Reference potential generators
The present invention relates to reference potential generators. 
     Generators providing reference potentials composed of a negative-temperature-coefficient component proportional to the offset potential across a semiconductor junction and of a positive-temperature-component proportional to the difference between the offset potentials of a pair of semiconductor junctions operated at different current densities are known. They are favored for obtaining zero-temperature-coefficient reference potentials in monolithic integrated circuitry. See U.S. Pat. Nos. 3,271,660; 3,648,153; 3,887,863 and 3,893,018. An important difference between reference potential generators embodying the present invention and those of the prior art is the manner in which the positive-temperature-coefficient component of the reference potential is obtained. This and other significant features of the present invention will be dealt with in detail below. 
    
    
     In the drawing: 
     FIGS. 1 and 2 are schematic diagrams of different reference potential generators, each embodying the present invention; and 
     FIGS. 3 and 4 show alternative current amplifiers 20&#39; and 20&#34; to be used in implementing either of these reference potential generators. 
    
    
     In FIG. 1, current regulating circuitry 10 has a first terminal 11 and a second terminal 12 between which an operating potential V CC  is applied. Current regulating circuitry 10 comprises a regenerative feedback loop connection of current amplifier 20 and of current amplifier 30, which latter current amplifier is of the type described by Harford and by Frederikson in U.S. Pat. Nos. 3,579,133 and 3,659,133. The common terminals 21 and 31 of current amplifiers 20 and 30, respectively, are connected respectively to terminal 11 and to terminal 12 of the current regulating circuit 10. The regenerative feedback loop is formed by (a) the output terminal 23 of current amplifier 20 being galvanically coupled via resistive element 44 to the input terminal 32 of current amplifier 30 and (b) the output terminal 33 of current amplifier 30 being galvanically coupled by direct connection to the input terminal 22 of current amplifier 20. 
     Current amplifier 30 includes, in addition to a resistive element 34, a first transistor 35 and a second transistor 36 so connected that they function as a current mirror amplifier at low current levels where the potential drop across resistive element 34 is less than a millivolt or so. At these low current levels, the current gain of current amplifier 30 is -H O , H O  being a positive number, as between its input terminal 32 and output terminal 33. This is achieved by proportioning the transconductance of transistor 36 to that of transistor 35 in H O  -to-one ratio at low current levels. Assuming transistors 35 and 36 to have similar diffusion or implantation profiles this is done by making the effective area of the base-emitter junction of transistor 36 H O  times the effective area of the base-emitter junction of transistor 35. 
     The current gain of current amplifier 20 is -G, where G is a positive number. The product of H O  G, the low-current-level open loop gain of the regenerative feedback loop connection of amplifiers 20 and 30, is chosen to exceed unity. Accordingly, a small initial disturbance in the loop (as may be administered by any of several known starting circuits, if necessary) will initiate a steady build up of currents in amplifiers 20 and 30. With this build up in current levels, the current gain of current amplifier 30 decreases from -H O  until it reaches a value of -1/G, at which current levels the unity closed-loop gain condition obtains and the loop remains in equilibrium. 
     Under these equilibrium conditions, ΔV BE , the difference between the base-emitter potentials V 35  and V 36  of transistors 35 and 36, respectively, appearing as a potential drop across resistive element 34, can be determined proceeding from the following basic equation describing transistor action. 
     
         V.sub.BE = (kT/g)lnI.sub.E /AJ.sub.S)                      (1) 
    
     where 
     V BE  is the base-emitter potential of the transistor, 
     k is Boltzmann&#39;s constant, 
     T is absolute temperature of the transistor base-emitter junction, 
     q is the charge on an electron, 
     I E  is the emitter current of the transistor, 
     A is the area of the transistor base-emitter junction, and 
     J S  is the emitter current density during saturation of the transistor. 
     Numerical subscripts for these quantities relate them to the transistor having that identification numeral. J S  is assumed the same for integrated transistors 35 and 36 since they are fabricated by the same process steps, and their junction temperatures are caused to be substantially equal by locating them close by each other on the integrated circuit. 
     
         ΔV.sub.BE = V.sub.BE35 - V.sub.BE36                  (2) 
    
     substituting from equation 1 into equation 2, equation 3 is obtained. 
     
         ΔV.sub.BE = (kT/q)ln(I.sub.E35 /J.sub.S) - (kT/q)ln(I.sub.E36 /H.sub.O J.sub.S) = (kT/q)ln(H.sub.O I.sub.E35 /I.sub.E36) (3) 
    
     equation 4 describes the equilibrium loop condition and substituted into equation 3 yields equation 5. 
     
         I.sub.E35 /I.sub.E36 = G                                   (4) 
    
     
         Δv.sub.be = (kT/q)ln G H.sub.O                       (5) 
    
     the current flow I 1  through resistive element 34 with resistance R 34  is determined in accordance with Ohm&#39;s Law. 
     
         I.sub.1 = ΔV.sub.BE /R.sub.34 = (kT/q R.sub.34)ln G H.sub.O (6) 
    
     i 1  is substantially equal to the collector current of transistor 35, assuming the base current of transistor 36 to be negligibly small, which assumption closely approximates actuality if the common-emitter forward current gain, or h fe , of transistor 36 is of reasonably large value (e.g., more than 30). The collector current of a transistor is -α times its emitter current, α being a factor well-defined to within a percent or so and nearly equal to unity in a transistor with reasonably large h fe . 
     
         I.sub.E35 = I.sub.1 /α.sub.35 = (kT/q α.sub.35 R.sub.34)ln G H.sub.O                                                   (7) 
    
     the equilibrium value of I E36  is obtained by combining equations 4 and 7 per equation 8. 
     
         I.sub.E36 = (I.sub.E35 /G) = (kT/q) α.sub.35 G R.sub.34)ln G H.sub.0 (8) 
    
     the current I 2  flowing through resistive element 44 is substantially equal to I E35 . So, one can, by application of Ohm&#39;s and Kirchoff&#39;s Laws, derive the potential drop across resistive element 44, which drop is the resistance R 44  of element 44 times I 2 , in terms of the ΔV BE  potential drop across resistive element 34, which drop is the resistance R 34  of element 34 times I 1 . The positive-temperature-coefficient potential V + , which is the sum of the potential drops across resistive elements 34 and 44, will have substantially the following value. 
     
         V.sub.+ = ΔV.sub.BE [1 + (R.sub.44 /α.sub.35 R.sub.34)](9) 
    
     combining equations 6 and 9 one obtains the following. 
     
         V.sub.+ = (kT/q) [1 + (R.sub.44 /α.sub.35 R.sub.34)]ln G H.sub.0 (10) 
    
     as has been indicated in previous portions of the specification, α 35  and H 0  are both well-defined and k and q are universal constants. R 34  and R 44 , if resistive elements 34 and 44 are concurrently formed in a monolithic integrated circuit by identical process steps, are in constant ratio to each other. If current amplifier 20 is a current mirror amplifier, for example, G is substantially constant, despite changes in temperature and current levels. Accordingly, V +  is very well defined in terms of temperature. 
     The potential appearing between terminals 12 and 23 is the sum of V BE36  and V + . Applied to the input of a zero-offset potential follower 50, this potential causes a potential V OUT  at the output terminal 55 of follower 50 which will have substantially the following value. 
     
         V.sub.OUT = V.sub.BE36 +V.sub.+ = V.sub.BE36 +(kT/q) [1+R.sub.44 /α.sub.35 R.sub.34)]lnG H.sub.0                     (11) 
    
     v out  can then be applied to a load such as resistive load 56, the buffering action of potential follower 50 preventing such loading from affecting the current regulating actions in the positive feedback loop connection of current amplifiers 20 and 30. Knowing the value of I E36  the current regulator 10 will maintain and its temperature coefficient as affected by R 34 , one can determine by measurement on transistors of the type to be used for transistor 36 the value of V BE36  versus temperature. V BE36  will, as wellknown, display a negative-temperature-coefficient owing to the temperature-dependency of J S  predominating in equation 1. By choosing V +  of such magnitude its positive-temperature-coefficient equals the negative-temperature-coefficient of V BE36 , V OUT  will be temperature-independent. It can be shown that under these circumstances, V OUT  will be equal to the extrapolated bandgap potential of the semiconductor material from which transistors 35 and 36 are made. While potential follower 50 is shown as comprising an operational amplifier with its output terminal directly connected to its inverting terminal and with its non-inverting input terminal having the potential at terminal 23 thereto applied, potential follower 50 may take other known forms. Also, one may modify the structure as used as a potential follower 50 in FIG. 1, inserting a potential divider between the output terminal and inverting input terminal of the operational amplifier. This will increase V OUT  from the value given in equation 11 by a factor equal to the potential division ratio of the potential divider. 
     FIG. 2 shows a reference potential generator that is a modification and functional equivalent of the FIG. 1 reference potential generator. In FIG. 2, the current I 3  flowing through resistive element 54 having a resistance R 54  causes a potential drop equal to I 3  R 54 . I 3  equals the sum of I E35  and I E36 , so the drop across resistive element 54 is (I E35  + I E36 ) R 54 . In FIG. 2, as in FIG. 1, the positive feedback loop connection of current amplifiers 20 and 30 stabilizes with I E35  being in G:1 ratio with I E36 , so the drop across resistive element 54 is [1 + (1/G)] I E35  R 54 . Referring back to FIG. 1, the drop across resistive element 44 is I 2  R 44 . I 2  is substantially equal to I E35  so the drop across resistive element 44 is substantially I 35  R 44 . If the FIG. 1 and 2 circuits are to provide like potentials between their respective terminals 12 and 23, the potential drop across resistive element 54 must equal the potential drop across resistive element 44. 
     
         I.sub.E35 R.sub.44 = [1 + (1/G)] I.sub.E35 R.sub.54        (12) 
    
     therefore, R 54  should have the following value. 
     
         R.sub.54 = G R.sub.44 /(G+1)                               (13) 
    
     one familiar with circuit design will perceive that further modifications that are functional equivalents of the FIG. 1 circuit exist, in which resistive elements appear both between terminals 23 and 32 and between terminals 31 and 12. 
     FIG. 3 shows a specific current amplifier 20&#39; as may be used for current amplifier 20 in either of the reference potential generators shown in FIGS. 1 and 2. Current amplifier 20&#39; comprises transistors 24 and 25 having respective base-emitter junctions with respective effective areas in 1 to G 0  ratio. If the resistances of resistors 27 and 28 are in G 0  :1 ratio, current amplifier 20&#39; is a current mirror amplifier with a current gain of -G 0 . Transistor 24 is provided with direct coupled collector-to-base feedback to adjust its base-emitter potential to condition it to supply a collector current equal to the current demand presented to input terminal 22&#39; of the current mirror amplifier. This direct-coupled collector-to-base feedback might be a direct connection, but often includes a current amplifier such as the common-collector amplifier transistor 26 to reduce the effects of the base currents of transistors 24 and 25 in the current gain of amplifier 20&#39;. By proportioning the resistances of resistors 27 and 28 inversely as the transconductances of transistors 24 and 25, respectively, application of the same base potential to transistor 25 as to transistor 24 conditions it for supplying a collector current G 0  times as large as that of transistor 25. Alternatively, resistors 27 and 28 may be replaced by direct connections of the emitter electrodes of transistors 24 and 25 to common terminal 21, and current amplifier 20&#39; would still function as a current mirror amplifier. 
     Current amplifier 20 need not be a current mirror amplifier, however, nor need it be an amplifier with gain that is invariant with input current level either. It is desirable that the current gain of current amplifier 20 be independent of the h fe  &#39;s of its transistors so that current levels in the current regulating circuit 10 are predictable and have one less temperature-dependent factor determining them. The regulation exhibited by circuit 10 is improved as the amplitude G of the gain of current amplifier 20 is made larger, but achieving large values of G using current mirror amplifiers or other fixed current gain amplifier techniques takes up extensive area on the integrated circuit die. When current amplifier 20 is constructed with bipolar junction transistors rather than field effect transistors, it is advantageous to modify current amplifier 20&#39; so as to increase the ratio of the resistance of resistor 27 to that of resistor 28 to values larger than G 0  in current amplifier 20&#39;, which increases the current gain of transistor 20 above G 0  as current levels rise. This permits a circuit having smaller values of G 0  and H 0  (which can usually be realized in a smaller die area), but exhibiting the large G H 0  product in the range of current levels where equilibrium is achieved in the positive feedback loop which is required to get good current regulation. 
     The current amplifier 20&#34; of FIG. 4 results when this modification procedure is carried out fully. A variety of current mirror amplifiers besides those having the structural connections of current amplifier 20&#39; can be used as current amplifier 20 and also these current mirror amplifiers, as modified similarly to the modifications of the current mirror amplifier described above. The important thing to understand about these modified current mirror amplifier structures is that their current gains are still substantially independent of the h fe  &#39;s of the transistors and do not change with temperature. In the structures of FIGS. 3 and 4 to which all of these structures are analogous, this comes about because the small difference between the emitter potentials of transistors 24 and 25 is proportional to ΔV BE . Any potential drop across a resistive element 27 is proportional to the ΔV BE  drop across resistive element 34 because substantially the same current flows through them. Since the proportionality between collector currents of transistors 35 and 36 does not change with temperature, the potential drop across resistive element 27 responsive to the collector current of transistor 36 flowing therethrough is proportional to the ΔV BE  drop. In current amplifier 20&#34; of FIG. 4, the potential drop across resistive element 27 proportional to ΔV BE  is the potential difference linearly proportional to T known to be required between the emitter-to-base potentials of transistors 24 and 25 to maintain their collector currents in constant ratio. In current amplifier 20&#39; of FIG. 3 since each of the potential drops across resistive elements 27 and 28, respectively, are proportional to ΔV BE , so is their difference. This difference is equal to the difference between the emitter-to-base potentials of transistors 24 and 25, which must then be in the linear proportion to T known to cause the collector currents of transistors 24 and 25 to be in temperature-independent ratio. 
     The positive feedback loop including amplifier 30 and the other current amplifier 20, 20&#39; or 20&#34;, exhibits a tendency towards assuming a stable state in which no currents flow in the loop at the time potential is first applied between terminals 11 and 12. The loop can be forced out of this undesirable condition by applying a small starting current to the input terminal of either of these current amplifiers, a variety of apparatus suitable to this purpose being known. Or one may arrange for a relatively minute leakage current to be constantly applied to the input terminal of one of the current amplifiers--e.g., an open-base transistor may have its collector-to-emitter path connected between terminals 11 and 32.