention may take the form of a latch type circuit. Such circuits may be used as calibration circuits in which small signal parameters of the gain stages are calibrated, and are used in turn to calibrate a target circuit. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1A  is a block diagram of a calibration circuit in accordance with one embodiment of the present invention. 
       FIG. 1B  is a block diagram of a calibration circuit in accordance with another embodiment of the present invention. 
       FIG. 2A  is a graphical representation of a transfer function of a gain stage in accordance with an embodiment of the present invention. 
       FIG. 2B  is a phase response for the transfer function of  FIG. 2A . 
       FIG. 3A  is a schematic diagram of a controlled resistance in accordance with an embodiment of the present invention. 
       FIG. 3B  is a schematic diagram of a current source in accordance with an embodiment of the present invention. 
       FIG. 4  is a block diagram of a calibration circuit in accordance with a third embodiment of the present invention. 
       FIG. 5  is a block diagram of a system in accordance with one embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
   In various embodiments of the present invention, a small signal gain of a calibration circuit using positive feedback may be used to directly calibrate small signal parameters of a target circuit. In so doing, more accurate calibration may occur as a direct link between calibration circuit and the target circuit may be formed. Such a calibration circuit may be used in various situations where it is desired to calibrate the gain of a target circuit. Such a calibration circuit may find application at RF and baseband. For example, in certain embodiments, such a calibration circuit may be used in situations where an open loop gain at a high bandwidth is desired, such as a LNA, a mixer, a variable gain amplifier (VGA), and the like. 
   In various embodiments, different circuitry may be used to calibrate a target circuit. In certain embodiments, a calibration circuit may include at least one gm-Z stage (where Z represents a general impedance block, which may be as simple as a resistor). By calibrating the value of gm-Z, a similar gm-Z in a target device may be similarly calibrated or tuned. That is, a control signal used to calibrate the gm-Z value of the calibration circuit may also be coupled to the target circuit. Similarly, a measurement or calibration of an RC (in the case that Z is formed by a parallel resistor-capacitor pair) portion of the calibration circuit may concurrently be performed to calibrate a corresponding RC portion of the target circuit for applications where accurate pole frequencies need to be set. 
   Referring now to  FIG. 1A , shown is a block diagram of a calibration circuit in accordance with one embodiment of the present invention. As shown in  FIG. 1A , calibration circuit  10  may be implemented as a ring oscillator. Such a ring oscillator may include a plurality of gain stages  20   a – 120   c.    
   As shown in  FIG. 1A , each gain stage may include a transconductor  25  having a transconductance value of −gm. As further shown in  FIG. 1A , the output of each transconductor  25  (collectively transconductors  25   a–c ) may be coupled to an impedance  27  (collectively impedances  27   a–c ) coupled between the output of transconductor  25  and a ground potential. Further, each of the gain stages  20   a – 20   c  may be coupled together in series, and an output of the last gain stage  20   c  may be coupled to provide a feedback signal  40  to the input of the first gain stage  20   a.  While impedances  27  may take various forms, in certain embodiments, the impedances may be formed of a resistor and a capacitor (i.e., an RC circuit). In other embodiments, impedance  27  may be formed of an inductor and a capacitor (i.e., an LC circuit). 
   In certain embodiments, instead of a passive load an active load such as a PMOS device or an NMOS device may be coupled to each of the gain stages. Such active devices may be used to calibrate similar devices in a target circuit. 
   For further discussion with regard to  FIG. 1A , it may be assumed that each impedance  27  may be formed of a resistor (R) and a capacitor (C) coupled in parallel between an output of transconductor  25  and a ground potential. In one such embodiment, impedance  27  may be implemented using a controlled resistive element so that a gm-Z (in the form of gm·R) may be calibrated using a variable resistance. However, in other embodiments the transconductance may be varied in order to calibrate gm·Z. While shown in the embodiment of  FIG. 1A  as including three gain stages, it is to be understood that in other embodiments more or fewer gain stages may be present. If fewer gain stages are present, the gain of each stage may be higher than two, while if more than three gain stages are present, the gain of each stage may be lower than two (but greater than one). In one embodiment, ring oscillator  10  may be used in connection with a broadband target circuit, such as a mixer. In such an embodiment, the gain may be greater than one at the oscillation frequencies, and the low frequency gain may be whatever is needed to allow this to happen, as shown in the below equations. 
   During operation, ring oscillator  10  begins to oscillate at a frequency of ω 0  when feedback signal  40  becomes positive. That is, the ring oscillator begins to oscillate when each stage has a phase shift of 60° (for a total phase shift of 360°) and a gain of each stage becomes greater than two. In the embodiment shown in  FIG. 1A , the transfer function of each stage is: 
   
     
       
         
           
             
               
                 
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   A graphical representation of the absolute value of the transfer function as a function of frequency for the circuit of  FIG. 1A  is shown in  FIG. 2A . As shown in  FIG. 2A , the absolute value crosses zero at the 60° phase shift, when oscillation begins. The phase response for the transfer function of  FIG. 2A  is shown in  FIG. 2B . Thus oscillation occurs at ω 0  and the feedback becomes positive when ω 0 RC=√{square root over (3)} [2]. 
   
     
       
         
           
             
               
                 
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   Thus during operation, the resistance of each gain stage  20   a–c  may be varied by a control signal such that its gm·R is greater than two. While the gain may exceed two by different amounts, any value greater than two may suffice. In practice, the closer the gain is to two, the longer it takes for the oscillation to reach full scale, and the smaller the amplitude of the oscillation is. In certain embodiments, the gain may desirably be very close to two, e.g., between approximately 2.01–2.05. Due to certain process variations and secondary considerations, in certain embodiments oscillation may occur and a positive feedback may be reached when the gain of each stage is slightly less than two. In various embodiments, it may be desirable to keep the gain relatively close to two. 
   In other embodiments, a calibration circuit may be used to calibrate gain for use in a tuned RF circuit. For example, a tuned RF component, such as a tuned LNA may have its gain calibrated by a calibration circuit according to an embodiment of the present invention. 
   Referring now to  FIG. 1B , shown is a block diagram of a calibration circuit in accordance with another embodiment of the present invention. As shown in  FIG. 1B , ring oscillator  200  may be used to calibrate gain in a tuned RF component. As shown in  FIG. 1B , ring oscillator  200  may include a first transconductor  210  having a transconductance value of −gm. The output of transconductor  210  may be coupled to an input of a second transconductor  220 , which may also have a transconductance value of −gm. As shown in  FIG. 1B , the output of transconductor  220  may be coupled to an input of transconductor  210 . Accordingly, the outputs of each transconductor may act as a feedback signal. As further shown in  FIG. 1B , a first impedance  230  may be coupled between the output of transconductor  210  and the input of transconductor  220  and a second impedance  240  may be coupled to an input of transconductor  210  in an output of transconductor  220 . As further shown, impedances  230  and  240  may each be coupled to ground. While not shown in  FIG. 1B , in certain embodiments, an additional impedance may be coupled between transconductors  220  and  210 . 
   Each impedance  230  and  240  may have a generic value of Z (ω 0 ), where ω 0  is the resonance frequency of the tuned circuit. As shown in the close-up in  FIG. 1B , in one embodiment each of impedances  230  and  240  may be an LC circuit having an inductor (L)  242  and a capacitor (C)  244 . In such manner, 
   
     
       
         
           
             
               
                 
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   In operation, by programming the current of transconductors  210  and  220  of  FIG. 1B , the gain of a tuned RF component, such as an LNA may be calibrated. Ring oscillator  200  may reach oscillation when gm·Z (ω 0 ) is greater than one. 
   While in some embodiments, ring oscillator  200  may be implemented in a separate calibration circuit, in other embodiments, ring oscillator  200  may be added to circuitry already present in an RF component, such as a local oscillator, as such a circuit may already include desired impedances (e.g., LC circuits). In such manner, minimal real estate may be used, and process variations may be eliminated. 
   While not shown in  FIGS. 1A and 1B , it is to be understood that in various embodiments, a detection circuit may be present and coupled to receive the feedback signals. Such a detection circuit may be used to detect when the ring oscillators reach a full scale of oscillation. When oscillation reaches full scale, the detection circuit may provide a signal to a control circuit (not shown in  FIGS. 1A and 1B ) that provides a calibration or tuning signal to the controllable elements of the ring oscillators. Such a tuning control signal may be initiated at a low value (i.e., at system power up), and be gradually increased until oscillation begins, at which point the tuning signal remains at its then current value (in embodiments in which calibration is effected on system power up). Various algorithms may be implemented in order to effect control of the controllable elements of the ring oscillators. 
   Referring now to  FIG. 3A , shown is a block diagram of a controlled resistance in accordance with one embodiment of the present invention. Controlled resistance  50  of  FIG. 3A  may correspond to resistances within impedances  27   a–c  of  FIG. 1A . Thus each impedance  27   a–c  of ring oscillator  10  of  FIG. 1A  may be controlled within a desired predetermined range using a controlled resistance like that of  FIG. 3A . In one embodiment the switches in  FIG. 3A  may be implemented using transistors. Each resistance may be controlled within a wide range of values, extending between approximately 100 Ω to several MΩ. In other embodiments, the values may be between several kΩ to tens of kΩ. It is to be understood that each resistance  27   a–c  may be much smaller than the parasitic conductance of the gain stage. 
   As shown in  FIG. 3A , controlled resistance  50  may be synthesized from a digitally controlled parallel connection of a plurality of fixed resistors. As shown in  FIG. 3A , four fixed resistors having values of R unit , 2R unit , 4R unit , and 8R unit , respectively, may be selectively connected or disconnected in response to a tuning control signal. In various embodiments, R unit  may be between approximately 50 Ω and 100 kΩ. In the example shown in  FIG. 3A , a four-bit digital tuning signal (i.e., including bits b 0 -b 3 ) from a control circuit may be used to selectively connect or disconnect the individual resistors. Similarly, the digital tuning signal may be sent to the target circuit for calibration of associated gm-R values therein. 
   While shown as including four resistors in the specific embodiment of  FIG. 3A , it is to be understood that in other embodiments more or fewer such resistors may be possible. It is also to be understood that there are numerous other approaches that may be used to realize a controllable resistance. For example, a programmable or otherwise programmed impedance or a voltage controlled impedance may be used. Furthermore, instead of the parallel implementation shown in  FIG. 3A , a series implementation of impedances may be used. Also, instead of a digital tuning signal, other signals from a control circuit (other analog circuits, i.e., analog vs. digital control) may be used to control the controllable elements of a calibration circuit. 
   In other embodiments, gm·Z may be calibrated by varying gm and maintaining a fixed impedance. For example, gm may be adjusted by changing values of a bias current (I bias ) flowing therethrough. 
   In certain embodiments, calibration may be performed on system startup to calibrate a desired target circuit. Alternately, calibration may be performed continuously during system operation or at predetermined intervals. Such continuous calibration maybe desired when adjusting gm by varying a bias current. 
   After calibration of the desired components (i.e., gm or Z, or both in certain embodiments), the value of the oscillating frequency may be analyzed and used to measure the value of the impedance portion of gain stage. In such manner, the measured value of RC may be used to calibrate an impedance portion of the target circuit, for example, an RC filter coupled to the calibration circuit. 
   In certain embodiments, particularly with respect to a ring oscillator incorporating RC circuits such as the ring oscillator of  FIG. 1A , it may be desirable for a current source to provide a constant saturation voltage (i.e., V on ) to the transconductors. 
   Referring now to  FIG. 3B , shown is a schematic diagram of a constant current source  300  in accordance with one embodiment of the present invention. As shown in  FIG. 3B , current source  300  may be formed by dividing a reference voltage (i.e., V REF ) by a controlled resistance (e.g., a variable resistance). Such controlled resistance may be the same as that shown in  FIG. 3A . In such manner, the current source  300  is propagated to the transconductors so that as the current of the source is decreased, the gm of the transconductor is similarly decreased. Conversely, increasing the current increases the gain. Because there is a constant V on , the headroom of the transconductors is constant, which provides for process independence and makes headroom issues easier to maintain and provides linearity even for corner cases. 
   Thus, the gain of the stage is proportional to the transconductance times the resistance. More specifically, 
                 gm   ⁢           ⁢   α   ⁢     I             [   8   ]               gain   ⁢           ⁢   α   ⁢           V   ref     R       ·   R             [   9   ]               gain   ⁢           ⁢   α   ⁢     R             [   10   ]               
In such manner, by providing a current source to the transconductors, an additional bit of granularity may be effected for the controlled resistance shown in  FIG. 3A . In various embodiments, a current source may be coupled to each transconductor within a calibration circuit. For example, in the embodiment of  FIG. 1A , a current source may be coupled to each of transconductors  25   a–c  to provide a constant saturation voltage thereto. In certain embodiments, a temperature coefficient may be added to eliminate the need for continuous calibration. Because current increases with temperature, compensation for decreased gm at higher temperatures is thus provided. In such manner, a reduced variation in the constant saturation voltage may be effected. In one embodiment, the temperature coefficient may be a proportional to absolute temperature (PTAT) current, I PTAT , which may be generated and mirrored. The two currents may then be summed and converted to a bandgap voltage with a resistor. Alternately, I PTAT  itself may be used as the coefficient.
 
   In other embodiments, a latch type circuit may be used to calibrate a desired target circuit. Referring now to  FIG. 4 , shown is a block diagram of a calibration circuit  100  in accordance with another embodiment of the present invention. As shown in  FIG. 4 , calibration circuit  100  may be used to provide a calibration signal to a target circuit. Calibration circuit  100  may include a first transistor  105  and a second transistor  115  having emitters coupled to a current source  130  (I b ). Each of transistors  105  and  115  may be of the same size (i.e., m 1  of transistor  105  equals m 2  of transistor  115 ) and may have equal transconductance values (i.e., gm 1  of transistor  105  equals gm 2  of transistor  115 ). Transistors  105  and  115  may have bases coupled between a collector of the opposite transistor and a controlled resistance (respectively resistances  110  and  120 ). In such manner, nodes  135  and  140  situated between the respective collectors of transistors  105  and  115  and controlled resistances  110  and  120  may be provided as differential inputs into a comparator  150 , where they may be compared to a differential reference voltage V REF . While controlled resistors  110  and  120  may be implemented in different manners, in certain embodiments, they may be implemented with a plurality of fixed resistors as discussed above in regard to  FIG. 3A . 
   In operation, when the absolute value of gm·R is greater than one, calibration circuit  100  may turn into a regenerative latch and any stimulus may create a large differential voltage. However, if positive feedback is achieved, one can make a −gm, and thereby create either a near zero or near infinite resistance using a calibrated resistance (or gm) such that absolute value of gm·R equals one. Thus if a noise offset of the stimulus may be accounted for, a proper threshold for the comparator may be obtained to measure gm-R=1. In certain embodiments, calibration circuit  100  may be suitable for use at frequencies around DC, such as for calibrating a baseband circuit, for example, a baseband filter. 
   In certain embodiments, calibration may be effected using software (or a combination of software and hardware) that may be executed on a host system, such as, for example, a computer system, receiver, a wireless device, or the like. Accordingly, such embodiments may comprise an article in the form of a machine-readable storage medium onto which there are written instructions and data that constitute a software program that defines at least an aspect of the operation of the system. 
   While calibration in accordance with an embodiment of the present invention may have numerous applications, in one embodiment a calibration circuit may be used in a receiving system such as depicted in  FIG. 5 . The receiving system of  FIG. 5  is representative in its salient aspects of receiving systems that may be used in connection with Direct Broadcast Satellite (DBS) or other such satellite communications equipment and may be included in the familiar set-top box for satellite television systems. 
   As illustrated in  FIG. 5 , receiving system  500  includes a LNA  510  that serves as front end of the receiver. LNA  510  is, in operation, coupled to an appropriate antenna (not shown). The output of LNA  510  is frequency converted in a mixer  520 . As shown in  FIG. 5 , mixer  520  may be calibrated using a calibration circuit in accordance with an embodiment of the present invention, such as ring oscillator  10  of  FIG. 1A  or ring oscillator  200  of  FIG. 1B , for example. The frequency-converted output of mixer  520  is demodulated by demodulator  530 . In many receiver system architectures, an intermediate frequency (IF) amplifier is interposed between mixer  520  and demodulator  530 . The demodulated signal is coupled to a baseband filter  540 , e.g., a low-pass filter with a specified cutoff frequency. 
   As shown in  FIG. 5 , calibration circuit  10  receives control signals from control circuit  570 . For example, as discussed above, a digital tuning control signal may be provided to ring oscillator  10  to control impedances  27 . Similarly, as shown in  FIG. 5 , such a control signal may also be provided to mixer  520  to calibrate one or more associated gm·Z stages therein. As shown in  FIG. 5 , an output of calibration circuit  10  (which may be feedback signal  40  of  FIG. 1A ), may be provided as an input to a detector  560 , which may be used to detect when calibration circuit  10  reaches a full stage of oscillation. When it does, detector  560  may send a signal to control circuit  570  to indicate that calibration circuit  10  has reached full stage oscillation, and to cease varying the digital tuning signal. 
   In various embodiments, the gm·Z of calibration circuit  10  may be substantially matched to that of a gm·Z value of mixer  520 . In such manner, mixer  520  may be calibrated using the same control signals used to cause calibration circuit  10  to reach full stage oscillation. In other embodiments, such control signals may be scaled as appropriate to calibrate a target circuit as desired. 
   In other embodiments, a calibration circuit in accordance with an embodiment of the present invention may be used to calibrate other system components, such as a tunable baseband filter. Accordingly, baseband filter  540  may be coupled to, and be tuned by, a calibration unit in accordance with one embodiment of the present invention. 
   While the present invention has been described with respect to a limited number of embodiments, those skilled in the art will appreciate numerous modifications and variations therefrom. It is intended that the appended claims cover all such modifications and variations as fall within the true spirit and scope of this present invention.