Abstract:
Low noise bandgap references of the type providing a temperature independent output by balancing the proportional to absolute temperature dependence of the difference in base-emitter voltages of two transistors operating at different current densities with the negative temperature coefficient of the base-emitter voltage of a transistor. The bandgap references disclosed reduce the noise characteristic of such references by balancing the difference in base-emitter voltages of a first number of pairs of transistors, each pair having two transistors operating at different current densities, with the negative temperature coefficient of the base-emitter voltage of a second number of transistors, the second number being less than the first number. Various embodiments are disclosed, including embodiments having an output corresponding to the bandgap of the transistor material, and multiples of the bandgap of the transistor material.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the field of bandgap references. 
     2. Prior Art 
     Bandgap references are well known in the prior art, and are commonly used in integrated circuits to provide a reference that is independent of temperature. These references make use of two characteristics of the base-emitter voltage (VBE) of a bipolar transistor. In particular, the base-emitter voltage VBE of a junction transistor may be expressed as follows:          V   BE     =       V   g0     +       (       V   BE0     -     V   g0       )          (     T     T   0       )       +       NKT   q          ln        (       T   0     T     )         +       KT   q          ln        (       I   C       I   C0       )                                  
     where: 
     T=temperature 
     I C =the transistor collector current 
     I C0 =collector current for which V BEO  was determined 
     V g0 =bandgap voltage of silicon at temperature T 0    
     V BE0 =base to emitter voltage V at T 0  and I CO    
     q=electron charge 
     N=structure factor 
     K=Boltzmann&#39;s constant 
     The dominant terms are the first two terms:          V   g0     +       (       V   BE0     -     V   g0       )          (     T     T   0       )                              
     and since V g0  is larger than V BE0 , the net result is a negative temperature coefficient for the V BE  of a transistor. 
     If one subtracts the VBEs of two identical transistors Q 1  and Q 2  operating with unequal collector currents, there results:              V   BE1     -     V   BE2       =         KT   q          ln        (       I   C1       I   C0       )         -       KT   q          ln        (       I   C2       I   C0       )                                  or   :     
            V   BE1     -     V   BE2         =       KT   q          ln        (       I   C1       I   C2       )                                
     This frequently is expressed in terms of current densities J 1  and J 2  in the two transistors as follows:            V   BE1     -     V   BE2       =       KT   q          ln        (       J   1       J   2       )                                
     or for transistors that are of different areas (area ratio of 1 to n) but otherwise identical and having the same collector currents, can be expressed in terms of the transistor areas A as follows:            V   BE1     -     V   BE2       =         KT   q          ln        (       A   2       A   1       )         =       KT   q          ln        (   n   )                                  
     In bandgap references, two transistors are usually operated at different current densities, typically by using two transistors of different areas, but having equal collector currents. Accordingly, for specificity in the descriptions to follow, it will be assumed that the respective two transistors have different areas and have substantially equal collector currents, though this is not a specific limitation of the invention, as transistors of the same area could be operated at different collector currents, or transistors of different areas could be operated at different collector currents in the practice of the present invention. 
     Now referring to FIG. 1, a circuit diagram for a classic bandgap reference may be seen. In such a circuit, resistors R 2  and R 3  could be equal resistors with amplifier A 1 , preferably a high input impedance amplifier, driving the output voltage VBG to the voltage required to provide a zero differential input to the amplifier. Accordingly, under these conditions, the currents through resistors R 2  and R 3  are equal currents, and accordingly, neglecting the base currents of transistors Q 1  and Q 2 , provide equal collector currents to transistors Q 1  and Q 2 . In such a circuit, transistor Q 2  could have an area n times the area of transistor Q 1 , so that the current density in transistor Q 2  is only 1/n times the current density in transistor Q 1 . 
     Amplifier A 1  forces the collector voltages of transistors Q 1  and Q 2  to be equal. Because the collector voltages are equal, the voltage V R1  across resistor R 1  is as follows: 
     
       
         V R1 =VBE q1 −VBE q2   
       
     
     Where: 
     VBE q1  is the base emitter voltage of transistor Q 1 , and 
     VBE q2  is the base emitter voltage of transistor Q 2   
     Referring back to the prior equations, it may be seen that the difference in these two VBE&#39;S, the voltage across resistor R 1 , is proportional to absolute temperature. Also, since the current in resistor R 2  equals the current in resistor R 1 , the voltage across resistor R 2  is also proportional to absolute temperature, and can be thought of as amplifying the voltage across resistor R 1  by a factor of (R 1 +R 2 )/R 1 . 
     In addition to the voltages proportional to absolute temperature (PTAT) across resistors R 1  and R 2 , that leg of the circuit also includes the base emitter voltage VBE of transistor Q 2 . Again, referring to the prior equations, the VBE of a transistor linearly decreases with increases in temperature. Accordingly, by proper selection of the value of resistor R 2  in relation to the value of resistor R 1 , the linear rate of increase in the PTAT voltage across the combination of resistors R 1  and R 2  with temperature increase may be made to equal the linear rate of decrease of the base emitter voltage V BE  of transistor Q 2  with temperature increases, so that the bandgap voltage output of the circuit VBG is substantially temperature insensitive. 
     In typical prior art bandgap references, the area ratio for transistors Q 1  and Q 2  may be, by way of example, on the order of 10 to 1, which area ratio will provide a VBE difference, the voltage across resistor R 1 , on the order of 60 millivolts. The output voltage of the bandgap reference needed to balance the positive temperature coefficient of the voltage across resistors R 1  and R 2  with the negative temperature coefficient of the VBE of transistor Q 2  for a silicon transistor is typically a little over 1.2 volts. Accordingly, resistor R 2  typically is approximately an order of magnitude larger in resistance than resistor R 1 . 
     The resistor R 2  effectively amplifies the voltage across resistor R 1 , including the noise across resistor R 1 . In a typical bandgap reference circuit, resistor R 1  is the single largest source of wideband noise. The noise across resistor R 1  includes not only the thermal noise of resistor R 1 , but also the shot noise of transistors Q 1  and Q 2 , and for that matter, the noise associated with the base resistance of transistors Q 1  and Q 2 . 
     In electronic systems, the voltage reference provides the known standard that the rest of the system relies upon. Electronic circuit noise present in voltage references can limit the overall accuracy and ultimately the usefulness of the reference. Previous methods of reducing noise have depended on increased circuit power consumption or expensive semiconductor process development. The present invention improves the noise performance of bandgap references using a new circuit arrangement with existing process technology. 
     BRIEF SUMMARY OF THE INVENTION 
     Low noise bandgap references of the type providing a temperature independent output by balancing the proportional to absolute temperature dependence of the difference in base-emitter voltages of two transistors operating at different current densities with the negative temperature coefficient of the base-emitter voltage of a transistor are disclosed. The bandgap references disclosed reduce the noise characteristic of such references by balancing the difference in base-emitter voltages of a first number of pairs of transistors, each pair having two transistors operating at different current densities, with the negative temperature coefficient of the base-emitter voltage of a second number of transistors, the second number being less than the first number. Various embodiments are disclosed, including embodiments having an output corresponding to the bandgap of the transistor material (silicon in the exemplary embodiment), and multiples of the bandgap of the transistor material. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a circuit diagram for a prior art band gap reference. 
     FIG. 2 is a circuit diagram for an exemplary embodiment of the present invention. 
     FIG. 3 is a circuit diagram for a first alternate embodiment of the present invention. 
     FIG. 4 is a circuit diagram for a second alternate embodiment of the present invention. 
     FIG. 5 is a further alternate embodiment of the present invention using a combination of transistors of differing conductivity types. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Now referring to FIG. 2, a circuit diagram for one embodiment of the present invention may be seen. Again for purposes of specificity and not for purposes of limitation, it will be assumed that different current densities are obtained in any respective pair of transistors by providing equal (or substantially equal) collector currents to transistors of different sizes. Thus, for instance in FIG. 2, the resistance of resistor R 3  could be equal-to the value of resistor R 2 , and resistor R 11  could be equal to resistor R 12 . Similarly, transistor Q 2  could be n times the area of transistor Q 1  and transistor Q 4  could be n times the area of transistor Q 3 . Further, for convenience, the resistance of resistor R 3  and resistor R 2  could each equal the resistance of each of resistors R 11  and R 12 . Alternatively, there is a benefit in making R 11  and R 12  relatively large, in that it increases the gain of transistors Q 3  and Q 4 . Any noise from the operational amplifier A 1  has to be referred back through this gain. Therefore the higher gain reduces the noise contribution of the amplifier, which eases the design constraints on the amplifier. Resistor R 10  might be one half of resistor R 1 , transistors Q 1  and Q 3  could be identical, and transistors Q 2  and Q 4  also could be identical. Further, while transistor Q 2  in FIG. 2 is shown as n times the area of transistor Q 1 , as is transistor Q 4  relative to transistor Q 3 , the ratio of the areas between transistors Q 4  and Q 3  need not be the same as the ratio of the areas between transistors Q 2  and Q 1 . 
     Because transistors Q 1  and Q 2  are diode connected, the base and the collector of each respective transistor are at the same voltage. Accordingly, one may write the equation for the voltages around the closed loop that includes resistor R 1  as follows: 
     
       
         V R1 +VBE Q2 −VBE Q3 +VBE Q4 −VBE Q1 =0 
       
     
     or: 
     
       
         V R1 =(VBE Q1 −VBE Q2 )+(VBE Q3 −VBE Q4 ) 
       
     
     Consequently, with the relative values of resistors and transistors previously mentioned:          (       VBE   Q1     -     VBE   Q2       )     =       (       VBE   Q3     -     VBE   Q4       )     =         KT   q          ln        (       A   2       A   1       )         =       KT   q          ln        (   n   )                       and   :     
          V   R1       =       2        KT   q          ln        (   n   )         =       KT   q          ln        (     n   2     )                                  
     It may be seen from the foregoing that the voltage across the resistor R 1  is now equal to two differences in VBEs, or under the conditions stated, equivalent to the difference in one pair of VBEs for transistors having an area ratio of n 2  instead of simply n. Because the PTAT voltage across resistor R 1  is now effectively twice the voltage across resistor R 1  of the prior art bandgap reference of FIG. 1, the thermal noise voltage due to R 1  is increased by {square root over (2)} (because it&#39;s resistance is doubled to maintain the same current in Q 2  &amp; Q 1 ). However, the amplification required by resistor R 2  is reduced by a factor of more than 2, so the net result of the circuit of FIG. 2 is a reduction in the noise in the output voltage VBG of more than 1/{square root over (2)} times the noise voltage characteristic of the prior art. Also, the noise contribution due to the base resistance and shot noise of Q 1  and Q 2  is reduced by slightly greater than a factor of 2 because this noise appears across R 1  and the amplification factor has been reduced. This noise reduction is partially offset by the additional noise contributed by Q 3  and Q 4 . 
     The output voltage VBG itself, a voltage independent of temperature, is the same as that of the prior art (approximately 1.2 volts). In particular, as in the prior art, there is only a single VBE (with the associated negative temperature coefficient) which must be balanced by the PTAT voltages across resistors R 1  and R 2  that yield the temperature independence of the bandgap reference output voltage VBG. 
     Referring again to FIG. 2, it will be noted that for the values stated, amplifier A 1  forces the collector currents in transistors Q 3  and Q 4  to be equal. Since the emitter voltages of transistors Q 3  and Q 4  are equal, the base voltages of transistors Q 3  and Q 4 , and thus the collector voltages of transistors Q 1  and Q 2 , differ by VBE Q4 −VBE Q3 . Consequently, even with the resistance of resistor R 3  equaling the resistance of resistor R 2 , the collector currents of transistors Q 1  and Q 2  are not exactly equal. However the difference in the VBEs is on the order of 60 millivolts, whereas the voltage across the collector resistors is on the order of 0.5 volts. Accordingly, the collector currents are approximately equal, and the current densities in transistors Q 1  and Q 2  are approximately n to 1 under the stated exemplary assumptions. 
     In addition to reducing the noise in the bandgap output, another benefit of this circuit configuration is that the tail current of transistors Q 3  and Q 4  is self-biased by appropriate selection of resistor R 10 . In other circuit implementations, it would often be necessary to use an active current source to bias the transistor pair, which generally would contribute more noise that this simple resistor biasing scheme. 
     The present invention provides substantial flexibility with respect to noise reduction. Because transistors Q 1  and Q 2  are diode connected, their flicker noise contribution to the circuit is reduced. Therefore the primary source of flicker noise will be from transistors Q 3  and Q 4 , primarily transistor Q 3 . On the other hand, the primary source of wideband noise is resistor R 1 . Thus the design tradeoff between flicker noise and wideband noise has been substantially decoupled. Consequently, the present invention allows operation of the left side of the circuit, which dominates wide band noise, at higher current to keep the wideband noise low, and the right side of the circuit, which dominates flicker noise, at a lower current to reduce the flicker noise. Lowering the current in transistors Q 3  and Q 4  too low, however, will cause the shot noise from these transistors to become significant contributions to the overall noise. Still, normally it is preferable to operate the left side of the circuit at a higher current than the right side. 
     Now referring to FIG. 3, an alternate embodiment of the present invention may be seen. Again, while not a limitation of the invention, for convenience in explanation, one selection of the various components shown therein could be to make resistor R 2 , resistor R 3 , resistor R 11  and resistor R 12  all equal, to make transistors Q 1 , Q 2 , and Q 5  identical, to make transistors Q 3 , Q 4 , Q 6 , and Q 7  identical, each with an area equal to n times the area of each of transistors Q 1 , Q 2 , and Q 5 , and to make resistor R 10  one third the value of resistor R 1 . As with the other embodiments and the prior art, amplifier A 1  drives the output voltage VBG to a level required to make the collector voltages on transistors Q 5  and Q 6  equal. Looking at the closed loop, including the resistor R 1 , there results: 
     
       
         V R1 +VBE Q4 +VBE Q3 −VBE Q5 +VBE Q6 −VBE Q2 −VBE Q1 =0 
       
     
     or: 
     
       
         V R1 =(VBE Q2 −VBE Q3 )+(VBE Q1 −VBE Q4 )+(VBE Q5 −VBE Q6 ) 
       
     
     Consequently, with the relative values of resistors and transistors previously mentioned:          (       VBE   Q2     -     VBE   Q3       )     =       (       VBE   Q1     -     VBE   Q4       )     =       (       VBE   Q5     -     VBE   Q6       )     =         KT   q          ln        (       A   2       A   1       )         =         KT   q          ln        (   n   )                       and   :     
          V   R1         =       3        KT   q          ln        (   n   )         =       KT   q          ln        (     n   3     )                                          
     Thus it may be seen that in embodiment of FIG. 3, the voltage across the resistor R 1  is increased to the difference in VBEs of three pairs of transistors having an area ratio of n to 1, which is equivalent to a single pair of transistors having an area ratio of n 3 . Since the voltage across resistor R 1  is increased over that of the prior art by a factor of 3, whereas the thermal noise of R 1  will only be increased by {square root over (3)} (because the resistance of R 1  is tripled to maintain the same bandgap current), a further increase in the output to noise ratio across resistor R 1  is achieved. Again, the noise contribution from shot noise and base resistance noise of Q 1  and Q 2  is reduced because the amplification factor between R 1  and R 2  has been reduced. However, in this embodiment, the circuit leg that includes resistor R 1  also includes the VBE of two transistors, namely transistors Q 3  and Q 4 , the temperature dependence of both of which must be cancelled by the PTAT voltages across resistors R 1  and R 2 . The net result is that the bandgap reference output voltage VBG is doubled in comparison to that of the prior art of FIG. 1, or approximately 2.4 volts. Obviously this circuit requires greater headroom, though if the headroom is available, the output (VBG) to noise ratio is further improved. (The collector currents in transistors Q 2  and Q 3 , etc. would only be approximately equal for the same reasons as given for transistors Q 1  and Q 2  of FIG. 2.) 
     Now referring to FIG. 4, a still further embodiment of the present invention may be seen. Again, for purposes of explanation, it is convenient to consider the values of resistors R 2 , R 3 , R 11  and R 12  to all be equal, to set resistor R 10  to be one-half that of resistor R 1 , to make transistors Q 1 , Q 2 , Q 10 , and Q 12  identical transistors, and transistors Q 3 , Q 4 , Q 11 , and Q 13  identical transistors each having an area n times the area of each of transistors Q 1 , Q 2 , Q 10 , and Q 12 . With amplifier A 1  driving the bandgap reference voltage output VBG to that required to equalize the collector voltages and thus the collector currents in transistors Q 10  and Q 11 , the voltages around the loop that includes resistor R 1  is as follows: 
     
       
         V R1 +VBE Q4 +VBE Q3 −VBE Q10 −VBE Q12 +VBE Q13 +VBE Q11 −VBE Q2 −VBE Q1 =0 
       
     
     or: 
     
       
         V R1 =(VBE Q2 −VBE Q3 )+(VBE Q1 −VBE Q4 )+(VBE Q10 −VBE Q11 )+(VBE Q12 −VBE Q13 ) 
       
     
     Consequently, with the relative values of resistors and transistors previously mentioned:          (       VBE   Q2     -     VBE   Q3       )     =       (       VBE   Q1     -     VBE   Q4       )     =     (         VBE   Q10     -     VBE   Q11       =       (       VBE   Q12     -     VBE   Q13       )     =         KT   q          ln        (       A   2       A   1       )         =         KT   q          ln        (   n   )                       and   :     
          V   R1         =       4        KT   q          ln        (   n   )         =       KT   q          ln        (     n   4     )                                              
     Thus the embodiment of FIG. 4 provides a PTAT voltage across resistor R 1  equivalent to the difference in VBEs of four transistor pairs, further increasing the output to noise ratio in the bandgap reference voltage VBG. Like the embodiment of FIG. 3, there are two VBEs in the leg of resistor R 1 , namely the VBEs of transistors Q 3  and Q 4 , so that the bandgap reference output voltage VBG is again twice the voltage characteristic of the prior art bandgap reference of FIG.  1 . Also, even with resistor R 3  equaling resistor R 2 , the collector currents in transistors Q 2  and Q 3  are only approximately equal. Obviously resistor R 3  could be chosen to make the collector currents equal if desired. 
     As stated before, for specificity in the previous descriptions of the exemplary embodiments of the invention, it was generally assumed that the pairs of transistors operating at different current densities have different areas and have substantially equal collector currents, though again, this is not a specific limitation of the invention, as transistors of the same area could be operated at different collector currents, or transistors of the different areas could be operated at different collector currents, all in the practice of the present invention. As only one example, it was pointed out before that for the embodiment of FIG. 2, the tail current of transistors Q 3  and Q 4  can be reduced to lower the flicker noise of the circuit at the expense of a minor increase in the overall wideband noise. Obviously this reduces the collector current for these two transistors. 
     In the embodiments described, NPN transistors have been used. In some situations it may be advantageous to use PNP transistors. Subject to the specifics of the semiconductor processing used to manufacture the circuit, either PNP or NPN transistors may lend themselves to better noise performance, especially flicker noise, or improved DC accuracy or more reliable manufacturing of the voltage reference. It is also possible to use a combination of PNP and NPN transistors to build the circuits of the present invention. 
     In the embodiment of the invention shown in FIG. 2, it will be noted that the voltage on the base of transistor Q 3  is equal to the VBE of transistor Q 2  plus the voltage across resistor R 1 . Consequently, transistor Q 2  may be placed below resistor R 1  rather than above the resistor, provided the base of transistor Q 3  is coupled to the top of the series combination of the resistor R 1  and the transistor Q 2 . Similarly, in the embodiment of FIG. 3, resistor R 1  may be between transistors Q 3  and Q 4 , or even above transistor Q 3 , provided the base of transistor Q 5  is coupled to the top of the series combination of transistors Q 3  and Q 4  and resistor R 1 . A similar rearrangement is applicable to the embodiment of FIG.  4 . 
     It is also possible to combine a portion of R 2  and R 3  into a single series resistor. It would be convenient to do this because the output voltage of the bandgap could be trimmed by altering the value of this combined resistor. 
     Now referring to FIG. 5, an embodiment similar to FIG. 2, but incorporating a number of alternatives may be seen. In particular, NPN transistors Q 1  and Q 2  of FIG. 2 have been replaced in FIG. 5 by PNP transistors, providing an embodiment using a combination of NPN and PNP transistors. Also the positions of transistor Q 2  and resistor R 1  have been reversed, as it is the series combination of transistor Q 2  and resistor R 1 , not their position in the series combination, that is important. Finally, a portion of resistors R 2  and R 3  of FIG. 2 have been combined into a single series resistor R 4 , convenient for trimming the output voltage of the bandgap reference by altering the value of this combined resistor. 
     While certain preferred embodiments of the present invention have been disclosed and described herein, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.