Bandgap voltage reference circuit with an increased difference voltage

Abstract

A reference voltage output by a bandgap voltage reference circuit is formed by summing an amplified voltage that has a positive temperature coefficient with a base-to-emitter voltage that has a negative temperature coefficient. The amplified voltage is formed by amplifying a difference voltage ΔVBE. Variations over temperature of the reference voltage are reduced by increasing the magnitude of the difference voltage ΔVBE. By increasing the magnitude of the difference voltage ΔVBE, a smaller gain can be used to form the amplified voltage. By utilizing a smaller gain, less of the error associated with the difference voltage ΔVBE is present in the amplified voltage.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a bandgap voltage reference circuit and, more particularly, to a bandgap voltage reference circuit with an increased difference voltage ΔV BE .

2. Description of the Related Art

A bandgap voltage reference circuit is a circuit that provides a reference voltage that is ideally temperature independent. Bandgap voltage reference circuits are commonly used as stand-alone voltage sources, and as building blocks in analog-to-digital converters, digital-to-analog converters, bias line generators, and other common analog circuits.

FIG. 1 shows a schematic diagram that illustrates a conventional bandgap voltage reference circuit 100 . As shown in FIG. 1 , circuit 100 includes a current source 110 that outputs a current I that is proportional to absolute temperature (PTAT), and transistors Q 1 , Q 2 , and Q 3 . The collectors of transistors Q 1 and Q 2 are connected to current source 110 through resistors R 1 and R 2 , respectively, while the collector of transistor Q 3 is directly connected to current source 110 .

In addition, the emitters of transistors Q 1 and Q 3 are connected together, while the emitter of transistor Q 2 , which has an emitter area that is N times larger than the emitter area of transistor Q 1 , is connected to the emitter of transistor Q 1 through resistor R 3 . Further, the bases of transistors Q 1 and Q 2 are connected to the collector of transistor Q 1 , while the base of transistor Q 3 is connected to the collector of transistor Q 2 .

In operation, circuit 100 provides a nearly temperature independent reference voltage V REF between the collector and emitter of transistor Q 3 by summing a voltage that has a positive temperature coefficient with voltage that has a negative temperature coefficient of equal value.

For example, when the temperature increases by one degree, the voltage with the positive temperature coefficient increases by, for example, 2 mV while the voltage with the negative temperature coefficient decreases by 2 mV. Since the voltages vary an equal amount in opposite directions, the reference voltage V REF remains unchanged when the temperature increases by one degree.

With respect to the voltage with the positive temperature coefficient, it is known that the difference between the base-to-emitter voltages of a pair of bipolar transistors that are forced to operate with unequal emitter current densities is a voltage with a positive temperature coefficient.

In circuit 100 , since transistor Q 2 has an emitter area that is N times larger than the emitter area of transistor Q 1 , transistors Q 1 and Q 2 operate with unequal emitter current densities. As a result, a difference voltage ΔV BE , which is equal to V BEQ1 −V BEQ2 , has a positive temperature coefficient.

As shown in FIG. 1 , the base-to-emitter voltage V BEQ1 of transistor Q 1 is equal to the base-to-emitter voltage V BEQ2 of transistor Q 2 and the voltage VR 3 across resistor R 3 , i.e., V BEQ1 =V BEQ2 +VR 3 . Rearranging yields V BEQ1 −V BEQ2 =VR 3 .

Since the difference voltage ΔV BE is equal to the difference between the base-to-emitter voltages (ΔV BE =V BEQ1 −V BEQ2 ), the difference voltage ΔV BE is also equal to the voltage VR 3 across resistor R 3 . Since the difference voltage ΔV BE has a positive temperature coefficient, the voltage VR 3 across resistor R 3 must also have a positive temperature coefficient.

The voltage VR 3 across resistor R 3 (and the value of resistor R 3 ) define the resistor current which, in turn, defines the emitter current I EQ2 of transistor Q 2 . As a result, the emitter current I EQ2 is proportional to the difference voltage ΔV BE and, therefore, must have a positive temperature coefficient.

In addition, the collector current I CQ2 of transistor Q 2 is approximately equal to the emitter current I EQ2 of transistor Q 2 due to the beta of transistor Q 2 . As a result, the collector current I CQ2 of transistor Q 2 is proportional to the difference voltage ΔV BE and, therefore, must have a positive temperature coefficient.

Thus, since the collector current I CQ2 is proportional to the difference voltage ΔV BE , the voltage VR 2 across resistor R 2 is proportional to the difference voltage ΔV BE , and therefore must also have a positive temperature coefficient.

The voltage VR 2 is also known as an amplified difference voltage ΔV BE because the voltage VR 2 is approximately equal to R 2 /R 3 times the voltage VR 3 which, in turn, is equal to the difference voltage ΔV BE .

With respect to the voltage with the negative temperature coefficient, it is known that the base-to-emitter voltage of a bipolar transistor has a negative temperature coefficient when the collector current of the transistor is proportional to absolute temperature.

As noted above, current source 110 outputs a current I that is proportional to absolute temperature. As a result, the base-to-emitter voltage V BEQ3 of transistor Q 3 has a negative temperature coefficient.

Thus, circuit 100 provides a nearly temperature independent reference voltage V REF between the collector and emitter of transistor Q 3 by summing the voltage VR 2 , the amplified difference voltage ΔAV BE , with the base-to-emitter voltage V BEQ3 across the base-to-emitter junction of transistor Q 3 .

The amplified difference voltage ΔAV BE (VR 2 ) has a positive temperature coefficient of approximately +2 mV/° C., while the base-to-emitter voltage V BEQ3 has a negative temperature coefficient of approximately −2 mV/° C. Thus, by summing voltages which have equal and opposite temperature coefficients, the total voltage, i.e., the reference voltage V REF , remains unchanged as the temperature changes. (See also U.S. Pat. No. 3,617,859 to Dobkin which is hereby incorporated by reference.)

FIG. 2 shows a schematic diagram that illustrates a conventional bandgap voltage reference circuit 200 . Circuit 200 is similar to circuit 100 and, as a result, utilizes the reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 2 , circuit 200 differs from circuit 100 in that circuit 200 eliminates both current source 110 and transistor Q 3 , and instead utilizes an operational amplifier (op amp) 210 and a resistor R 4 . As with circuit 100 , transistor Q 2 of circuit 200 has an emitter area that is N times larger than the emitter area of transistor Q 1 of circuit 200 .

Op amp 210 has a positive input connected to the collector of transistor Q 1 , a negative input connected to the collector of transistor Q 2 , and an output connected to the bases of transistors Q 1 and Q 2 . Resistor R 4 , in turn, has a first end connected to resistor R 3 and the emitter of transistor Q 1 , and a second end connected to ground.

In operation, the resistances of resistors R 1 and R 2 are equal, and develop voltages at the collectors of transistors Q 1 and Q 2 which are equal when the collector currents are equal. When the collector currents, which are proportional to absolute temperature, are not equal, op amp 210 responds to the unequal collector voltages by changing the base voltages of transistors Q 1 and Q 2 until the collector currents of transistors Q 1 and Q 2 are equal.

In circuit 200 , transistors Q 1 and Q 2 are again forced to operate with unequal emitter current densities due to the difference in emitter areas. As a result, the difference voltage ΔV BE is again equal to the voltage VR 3 across resistor R 3 , and the voltage VR 3 again has a positive temperature coefficient.

The voltage VR 3 across resistor R 3 defines the emitter current I EQ2 of transistor Q 2 . As a result, the emitter current I EQ2 is proportional to the difference voltage ΔV BE , and must have a positive temperature coefficient.

Since the collector currents, the base currents, and the betas of transistors Q 1 and Q 2 are nominally the same, the emitter current I EQ1 of transistor Q 1 is nominally the same as the emitter current I EQ2 of transistor Q 2 . Thus, the emitter current I EQ1 of transistor Q 1 is also proportional to the difference voltage ΔV BE .

Since both the emitter current I EQ1 of transistor Q 1 and the emitter current I EQ2 of transistor Q 2 are proportional to the difference voltage ΔV BE , the combined currents through resistor R 4 must also be proportional to the difference voltage ΔV BE , and must also have a positive temperature coefficient.

Since the combined emitter currents have a positive temperature coefficient, the voltage VR 4 across resistor R 4 must also have a positive temperature coefficient. Thus, by properly sizing resistor R 4 to obtain the proper gain, the amplified difference voltage ΔAV BE is defined across resistor R 4 .

In circuit 200 , the amplified difference voltage ΔAV BE (the voltage VR 4 ) is summed with the base-to-emitter voltage V BEQ1 of transistor Q 1 to produce the reference voltage V REF . The base-to-emitter voltage V BEQ1 of transistor Q 1 has a negative temperature coefficient as op amp 210 insures that transistor Q 1 receives a collector current that is proportional to absolute temperature. (See also U.S. Pat. No. 3,887,863 to Browkaw which is hereby incorporated by reference.)

Although circuits 100 and 200 output reference voltages V REF which are, to a first degree, constant over variations in temperature, in actual practice the reference voltages V REF vary slightly with changes in temperature. Thus, with the need to produce highly-accurate, low-voltage reference voltages, there is a need for a bandgap voltage reference circuit that reduces these slight changes in the reference voltage V REF over changes in temperature.

SUMMARY OF THE INVENTION

The present invention provides a bandgap voltage reference circuit that reduces variations in the reference voltage V REF over temperature by significantly increasing the magnitude of the difference voltage ΔV BE . By increasing the magnitude of the difference voltage ΔV BE , a smaller gain can be used to form the amplified difference voltage ΔAV BE . By utilizing a smaller gain, less of the error associated with the difference voltage ΔAV BE is present in the amplified difference voltage ΔAV BE .

In accordance with the present invention, a voltage reference circuit includes a current source that outputs a first current and a second current, and a difference circuit that is connected to the current source. The difference circuit has a first transistor which has a collector connected to receive the first current, a base, and an emitter that outputs a first emitter current.

The difference circuit also includes a second transistor which has a collector connected to receive the second current, a base connected to the base of the first transistor, and an emitter. The voltage on the base of the first transistor and the base of the second transistor is defined by a voltage on the collector of the second transistor. The difference circuit further includes a third transistor which has a collector connected to the emitter of the first transistor, a base connected to receive a voltage defined by a voltage on the collector of the third transistor, and an emitter.

The difference circuit additionally includes a fourth transistor which has a collector connected to the emitter of the second transistor, a base connected to receive a voltage defined by a voltage on the collector of the fourth transistor, and an emitter. Further, a first resistor has a first end connected to the emitter of the third transistor, and a second end connected to the emitter of the fourth transistor. A difference voltage, which has a positive temperature coefficient, is formed across the first resistor.

A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description and accompanying drawings which set forth an illustrative embodiment in which the principles of the invention are utilized.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a conventional bandgap voltage reference circuit 100 .

FIG. 2 is a schematic diagram illustrating a conventional bandgap voltage reference circuit 200 .

FIG. 3 is a schematic diagram illustrating a bandgap voltage reference circuit 300 in accordance with the present invention.

FIG. 4 is a schematic diagram illustrating a voltage reference circuit 400 in accordance with the present invention.

FIG. 5 is a schematic diagram illustrating a voltage reference circuit 500 in accordance with the present invention.

FIG. 6 is a schematic diagram illustrating a voltage reference circuit 600 in accordance with the present invention.

FIG. 7 is a schematic diagram illustrating a voltage reference circuit 700 in accordance with the present invention.

FIG. 8 is a schematic diagram illustrating a thermal shutdown circuit 800 in accordance with the present invention.

FIG. 9 is a schematic diagram illustrating a bandgap voltage reference circuit 900 in accordance with the present invention.

FIG. 10 is a schematic diagram illustrating a bandgap voltage reference circuit 1000 in accordance with the present invention.

FIG. 11 is a schematic diagram illustrating a bandgap voltage reference circuit 1100 in accordance with the present invention.

FIG. 12 is a schematic diagram illustrating a bandgap voltage reference circuit 1200 in accordance with the present invention.

FIG. 13 is a block diagram illustrating the cross-quading of transistors Q 1 -Q 4 in accordance with the present invention.

DETAILED DESCRIPTION

FIG. 3 shows a schematic diagram that illustrates a bandgap voltage reference circuit 300 in accordance with the present invention. As shown in FIG. 3 , circuit 300 includes a current source circuit 310 that outputs a first current I 1 and second current I 2 which has a magnitude defined by current I 1 , and a difference circuit 312 that is connected to current source 310 . Circuit 312 , in turn, includes a transistor Q 1 which has a collector connected to receive the first current I 1 , a base, and an emitter.

Difference circuit 312 further includes a transistor Q 2 which has a collector connected to receive the second current I 2 , a base connected to the base of transistor Q 1 and the collector of transistor Q 2 , and an emitter. In addition, transistor Q 1 is formed to have an emitter area that is N times larger than the emitter area of transistor Q 2 .

Further, difference circuit 312 also includes a transistor Q 3 which has a collector connected to the emitter of transistor Q 1 , a base connected to the collector of transistor Q 3 , and an emitter. In addition, a transistor Q 4 has a collector connected to the emitter of transistor Q 2 , a base connected to the collector of transistor Q 4 , and an emitter.

In circuit 312 , transistor Q 3 is formed to have an emitter area that is N times larger than the emitter area of transistor Q 4 , while transistor Q 4 is formed to have an emitter area that is equal to the emitter area of transistor Q 2 .

Difference circuit 312 additionally includes a resistor R 1 which has a first end connected to the emitter of transistor Q 3 , and a second end connected to the emitter of transistor Q 4 . As described in greater detail below, difference circuit 312 develops a difference voltage ΔV BE , which has a positive temperature coefficient, across resistor R 1 .

As further shown in FIG. 3 , circuit 300 also includes an amplification circuit 314 that is connected to difference circuit 312 . Amplification circuit 314 includes a transistor Q 5 that has a collector, a base connected to the base of transistor Q 3 , and an emitter. Transistor Q 5 has an emitter area that is equal to the size of the emitter area of transistor Q 3 .

Amplification circuit 314 also includes a second resistor R 2 having a first end connected to the emitter of transistor Q 5 , a second end connected to the second end of resistor R 1 , and a resistance equal to the resistance of resistor R 1 . In addition, a third resistor R 3 has a first end connected to the collector of transistor Q 5 , and a second end.

As described in greater detail below, amplification circuit 314 develops the difference voltage ΔV BE across resistor R 2 , and an amplified difference voltage ΔAV BE across resistor R 3 . Thus, since the difference voltage ΔV BE has a positive temperature coefficient, the amplified difference voltage ΔAV BE also has a positive temperature coefficient.

In addition, circuit 300 further includes an output circuit 316 that is connected to amplification circuit 314 . Circuit 316 includes an output transistor Q 6 which has a collector connected to receive a current, a base connected to the collector of transistor Q 5 , and an emitter connected to the second end of resistor R 2 .

In addition, transistor Q 6 has a base-to-emitter voltage V BEQ6 which has a negative temperature coefficient. The magnitudes of the positive and negative temperature coefficients are substantially the same.

Output circuit 316 also includes a current source 318 that outputs a current I 3 which is proportional to absolute temperature (PTAT), and a buffer 320 having an input connected to the collector of transistor Q 6 , and an output connected to the second end of resistor R 3 .

In operation, the output circuit 316 outputs a reference voltage V REF that is the sum of the amplified difference voltage ΔAV BE and the base-to-emitter voltage V BEQ6 .

Since the amplified difference voltage ΔAV BE and the base-to-emitter voltage V BEQ6 have equal but opposite temperature coefficients, changes in temperature cause the amplified difference voltage ΔAV BE and the base-to-emitter voltage V BEQ6 to vary in equal and opposite directions, thereby leaving the reference voltage V REF unchanged.

For example, if the amplified difference voltage ΔAV BE has a temperature coefficient of +2 mV/° C. and the base-to-emitter voltage V BEQ6 has a temperature coefficient of −2 mV/° C., then a one degree increase in temperature raises the amplified difference voltage ΔAV BE by 2 mV while lowering the base-to-emitter voltage V BEQ6 by 2 mV, thereby leaving the reference voltage V REF , the sum of the voltages, unchanged.

The amplified difference voltage ΔAV BE , which is dropped across resistor R 3 , is developed by utilizing bipolar transistors which are forced to operate with emitter currents that have unequal current densities. As noted above, when bipolar transistors operate with unequal emitter current densities, the difference voltage between the base-to-emitter voltages of the transistors has a positive temperature coefficient.

In circuit 300 , when first and second currents I 1 and I 2 are equal, transistors Q 1 /Q 3 and Q 2 /Q 4 are forced to operate with unequal emitter current densities since transistors Q 1 and Q 3 have emitter areas that are N times larger than the emitter areas of transistors Q 2 and Q 4 , respectively.

As a result, the difference voltage ΔV BE , which has a positive temperature coefficient, is defined as the difference between the combined base-to-emitter voltages of transistors Q 2 and Q 4 ; and the combined base-to-emitter voltages of transistors Q 1 and Q 3 , i.e., ΔV BE =(V BEQ2 +V BEQ4 )−(V BEQ1 +V BEQ3 ).

As shown in FIG. 3 , the combined base-to-emitter voltages V BEQ2 and V BEQ4 of transistors Q 2 and Q 4 are equal to the combined base-to-emitter voltages V BEQ1 and V BEQ3 of transistors Q 1 and Q 3 , and a voltage VR 1 across resistor R 1 , i.e., V BEQ2 +V BEQ4 =V BEQ1 +V BEQ3 +VR 1 . Rearranging yields (V BEQ2 +V BEQ4 )−(V BEQ1 +V BEQ3 )=VR 1 .

Since the difference voltage ΔV BE is equal to the difference between the base-to-emitter voltages (ΔV BE =(V BEQ2 +V BEQ4 )−(V BEQ1 +V BEQ3 )), the difference voltage ΔV BE is also equal to the voltage VR 1 across resistor R 1 . In addition, since the difference voltage ΔV BE has a positive temperature coefficient, the voltage VR 1 across resistor R 1 must also have a positive temperature coefficient.

Since the difference voltage ΔV BE is equal to the voltage VR 1 across resistor R 1 , the emitter current I E3 flowing through resistor R 1 is proportional to the difference voltage ΔV BE and, therefore, must have a positive temperature coefficient.

Further, the collector current I CQ3 of transistor Q 3 is approximately equal to the emitter current I E3 of transistor Q 3 due to the beta of transistor Q 3 . As a result, the collector current I CQ3 is approximately proportional to the difference voltage ΔV BE and, therefore, must have a positive temperature coefficient.

Transistors Q 3 and Q 5 form a resistor-ratioed current mirror. Since transistors Q 3 and Q 5 have the same-sized emitter areas, resistors R 1 and R 2 provide equal resistances, and the current mirror configuration forces the base-to-emitter voltages V BE of transistors Q 3 and Q 5 to be equal, the emitter current I EQ5 and the collector current I CQ5 of transistor Q 5 are the same as the emitter current I EQ3 and collector current I C3 of transistor Q 3 , respectively.

Since the emitter current I EQ5 is the same as the emitter current I EQ3 , and the resistances of resistors R 1 and R 2 are the same, the voltage VR 2 across resistor R 2 is also equal to the difference voltage ΔV BE .

Further, the collector current I CQ5 of transistor Q 5 is approximately equal to the emitter current I E5 of transistor Q 5 due to the beta of transistor Q 5 . As a result, the collector current I CQ5 is proportional to the difference voltage ΔV BE and, therefore, must have a positive temperature coefficient.

In addition, since the collector current I CQ5 has a positive temperature coefficient, the voltage VR 3 across resistor R 3 , i.e., the amplified difference voltage ΔAV BE , must also have a positive temperature coefficient. Since the collector current I CQ5 is approximately equal to the emitter current I EQ5 , the amplified difference voltage ΔAV BE is equal to the resistor ratio R 3 /R 2 times the difference voltage ΔV BE .

As noted above, the amplified difference voltage ΔAV BE is summed with the base-to-emitter voltage V BEQ6 to produce the reference voltage V REF . Since the current I 3 output by current source 318 is proportional to absolute temperature, the base-to-emitter voltage V BEQ6 of transistor Q 6 changes only with temperature, and decreases as temperature increases.

Thus, by setting the positive and negative temperature coefficients of the amplified difference voltage ΔAV BE and the base-to-emitter voltage V BEQ6 to be equal, changes in temperature cause the amplified difference voltage ΔAV BE and the base-to-emitter voltage V BEQ6 to vary in equal and opposite directions, thereby leaving the reference voltage V REF unchanged.

One of the advantages of the present invention is that the present invention significantly increases the magnitude of the difference voltage ΔV BE . The base-to-emitter voltage V BEQ6 of transistor Q 6 is approximately 625 mV@50° C. Thus, to provide a positive temperature coefficient that matches the negative temperature coefficient of the base-to-emitter voltage V BEQ6 of transistor Q 6 , 625 mV@50° C. must also be dropped across resistor R 3 .

In circuit 100 , approximately 64.2 mV@50° C. is dropped across resistor R 3 when the current densities differ by a factor of 10. Similarly, approximately 64.2 mV@50° C. is dropped across resistor R 3 in circuit 200 when the ratio of the emitter area A 2 of transistor Q 2 to the emitter area A 1 of transistor Q 1 is 10, i.e., A 2 /A 1 =10.

As noted above, in circuit 100 , the amplified difference voltage ΔAV BE (VR 2 ) is equal to the resistor ratio R 2 /R 3 times the difference voltage ΔV BE . Thus, in circuit 100 , a resistor ratio of 9.7 is needed to amplify the 64.2 mV to 625 mV. The difference voltage ΔV BE typically varies by approximately ±2.66 mV (based on a statistical estimate). Thus, after being amplified 9.7 times, the amplified difference voltage ΔAV BE across resistor R 2 in circuit 100 varies by approximately ±25.802 mV.

In accordance with the present invention, as shown in FIG. 3 , since transistors Q 1 and Q 3 have the same-sized emitter areas, and transistors Q 2 and Q 4 have the same-sized emitter areas, transistors Q 3 and Q 4 double the magnitude of the difference voltage ΔV BE (VR 1 across resistor R 1 and VR 2 across resistor R 2 ) to approximately 128.4 mV@50° C. (when currents I 1 and I 2 are equal).

Thus, to cancel the negative temperature coefficient of the base-to-emitter voltage V BEQ6 of transistor Q 6 , the 128.4 mV dropped across resistor R 2 in circuit 300 must be amplified by approximately 4.9 to obtain the same 625 mV. As a result, the amplified difference voltage ΔAV BE across resistor R 3 in circuit 300 only varies by approximately ±12.9 mV, a 50% reduction over the prior art.

In the preferred embodiment of the present invention, first and second currents I 1 and I 2 are not equal. Instead, second current I 2 is L times larger than first current I 1 . By setting second current I 2 to be L times larger than first current I 1 , the emitter current densities of transistors Q 2 /Q 4 are not just N times larger than the emitter current densities of transistors Q 1 /Q 3 , but are L*N times larger.

This further increases the magnitude of the difference voltage ΔV BE (VR 1 across resistor R 1 and VR 2 across resistor R 2 ) which is defined in equation 1 as:

ΔV BE =2V T (ln(L*N))  EQ. 1

where V T is the thermal voltage kT/q.

For N=L=8, the difference voltage ΔV BE is approximately 232 mV@50° C. As a result, the gain required to amplify 232 mV to 625 mV is only 2.7. Thus, in this example, the amplified difference voltage ΔAV BE across resistor R 3 varies by approximately ±7.18 mV.

Another advantage of the present invention is that circuit 300 can be easily trimmed. As discussed above, resistors R 1 and R 2 are nominally the same. However, by modifying the resistance provided by resistor R 2 , the magnitude of the collector current I CQ5 can be adjusted as needed.

FIG. 4 shows a schematic diagram that illustrates a voltage reference circuit 400 in accordance with the present invention. Circuit 400 is similar to circuit 300 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 4 , circuit 400 differs from circuit 300 in that circuit 400 includes a current source 408 that outputs a current I 4 which defines the magnitude of current I 3 . Circuit 400 also differs from circuit 300 in that circuit 400 includes a base width compensation circuit 410 which is connected to output circuit 316 . Circuit 410 reduces variations in the base-to-emitter voltage V BE6 of transistor Q 6 by reducing the effect of the base width on the base-to-emitter voltage V BE6 .

The base-to-emitter voltage V BE6 of transistor Q 6 is given by equation 2 as:

V BE6 =(kT/q)ln(I CQ6 /I S6 )  EQ. 2

where I CQ6 represents the collector current of transistor Q 6 , and I S6 represents the substrate current of transistor Q 6 .

The collector current I CQ6 , in turn, is highly influenced by variations in the base width of transistor Q 6 due to the relationship between the collector current I CQ6 and the beta of transistor Q 6 (i B β=i C ). Beta β is given by equation 3 as:

1/β=((W B /L PB ) 2 )/2+(N DB W B D nE )/(D PB N AE W E )+(W EB /τ 0 )(N DB W B /D PB 2n i e qVeb/2kT )  EQ. 3

where W B represents the base width, L PB represents the diffusion length of the minority carriers in the base region, N DB represents the donor concentration within the base region, D nE represents the diffusivity of electrons in the emitter, D PB represents the diffusivity of holes in the base region, N AE represents the acceptor concentration in the emitter, W E represents the emitter depth, W EB/τ represents the recombination factor, and 2n i e qVeb/2kT represents the recombination rate. (Also see “The Physics and Technology of Semiconductor Devices”, page 220, A. S. Grove which is hereby incorporated by reference.)

In addition, the substrate current I S6 is also influenced by variations in the base width of transistor Q 6 , and is given by equation 4 as:

I S6 =qAn PO D N /W B   EQ. 4

where q represents the charge of an electron, A represents the effective emitter area of transistor Q 6 , n PO represents the equilibrium concentration of electrons in the base, and D N represents the electron diffusion constant.

Since both the collector current I CQ6 and the substrate current I S6 are influenced by variations in the base width W B of transistor Q 6 , variations in the base width W B of transistor Q 6 also cause variations in the base-to-emitter voltage V BE6 of transistor Q 6 which, in turn, causes variations in the reference voltage V REF .

Returning to FIG. 4 , circuit 410 includes an amplifying transistor Q 7 , current dividing transistors Q 8 -Q 10 , an amplifying transistor Q 11 , and a resistor R 4 . Transistor Q 7 , which is formed to have an emitter area that is the same size as the emitter area of transistor Q 4 , has a collector, a base connected to the base of transistors Q 3 and Q 5 , and an emitter.

Resistor R 4 , in turn, has a first end connected to the emitter of transistor Q 7 and a second end connected to the second end of resistor R 2 , and has a resistance which is N times larger than the resistance provided by resistors R 1 and R 2 .

Transistor Q 8 has a collector and a base connected to the collector of transistor Q 7 , and an emitter connected to a bias voltage V BIAS . Transistor Q 9 has a collector connected to the base of transistor Q 6 , a base connected to the base of transistor Q 8 , and an emitter connected to the bias voltage V BIAS .

Transistor Q 10 has a collector, a base connected to the base of transistor Q 8 , and an emitter connected to the bias voltage V BIAS . Transistors Q 9 and Q 10 have collector areas that are the 1/Mth the size as the collector area of transistor Q 8 . Further, transistor Q 11 , which is matched to transistor Q 6 , has a collector connected to current source 408 to receive the current I 4 , a base connected to the collector of transistor Q 10 , and an emitter connected to the second end of resistor R 2 .

Transistors Q 3 , Q 5 , and Q 7 also form a resistor-ratioed current mirror. Since transistor Q 7 has an emitter area that is 1/Nth the size of the emitter areas of transistors Q 3 and Q 5 , resistor R 4 provides a resistance that is N times larger than resistors R 1 and R 2 , and the current mirror configuration forces the base-to-emitter voltages V BE of transistors Q 3 , Q 5 , and Q 7 to be equal, the collector current I CQ7 of transistor Q 7 is 1/Nth the size of the collector current I CQ5 of transistor Q 5 .

The collector current I CQ7 of transistor Q 7 is divided by M by transistors Q 8 -Q 10 , utilizing collector area ratioing, to produce two matched collector currents I CQ9 and I CQ10 . Thus, the collector current I CQ9 , which provides the base current for transistor Q 6 , and the collector current I CQ10 , which provides the base current for transistor Q 11 , are both equal to the collector current of transistor Q 5 divided by M*N (I CQ5 /M*N). (The value N*M can be chosen to be equal to the nominal (npn) beta of the process.)

The beta of transistor Q 11 , which is nominally the same as the beta of transistor Q 6 , defines the collector current of transistor Q 11 . Current source 408 , in turn, forms the current I 3 by mirroring the current I 4 so that the collector current I CQ6 of transistor Q 6 matches the collector current I CQ11 of transistor Q 11 .

Thus, since the base and collector currents of transistor Q 6 are defined, the beta of transistor Q 6 is also defined (i c /i B =β). The underlying assumption is that the substrate current is inversely proportional to beta. This assumption, however, is not exact. As a result, defining the beta of transistor Q 6 in this manner reduces by approximately one-half the variation in the base-to-emitter voltage V BE6 (EQ. 2) due to the influence of the base width W B . The compensation that is provided to the base-to-emitter voltage V BE6 , however, is precise to within the beta matching of transistors Q 6 and Q 11 when operated under identical conditions.

Conventionally, the base-to-emitter voltage V BE of a transistor varies by approximately +18 mV at 50° C. due to the influence of the base width W B when the diffused regions are formed by chemical doping processes, and by approximately ±4 mV at 50° C. when the diffused regions are formed by ion implantation processes.

Thus, circuit 410 reduces the variation in the base-to-emitter voltage V BE of transistor Q 6 to approximately ±9 mV at 50° C. when the diffused regions are formed by chemical doping processes, and to approximately ±2 mV at 50° C. when the diffused regions are formed by ion implantation processes.

As with circuit 300 , circuit 400 can also be easily trimmed. As discussed above, resistors R 1 and R 2 are nominally the same, while resistor R 4 is N times larger. By modifying the resistance provided by resistor R 4 , the magnitudes of the collector current I CQ7 can be adjusted as needed.

FIG. 5 shows a schematic diagram that illustrates a voltage reference circuit 500 in accordance with the present invention. Circuit 500 is an example of a specific embodiment of circuit 400 when circuit 400 is operated with substantially equal first and second currents I 1 and I 2 .

As shown in FIG. 5 , circuit 500 includes a start-up circuit 510 that insures that the difference voltage ΔV BE is developed across resistor R 1 when power is applied. In operation, when the difference voltage ΔV BE is collapsed to ground (the off condition), transistor QSU 2 sinks current from the PNP current source transistors QSU 3 -QSU 6 which, in turn, causes a current ISU to flow into current source 310 from output circuit 316 .

FIG. 6 shows a schematic diagram that illustrates a voltage reference circuit 600 in accordance with the present invention. Circuit 600 is another example of a specific embodiment of circuit 400 when circuit 400 is operated with the second current I 2 being L times greater than the first current I 1 . Circuit 600 is similar to circuit 500 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 6 , circuit 600 differs from circuit 500 in that circuit 600 includes a saturation prevention transistor 610 which is placed between transistors Q 6 and Q 11 , and ground. When the second current I 2 is larger than the first current I 1 , transistor Q 5 can saturate. Transistor 610 prevents this from happening, and also doubles the value of the reference voltage V REF , i.e., from 1.25 volts to 2.50 volts.

FIG. 7 shows a schematic diagram that illustrates a voltage reference circuit 700 in accordance with the present invention. Circuit 700 is similar to circuit 400 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 7 , circuit 700 differs from circuit 400 in that circuit 700 includes a base width compensation circuit 710 which is connected to circuit 316 . As noted above, the compensation provided to the base-to-emitter voltage V BE6 by compensation circuit 410 is based on the assumption that the substrate current is inversely proportional to beta.

Experimentally, the base-to-emitter voltage V BE of transistor Q 6 has been found to vary as the −⅔ power of beta β (this corresponds to about equal contributions from the linear and squared base width W B terms in equation 3). Circuit 710 provides this compensation and, as a result, substantially eliminates the variation in the base-to-emitter voltage V BE of transistor Q 6 .

Circuit 710 includes a transistor Q 12 that has a collector, a base connected to the collector, and an emitter connected to the collector of transistor Q 11 ; and a transistor Q 13 that has a collector connected to a voltage Vcc, a base, and an emitter connected to the collector of transistor Q 12 .

In addition, circuit 710 also includes a transistor Q 14 which has a collector, a base connected to the emitter of transistor Q 12 , and an emitter; and a current source 712 which has a first end connected to the voltage Vcc, and a second end connected to the base of transistor Q 13 and the collector of transistor Q 14 .

Circuit 710 further includes a transistor Q 15 that has a collector, a base connected to the collector, and an emitter connected to the emitter of transistor Q 14 and ground; a transistor Q 16 that has a collector, a base connected to the collector, and an emitter connected to the collector of transistor Q 15 ; and a transistor Q 17 that has a collector connected to current source 408 , a base connected to the base of transistor Q 13 , and an emitter connected to the collector of transistor Q 16 .

In operation, as discussed above with respect to FIG. 4 , the base current of transistor Q 11 is equal to the collector current of transistor Q 5 divided by M*N, i.e., I CQ5 /M*N. As a result, the collector current of transistor Q 11 is equal to βI CQ5 /M*N (the beta of transistor Q 11 times the base current).

Compensation circuit 710 sinks the current I 4 from current source 408 , which is equal to I CQ5 (β/M*N) ⅔ , and changes the current I 4 to be equal to the collector current βI CQ5 /M*N of transistor Q 11 . Current source 408 mirrors the current I 4 to output the current I 3 .

As a result, the collector current of transistor Q 6 is equal to I CQ5 (β/M*N) ⅔ . Thus, since the collector current of transistor Q 6 varies as the −⅔ power of beta β, the variation in the base-to-emitter voltage V BE of transistor Q 6 is substantially eliminated.

With respect to circuit 710 , the collector current of transistor Q 11 , which is equal to βI CQ5 /M*N, flows through transistors Q 12 and Q 13 . In addition, current source 712 sources a current I 5 which flows through transistor Q 14 . Current I 5 is independently derived and is also proportional to absolute temperature. Further, the current I 4 flows through transistors Q 15 -Q 17 .

The relationship between these currents is given by equation 5 as:

(kT/q)[(ln(I5/I S )+(2ln(βI CQ5 /M*N*I S ))]=3(kT/q)ln(I4/I S )  EQ. 5

where kT/q represents the thermal voltage, and I S represents the substrate current.

Simplifying provides the equality given in equation 6:

((I5 3 )(β/M*N) 2 )/I S 3 =I4 3 /I S 3 .  EQ. 6

Further simplifying provides equations 7 and 8 as:

((I5) 3 )(β/M*N) 2 =I4 3 ,  EQ. 7 and

I4=I5(β/M*N) ⅔ .  EQ. 8

Thus, since the current I 4 defines the current I 3 (mirrors the current in this case), the current I 3 is also equal to I 5 (β/M*N) ⅔ . Since the current I 3 varies as the −⅔ power of beta β, variations due to the base width of transistor Q 6 are effectively eliminated.

Thermal shutdown circuits are frequently used in conjunction with bandgap reference circuits to prevent the destruction of the device under extreme loading or temperature conditions. FIG. 8 shows a schematic diagram that illustrates a thermal shutdown circuit 800 in accordance with the present invention.

As shown in FIG. 8 , circuit 800 includes first and second dividing resistors RD 1 and RD 2 . Resistor RD 1 has a first end connected to the reference voltage V REF , and a second end; while resistor RD 2 has a first end connected to the second end of resistor RD 1 , and a second end connected to ground.

In addition, circuit 800 also includes a sense transistor 812 that has a base connected to the first end of resistor RD 2 , an emitter connected to ground, and a collector connected to the power dissipating functions of the device.

In operation, a resistively divided fraction of the reference voltage V REF is applied to the base of transistor 812 which, during normal operation, turns off transistor 812 . When temperature increases, the base-to-emitter voltage of transistor 812 falls which turns on transistor 812 . Further decreases in the base-to-emitter voltage from increasing temperature cause an exponential increase in the collector current which, in turn, shuts down some or all of the power dissipating functions of the device.

It is frequently desirable to have sense transistor 812 placed close to the power devices that are monitored by sense transistor 812 , while having circuit 300 or 400 placed away from such devices to minimize thermal gradients that would disturb the circuit.

Since the thermal drift of the base-to-emitter voltage V BE of transistor 812 is −2 mV/° C., the shutdown will occur at some elevated temperature determined by the base voltage. Given that the sensing transistor 812 senses the reference voltage V REF , the variation in the conduction of transistor 812 is dependent on the variation in the reference voltage V REF .

These combined effects can cause a large variability in the thermal shutdown temperature. If only the reference voltage V REF is trimmed, the remaining variability of circuit 800 is left unaffected. The still fairly large uncertainty in the shutdown temperature is usually tolerated rather than committing more resources for a second trim network.

For circuit 800 , if the reference voltage V REF is assumed to have been trimmed, the remaining variability is mostly due to the large range in the base width of transistor 812 which effects the substrate current Is term in the base-to-emitter voltage of transistor 812 .

At a typical shutdown temperature of 170° C., a thermal voltage of approximately 38 mV implies that the range of shutdown temperatures is V BEQ6 /(2 mV/° C.)=(38 mV)ln2/(2 mV/° C.) or about ±13° C. (This is the result for a trimmed bandgap circuit where transistor 812 has been removed from the bandgap circuit area, and has diffusion regions from applied chemicals. When transistor 812 has diffusion regions formed from ion implantation, the result is (38 mV)ln1.2/(2 mV/° C.)=±6.9 mV or about ±3.45° C.)

FIG. 9 shows a schematic diagram that illustrates a bandgap voltage reference circuit 900 in accordance with the present invention. Circuit 900 is similar to circuit 400 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 9 , circuit 900 differs from circuit 400 in that circuit 900 includes a shutdown circuit 910 . Circuit 910 , in turn, includes first and second dividing resistors RD 1 and RD 2 . Resistor RD 1 has a first end connected to the output of buffer 320 , and a second end; while resistor RD 2 has a first end connected to the second end of resistor RD 1 , and a second end connected to ground.

In addition, circuit 910 also includes an operational amplifier (op amp) 920 that has a positive input connected to the first end of resistor RD 2 , a negative input connected to the base of transistor Q 6 , and an output.

In operation, a resistively divided fraction of the reference voltage V REF is applied to the non-inverting (positive) input of op amp 920 , while the base voltage of transistor Q 6 is applied to the inverting (negative) input of op amp 920 . As the temperature changes, the base voltage of transistor Q 6 changes.

The changing base voltage changes the difference between the voltages on the inverting and non-inverting inputs of op amp 920 which, in turn, places a voltage on the output in response to the change. The power dissipating functions of the device response to the output voltage and shut down the operation of the circuit when the output voltage reaches a predefined level.

If circuit 900 is untrimmed (via resistors R 2 or R 4 ), op amp 920 provides a significant reduction in the thermal voltage, and an even greater reduction when trimmed. (Remote sensing can also be accomplished by placing a diode-connected sense device, identical to transistor Q 6 and similarly biased, close to the point to be monitored. A small additional error (±1° C.) is incurred mostly due to the area mismatch between the sense device and transistor Q 6 .)

FIG. 10 shows a schematic diagram that illustrates a bandgap voltage reference circuit 1000 in accordance with the present invention. Circuit 1000 is similar to circuit 900 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 10 , circuit 1000 differs from circuit 900 in that circuit 1000 includes a current source 1010 that, in addition to currents I 3 and I 4 , outputs a current I 3 ′ which is mirrored equivalent of current I 3 , and a sense transistor 1012 that has a collector connected to receive the current I 3 ′, a base connected to receive a voltage from the collector of transistor 1012 , and an emitter connected to the second end of resistor R 2 . As further shown in FIG. 10 , the negative input of op amp 920 is connected to the base of transistor 1012 rather than to the base of transistor Q 6 .

In operation, circuit 1000 operates the same as circuit 900 except that op amp senses the base-to-emitter voltage of transistor 1012 rather than the base-to-emitter voltage of transistor Q 6 . The advantage provided by transistor 1012 is that transistor 1012 may be located away from the bandgap circuit and closer to the power generating circuits which tend to overheat before the bandgap circuit.

FIG. 11 shows a schematic diagram that illustrates a bandgap voltage reference circuit 1100 in accordance with the present invention. Circuit 1100 is similar to circuit 300 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 11 , circuit 1100 differs from circuit 300 in that circuit 1100 includes a unity-gain buffer 1110 which has a high input impedance, and resistors R 5 and R 6 in lieu of amplification circuit 314 and output circuit 316 .

As further shown in FIG. 11 , the collector of transistor Q 2 is connected to the bases of transistors Q 1 and Q 2 through buffer 1110 . In addition, resistor R 5 is connected between the output of buffer 1110 and ground, while resistor R 6 is connected between resistor R 1 and ground, and to the emitter of transistor Q 4 .

In operation, circuit 1100 outputs a reference voltage V REF which is defined by the voltage VR 5 across resistor R 5 . The voltage VR 5 , in turn, is defined by a voltage V BEC which represents the combined base-to-emitter voltage drops of transistors Q 1 and Q 3 , and a voltage VRC which represents the combined voltage drops across resistors R 1 and R 6 . The voltage V BEC has a negative temperature coefficient, while the voltage VRC has a positive temperature coefficient that is equal in magnitude to the negative temperature coefficient of the voltage V BEC .

Since the voltages V BEC and VRC have equal but opposite temperature coefficients, changes in temperature cause the voltages V BEC and VRC to vary in equal and opposite directions, thereby leaving the voltage VR 5 unchanged. As a result, the voltage VR 5 is temperature compensated.

The voltage VRC is developed by utilizing bipolar transistors which are forced to operate with emitter currents that have unequal current densities. As noted above, transistors Q 1 /Q 3 and Q 2 /Q 4 are forced to operate with unequal emitter current densities when the second current I 2 is L times greater than the first current I 1 , and the emitter area of transistors Q 1 and Q 3 are N times larger than the emitter areas of transistors Q 2 and Q 4 , respectively.

As a result, the difference voltage ΔV BE , which has a positive temperature coefficient, is defined as the difference between the combined base-to-emitter voltages of transistors Q 2 and Q 4 ; and the combined base-to-emitter voltages of transistors Q 1 and Q 3 , i.e., ΔV BE =(V BEQ2 +V BEQ4 )−(V BEQ1 +V BEQ3 ).

As shown in FIG. 11 , the combined base-to-emitter voltages V BEQ2 and V BEQ4 of transistors Q 2 and Q 4 are equal to the combined base-to-emitter voltages V BEQ1 and V BEQ3 of transistors Q 1 and Q 3 , and a voltage VR 1 across resistor R 1 , i.e., V BEQ2 +V BEQ4 =V BEQ1 +V BEQ3 +VR 1 .

Since the difference voltage ΔV BE is equal to the difference between the base-to-emitter voltages (ΔV BE =(V BEQ2 +V BEQ4 )−(V BEQ1 +V BEQ3 )), the difference voltage ΔV BE is also equal to the voltage VR 1 across resistor R 1 . In addition, since the difference voltage ΔV BE has a positive temperature coefficient, the voltage VR 1 across resistor R 1 must also have a positive temperature coefficient. Thus, when the second current I 2 is L times greater than the first current I 1 , approximately 232 mV are dropped across resistor R 1 (for N=L=8) at 50° C.

Since the voltage VR 1 is equal to the difference voltage ΔV BE the emitter current I EQ3 of transistor Q 3 , which flows through resistor R 1 , is also proportional to the voltage difference ΔV BE . In addition, the emitter current I E4 of transistor Q 4 is additionally proportional to ΔV BE since the second current I 2 is L times greater than the first current I 1 .

As a result, the combined emitter currents I EQ3 and I EQ4 flowing through resistor R 6 are proportional to the difference voltage ΔV BE . Thus, the voltage VR 6 across resistor R 6 is proportional to the difference voltage ΔV BE and, therefore, has a positive temperature coefficient.

The voltage V BEC , which represents the combined base-to-emitter voltage drops of transistors Q 1 and Q 3 , is approximately equal to 1250 mV at 50° C. Since 232 mV are dropped across resistor R 1 , approximately 1,018 mV need to be dropped across resistor R 6 . As a result, the difference voltage ΔV BE (VR 1 ) across resistor R 1 need only be amplified by a gain factor of 5.4.

FIG. 12 shows a schematic diagram that illustrates a bandgap voltage reference circuit 1200 in accordance with the present invention. Circuit 1200 is similar to circuit 1100 and, as a result, utilizes the same reference numerals to designate the structures which are common to both circuits.

As shown in FIG. 12 , circuit 1200 differs from circuit 1100 in that circuit 1200 includes a resistor R 7 between the output of buffer 1110 and resistor R 5 . Resistor R 7 allows the magnitude of the reference voltage V REF to be amplified.

The voltage VR 5 across resistor R 5 (along with the resistance of resistor R 5 ) defines the current through resistor R 5 which, in turn, defines the voltage VR 7 across resistor R 7 . Thus, since the voltage VR 5 is temperature compensated, the voltage VR 7 is also temperature compensated, thereby leaving the reference voltage V REF temperature compensated.

In further accordance with the present invention, by cross-quading transistors Q 1 -Q 4 of circuits 1100 and 1200 , the variability of the difference voltage ΔV BE can be reduced by 2 (the square root of two). FIG. 13 shows a block diagram that illustrates the cross-quading of transistors Q 1 -Q 4 in accordance with the present invention.

It should be understood that various alternatives to the embodiment of the invention described herein may be employed in practicing the invention. Thus, it is intended that the following claims define the scope of the invention and that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

1. A voltage reference circuit comprising:a first current source that outputs a first current and a second current; and a difference circuit connected to the first current source, the difference circuit having: a first transistor having a collector connected to receive the first current, a base, and an emitter that outputs a first emitter current; a second transistor having a collector connected to receive the second current, a base connected to the base of the first transistor, and an emitter, the base of the first transistor and the base of the second transistor being electrically coupled to the collector of the second transistor; a third transistor having a collector connected to the emitter of the first transistor, a base coupled to the collector of the third transistor, and an emitter; a fourth transistor having a collector connected to the emitter of the second transistor, a base coupled to the collector of the fourth transistor, and an emitter; and a first resistor having a first end connected to the emitter of the third transistor, and a second end connected to the emitter of the fourth transistor, the first resistor having a first difference voltage across the first and second ends, the first difference voltage having a positive temperature coefficient.

2. The circuit of claim 1 wherein the base of the first transistor and the base of the second transistor are connected to the collector of the second transistor.

3. The circuit of claim 2 wherein the first transistor has an emitter area that is N times larger than the emitter area of the second transistor.

4. The circuit of claim 3 wherein the third transistor has an emitter area that is N times larger than the emitter area of the fourth transistor.

5. The circuit of claim 4 wherein the second current is L times larger than the first current.

6. The circuit of claim 4 wherein the first and second currents are equal.

7. The circuit of claim 2 and further comprising an amplification circuit connected to the difference circuit, the amplification circuit forming a second difference voltage that is proportional to the first difference voltage, and amplifying the second difference voltage to form an amplified difference voltage, the amplified difference voltage having a positive temperature coefficient.

8. The circuit of claim 7 wherein the amplification circuit includes:a fifth transistor that has a collector, a base connected to the base of third transistor, and an emitter; a second resistor having a first end connected to the emitter of the fifth transistor, a second end connected to the second end of the first resistor, and a resistance equal to the resistance of the first resistor, the second resistor having the difference voltage across the first and second ends of the second resistor; and a third resistor having a first end connected to the collector of the fifth transistor, and a second end, the third resistor having the amplified difference voltage across the first and second ends of the third resistor.

9. The circuit of claim 8 wherein the second resistor is variable.

10. The circuit of claim 8 wherein the third transistor and the fifth transistor have equal emitter areas.

11. The circuit of claim 8 and further comprising an output circuit having a sixth transistor connected to the amplification circuit, the sixth transistor having a base-to-emitter voltage, the output circuit summing the amplified difference voltage and the base-to-emitter voltage to output a reference voltage, the base-to-emitter voltage having a negative temperature coefficient.

12. The circuit of claim 11wherein the output circuit includes a second current source that outputs a third current; wherein the sixth transistor has a collector connected to receive the third current, a base connected to the collector of the fifth transistor, and an emitter connected to the second end of the second resistor; and wherein the output circuit includes a buffer having an input connected to the collector of the sixth transistor, and an output connected to the second end of the third resistor.

13. The circuit of claim 11wherein the output circuit includes a second current source that outputs a third current and a fourth current; wherein the sixth transistor has a collector connected to receive the third current, a base connected to the collector of the fifth transistor, and an emitter connected to the second end of the second resistor, the sixth transistor having the base-to-emitter voltage; and wherein the output circuit includes a buffer having an input connected to the collector of the sixth transistor, and an output connected to the second end of the third resistor.

14. The circuit of claim 13 and further comprising a first compensation circuit connected to the output circuit that provides a base current and a collector current to the sixth transistor where the substrate current of the sixth transistor is defined to be inversely proportional to the beta of the sixth transistor.

15. The circuit of claim 14 wherein the first compensation circuit includes:a seventh transistor that has a collector, a base connected to the base of the third and fifth transistors, and an emitter, the seventh transistor and the fourth transistor having equal emitter areas; a fourth resistor that has a first end connected to the emitter of the seventh transistor, a second end connected to the second end of the second resistor, and a resistance that is N times larger than the resistance of the second resistor; an eighth transistor that has a collector and a base connected to the collector of the seventh transistor, and an emitter connected to a bias voltage; a ninth transistor that has a collector connected to the base of the sixth transistor, a base connected to the base of the eighth transistor, and an emitter connected to the bias voltage; a tenth transistor that has a collector, a base connected to the base of the eighth transistor, and an emitter connected to the bias voltage, the ninth and tenth transistors having a collector area that is 1/Mth the area of the collector area of the eighth transistor; and an eleventh transistor that has a collector connected to the second current source to receive the fourth current, a base connected to the collector of the tenth transistor, and an emitter connected to the second end of the second resistor, the eleventh transistor being matched to the sixth transistor.

16. The circuit of claim 14 and further comprising a second compensation circuit connected to the first compensation circuit and the output circuit, the second compensation providing a base current and a collector current to the sixth transistor where the substrate current of the sixth transistor is defined to be equal to −⅔ power of the beta of the sixth transistor.

17. The circuit of claim 11 and further comprising a thermal shut-down circuit connected to the output circuit, the thermal shut-down circuit including:a resistive divider that establishes a voltage at a node that is a fraction of the reference voltage; and a shut-down transistor having a collector, a base connected to the node, and an emitter.

18. The circuit of claim 11 and further comprising a thermal shut-down circuit connected to the output circuit, the thermal shut-down circuit including:a resistive divider that establishes a voltage at a node that is a fraction of the reference voltage; and an operational amplifier having a positive input connected to the node, and a negative input connected to the base of the sixth transistor.

19. The circuit of claim 12wherein the current source outputs a compensation current equal to the third current, and further comprising a thermal shut-down circuit connected to the output circuit, the thermal shut-down circuit including: a resistive divider that establishes a voltage at a node that is a fraction of the reference voltage; an operational amplifier having a positive input connected to the node, and a negative input; and a shut-down transistor having a collector connected to receive the compensation current, a base connected to the negative input of the operational amplifier and to receive a voltage on the collector of the shut-down transistor, and an emitter.

20. The circuit of claim 1 and further including:a buffer having an input connected to the collector of the second transistor, and an output connected to the base of the first transistor and the base of the second transistor, wherein the bases of first and second transistors are electrically coupled to the collector of the second transistor via the buffer; a second resistor having a first end connected to the second end of the first resistor and the emitter of the fourth transistor, and a second end; and a third resistor having a first end connected to the base of the first transistor, and a second end.

21. The circuit of claim 20 and further including a fourth resistor having a first end connected to the output of the buffer, and a second end connected to the first end of the third resistor.