Patent Publication Number: US-7710198-B2

Title: Methods and apparatus for process invariant transconductance

Description:
RELATED APPLICATIONS 
   This application is a continuation of U.S. application Ser. No. 11/656,214, issued as U.S. Pat. No. 7,482,872, entitled “METHODS AND APPARATUS FOR PROCESS INVARIANT TRANSCONDUCTANCE,” filed on Jan. 22, 2007, which claims priority under 35 U.S.C. §119(e) to U.S. Provisional Application Ser. No. 60/760,780, entitled “METHODS AND APPARATUS FOR PROCESS INVARIANT TRANSCONDUCTANCE,” filed on Jan. 20, 2006, each of which is herein incorporated by reference in its entirety. 

   FIELD OF INVENTION 
   The present invention relates to integrated circuits, and more particularly, to obtaining a transconductance within an integrated circuit that is substantially constant across a desired set of operating parameters. 
   BACKGROUND 
   Transconductance is often an important measure of the performance of an electronic circuit, affecting many performance parameters including, but not limited to, bandwidth, gain and noise. Transconductance is an expression of the performance of certain electronic circuits, and traditionally refers to the ratio of output current to input voltage of a particular circuit, or mutual conductance. The term “transconductance” refers to herein as the control of an output current as a result of an input voltage, and is given by the expression: 
   
     
       
         
           
             
               
                 
                   
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   or more generally as, 
   
     
       
         
           
             
               
                 
                   
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   where g m  is the transconductance with units of siemens, I out  is the output current and V in  is the input voltage. In general, the larger the transconductance figure for a device or circuit, the greater the gain (amplification) it is capable of delivering, when all other factors are held constant. 
   In integrated circuits, it may be important for the transconductance of an electronic circuit to remain constant over one or more operating parameters as well as processing variation. The stability or robustness of transconductance of transistors may be an important design parameter, as it may be affected by many operation and processing conditions, such as temperature, carrier mobility, supply voltage, etc. A conventional solution to the problem of achieving constant transconductance is to use the conductance of a stable and precise external (e.g., off-chip) resistor. In the context of an amplifier, for example, a constant reference voltage provided off-chip may be placed across an external resistor to achieve a substantially constant bias current for the amplifier. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  illustrates a integrated amplifier having a substantially constant transconductance, in accordance with some embodiments of the present invention; 
       FIG. 2  illustrates an integrated circuit having a substantially constant transconductance across resistance variation, in accordance with some embodiments of the present invention; 
       FIG. 3  illustrates an integrated circuit having a substantially constant transconductance across resistance variation implemented using transistors, in accordance with some embodiments of the present invention; and 
       FIG. 4  illustrates a circuit for implementing one or more of the bias currents for a transconductor, in accordance with some embodiments of the present invention. 
   

   DETAILED DESCRIPTION 
   As discussed above, conventional circuits attempt to achieve a constant transconductance by forcing a constant reference voltage across a resistor to obtain a constant bias current, for example, to bias one or more amplifiers. Accordingly, the transconductance is dependent on the absolute value of the resistor. However, this solution has several problems. First, the resistor is often provided external to the integrated circuit to avoid resistor variation resulting from process conditions of the integrated circuit. Providing external components and packaging infrastructure necessary for the integrated circuit to connect to the external resistor is relatively expensive and inconvenient to manufacture. 
   Alternatively, the resistor can be provided internal to the integrated circuit. However, the resistor may then be vulnerable to process variation within the integrated circuit. To address this dependence, integrated circuit designers must take into consideration this variation in the resistance of the bias resistor. However, this variation may be as much as ±20%. As a result, the design of the integrated circuit must compensate for this variation. That is, the integrated circuit must be able to handle conditions where the bias resistance is 20% higher and 20% lower than an expected or nominal value. This additional design overhead is relatively expensive, increases power requirements, and complicates the design of the integrated circuit. Integrated resistors may be trimmed during manufacture to achieve low variation, but the extra processing required for resistor trimming is relatively expensive and inconvenient. 
   Applicant has appreciated the benefit of an integrated amplifier with a transconductance that is substantially independent of variation within the integrated circuit. is Applicant has recognized that an integrated amplifier may be appropriately designed such that the transconductance may not substantially vary and/or depend on resistor process variation of the integrated circuit, nor substantially vary and/or depend on resistor variation due to operating conditions. In some embodiments, a fully integrated transconductance amplifier that is substantially constant across resistor process variation and operating conditions is provided, A transconductance that is independent of resistor process variation and operating conditions may allow for more optimal performance, such as low power for a given bandwidth, without the need for trimming or external components. 
   Following below are more detailed descriptions of various concepts related to, and embodiments of, methods and apparatus according to the present invention. It should be appreciated that various aspects of the invention described herein may be implemented in any of numerous ways. Examples of specific implementations are provided herein for illustrative purposes only. In addition, the various aspects of the invention described in the embodiments below may be used alone or in any combination, and are not limited to the combinations explicitly described herein. 
     FIG. 1  illustrates an integrated amplifier, in accordance with some embodiments of the present invention. Amplifier  100  may be fully formed in on a single substrate  150 . In particular, amplifier  100  may be fully integrated such that it does not rely on connections to external resistors to provide a substantially constant transconductance. Amplifier  100  includes a voltage input  105  adapted to receive one or more voltage signals, and current output  125  adapted to provide one or more current signals. The ratio between the at least one voltage signal and the at least one current signal form the transconductance of the amplifier  100 . 
   Amplifier  100  includes a circuit  110  adapted to maintain a substantially constant transconductance over resistor process variation. For example, circuit  110  may include one or more integrated resistor used to establish a bias current to bias components of the amplifier. Circuit  110  may be configured to ensure that the transconductance is substantially constant and independent of variation in the one or more integrated resistors, for example, due to temperature changes within the amplifier. Various methods of configuring circuit  110  are discussed in further detail below. 
   In  FIG. 1 , amplifier  100  is described as an operational transconductance amplifier (OTA), because it provides an output current in response to an input voltage. It should be appreciated, however, that the aspects of the invention are not limited to OTAs, and may be used with any amplifier circuit, For example, an operational amplifier (op-amp) can be considered an OTA with a voltage buffer at the output. In an amplifier, there is generally at least one transconductance element, and some embodiments of the invention are directed to providing at least one transconductance that is substantially independent of variation in one or more integrated resistors (e.g., one or more resistors included in the amplifier, one or more resistors used to establish a bias current, or both). 
     FIG. 2  illustrates a resistor invariant amplifier, in accordance with some embodiments of the present invention. Amplifier  200  includes a first transconductance stage  210  having a transconductance of G M1  and a second transconductance stage  220  having a transconductance G M2 , two bias currents for the two transconductance stages, I B1  and I B2 , respectively, and a resistor R L . G M     —     TOTAL , the total transconductance of amplifier  200 , is equal to I out /V in  and is configured to be substantially independent of resistor variation. 
   Since G M1  has ideally infinite output impedance, the current output by G M1  will flow into the resistor R L , producing some voltage gain from the input  205  to node INT. Accordingly, integrated resistor R L  is arranged in the signal path of the amplifier. The voltage gain will be G M1 R L . The voltage swing at INT will cause G M2  to output current, and the total transconductance (defined as the current at output  225  caused by the voltage at input  205 ) can be expressed as,
 
G M     —     TOTAL =G M1 R L G M2   (3).
 
   Transconductances G M1  and G M2  are proportional to some power of the bias currents I B1  and I B2 . For example, if the transconductors were MOSFET devices in strong inversion, the transconductances would be proportional to the square root of the bias current. If the transconductors were bipolar transistors, the transconductances would be directly proportional to the bias current. In general, the relationship between the two transconductances and the respective bias current can be expressed as a proportionality based on some factor K, which is a function of the transistor type, circuit topology, and operating conditions used to implement the two transconductance stages. For example, the proportionality described above is shown below in Equations 4 and 5 below using constants K 1  and K 2  as power factors for the respective proportionalities.
 
G M1 ∝I B1   K     1     (4)
 
G M2 ∝I B2   K     2     (5)
 
   The bias currents I B1  and I B2  may be generated in a way such that they are also proportional to some power of the resistance R L . In general, the relationship between the two bias currents I B1  and I B2  and the resistance can be expressed as a proportionality based on factors H 1  and H 2 , respectively. This relationship is expressed in Equations 6 and 7, as
 
I B1 ∝R L   H     1     (6)
 
I B2 ∝R L   H     2     (7).
 
   By combining Equations 3 through 7, the relationship between the total transconductance and the resistance R L  can be expressed as,
 
G M     —     TOTAL ∝R L   K     1     H     1     +K     2     H     2     +1   (8).
 
   Applicant has appreciated that the total transconductance can be made independent of the resistance if the exponent is designed to be zero, That is, if
 
 H   1   K   1   +H   2   K   2 +1=0  (9),
 
   then the total transconductance, G M     —     TOTAL , will be constant across resistor variation, e.g., the total transconductance can be made to be independent of variations in the resistance R L . As a result, as the integrated resistance (e.g., resistance R L ) varies or fluctuates as a result of processing or operating conditions within the integrated circuit (e.g., temperature change, etc.), the total transconductance G M     —     TOTAL  remains substantially constant. Accordingly, the expense and inconvenience of an external resistor and/or trimming one or more resistors during manufacture may be eliminated while avoiding transconductance variation resulting from resistor variation. It should be appreciated that while G M     —     TOTAL  shown in  FIG. 2  is illustrated as a differential input  205 , and a single-ended output  225 , the aspects of the invention are not limited in this respect and can be implemented in any suitable manner. For example, the input may be single-ended and the output differential, or both the input and output may be either differential or single-ended. 
     FIG. 3  illustrates an integrated circuit having a transconductance substantially invariant to resistor variation, in accordance with some embodiments of the present invention. In  FIG. 3 , transconductors G M1  and G M2  illustrated in  FIG. 2  are implemented as NMOS devices. The first stage transconductor, comprised of M 1  and M 2 , has a differential output connected to the load resistors R L . The second stage transconductor, comprised of M 3  and M 4 , is loaded with a current mirror, comprised of M 5  and M 6 . In some embodiments, the transconductors are formed from MOSFETs biased so as to operate in strong inversion. As a result, the transconductances G M1  and G M2  will be proportional to the square root of the bias currents. That is power factors K 1  and K 2  introduced in equations 4 and 5 may be chosen as,
 K 1 =K 2 =0.5  (10). 
   In order to satisfy equation 7 given K 1  and K 2  shown in equation 9, the sum of factors H 1  and H 2  should be equal to −2. If the bias currents I B1  and I B2  are generated from the same current reference circuit, the factors H 1  and H 2  may be established to be the same. In this case, Equations 9 and 10 are both satisfied for the relationship,
 
H 1 =H 2 =−1  (11).
 
   Equation 11 illustrates that if both bias currents are inversely proportional to the resistance R L , then Equation 9 will be satisfied and the total transconductance G M     —     CONSTANT  will be substantially constant across resistor variations. Providing a substantially constant transconductance may be achieved using other suitable integrated circuits, as the aspects of the invention are not limited for use with any particular implementation. 
     FIG. 4  illustrates a circuit suitable for generating bias currents inversely proportional to resistance, that can be used to implement a transconductor in accordance with some embodiments of the present invention. Circuit  400  benefits from a substantially stable reference voltage V ref  as an input. This reference voltage may be constant across resistor processing variations, such as a bandgap voltage. Amplifier  410  forces this voltage to appear at the source of M 7 , across R L , Accordingly, resistor R L  appears in the bias current signal path of circuit  400 . Assuming infinite amplifier gain, the current that will flow through the drain of M 7  can be expressed as, 
   
     
       
         
           
             
               
                 
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   Circuit  400  may be used to implement bias currents I b1  and/or I b2  in  FIGS. 2 and 3 . However, the bias currents may be implemented in other ways as the aspects of the invention are not limited in this respect It should be appreciated that RL in  FIG. 4  need not be the same resistor as the load resistors illustrated in  FIGS. 2 and 3 . However, utilizing the same type of resistor may yield a transconductance with superior independence from resistor process variation. 
   As should be appreciated from the foregoing, there are numerous aspects of the present invention described herein that can be used independently of one another or in any combination. In particular, various aspects of the present invention may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing, and the aspects of the present invention described herein are not limited in their application to the details and arrangements of components set forth in the foregoing description or illustrated in the drawings. The aspects of the invention are capable of other embodiments and of being practiced or of being carried out in various ways. Various aspects of the present invention may be implemented using any type of circuit and no limitations are placed on the circuit implementation. Accordingly, the foregoing description and drawings are by way of example only. 
   Use of ordinal terms such as “first”, “second”, “third”, etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements, 
   Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing”, “involving”, and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.