Abstract:
Disclosed herein is technology for, among other things, a current feedback fully differential amplifier. The amplifier includes an input stage operable to sense an input current at a first terminal and a second terminal. The input stage includes a first buffer having an input coupled with the first terminal and an output coupled with said the terminal. The input stage further includes a second buffer having an output coupled with the first terminal and an input coupled with the second terminal.

Description:
BACKGROUND 
       [0001]    1. Field 
         [0002]    Embodiments of the present invention relate generally to the field of feedback amplifiers. 
         [0003]    2. Background 
         [0004]    The fully differential amplifier (FDA) has become a key component in signal processing applications where high speed and signal fidelity are essential system requirements. Advantages offered by fully differential amplifiers over single ended amplifiers include inherent resistance to external noise sources, reduced even order harmonics, and increased dynamic range.  FIG. 1  shows a circuit  100  illustrating a general purpose FDA  110  in a typical data acquisition application. Within the scope of this discussion, the term “general purpose” will refer to an amplifier circuit generally having the following properties: 1) a pair of differential inputs, ν ip  and ν im ; 2) a pair of differential outputs, ν op  and ν om ; 3) a common mode reference input, ν cm , to control the common mode voltage level at the FDA&#39;s outputs; 4) a feedback network external to the chip (i.e., user configurable gain); 5) the ability to DC couple both inputs and outputs; and 6) the ability to drive the closed loop FDA from either a differential or single ended source. The FDA in this example shall be considered ideal, meaning infinite differential open loop gain and input impedance across the frequency domain. The closed loop gain of circuit  100 , assuming an ideal FDA  110 , is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       v 
                       
                         o 
                         , 
                         dm 
                       
                     
                     = 
                     
                       
                         2 
                         
                           
                             f 
                             1 
                           
                           + 
                           
                             f 
                             2 
                           
                         
                       
                       * 
                       
                         [ 
                         
                           
                             
                               v 
                               sp 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   1 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               v 
                               sm 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where ν o,dm , the differential mode output voltage, is defined as 
         [0000]      ν o,dm ≡ν op −ν om ,  (2) 
         [0000]    f 1  and f 2  are the respective gain factors for positive and negative feedback networks 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                       x 
                     
                     = 
                     
                       
                         R 
                         gx 
                       
                       
                         
                           R 
                           fx 
                         
                         + 
                         
                           R 
                           gx 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and ν sp  and ν sm  refer to the positive and negative terminals of the source. For the balanced feedback network case, R f1 =R f2 =R f  and R g1 =R g2 =R g , and Equation 1 reduces to: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       v 
                       
                         o 
                         , 
                         dm 
                       
                     
                     = 
                     
                       
                         v 
                         
                           s 
                           , 
                           dm 
                         
                       
                       * 
                       
                         ( 
                         
                           
                             R 
                             f 
                           
                           
                             R 
                             g 
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     v 
                     
                       s 
                       , 
                       dm 
                     
                   
                   ≡ 
                   
                     
                       v 
                       sp 
                     
                     - 
                     
                       
                         v 
                         sm 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
       The output common mode voltage level, defined as 
       [0005]    
       
         
           
             
               
                 
                   
                     
                       v 
                       
                         o 
                         , 
                         cm 
                       
                     
                     ≡ 
                     
                       
                         ( 
                         
                           
                             v 
                             op 
                           
                           + 
                           
                             v 
                             om 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    is controlled by means of a separate integrated amplifier circuit. The inverting terminal of this amplifier is connected to both output terminals of the FDA through a matched resistive divider network while the non-inverting terminal is connected to a reference voltage, V cm . The closed loop gain of this amplifier, usually referred to as the common mode feedback amplifier (CMFB), is set to unity in most FDA integrated circuits. 
         [0006]      FIG. 2  illustrates one possible implementation of the FDA  110  of  FIG. 1 . The architecture in  FIG. 2  is based on a voltage feedback approach. Using this architecture, the balanced FDA gain relationship given in Equation 4 becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                     v 
                     
                       o 
                       , 
                       dm 
                     
                   
                   = 
                   
                     
                       v 
                       
                         s 
                         , 
                         dm 
                       
                     
                     * 
                     
                       
                         
                           ( 
                           
                             
                               R 
                               f 
                             
                             
                               R 
                               g 
                             
                           
                           ) 
                         
                         [ 
                         
                           1 
                           
                             1 
                             + 
                             
                               1 
                               
                                 2 
                                  
                                 
                                   
                                     G 
                                     dm 
                                   
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     Z 
                                     t 
                                   
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                  
                                 f 
                               
                             
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    This is the conventional closed loop gain expression for a linear voltage feedback FDA with finite open loop gain, where G dm (s) is the transconductance of the differential input stage  210 , and Z t (s) is the transimpedance gain of each half of the forward amplifier&#39;s signal path. 
         [0007]    The amplifier&#39;s loop gain is given by: 
         [0000]        T ( s )=2 G   dm ( s ) Z   t ( s ) f.   (10) 
         [0000]    This equation reveals the fundamental limitation of voltage feedback amplifier architectures, whether differential or single ended out, which is the direct proportionality of loop gain to the feedback factor f. As closed loop gain is increased (i.e., f is decreased), the loop gain is reduced, resulting in a corresponding reduction in closed loop bandwidth. 
         [0008]    Another limitation of the voltage feedback FDA architecture depicted in  FIG. 2  is the sensitivity of its high impedance inputs to parasitic capacitance at the ν ip  and ν im  nodes. Analysis of the circuit of  FIG. 2 , introducing capacitors C ip  and C im  at ν ip  and ν im  respectively and ground, shows that the loop gain equation is modified by an additional high frequency pole: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       T 
                        
                       
                         ( 
                         s 
                         ) 
                       
                     
                     = 
                     
                       
                         2 
                          
                         
                           
                             G 
                             dm 
                           
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                          
                         
                           
                             Z 
                             t 
                           
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                          
                         f 
                       
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               sC 
                               i 
                             
                              
                             
                               R 
                               eq 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where it is assumed for simplicity that C ip =C im =C i  and R eq  is simply R f ∥R g . Typically, the parasitic capacitance contributions from PCB, package, and ESD protection circuits can add up to 1-2 pF. For example, a FDA configured for a gain of +1, with R f  equal to 500 ohms, will exhibit a parasitic pole between 318 MHz and 636 MHz. Any attempt to improve bandwidth by decompensation of the open loop amplifier will be limited by the loss of phase margin in the vicinity of this pole frequency. 
         [0009]    The noise power spectral density at the differential output of the FDA is given by the following equation, where contributions from the resistive feedback network elements have been ignored for simplicity. 
         [0000]    
       
         
           
             
               
                 
                   
                     Pn 
                     o 
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     Vn 
                                     i 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     In 
                                     ip 
                                   
                                    
                                   
                                     R 
                                     
                                       eq 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     In 
                                     im 
                                   
                                    
                                   
                                     R 
                                     
                                       eq 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     
                                       Vn 
                                       cm 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           f 
                                           1 
                                         
                                         - 
                                         
                                           f 
                                           2 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             f 
                             1 
                           
                           + 
                           
                             f 
                             2 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0010]    Vn i  is the input referred voltage noise, In ip  and In im , are the input referred current sources at the positive and negative input terminals respectively, and Vn cm  is the input referred noise of the CMFB amplifier. R eqx  is defined as R fx ∥R gx . If the feedback networks are balanced, the noise equation reduces to: 
         [0000]    
       
         
           
             
               
                 
                   
                     Pn 
                     o 
                   
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               2 
                                
                               
                                 Vn 
                                 i 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             
                               ( 
                               
                                 2 
                                  
                                 
                                   R 
                                   eq 
                                 
                               
                               ) 
                             
                             2 
                           
                           * 
                           
                             ( 
                             
                               
                                 In 
                                 ip 
                                 2 
                               
                               + 
                               
                                 In 
                                 im 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           ( 
                           
                             2 
                              
                             f 
                           
                           ) 
                         
                         2 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Since the differential input to the voltage feedback FDA is high impedance, the noise contribution from circuit elements referred to the input as voltage sources will usually dominate the differential noise spectral density at the FDA output. The noise gain of the voltage feedback FDA will be proportional to the closed loop amplifier&#39;s feedback factor f. 
         [0000]    
       
         
           
             
               Pn 
               o 
             
             = 
             
               
                 Vn 
                 i 
                 2 
               
               
                 f 
                 2 
               
             
           
         
       
     
         [0011]    Thus, operation at higher signal path gains will necessarily be accompanied by higher noise levels at the FDA outputs. 
         [0012]    In addition to voltage feedback, current feedback techniques have been applied in the design of high speed single ended output op-amps for a number of years. Advantages of current feedback (CFB) op-amps over their voltage feedback (VFB) counterparts include gain-bandwidth independence, generally higher slew rates, and improved even order non-linearity rejection. These performance benefits usually come at the price of less precision, smaller input common mode voltage range, and higher inverting input referred noise current. CFB techniques have not easily migrated to FDAs, primarily due to the difficulty in developing practical, low input impedance, fully differential input stage architectures with good common mode voltage rejection. However, the case for integrating current feedback techniques into the design of fully differential amplifiers is becoming more and more compelling as the demands of data acquisition systems continue to drive signal path components to provide high signal fidelity across much wider system bandwidths. 
         [0013]    Previous attempts at designing a current feedback FDA have involved using two single-ended CFB amplifiers to form a differential amplifier. For example, U.S. Pat. No. 6,636,116, entitled “FULLY DIFFERENTIAL CURRENT FEEDBACK AMPLIFIER” and assigned to Texas Instruments Incorporated, discloses a CFB FDA that develops a differential low impedance input from the outputs of a pair of buffers, both referenced to a potential at their respective high impedance inputs. However, a dual, “un-balanced” input approach such as this results in an input stage that cannot discriminate between differential and common mode signals. In order to correct the balance error that results from such an implementation, the interfering input common mode signal must be cancelled elsewhere in the circuit. This is achieved by means of an additional circuit that replicates and 180° phase shifts the output current from one input buffer and combines it with the output current from the other, and vice versa. Moreover, in single ended input to differential output applications, where the common mode voltage at the FDA inputs is “boot strapped” to the differential voltage at the FDA outputs, holding the input buffer inputs to a fixed reference voltage could cause heavy current loading on each of the input buffers, and therefore introduce a significant distortion in the input stages of these circuits. 
       SUMMARY 
       [0014]    This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
         [0015]    Disclosed herein is technology for, among other things, a current feedback fully differential amplifier. The amplifier includes an input stage operable to sense an input current at a first terminal and a second terminal. The input stage includes a first buffer having an input coupled with the first terminal and an output coupled with said the terminal. The input stage further includes a second buffer having an output coupled with the first terminal and an input coupled with the second terminal. 
         [0016]    Thus, embodiments are able to achieve fully differential current feedback amplifiers, as opposed to amplifiers that use dual single-ended output topography. As a consequence, embodiments have inherent common mode signal rejection. In other words, the sensitivity of input stages of some embodiments to common mode voltage is small and due entirely to a second order effect. Thus, embodiments are able to achieve very low harmonic distortion even in the presence of significant common mode interference. Furthermore, embodiments are able to achieve high gains without sacrificing bandwidth and noise performance. Additionally, embodiments have reduced sensitivity to parasitic capacitances at the input, which moves a higher order parasitic system pole further up in frequency. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]    The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of embodiments of the invention: 
           [0018]      FIG. 1  shows a circuit illustrating a general purpose fully differential amplifier in a typical data acquisition application. 
           [0019]      FIG. 2  illustrates one possible implementation of the fully differential amplifier of  FIG. 1 . 
           [0020]      FIG. 3  illustrates a block diagram of an amplifier that employs current feedback architecture, in accordance with various embodiments of the present invention. 
           [0021]      FIG. 4  illustrates an input stage for a current feedback fully differential amplifier, in accordance with various embodiments of the present invention. 
           [0022]      FIG. 5  illustrates an alternative input stage for a current feedback fully differential amplifier, in accordance with various embodiments of the present invention. 
           [0023]      FIG. 6  illustrates an exemplary input stage for a current feedback fully differential amplifier, in accordance with various embodiments of the present invention. 
           [0024]      FIG. 7  illustrates a detailed schematic for a current feedback fully differential amplifier, in accordance with various embodiments of the present invention. 
           [0025]      FIG. 8  illustrates a cascode-enhanced input stage for a current feedback fully differential amplifier, in accordance with various embodiments of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0026]    Reference will now be made in detail to the preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with the preferred embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention as defined by the claims. Furthermore, in the detailed description of the present invention, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be obvious to one of ordinary skill in the art that the present invention may be practiced without these specific details. In other instances, well known methods, procedures, components, and circuits have not been described in detail as not to unnecessarily obscure aspects of the present invention. 
         [0027]    Generally speaking, embodiments of the present invention are directed to current feedback fully differential amplifiers. In other words, embodiments are able to achieve a true differential input/output amplifier, as opposed to two single-ended input/output amplifiers. Embodiments are able to achieve a true differential input/output amplifier by incorporating input stages discussed below. 
         [0028]      FIG. 3  illustrates a block diagram of an amplifier  300  that employs a CFB architecture, in accordance with various embodiments of the present invention. One difference between the amplifier  300  and the VFB architecture shown in  FIG. 2  is that amplifier  300  uses what will be hereinafter referred to as a differential current conveyor  310 , rather than the differential input transconductor  210  of  FIG. 2 . In one embodiment, the differential current conveyor  310  is, in effect, a current dependent current source where the differential input current is sensed through a pair of low impedance (ideally zero) inputs and replicated (or “conveyed”) at a high impedance differential output. Each sense of the differential output current is then fed into one of a pair of transimpedance amplifiers (TIAs), one corresponding to the “+” output (i.e., TIA+), and the other to the “−” output (i.e., TIA−). The high impedance nodes are isolated from the external loading environment at the differential output by a pair of high speed, high input impedance buffers  320  and  325 . 
         [0029]    The equations governing the closed loop response of CFB FDA  300  are developed in the following analysis. For simplicity it is assumed once again that: 
         [0000]      R f1 =R f2 =R f ,  (12) 
         [0000]      R g1 =R g2 =R g ,  (13) 
         [0000]    and that V cm  is set to ground. It will also be assumed that the differential input has a small non-zero series resistance, r id , associated with it. Substituting the CFB FDA  300  of  FIG. 3  for the generic FDA  110  of  FIG. 1  and performing the same nodal analysis as above yields the following equations for the voltages at the inputs of CFB FDA  300 : 
         [0000]      ν ip =ν om   *f+ν   sp *(1− f )− i   dm   *R   eq ;  (13) 
         [0000]      ν im =ν op   *f+ν   sm *(1− f )+ i   dm   *R   eq .  (14) 
         [0000]    Subtracting Equation 13 from Equation 14, and using the definitions for differential source and output signals gives: 
         [0000]      ν ip −ν im =ν o,dm   *f+ν   s,dm *(1− f )−2 i   dm   *R   eq .  (15) 
         [0000]    Inspection of  FIG. 3  shows that: 
         [0000]      ν ip −ν im   =i   dm   *R   id .  (16) 
         [0000]    Substituting this into Equation 15 and rearranging gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     v 
                     
                       o 
                       , 
                       dm 
                     
                   
                   = 
                   
                     
                       
                         v 
                         
                           s 
                           , 
                           dm 
                         
                       
                       * 
                       
                         [ 
                         
                           
                             1 
                             - 
                             f 
                           
                           f 
                         
                         ] 
                       
                     
                     - 
                     
                       
                         i 
                         dm 
                       
                       * 
                       
                         
                           [ 
                           
                             
                               2 
                                
                               
                                 R 
                                 f 
                               
                             
                             + 
                             
                               
                                 r 
                                 id 
                               
                               f 
                             
                           
                           ] 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The differential output voltage, ν o,dm , is related to the differential input current, i dm , by the amplifier&#39;s open loop transimpedance multiplied by the input current mirror gain: 
         [0000]      ν o,dm   =i   dm *2 mZ   t ( s ).  (18) 
       Solving for i dm  and substituting into Equation 17 gives the gain equation for a closed loop current feedback FDA (such as CFB FDA  300 ): 
       [0030]    
       
         
           
             
               
                 
                   
                     v 
                     
                       o 
                       , 
                       dm 
                     
                   
                   = 
                   
                     
                       v 
                       
                         s 
                         , 
                         dm 
                       
                     
                     * 
                     
                       
                         
                           ( 
                           
                             
                               R 
                               f 
                             
                             
                               R 
                               g 
                             
                           
                           ) 
                         
                         [ 
                         
                           1 
                           
                             1 
                             + 
                             
                               
                                 
                                   2 
                                    
                                   
                                     R 
                                     f 
                                   
                                 
                                 + 
                                 
                                   
                                     r 
                                     id 
                                   
                                   f 
                                 
                               
                               
                                 2 
                                  
                                 
                                   
                                     mZ 
                                     t 
                                   
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0000]    This is a linear feedback equation identical to that for the VFB case except that now the loop gain is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           
                             mZ 
                             t 
                           
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                       
                       
                         
                           2 
                            
                           
                             R 
                             f 
                           
                         
                         + 
                         
                           
                             r 
                             id 
                           
                           f 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0031]    It should be appreciated that if the input impedance of the differential current conveyor input stage is small compared to R f , varying the feedback factor f will have little or no effect on the loop gain of FDA  300 , except at small f. An alternate way of stating this result is that the closed loop bandwidth of FDA  300  is proportional to the size of the feedback resistor R f , rather than to the value of the closed loop gain. In one embodiment, the CFB FDA  300  can therefore be configured to simultaneously provide both high signal path bandwidth and high gain with a suitable choice of feedback resistor—a unique property of the CFB architecture. 
         [0032]    As stated above, VFB FDAs are sensitive to input capacitance, which limits the maximum achievable bandwidth of the VFB FDA. Proceeding as above, with the inclusion of C ip  and C im  in the nodal equations for ν ip  and ν im  respectively, results in the new loop gain equation shown below: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                      
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           
                             mZ 
                             t 
                           
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                       
                       
                         
                           ( 
                           
                             
                               2 
                                
                               
                                 R 
                                 f 
                               
                             
                             + 
                             
                               
                                 r 
                                 id 
                               
                               f 
                             
                           
                           ) 
                         
                          
                         
                           ( 
                           
                             1 
                             + 
                             
                               
                                 sC 
                                 p 
                               
                                
                               
                                 R 
                                 eq 
                               
                                
                               
                                  
                                 
                                   r 
                                   id 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Note that the pole due to the parasitic capacitance at the inputs is now: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       p 
                       
                         2 
                         , 
                         CFB 
                       
                     
                     = 
                     
                       1 
                       
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           C 
                           p 
                         
                          
                         
                           R 
                           eq 
                         
                          
                         
                            
                           
                             r 
                             id 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
         [0000]    compared to: 
         [0000]    
       
         
           
             
               
                 
                   
                     p 
                     
                       2 
                       , 
                       VFB 
                     
                   
                   = 
                   
                     1 
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                           
                       
                        
                       
                         C 
                         p 
                       
                        
                       
                         R 
                         eq 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
         [0000]    for the VFB architecture. This represents a pole frequency shift of: 
         [0000]    
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         
                           R 
                           eq 
                         
                         + 
                         
                           r 
                           id 
                         
                       
                       
                         r 
                         id 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
       With the assumption that r id &lt;&lt;R eq , and that the other system poles occur at much higher frequencies yet, the maximum achievable closed loop bandwidth of the current feedback FDA  300  is extended by the same factor. 
       [0033]    The noise response for the closed loop CFB FDA  300  is identical to that given by Equation 7 for the VFB FDA  200 . However, since the input impedance of the CFB FDA  300  is low, circuit noise elements referred to the inputs as current sources will dominate the amplifier&#39;s noise response. If the noise contribution from the input referred voltage source can be ignored, and assuming small r id  and matched feedback, Equation 7 reduces to 
         [0000]    
       
         
           
             
               
                 
                   
                     Pn 
                     0 
                   
                   ≅ 
                   
                     
                       
                         ( 
                         
                           
                             In 
                             ip 
                             2 
                           
                           + 
                           
                             In 
                             im 
                             2 
                           
                         
                         ) 
                       
                        
                       
                         R 
                         eq 
                         2 
                       
                     
                     
                       f 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
       Using the definitions of R eq  and f given earlier, Equation 25 further reduces to 
       [0034]        Pn   o =( In   ip   2   +In   im   2 ) Rf   2   (26) 
         [0000]    Equation 26 demonstrates an important and useful property of the current feedback FDA architecture. Unlike the voltage feedback FDA noise response described earlier, the noise gain of the closed loop current feedback FDA is not proportional to the magnitude of the signal gain; rather it depends only on the size of the feedback resistor. This is an important result for many differential signaling applications that require high signal path gain but low noise figure. 
         [0035]      FIG. 4  illustrates an input stage  400  for a current feedback fully differential amplifier (such as CFB FDA  300 ), in accordance with various embodiments of the present invention. Input stage  400  may also be referred to as a differential current conveyor. In one embodiment, input stage  400  includes a pair of back-to-back connected (i.e., the output of each is connected to the input of the other) open loop buffers  410  and  420 . It should be appreciated that additional buffers connected in a similar fashion may be used. Because buffers  410  and  420  are connected in a back-to-back fashion, they are self-biasing. In other words, buffers  410  and  420  do not need to be referenced to an external potential. Additionally, since such buffers tend to have low impedance outputs and high impedance inputs, connecting buffers  410  and  420  in this manner creates a virtual low impedance path between the two terminals, i ip  and i im . In one embodiment, an increase in i dm  in the direction indicated is reflected as increases in i C2  and i C8  and decreases in i C4  and i C6 . Thus, the differential current i dm  at the inputs of the input stage  400  creates corresponding differential currents at the outputs of the input stage  400 . 
         [0036]      FIG. 5  illustrates another input stage  500  for a current feedback fully differential amplifier (such as CFB FDA  300 ), in accordance with various embodiments of the present invention. Input stage  500  may also be referred to as a differential current conveyor. In one embodiment, input stage  500  includes a pair of hyperbolic sine transconductors  510  and  520 , where transconductor  520  is complementary to transconductor  510 . Hyperbolic sine transconductors  510  and  520  have a sinh I-V transfer characteristic. It should be appreciated that additional sinh transconductors connected in a similar fashion may be used. Additionally, the configuration of transconductors  510  and  520  maintains a virtual low impedance path between the two terminals, i ip  and i im . In one embodiment, an increase in i dm  in the direction indicated is reflected as increases in i C2  and i C8  and decreases in i C4  and i C6 . Thus, the differential current i dm  at the inputs of the input stage  500  creates corresponding differential currents at the outputs of the input stage  500 . 
         [0037]      FIG. 6  illustrates an exemplary input stage  600  for a current feedback fully differential amplifier (such as CFB FDA  300 ), in accordance with various embodiments of the present invention. In one embodiment, transistors Q 1 , Q 2 , Q 5 , and Q 6  form a first four-transistor buffer (such as buffer  410 ), and transistors Q 3 , Q 4 , Q 7 , and Q 8  form a second four-transistor buffer (such as buffer  420 ). It should be appreciated that buffers such as buffers  410  and  420  may be implemented using different configurations with different numbers of transistors. In another embodiment, transistors Q 1 -Q 4  form a first hyperbolic sine transconductor (such as sinh transconductor  510 ), and transistors Q 5 -Q 8  form a second hyperbolic sine transconductor (such as sinh transconductor  520 ), which is complementary to the first hyperbolic sine transconductor (e.g., sinh transconductor  510 ). 
         [0038]    As stated above, the buffering action of each half-circuit maintains a virtual low impedance path between the two terminals, i ip  and i im . Solving for the currents at nodes i ip  and i im  gives: 
         [0000]        i   dm   +i   C1   +i   C4   −i   C5   −i   C8 =0; and  (27) 
         [0000]        i   dm   +i   C6   +i   C7   −i   C2   −i   C3 =0,  (28) 
         [0000]    where base currents have been ignored for simplicity. Summing Equation 27 and Equation 28 and recognizing that: 
         [0000]      i C1 =i C3 =i C5 =i C7 =I S1   (29) 
         [0000]    yields the following relationship between the differential input current and the differential collector output currents from the complimentary half circuits: 
         [0000]      [ i   C2   −i   C4   ]−[i   C6   −i   C8 ]=2 i   dm   (30) 
         [0000]      or 
         [0000]        i   o,dm =2 i   dm ,  (31) 
         [0000]    where i o,dm  is defined as the differential output current between left and right half circuits. The gain of the differential current conveyor  600  is 2. AC analysis of the current conveyor  600  gives the same result as Equation 31 above with the exception that the dependence of the current gain on finite, band limited beta is also shown: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       i 
                       
                         o 
                         , 
                         dm 
                       
                     
                     = 
                     
                       2 
                        
                       
                         i 
                         dm 
                       
                       * 
                       
                         
                           β 
                           o 
                         
                         
                           
                             β 
                             o 
                           
                           + 
                           2 
                         
                       
                       * 
                       
                         1 
                         
                           1 
                           + 
                           
                             s 
                              
                             
                               
                                 2 
                                  
                                 
                                   C 
                                   π 
                                 
                                  
                                 
                                   r 
                                   π 
                                 
                               
                               
                                 
                                   β 
                                   o 
                                 
                                 + 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the following notational shorthands have been used: 
         [0000]      β o =β pnp ∥β npn ;  (33) 
         [0000]        r   π   =r   πpnp   |r   πnpn ;  (34) 
         [0000]        C   π   =C   πpnp   +C   πnpn .  (35) 
       For good high speed bipolar process technology, frequencies greater than 2 GHz maybe achieved for this pole. 
       [0039]    With respect the differential input resistance of input stage  600 , application of a differential current will result in a small voltage drop between the input terminals: 
         [0000]      ν i,dm =ν ip −ν im .  (36) 
         [0000]    There are four distinct diode paths to get from node ν ip  to node ν im . Choosing the path formed by Q 1  and Q 2  gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       v 
                       
                         i 
                         , 
                         dm 
                       
                     
                     = 
                     
                       
                         V 
                         
                           BE 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       - 
                       
                         V 
                         
                           BE 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       v 
                       
                         i 
                         , 
                         dm 
                       
                     
                     = 
                     
                       
                         V 
                         t 
                       
                        
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               i 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             
                               i 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
             
               
                 
                   
                     v 
                     
                       i 
                       , 
                       dm 
                     
                   
                   = 
                   
                     
                       V 
                       t 
                     
                      
                     
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               i 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             
                               i 
                               
                                 S 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Taking e x  of both sides gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     
                       C 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       I 
                       
                         S 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     * 
                     
                       
                          
                         
                           ( 
                           
                             
                               v 
                               
                                 i 
                                 , 
                                 dm 
                               
                             
                             
                               V 
                               T 
                             
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
       A similar equation is established for the path formed by Q 5  and Q 6 : 
       [0040]    
       
         
           
             
               
                 
                   
                     i 
                     
                       C 
                        
                       
                           
                       
                        
                       6 
                     
                   
                   = 
                   
                     
                       I 
                       
                         S 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     * 
                     
                       
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 v 
                                 
                                   i 
                                   , 
                                   dm 
                                 
                               
                               
                                 V 
                                 T 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
       Substituting Equations 40 and 41 into Equation 28 gives: 
       [0041]    
       
         
           
             
               
                 
                   
                     i 
                     dm 
                   
                   = 
                   
                     
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       - 
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           6 
                         
                       
                     
                     = 
                     
                       
                         I 
                         
                           S 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       * 
                       
                         
                           [ 
                           
                             
                                
                               
                                 ( 
                                 
                                   
                                     v 
                                     
                                       i 
                                       , 
                                       dm 
                                     
                                   
                                   
                                     V 
                                     T 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                                
                               
                                 - 
                                 
                                   ( 
                                   
                                     
                                       v 
                                       
                                         i 
                                         , 
                                         dm 
                                       
                                     
                                     
                                       V 
                                       T 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Applying the definition of the hyperbolic sine function produces: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     dm 
                   
                   = 
                   
                     
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       - 
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           6 
                         
                       
                     
                     = 
                     
                       2 
                        
                       
                         I 
                         
                           S 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       * 
                       
                         
                           sinh 
                            
                           
                             ( 
                             
                               
                                 v 
                                 
                                   i 
                                   , 
                                   dm 
                                 
                               
                               
                                 V 
                                 T 
                               
                             
                             ) 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
       Similarly, since i C2 −i c6 =i C8 −i C4 : 
       [0042]    
       
         
           
             
               
                 
                   
                     i 
                     dm 
                   
                   = 
                   
                     
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           8 
                         
                       
                       - 
                       
                         i 
                         
                           C 
                            
                           
                               
                           
                            
                           4 
                         
                       
                     
                     = 
                     
                       2 
                        
                       
                         I 
                         
                           S 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       * 
                       
                         
                           sinh 
                            
                           
                             ( 
                             
                               
                                 v 
                                 
                                   i 
                                   , 
                                   dm 
                                 
                               
                               
                                 V 
                                 T 
                               
                             
                             ) 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equations 43 and 44 show the signature I-V transfer characteristic for this class of transconductors. For small x, sin h(x)≈x, so for ν i,dm &lt;&lt;V T  Equation 42 reduces to the approximate relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     v 
                     
                       i 
                       , 
                       dm 
                     
                   
                   ≈ 
                   
                     
                       i 
                       dm 
                     
                     * 
                     
                       
                         
                           V 
                           T 
                         
                         
                           2 
                            
                           I 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
       Differentiating this equation with respect to i dm  gives the input resistance of the differential current conveyor  600 : 
       [0043]    
       
         
           
             
               
                 
                   
                     
                       r 
                       id 
                     
                     ≡ 
                     
                       
                         ∂ 
                         
                           v 
                           
                             i 
                             , 
                             dm 
                           
                         
                       
                       
                         ∂ 
                         
                           i 
                           dm 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         V 
                         T 
                       
                       
                         2 
                          
                         I 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
           
         
       
     
         [0044]      FIG. 7  illustrates a schematic for a CFB FDA  700 , in accordance with various embodiments of the present invention. CFB FDA  700  includes current conveyor  600  as its input stage. The left half of current conveyor  600  is coupled with folded cascode transistors Q 15  and Q 16 , which together form a first trans-resistor, and the right half of current conveyor  600  is coupled with folded cascode transistors Q 9  and Q 10 , which together form a second trans-resistor. 
         [0045]    As stated above, an increase in i dm  causes a corresponding increase in i C2  and a decrease in i C6  with respect to the left half of current conveyor  600 . In a similar fashion, an increase in i dm  causes a corresponding increase in i C8  and a decrease in i C4  with respect to the right half of current conveyor  600 . Focusing on the left half of  FIG. 7 , the increased current through Q 2  draws current away from Q 15 . The decreased current through Q 15  consequently pushes the voltage at the hiz_m node lower. Simultaneously, the decreased current through Q 6  directs more current through Q 16 , which in turn pulls the voltage at hiz_m lower. Similar but complementary operations occur in the right half of  FIG. 7  at transistors Q 4 , Q 8 , Q 9 , and Q 10 , and node hiz_p, with respect to an increase in i dm . Thus, an increase in idm ultimately causes a differential voltage by increasing the voltage at hiz_p and decreasing the voltage at hiz_m. It should be appreciated that the opposite result will occur in response to a decrease in i dm . The voltages at nodes hiz_p and hiz_m drive respective output buffers. In one embodiment, transistors Q 17 -Q 22  form a first output buffer and transistors Q 11 -Q 14 , Q 66  and Q 71  form a second output buffer. 
         [0046]    To understand how the input resistance of CFB FDA  600  affects the frequency of the pole due to the input capacitance discussed above, consider the following example. If the biasing current I S1  is set to 1 mA, the differential input resistance would be about 13 Ohms. If R eq =250 Ohms, then the pole due to capacitance at the inputs is shifted up in frequency by a factor of ˜19. In this example, using the proposed CFB FDA architecture results in a parasitic pole frequency translation of greater than one decade, preserving the amplifier&#39;s phase margin over a much larger system bandwidth than the corresponding voltage feedback architecture. 
         [0047]    Further modifications may be made to input stage  600  to improve the circuit&#39;s common mode rejection and thus the balance error response of the current feedback FDA. For example,  FIG. 8  illustrates a cascode-enhanced input stage  800 , in accordance with various embodiments of the present invention. In addition to transistors Q 1 -Q 8 , input stage  800  includes transistors Q 23 -Q 24 , which form a cascode with Q 2 , transistors Q 25 -Q 26 , which form a cascode with Q 4 , transistors Q 27 -Q 28 , which form a cascode with Q 6 , and transistors Q 29 -Q 30 , which form a cascode with Q 8 . With the addition of the cascoded transistors, input stage  800  has improved output resistance (ideally high) over input stage  600 . However, it should be appreciated that the improved output resistance of input stage  800  comes at the expense of voltage headroom. 
         [0048]    Thus, embodiments are able to achieve fully differential current feedback amplifiers, as opposed to amplifiers that use dual single-ended input/output topography. As a consequence, embodiments have inherent common mode signal rejection. In other words, the sensitivity of input stages of some embodiments to common mode voltage is small and due entirely to a second order effect, because embodiments have reduced sensitivity to parasitic capacitances at the input, which moves a system pole further up the spectrum. Consequently, embodiments are able to achieve very low harmonic distortion even in the presence of significant common mode interference. Furthermore, embodiments are able to achieve high gains without sacrificing bandwidth and noise performance. 
         [0049]    The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.