Abstract:
A bandgap-based reference voltage generator circuit with an increased output reference voltage and a reduced temperature coefficient uses a curvature correction bias voltage to significantly reduce the degree of variation of the bandgap-based reference voltage over temperature. A current having a negative temperature coefficient is conducted by a resistor having a positive temperature coefficient. The resultant voltage across the resistor has an arcuate voltage-versus-temperature characteristic with a direction of incurvature that is substantially opposite the direction of incurvature of the corresponding arcuate voltage-versus-temperature characteristic of the voltage generated by a conventional bandgap reference voltage generator circuit. These voltages are summed together to produce a bandgap-based reference voltage which is greater in magnitude than a conventional bandgap reference voltage and has a significantly reduced temperature coefficient.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to bandgap reference voltage generator circuits, and in particular, to bandgap-based reference voltage generator circuits with compensation for reducing the temperature coefficient. 
     2. Description of the Related Art 
     Electronic systems which require a precision reference voltage typically use a bandgap voltage reference circuit, which is advantageously capable of operating with a low power supply potential. As is well known, the basic principle of a bandgap voltage reference circuit is based upon the summation of the negative temperature drift of the base-emitter voltage (Vbe) of a bipolar junction transistor with an appropriate magnitude of a positive temperature drift of a thermal voltage (Vt) in order to achieve a net zero temperature drift sum. 
     Referring to FIG. 1, a conventional bandgap reference circuit includes two bipolar junction transistors Q 2 , Q 3  biased by a voltage divider circuit composed of resistors R 1 , R 2 , R 3  and a diode-connected transistor Q 1  and a current sinking circuit IS. The size of the emitter area of transistor Q 2  is ten times the size of the emitter area of transistor Q 3 . The collector currents of these transistors Q 2 , Q 3  are amplified differentially by a differential transconductance amplifier which produces the bandgap reference voltage Vbg (Vref), which, in turn, drives the voltage divider circuit. The diode-connected transistor Q 1  introduces a voltage into the voltage divider circuit which has a negative temperature coefficient. The difference between the base-emitter voltages Vbe of transistors Q 2 , Q 3  (ΔVbe=Vbe(Q 3 )−Vbe(Q 2 )) has a positive temperature coefficient. The value of the resulting bandgap voltage Vbg (Vref) can be determined in accordance with Equation 1:                Vref   =     Vbg   =       V     be   -     Q   1         +       (     1   +         R   1     +     R   3         R   2         )        Δ                   V   be                           Where                       Δ                   V   be       =         V     be   -     Q   3         -     V     be   -     Q   2           =       kT   q        ln                 A         ,                  V     be   -     Q   1         =       kT   q        ln        IE1   IES         ,                  k   /   q     =     8.6167   ×     10     -   5                                 I   ES     =       RT   m                 -     qV   G0       kT           ,                  I   E1     =       Δ                   V   be         R   2                 1                              
     Equation 1 can be rearranged and written as Equation 2:              Vbg   =       V   G0     +       kT   q          [         (     1   +         R   1     +     R   3         R   2         )        ln                 A     +     ln      k                 ln                   A     qRR   2         -       (     m   -   1     )        ln                 T       ]               2                              
     To establish a zero temperature coefficient (OTC) at the expected operating temperature (T 0 ) Equation 2 is differentiated and set equal to zero. This produces Equations 3 and 4:                               ∂   Vbg       ∂   T              T   =     T   0         =                    k   q          [         (     1   +         R   2     +     R   3         R   2         )        ln                 A     +     ln      k                 ln                   A     qRR   2         -       (     m   -   1     )        ln                 T       ]       +                                kT   q                 [       m   -   1     T     ]            T   =     T   0                       =              0               3                 (     1   +         R   1     +     R   3         R   2         )        ln                 A     =       (     m   -   1     )     -     ln      k                 ln                   A       qRR   2          T     m   -   1                     4                              
     Substituting Equation 4 into Equation 2 produces Equation 5 which defines the reference voltage Vref:              Vref   =     Vbg   =       V   G0     +       kT   q          (     m   -   1     )       -       kT   q          (     m   -   1     )        ln                   T     T   0                   5                              
     Referring to FIG. 2, the reference voltage Vref with respect to temperature T is graphed in accordance with Equation 5. From this graph it can be seen that, assuming a bandgap energy voltage V G0 =1.12 V, a constant m=5, an emitter-base junction constant of R=0.2818, an emitter area ratio A=10 and an operating temperature T 0 =20° C., the reference voltage Vref has a temperature coefficient of approximate 12.6 ppm/° C. 
     However, as the precision requirements for the operating characteristics of modem electronic systems increase, particular as the magnitude of the available power supply voltage decreases, temperature coefficients of such magnitude become increasingly unacceptable. Accordingly, it would be desirable to have a bandgap-based reference voltage generator circuit with compensation which provides for significantly reduced temperature coefficients. Additionally, it would be further desirable to be able to adjust such compensation and provide for such compensation using standard semiconductor processing techniques. 
     SUMMARY OF THE INVENTION 
     A bandgap-based reference voltage generator circuit in accordance with the present invention provides an increased output reference voltage and a reduced temperature coefficient. Such a circuit uses circuit components commonly available with standard semiconductor processing techniques. A temperature coefficient curvature correction voltage is generated based upon an IR (current times resistance) voltage drop. The resistance R exhibits a natural curvature over temperature and nonlinear cross products of the IR voltage drop provide for fine tuning of such curvature. This curvature correction voltage is provided as a separate and independent bias voltage that is introduced externally to a standard bandgap reference voltage generator circuit, thereby providing a simpler solution than those in which components with high temperature coefficients are integrated internally to the bandgap reference voltage generator circuit. This correction voltage can be turned off without adversely affecting standard bandgap circuit operation, and the first order temperature coefficient of the correction voltage curvature can be adjusted to be sufficiently minimized so as to not skew the temperature coefficient operation of the standard bandgap circuit. This is done by selecting the temperature coefficient of the current (TCI) to be the approximate inverse (−TCR) of the temperature coefficient for the resistor (TCR), thereby making the overall current-times-resistance (IR) temperature coefficient extremely low. 
     In accordance with one embodiment of the present invention, a bandgap-based reference voltage generator circuit with an increased output reference voltage and a reduced temperature coefficient includes a bandgap voltage generator circuit and a control voltage generator circuit. The bandgap voltage generator circuit is configured to receive a bandgap-based reference voltage and a curvature correction control voltage and in accordance therewith provide the bandgap-based reference voltage with a first arcuate voltage-versus-temperature characteristic having a first direction of incurvature. The control voltage generator circuit, coupled to the bandgap voltage generator circuit, is configured to provide the curvature correction control voltage with a second arcuate voltage-versus-temperature characteristic having a second direction of incurvature which is substantially opposite the first direction of incurvature. 
     In accordance with another embodiment of the present invention, a bandgap-based reference voltage generator circuit with an increased output reference voltage and a reduced temperature coefficient includes: a bias voltage generator circuit; a voltage divider circuit; first and second circuit branches; a differential amplifier circuit; a current source circuit; and a resistive circuit element. The bias voltage generator circuit is configured to receive a curvature correction control voltage and in accordance therewith provide a bias voltage, wherein a voltage difference between the curvature correction control voltage and the bias voltage has a negative temperature coefficient. The voltage divider circuit, coupled to the bias voltage generator circuit, is configured to receive the bias voltage and a bandgap-based reference voltage and in accordance therewith provide first and second intermediate voltages. The first and second circuit branches, coupled to the voltage divider circuit, are configured to receive the first and second intermediate voltages and in accordance therewith conduct first and second substantially equal branch currents at first and second substantially unequal current densities and provide first and second branch voltages, respectively, wherein a voltage difference between the first and second intermediate voltages has a positive temperature coefficient. The differential amplifier circuit, coupled to the first and second circuit branches and the voltage divider circuit, is configured to receive the first and second branch voltages and in accordance therewith provide the bandgap-based reference voltage. The current source circuit is configured to provide a control current with a negative temperature coefficient. The resistive circuit element, having a resistance with a positive temperature coefficient and coupled to the current source circuit and the bias voltage generator circuit, is configured to receive the control current and in accordance therewith provide the curvature correction control voltage. The bandgap-based reference voltage has a first arcuate voltage-versus-temperature characteristic with a first direction of incurvature and the curvature correction control voltage has a second arcuate voltage-versus-temperature characteristic with a second direction of incurvature which is substantially opposite the first direction of incurvature. 
     These and other features and advantages of the present invention will be understood upon consideration of the following detailed description of the invention and the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a circuit schematic of a conventional bandgap reference voltage generator circuit. 
     FIG. 2 is a graph of the voltage-versus-temperature characteristic of the circuit of FIG.  1 . 
     FIG. 3 is a circuit schematic of a bandgap-based reference voltage generator circuit with an increased output reference voltage and a reduced temperature coefficient in accordance with one embodiment of the present invention. 
     FIG. 4 is a more detailed circuit schematic of one embodiment of the circuit of FIG.  3 . 
     FIG. 5 is a graph of the resistance-versus-temperature characteristic of the resistor used for generating the curvature correction voltage in the circuit of FIG.  3 . 
     FIG. 6 is a graph of the current-versus-temperature characteristic of the source current used to generate the curvature correction voltage in the circuit of FIG.  3 . 
     FIG. 7 is a graph of the voltage-versus-temperature characteristic for the curvature correction voltage generated in the circuit of FIG.  3 . 
     FIG. 8 is a graph of the voltage-versus-temperature characteristic of the bandgap-based reference voltage generated by the circuit of FIG.  3 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 3, a bandgap-based reference voltage generator circuit in accordance with one embodiment of the present invention introduces a curvature correction voltage generator in the form of a current source IC and resistor R C  for driving the base of transistor Q 1  as shown. (One example of the current source circuit IC which is well suited for providing the bias current I C  is the subject of commonly assigned, co-pending U.S. patent application Ser. No. 09/368,321, entitled “Low Voltage Circuit For Generating Current With A Negative Temperature Coefficient,” filed on even date herewith, the disclosure of which is incorporated herein by reference. A proper selection of the magnitude for the bias current I C  and the curvature correction resistor R C , which should be a resistor having a non-linear temperature coefficient, provides a voltage V C  that has a voltage with a voltage-versus-temperature characteristic having a substantially equal but opposite direction of incurvature, or inflection, as the reference voltage Vbg′. This voltage V C  is added to the “quasi” bandgap voltage Vbg′. Assuming a resistance R C  as defined below, the correction voltage V C  can be determined in accordance with Equation 6: 
     
       
           R   C   =R   C0 (1+ TC   1−R   •T+TC   2−R   •T   2 )and  I   C   =I   C0 (1+ TC   1−1   •T ),  
       
     
     
       
           V   C   =I   C   •R   C   =I   C0 (1+ TC   1−1   •T ) R   C0 (1+ TC   2−R   •T   2 )   6  
       
     
     Equation 6 can be expanded to produce Equation 7: 
     
       
           V   C   =I   C0   R   C0 (1+ TC   1−R   •T+TC   2−R   T   2   TC   1−1   •T+(   TC   1−1   •TC   1−R )• T   2   +TC   1−1   •TC   1−1   •TC   2−R   •T   3 )   7  
       
     
     Disregarding the third order term in Equation 7 produces Equation 8: 
     
       
           V   C   =I   C0   R   C0 [1+( TC   1−R   +TC   1−1 ) T+(   TC   2−R   +TC   1−1   •TC   1−R ) T   2 ]  8  
       
     
     Differentiating this expression for the correction voltage V C  with respect to temperature produces Equations 9 and 10:                  ∂     V   C         ∂   T       =       I   C0            R   C0          [       (       TC     1   -   R       +     TC     1   -   I         )     +     2        (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )        T       ]               9                   ∂   2          V   C         ∂     T   2         =       I   C0            R   C0          [     2        (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )       ]               10                              
     Defining the correction voltage V C0  at the desired operating temperature T 0  being equal to the product of a corresponding bias current I C0  and R C0  (i.e., V C0 =I C0 R C0 ) and expanding Equation 8 in accordance with a Taylor Series produces Equation 11: 
     
       
           V   C ( T   0   +ΔT)=   V   C ( T   0 )+(Δ T ) V   C0   [TC   1−R   +TC   1−1 )+2( TC   2−R   +TC   1−1   •TC   1−R ) T   0 ]+½(Δ T)   2   •V   C0 [2( TC   2−R   +TC   1−1   •TC   1−R )]+  11  
       
     
     Additionally, Equation 5 can also be expanded using a Taylor Series to produce Equation 12:                            Vbg        (       T   0     +     Δ                 T       )       =                  Vbg        (     T   0     )       +       (     Δ                 T     )     ·            ∂   Vbg       ∂   T                      T   =     T   0         +                                  1   2              (     Δ                 T     )     2     ·              ∂   2        Vbg       ∂     T   2                      T   =     T   0         +   ⋯               12                              
     Ignoring those terms of Equations 11 and 12 which are higher than second order produces Equation 13 and 14: 
     
       
           V   C ( T   0   +ΔT)+   V   C ( T   0 )+(Δ T)   V   C0 [( TC   1−R   +TC   1−1   )+ 2( TC   2−R   +TC   1−1   •TC   1−R   )   T   0 ]+½(Δ T ) 2   •V   C0 [2( TC   2−R   +TC   1−1   •TC   1-R )]+  13  
       
     
     
       
         
           
             
               
                 
                   
                     Vbg 
                      
                     
                       ( 
                       
                         
                           T 
                           0 
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           T 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       Vbg 
                        
                       
                         ( 
                         
                           T 
                           0 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           kT 
                           0 
                         
                         q 
                       
                        
                       
                         ( 
                         
                           m 
                           - 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         1 
                         2 
                       
                        
                       
                         
                           kT 
                           0 
                         
                         q 
                       
                        
                       
                         ( 
                         
                           m 
                           - 
                           1 
                         
                         ) 
                       
                        
                       
                         
                           ( 
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               T 
                             
                             
                               T 
                               0 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 14 
               
             
           
         
                 
         
             
         
      
     
     From FIG. 3 it is known that the voltage V R3  across resistor R 3  is as defined in Equation 15:                V   R3     =           Δ                 Vbe       R   2       ·     R   3       =         (     Vt                 ln                 A     )     ·       R   3       R   2         =       (       k   q        ln                 A     )              R   3       R   2       ·   T                 15                              
     Expanding Equation 15 produces Equation 16:                  V   R3          (       T   0     +     Δ                 T       )       =         (       k   q        ln                 A     )            R   3       R   2            T   0       +         (       k   q        ln                 A     )     ·       R   3       R   2       ·   Δ                   T             16                              
     If the value of resistor R 3  in Equation 16 is adjusted so as to cancel the first order term (i.e., the slope) in Equation 13 and substituting for resistor R C0 (R Z0 =V C0 /I C0 ), also in Equation 13, so as to cancel the second order term in Equation 14, a flat reference voltage Vref can be produced. This produces Equations 17, 18, 19 and 20:        {                 V   C0          [       (       TC     1   -   R       +     TC     1   -   I         )     +     2        (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )          T   0         ]       =       -     (       k   q        ln                 A     )          Δ                     R   3       R   2               17                 1   2            kT   0     q          (     m   -   1     )          1     T   0   2         =       1   2            V   0          [     2        (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )       ]               18                         {               Δ                   R   3       =     -           V   0          (       TC     1   -   R       +     TC     1   -   I         )       +     2        (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )           {       [         (     k   /   q     )     ·   ln                   A     ]     /     R   2       }                                         19                 R   C0     =         V   C0       I   C0       =         (     k   /   q     )          (     m   -   1     )         2          T   0          (       TC     2   -   R       +       TC     1   -   I       ·     TC     1   -   R           )            I   0                 20                                    
     Accordingly, the “quasi” bandgap voltage Vbg′ and the bandgap-based reference voltage Vref (FIG. 3) can be determined using Equations 21 and 22. 
     
       
           Vbg′=Vbg+ΔV   R3    21  
       
     
      Vref′=Vbg′+V C    22 
     The term ΔV R3  is the adjustment voltage across resistor R 3  used to cancel the first order term (slope) of the correction voltage V C . Rearranging the foregoing equations to solve for the bandgap-based reference voltage Vref produces Equation 23:                  Vref   ′          (     T   +     Δ                 T       )       =       Vbg        (     T   0     )       +         kT   0     q          (     m   -   1     )       +       V   C          (     T   0     )       +       (     k   q     )        ln                   A   ·       Δ                   R   3         R   2                   23                              
     The term ΔR 3  is the differential resistance of resistor R 3  before and after adding the curvature correction voltage V C . (As will be seen in more detail below, this differential resistance for R 3  can be achieved by splitting the resistor R 3  into two series resistances and tapping off an appropriate amount of current from the node intermediate to such resistances.) 
     Referring to FIG. 4, one embodiment of the circuit of FIG. 3 can be implemented as shown. In accordance with well-known bandgap circuit techniques, the emitter area of transistor Q 211  is ten times the size of the emitter area of transistor Q 210  in order to generate a positive temperature drift voltage across resistor R 203 . A “bootstrap” operational amplifier is formed by transistors Q 210 , Q 211 , Q 214 , Q 213 , Q 208 , Q 218  and Q 219 . Transistor Q 206  serves as a current source and the loop formed by transistors Q 219 , Q 209 , Q 207  and Q 206  forces transistor Q 206  to source only that amount of bias current needed to generate the bandgap-based reference voltage Vref. Transistors Q 202 , Q 222 , Q 227 , Q 228 , Q 203 , Q 204 , Q 217  and Q 216  are also current sources. As discussed above, resistor R 201  and the bias current I C  cause the curvature correction voltage V C  to be generated at the base of transistor Q 215 . A diode string formed by diode-connected transistors Q 224 , Q 225  and Q 226  prevents the circuit from latching up during the initial application of DC power. 
     As noted above, resistor R 3  is formed with two resistors R 204 , R 205  in series. By tapping off a current Islope from the intermediate node connecting these resistors R 204 , R 205 , the original incoming current IBG is reduced to a lessor value of current I 204 , thereby allowing for an adjustment in the effective value of this overall resistance R 3 . 
     Referring to FIG. 5, it can be seen that the resistance of resistor of R 201  varies over temperature with a positive direction of incurvature. This resistor R 201  is formed by the P-type diffusion that forms the base regions of NPN bipolar junction transistors. 
     Referring to FIG. 6, it can be seen that the curvature correction current I C  varies over temperature with a negative slope. 
     Referring to FIG. 7, combining this curvature correction current I C  with the resistance of resistor R 201  produces a curvature correction voltage V C  which also has a positive direction of incurvature. The slope, i.e., the first order temperature coefficient, of this product of correction current I C  and resistance R C  (i.e., R 201 ) requires compensation by adjusting the first order slope of the “quasi” bandgap voltage Vbg′ to have an equal but opposite slope, thereby producing a bandgap-based reference voltage Vref having a zero temperature coefficient. The net result of this compensation, due to the introduction of the correction voltage V C  is a bandgap-based reference voltage Vref that is greater than the normal bandgap voltage Vbg by approximately 200 millivolts. 
     Referring to FIG. 8, the result of this compensation produces a bandgap-based reference voltage Vref which varies over temperature as shown. As can be seen, the temperature coefficient for this voltage Vref is approximately 0.77 ppm/° C. A comparison of this voltage variation (FIG. 8) with that shown in FIG. 2 reveals an improvement, i.e., reduction, in temperature coefficient by a factor of approximately 16. 
     One example of a host system for which a circuit in accordance with the present invention is well suited for use is the subject of commonly assigned and co-pending U.S. patent application Ser. No. 09/366,237entitled “Precision Voltage Reference Circuit With Temperature Compensation,” filed on even date herewith, the disclosure of which is incorporated herein by reference. 
     Various other modifications and alterations in the structure and method of operation of this invention will be apparent to those skilled in the art without departing from the scope and spirit of the invention. Although the invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. It is intended that the following claims define the scope of the present invention and that structures and methods within the scope of these claims and their equivalents be covered thereby.