Temperature compensated bandgap IC voltage references

Bandgap voltage reference circuits have been developed for integrated circuit applications. Typically, a negative temperature coefficient first voltage is developed related to the base to emitter potential of a transistor. A positive temperature coefficient second voltage related to the difference in base to emitter potential between two transistors operating at different current densities is developed and combined with the first voltage so as to produce a temperature compensated reference voltage. Such first order compensation leaves second order effects uncompensated. In the invention, a third voltage having a suitable temperature coefficient is combined with the first and second voltages so that the resultant reference voltage is compensated to a second order.

BACKGROUND OF THE INVENTION 
The invention relates to an improvement in temperature compensated voltage 
reference circuits. U.S. Pat. No. 3,617,859 issued to Robert C. Dobkin and 
Robert J. Widlar on a basic voltage reference circuit and is incorporated 
herein by reference. 
An improved form of temperature compensated voltage reference circuit is 
disclosed in copending application Ser. No. 888,721 filed Mar. 21, 1978, 
by Robert C. Dobkin and titled AN IMPROVED BANDGAP VOLTAGE REFERENCE. 
In the design of electronic circuits constant voltage references are often 
useful. The object is to develop a potential that has an absolute known 
magnitude that is substantially independent of current supply and load 
conditions. The avalanche or zener diode is characteristic of such a 
device but it has a temperature responsive voltage characteristic that is 
established by physical parameters. Furthermore, such devices have a knee, 
or transition region from variable to constant voltage, that produces 
noise. The so-called bandgap voltage reference devices have been developed 
in integrated circuit (IC) form in which the fundamental electronic 
properties of the semiconductor material are employed to develop a 
reference potential. 
DESCRIPTION OF THE PRIOR ART 
The prior art circuits are arranged to develop an output potential that is 
obtained by combining two potentials, one having a positive temperature 
coefficient and one having a negative temperature coefficient, in such a 
way that a temperature compensated output potential is produced. 
The base to emitter voltage (V.sub.BE) of a transistor is typically the 
source of potential with a negative temperature coefficient. The 
differential in base to emitter voltage (.DELTA.V.sub.BE) of two 
transistors operating at different current densities is typically the 
source of potential with a positive temperature coefficient. When those 
potentials are combined to produce a potential equal to the semiconductor 
bandgap extrapolated to 0.degree. K., the temperature dependent terms 
cancel for zero coefficient. Hence, the devices are often called bandgap 
references. Using silicon devices V.sub.BE at 300.degree. K. is typically 
about 600 mV. With a current density ratio of abut ten, .DELTA.V.sub.BE is 
typically about 60 mV at 300.degree. K. Since the extrapolated bandgap is 
about 1.205 volts, .DELTA.V.sub.BE is multiplied by ten and combined with 
V.sub.BE to produce 1.2 volts. It has been determined that if the 
reference is actually adjusted to 1.237 volts, the drift over the range of 
220.degree. to 400.degree. K. is minimized, provided that the current in 
the V.sub.BE transistor varies directly with temperature. Thus, in the 
vicinity of 300.degree. K. (close to normal room temperature) the 
reference voltage will not vary significantly with temperature. 
In effect, as V.sub.BE falls at about 2mV for each degree K. rise in 
temperature, .DELTA.V.sub.BE will rise about 0.2 mV for each degree K. 
temperature rise. When .DELTA.V.sub.BE is multiplied by ten the rise 
compensates the fall. 
The .DELTA.V.sub.BE potential is linearly related to temperature, as shown 
in patent 3,617,859. However, V.sub.BE, while linear with respect to 
temperature to a first order, includes second order dependencies that make 
the temperature compensation imperfect, particularly over large 
temperature ranges. 
In practice if a curve of potential versus temperature is plotted, it is 
quite flat in the vicinity of 300.degree. K. but shows curvature at 
temperatures remote from 300.degree. K. For example, even a good reference 
will display a change in excess of 0.5% over a .+-.80.degree. K. range. 
SUMMARY OF THE INVENTION 
It is an object of the invention to improve the temperature compensation of 
bandgap voltage reference circuits. 
It is a further object of the invention to reduce the curvature of the 
temperature-voltage characteristic in a bandgap voltage reference. 
It is a still further object of the invention to produce a bandgap voltage 
reference in which second order temperature dependence is compensated. 
These and other objects are achieved as follows. A bandgap voltage 
reference circuit is employed in the conventional manner. A V.sub.BE 
potential is generated and combined with a .DELTA.V.sub.BE related 
potential to produce a first order temperature-compensated reference 
potential. A third potential is developed, having a characteristic that 
matches the second order V.sub.BE temperature dependence, and combined 
with the first order terms to provide a reference potential, that is, 
compensates for the second order temperature dependence. In one embodiment 
the third potential is caused to vary with temperature by changing the 
current in a V.sub.BE transistor as a function of temperature raised to 
some power. The exponent is selected to be in the range of about 1.5 to 4, 
with 3 being preferred. In another embodiment the .DELTA.V.sub.BE 
potential is caused to vary by changing the ratio of current densities as 
a function of temperature.

DESCRIPTION OF THE INVENTION 
In the following discussions transistor base current will be largely 
ignored. Since IC transistors can consistently be manufactured to have 
beta values of 200, the base current typically represents only about 0.5% 
of the collector current. Accordingly, the simplification will not 
introduce serious error. In those instances where base current cannot be 
ignored without introducing a serious error, it will be accounted for. 
FIG. 1 shows a bandgap reference circuit of the kind disclosed in the 
above-referenced Dobkin application Ser. No. 888,721. A pair of terminals 
11 and 12 define the circuit which is energized by current source 10 
supplying I.sub.source. Transistors 13 and 14 are differentially connected 
and current source 15 supplies their combined current. Transistors 13 and 
14 are operated at different current densities to generate 
.DELTA.V.sub.BE. Since transistor 14 is at the lower current density, its 
base will be of a lower potential than the base of transistor 13. Ratioing 
can be achieved by designing transistor 14 to have about ten times the 
area of transistor 13. In this case, load resistors 16 and 17 are matched 
so that equal currents will flow in the transistors. However, the current 
density ratio can be achieved by ratioing the load resistors 16 and 17 and 
using equal area transistors. Furthermore, the resistors can be ratioed as 
well as the transistor areas to achieve the desired current density ratio. 
A voltage divider consisting of resistors 18-20 and diodeconnected 
transistor 21 in series is connected across terminals 11 and 12. Resistor 
19 is coupled between the bases of transistors 13 and 14 to develop the 
.DELTA.V.sub.BE component. As shown in the drawing resistor 19 is R, 
resistor 18 is xR, and resistor 20 is yR. Thus if .DELTA.V.sub.BE appears 
across register 19, the combined resistor voltage drop will be 
(x+y+1).DELTA.V.sub.BE . If a current density ratio of ten is used, 
.DELTA.V.sub.BE will be about 60 mV at 300.degree. K. If resistors 18 and 
20 have a combined value of nine times the value of resistor 19, the three 
resistors will develop a potential of about 600 mV at 300.degree. K. Since 
transistor 21 will develop a V.sub.BE of about 600 mV at 300.degree. K., 
the total potential across the series combination is about 1.2 volts at 
300.degree. K. As pointed out above, the temperature coefficients of the 
two potentials will be substantially equal and opposite thus compensating 
the circuit for temperature to a first order. 
The circuit is stabilized by amplifier 22 which senses the differential 
voltage at the collectors of transistors 13 and 14 and, by shunting a 
portion of I.sub.source, forces the potential across terminals 11 and 12 
to produce zero differential collector voltage. 
In accordance with the invention, the temperature compensation of the 
circuit can be improved by accounting for second order effects. This can 
be done by inserting a temperature dependent imbalance into the circuit as 
shown by the current source at 25 or the current source at 26. By making 
I.sub.25 in source 25 and/or I.sub.26 in source 26 temperature dependent, 
as will be shown hereinafter, the circuit can be compensated for second 
order temperature effects as well as the first order compensated of the 
prior art. A key point is that I.sub.25 and I.sub.26 vary as a function of 
temperature in a different way than I.sub.15. 
The formula for .DELTA.V.sub.BE is: 
EQU .DELTA.V.sub.BE =kT/q1n(J1/J2) (1) 
Where: 
q is the electron charge 
k is the Boltzmann's constant 
T is absolute temperature 
J1/J2 is the transistor current density ratio. 
The formula for V.sub.BE is: 
EQU V.sub.BE =V.sub.go (1-T/T.sub.o)+V.sub.BE.sbsb.o (T/T.sub.o)+nkT/q 1n 
(T.sub.o /T)+kT/q1n(I.sub.C /I.sub.C.sbsb.o) (2) 
Where: 
V.sub.go is the semiconductor bandgap extrapolated to absolute zero. 
V.sub.BE.sbsb.o is the base to emitter voltage at T.sub.o and 
I.sub.C.sbsb.o 
I.sub.C is collector current 
n is a transistor structure factor and is about 3 
for NPN double-diffused IC transistors. 
For the best compensation using silicon devices over a 220.degree. K. to 
400.degree. K. temperature range: 
EQU 1.237V=V.sub.BE +.alpha..DELTA.V.sub.BE (3) 
Where: 
.alpha.is a multiplying factor. 
Formula (1) shows that the .DELTA.V.sub.BE term is a linear function of 
temperature. However, V.sub.BE is not. The third term in Formula (2) is 
the one that causes the basic circuit of FIGS. 1 and 3 to depart from 
compensation and constitutes a significant second order effect. For small 
temperature changes T.sub.o /T.perspectiveto.1 and 1n T.sub.o /T is small 
and insignificant. However, over the temperature range demanded of 
operating devices, the logarithmic temperature ratio term becomes 
significant. 
The current sources 25 and 26 of FIG. 1 will act to introduce an effective 
offset potential into the circuit and shift the current ratio in 
transistors 13 and 14 as a function of temperature. The feedback loop 
around amplifier 22 will still force the differential collector voltage to 
zero. This offset will then cause .DELTA.V.sub.BE to vary with temperature 
differently. 
The circuit of FIG. 2 is a practical realization of the circuit of FIG. 1. 
In addition, it discloses a three-terminal circuit representation. It is 
to be understood that all of the circuits to be discussed herein can be 
implemented with a similar three-terminal equivalent. 
A source of potential is applied between terminals 101 (+V) and 112 (-V). 
This would be the conventional voltage supplied to the IC. The reference 
potential shown at terminal 111 (V.sub.REF) is in relation to terminal 
112. A positive potential (+V) is applied to differential operational 
amplifier 122 as a power supply so that the output terminal, when coupled 
to terminal 111, will supply current thereto. Thus, the current source 10 
of FIG. 1 is inherent in the circuit. 
Transistors 113 and 114 are operated at ratioed current densities and 
.DELTA.V.sub.BE appears across resistor 119. Amplifier 122 drives the 
potential between terminals 111 and 112 to force the input differential to 
zero. Basically the circuit functions as was described for FIG. 1. 
However, it can be seen that the voltage divider that includes resistors 
118, 119, and 120 also includes two diode connected transistors, 102 and 
121. Since resistor 119 develops about 60 mV at 300.degree. K., resistors 
118 and 120 should develop a total of about 1.24 volts to provide a 
V.sub.REF of about 2.5 volts, for basic compensation. 
Transistor 104 is connected to diode 121 to provide a current inverter. 
Thus the current flowing in resistor 103 mirrors the current flowing in 
resistor 119 which is proportional to .DELTA.V.sub.BE. Resistor 103 has a 
relatively small value so that it develops a few tens of millivolts at 
300.degree. K. and this voltage has a positive temperature coefficient. 
This voltage appears in series with resistor 117 and constitutes an offset 
potential at the input to amplifier 122. The amplifier will still act on 
the voltage at terminal 111 to force its differential input to zero. 
Transistor 115 acts as a current source to transistors 113 and 114. Since 
the base of transistor 115 is biased up two V.sub.BE values, the voltage 
across resistor 105 will be equal to one V.sub.BE. Thus resistor 105 sets 
the combined current flowing in transistors 113 and 114 and this current 
has a negative temperature coefficient because it is directly proportional 
to V.sub.BE. 
As temperature rises, the total current in transistors 113 and 114 will 
fall and the potential across resistor 103 will rise. These values can be 
proportioned so that the curvature of the temperature voltage curve of the 
uncompensated circuit is largely cancelled and the circuit is temperature 
compensated to a second order. 
FIG. 3 shows a bandgap reference designed to work at twice the 
semiconductor bandgap voltage when energized by current source 10. The 
basic operation is similar to the circuit disclosed in U.S. Pat. No. 
3,617,859. 
The .DELTA.V.sub.BE term is generated by transistors 32 thru 35 and appears 
across resistor 39. The actual value of .DELTA.V.sub.BE will be: 
EQU .DELTA.V.sub.BE =V.sub.BE 32 +V.sub.BE 33 -V.sub.BE 34 -V.sub.BE 35 (4) 
where the number subscripts denote the transistor. The current through 
transistor 32 is established by resistor 36, the current through 
transistor 33 by resistors 37 and 44, the current through transistor 34 by 
resistor 38, and the current through transistor 35 by resistor 39. Thus, 
each transistor can have its current independently set. The 
.DELTA.V.sub.BE of formula (4) will appear across resistor 39. If resistor 
40 is ratioed with respect to resistor 39, it will develop a multiple of 
.DELTA.V.sub.BE equal to the ratio. In operation, the V.sub.BE values of 
transistors 41 and 42 will combine with the .DELTA.V.sub.BE multiple 
across resistor 40 to provide a bandgap reference of about 2.5 volts 
across terminals 30-31. 
Transistors 41 and 42 are connected into a Darlington configuration along 
with resistor 43 Node 45 will be V.sub.BE 41 +V.sub.BE 42 above terminal 
31 and at 300.degree. K. will develop about 1.25 volts. This combined with 
the .DELTA.V.sub.BE related drop across resistor 40 will provide the 
temperature compensated 2.5 volts between terminals 30 and 31. 
As explained above, the compensation is to a first order and the 
temperature versus voltage characteristic is curved. Transistor 43 and 
resistor 44 are added to the circuit to provide the desired second order 
compensation. As temperature rises, the V.sub.BE across transistors 43 and 
32 falls with the V.sub.BE of 43 falling more rapidly since it operates at 
lower current density. This action increases the relative current in 
transistor 33. Thus, while .DELTA.V.sub.BE varies normally with 
temperature, an additional or compensating variation is introduced to 
provide a second order temperature compensation. 
FIG. 4 shows a very low voltage reference circuit that is compensated for 
second order temperature effects. In the circuit of FIG. 4 operation is 
from current source 10 supplying I.sub.1. A portion of I.sub.1, labeled 
I.sub.2, will flow through the voltage divider consisting of resistors 
50-52. Another portion, I.sub.3, flows through transistor 53 and the 
remainder, I.sub.4 flows through transistor 54 and back to node 55 by way 
of resistor 56. 
Transistor 54 is manufactured to have an emitter area large with respect to 
the emitter area of transistor 53 and the current in transistor 54 is made 
small with respect to the current in transistor 53. Thus, the current 
density in transistor 54 is much smaller than the current density in 
transistor 53. 
The circuit functions to develop a reference potential (V.sub.REF) at 
terminal 60 and is arranged to maintain this potential constant as a 
function of temperature. 
The V.sub.BE potential of transistor 53 appears at node 57. The voltage 
divider action of resistors 50-52 results in a fraction of this V.sub.BE 
to appear across resistor 50. Thus, at node 61 a potential of V.sub.BE 
plus a fraction thereof appears. Assuming resistor 59 to be zero for the 
moment, it can be seen that, with respect to terminal 60, the V.sub.BE of 
transistor 54 will subtract from the potential at node 61 so that 
V.sub.REF will contain a .DELTA.V.sub.BE term. This term will be: 
EQU .DELTA.V.sub.BE =kT/q1n(J.sub.53 /J.sub.54) (5) 
Where: 
k is Boltzman's constant 
T is absolute temperature 
q is electron charge 
J.sub.53 is current density in transistor 53 
J.sub.54 is current density in transistor 54 
If the current density ratio is set, for example, at 50, .DELTA.V.sub.BE at 
300.degree. kelvin will be about 100 mV. If the fraction of V.sub.BE 
appearing across resistor 50 is made about 100 mV at 300 .degree. kelvin, 
V.sub.REF will be about 200 mV. Accordingly, V.sub.REF is: 
EQU V.sub.REF =.DELTA.V.sub.BE +(V.sub.BE 53)/6 (6) 
The first term has a positive temperature coefficient and the second term 
has an equal negative temperature coefficient so that, to a first order, 
temperature compensation is achieved. 
Resistor 59 is present in the circuit to permit correction for current 
source variations. A portion of I.sub.1 will flow into the base of 
transistor 53 which will act as an inverting amplifier to node 58. Thus, 
if resistor 59 is made equal to the reciprocal of the transconductance of 
transistor 53, node 58 will be compensated for variations in I.sub.1. 
As shown above, the circuit is compensated for first order temperature 
effects. By returning resistor 56 to a tap, node 55, on the resistance 
associated with the V.sub.BE of transistor 53, a second order temperature 
compensation is achieved. 
Resistor 56 will determine the current flowing in transistor 54 and hence 
its current density, J.sub.54 of equation (5). Since the potential at node 
55 will fall within rising temperature, due to the V.sub.BE of transistor 
53, the current flowing in transistor 54 and hence its current density 
will increase with a rising temperature but less rapidly than the current 
in 53. Thus, the .DELTA.V.sub.BE term is varied non linearly as a function 
of temperature in such a direction as to compensate for the curvature in 
V.sub.BE (and that introduced by the temperature drift of diffused 
resistors). The degree of compensation can be adjusted by the ratio of 
resistors 51 and 52, to compensate the curvature of the first order 
compensation described above. 
FIG. 5 represents an alternative compensation method for the circuit of 
FIG. 1. However, the compensation in FIG. 5 is discontinuous. All of the 
part designations are as used in FIG. 1 and the first order compensation 
is as was described for FIG. 1. 
The second order compensation is achieved by the action of transistor 65 
and resistor 66. At the design temperature, for example, 300.degree. K. 
where .DELTA.V.sub.BE would be set to 60 mV which appears across resistor 
19, transistor 65 is inoperative. That is, the potential developed across 
resistors 18", 19, and 20 is less than one V.sub.BE so that negligible 
current will flow in resistor 66. As temperature rises and .DELTA.V.sub.BE 
increases, and V.sub.BE decreases, a point will be reached where 
transistor 65 will be turned on. As temperature further increases the 
current in transistor 65 will increase. Resistor 66 will determine how 
much the current in transistor 65 will rise and the tap on resistor 18 
which sets the relative values of resistors 18' and 18" will determine the 
temperature at which transistor 65 will turn on. This is selected to be 
the temperature at which curvature exceeds a certain value in the basic 
circuit. The increasing current flow in transistor 21 will cause its 
V.sub.BE value to increase. This will offset the normal tendency of 
V.sub.BE to decline excessively with temperature. The degree of 
compensation at the higher temperatures will be established by the value 
of resistor 66. 
FIG. 6 represents a discontinuously compensated bandgap reference of the 
kind disclosed in U.S. Pat. No. 3,617,859. Source 10 supplies I.sub.source 
to terminals 11 and 12. Transistors 70 and 71 generate .DELTA.V.sub.BE 
which appears across resistor 72. Assuming a ten to one current density 
ratio, .DELTA.V.sub.BE will be about 60 mV at 300.degree. K. If resistor 
72 is made 600 ohms, 100 microamperes will flow in transistor 71 at 
300.degree. K. If resistor 73 is made ten times the value of resistor 72, 
it will develop a drop of about 0.6 volt, proportional to V.sub.BE. Since 
this drop is combined with the V.sub.BE of transistor 74, a compensated 
1.2 volts appears across terminals 11 and 12. Clearly the required current 
density ratio can be established by current ratioing, area ratioing, or 
the combination of current and area ratioing. 
The circuit described thus far is temperature compensated to a first order. 
Transistor 77 and resistor 78 provide the second order compensation. Since 
the base is tapped into the divider consisting of resistors 75 and 76, 
less than a V.sub.BE at 300.degree. K. will be applied to the emitter-base 
circuit of transistor 77. It will therefore be non-conductive. As 
temperature rises the V.sub.BE in transistor 70 will drop thereby 
increasing the potential across resistor 75. At some temperature, as 
determined by the values of resistors 75 and 76, transistor 77 will turn 
on and act to shunt resistor 75 thereby tending to increase the V.sub.BE 
of transistor 70 and offset its tendency to fall excessively with rising 
temperature. The amount of compensation is established by the value of 
resistor 78. This provides a discontinuous compensation of the second 
order temperature effect 
EXAMPLE I 
The circuit of FIG. 4 was constructed using standard bipolar IC techniques. 
The transistors had a Beta of about 200. The following resistor values 
were established using ion implanted resistors; 
______________________________________ 
Resistor Value/ohms 
______________________________________ 
50 14.8K 
51 82.4K 
52 2.5K 
56 135K 
59 2.8K 
______________________________________ 
The circuit was operated at about 20 microamperes. The reference voltage 
drift was less than 0.1% over the range of 220.degree. K. to 400.degree. 
K. 
EXAMPLE II 
The circuit of FIG. 2 was constructed as described in EXAMPLE 1. All 
transistors were designed to have the same emitter area. The following 
resistor values were used: 
______________________________________ 
Resistor Value/ohms 
______________________________________ 
103 400 
105 6K 
116 3K 
117 30K 
118 6.2K 
119 600 
120 6.2K 
______________________________________ 
Amplifier 122 was a conventional high gain differential operational 
amplifier trimmed to have substantially zero offset voltage. 
V.sub.REF was 2.44 volts and varied less than 0.5 mv. over a temperature 
range of -55.degree. to +100.degree. C. 
The invention has been described and examples of its implementation set 
forth. A person skilled in the art when reading the foregoing disclosure 
will appreciate that there are other obvious alternatives and equivalents 
that come within the intent of the invention. Accordingly, it is intended 
that the scope of the invention be limited only by the following claims.