EP2067090B1 - Voltage reference electronic circuit - Google Patents

Abstract

The invention relates to a temperature-independent voltage reference circuit. The circuit comprises a first circuit of bandgap type providing a first-order temperature-stable voltage, on the basis of a bipolar transistor base-emitter voltage having a negative slope of variation as a function of temperature, and of a voltage or a current having a positive slope of variation as a function of temperature provided by a generator of current proportional to absolute temperature. The base currents of the PMOS transistors thereof are compensated in such a manner that the output current is proportional to a collector current and not an emitter current. A summator establishes a linear combination, with respective weighting coefficients, of three voltages which are respectively the output voltage of the first circuit, the output voltage of a second circuit providing a voltage proportional to the difference between the absolute temperature T and a reference temperature Tr, and the output voltage of a third circuit providing a voltage proportional to the square of this difference.

Description

The invention relates to electronic integrated circuits and more specifically to the production of a temperature-independent voltage reference circuit, based on the properties of silicon bipolar transistors.

The establishment of a reference voltage in a silicon integrated circuit most often comprises the realization of a circuit generically called a "bandgap reference circuit" because of the fact that it uses physical properties intrinsic silicon to ensure constant voltage despite temperature changes; the term bandgap refers to the difference in intrinsic energy that exists between the valence and conduction bands of silicon, a difference that is largely independent of temperature over a wide range of temperatures.

A bandgap reference circuit conventionally uses the combination of a base-emitter voltage of a transistor, which varies negatively (and approximately linearly) with the temperature, and a current or voltage that varies positively. (and almost linearly) with the temperature. For example, the difference of the base-emitter voltages of two different emitter surface transistors, diode-mounted and powered by the same current sources, is a voltage that varies positively with temperature.

The result of this combination is however not perfect over a wide range of temperatures, including a range that goes from -50 ° C to + 120 ° C: it can be seen that even with compensation circuits and with the finest adjustments circuit parameters (transistor sizes, resistor values, currents, etc.) result in a nearly flat voltage variation curve to ambient temperatures but which bends for both low temperatures and high temperatures .

Examples of bandgap reference circuits with temperature-dependent curvature corrections are given in the literature, for example: " A curvature corrected low-voltage bandgap reference "from Gunawan, Meijer, Fondrie, Huijsing in IEEE JSSC June 1993 ; or " A new Fahrenheit temperature sensor "by R. Pease in IEEE JSSC December 1984 . These corrections are complex.

The problem is made more critical for CMOS technology circuits, in which the bipolar transistors that are available to realize the voltage reference circuit, are PNP transistors of poor properties and widely dispersed characteristics from circuit to circuit. ; these transistors are in fact principally transistors that can be described as parasitic transistors formed from the P-type substrate, N-type wells of the PMOS transistors and source diffusions of these PMOS transistors. However, it is important to be able to achieve stable temperature voltages even in CMOS technology circuits that do not have other bipolar transistors available.

In general, obtaining a precise and reproducible reference voltage, stable over a wide range of temperatures (-50 ° C. to + 120 ° C.), poses problems. The object of the invention is to propose a solution that improves the performance of the previous circuits. The patent US 7,091,713 describes a bandgap type circuit with various compensations.

According to the invention there is provided a voltage reference circuit having a first bandgap circuit providing a first order temperature stable voltage or current from a PTAT current generator providing a temperature proportional current. absolute, this generator comprising, between a power supply and a ground, two parallel branches, one comprising a first MOS transistor in series with a bipolar transistor mounted diode, the other comprising a second MOS transistor identical to the first, a resistor and a second bipolar transistor having a transmitter area N times greater than the emitter area of the first, with a differential amplifier which drives the MOS transistors and which establishes in the resistor a voltage drop equal to the difference of the base voltages; emitter of the two bipolar transistors, characterized in that there is provided means for injecting at the junction point in be the first bipolar transistor and the first MOS transistor a current which is equal to the base current of the first bipolar transistor and means for injecting at the junction point of the second bipolar transistor and the resistor a current which is equal to the base current of the second bipolar transistor, so that the output current of the current generator proportional to the temperature is equal to the collector current and not the emitter current of the second bipolar transistor.

• d'une tension base-émetteur de transistor bipolaire ayant une pente de variation négative en fonction de la température
• et du courant issu du générateur de courant PTAT (ayant une pente de variation positive en fonction de la température).

The first bandgap circuit provides a stable first-order temperature current or voltage from

• a bipolar transistor base-emitter voltage having a negative variation slope as a function of temperature
• and current from the PTAT current generator (having a slope of positive variation as a function of temperature).

• la tension ou le courant de sortie du premier circuit de type bandgap,
• la tension ou le courant de sortie d'un deuxième circuit fournissant une tension ou un courant proportionnel à la différence entre la température absolue T et une température de référence Tr,
• la tension ou le courant de sortie d'un troisième circuit fournissant une tension ou un courant proportionnel au carré de cette différence.

The voltage reference circuit preferably comprises an adder to establish a linear combination, with respective weighting coefficients, of three values which are respectively

• the voltage or the output current of the first bandgap circuit,
• the output voltage or current of a second circuit providing a voltage or current proportional to the difference between the absolute temperature T and a reference temperature Tr,
• the output voltage or current of a third circuit providing a voltage or current proportional to the square of this difference.

Preferably, the first bandgap circuit comprises, in addition to the current generator PTAT supplying a current proportional to the absolute temperature, means for producing a current which is the ratio between a bipolar transistor base-emitter voltage and a resistance value. this current being applied to an input of an operational amplifier of the summator.

The circuit (called "thermometer" circuit) providing a voltage proportional to the difference (T-Tr) preferably comprises a current generator proportional to the absolute temperature (which may be the same as the previous one), means for applying this current a resistor and a bipolar transistor, and a differential amplifier for establishing a voltage which is the difference between the base-emitter voltage of this bipolar transistor and the voltage drop across the resistor.

The reference temperature is preferably the ambient temperature of about 25 ° C.

• la figure 1 représente le principe de base d'un circuit de type PTAT établissant un courant proportionnel à la température absolue, réalisé dans une technologie CMOS et utilisant les transistors PNP parasites de cette technologie ;
• la figure 2 représente le principe de base d'un circuit de type bandgap fondé sur l'équilibre au premier ordre entre la variation négative d'une tension base-émetteur de transistor bipolaire et la variation positive d'un courant de circuit de type PTAT ;
• la figure 3 représente un autre exemple de réalisation de circuit de type bandgap
• la figure 4 représente l'architecture générale d'un circuit de référence de tension stable en température selon l'invention ;
• la figure 5 représente l'utilisation d'un circuit classique de type bandgap, dans l'architecture selon l'invention ;
• la figure 6 représente un exemple de réalisation de circuit dit circuit "thermomètre" fournissant une tension proportionnelle à T-Tr ;
• la figure 7 représente un exemple de réalisation d'un circuit d'élévation au carré de la tension de sortie du circuit thermomètre ;
• la figure 8 représente un schéma de circuit permettant d'améliorer le comportement du circuit en éliminant l'influence néfaste du mauvais gain en courant des transistors bipolaires PNP utilisés dans le circuit lorsque celui-ci est réalisé dans une technologie purement CMOS.

Other features and advantages of the invention will appear on reading the detailed description which follows and which is given with reference to the appended drawings in which:

• the figure 1 represents the basic principle of a PTAT circuit establishing a current proportional to the absolute temperature, realized in a CMOS technology and using PNP transistors parasites of this technology;
• the figure 2 represents the basic principle of a bandgap-based circuit based on the first-order equilibrium between the negative variation of a bipolar transistor base-emitter voltage and the positive variation of a PTAT-type circuit current;
• the figure 3 represents another embodiment of a bandgap type circuit
• the figure 4 represents the general architecture of a temperature-stable voltage reference circuit according to the invention;
• the figure 5 represents the use of a conventional bandgap circuit, in the architecture according to the invention;
• the figure 6 represents an exemplary circuit embodiment "thermometer" circuit providing a voltage proportional to T-Tr;
• the figure 7 represents an exemplary embodiment of a squaring circuit of the output voltage of the thermometer circuit;
• the figure 8 is a circuit diagram for improving the behavior of the circuit by eliminating the detrimental influence of the bad current gain of PNP bipolar transistors used in the circuit when it is realized in a purely CMOS technology.

k est la constante de Boltzmann, q la charge de l'électron, T la température absolue, N le rapport des surfaces d'émetteur.On the figure 1 , PNP bipolar transistors T1 and T2 and PMOS transistors Q1 and Q2 form with a differential amplifier A1 the core of a current generator PTAT, that is to say a circuit providing a current proportional to the absolute temperature T. Transistors T1 and T2 are of different emitter surfaces, transistor T2 having a surface N times greater than that of transistor T1. Transistors Q1 and Q2 are identical and constitute variable but identical current sources. Their grids are brought to the same variable potential and their source is at a supply voltage Vdd. The transistor T1 is diode-mounted between the drain of Q1 and GND mass: T1 base and collector are joined and connected to ground, the transmitter is connected to the drain of Q1. The assembly is the same for T2 and Q2 but a resistor R2 is interposed between the drain of T2 and the emitter of Q2. The differential amplifier A1 has its two inputs respectively connected to the drains of Q1 and Q2; it carries out a counter-reaction by acting on the common potential of the gates of these two transistors, therefore on the identical currents which cross them, until finding a point of equilibrium where the potentials of the two drains are identical (at the voltage of input offset near the amplifier). The voltage drop R2.I2 in the resistor R2 then compensates exactly the difference ΔVbe between the base-emitter voltages of T1 and T2; it is known that this difference is proportional to the absolute temperature and the natural logarithm of the ratio N between their emitter surfaces if the two transistors T1 and T2 are of the same technology and placed under the same temperature conditions; the equation is: $$\mathrm{\Delta Vbe}=\left(\mathrm{kT}/\mathrm{q}\right)\mathrm{LOGN}$$

k is the Boltzmann constant, q the charge of the electron, T the absolute temperature, N the ratio of the emitter surfaces.

As a result, the current I2 traversing the resistor R2 automatically adjusts to a value of the form

12 = (kT / q) (LogN) / R2 (for transistors having a current gain sufficiently high so that the base current is negligible in front of the collector current).

The circuit of the figure 1 therefore constitutes a current generator I2 of value proportional to the absolute temperature and varying linearly and positively with the temperature.

From this current 12, with a positive variation, and a resistor R3, it is easy to realize a voltage with a positive variation R3.I2, and it is possible to add to the voltage R3.I2 a base-emitter voltage of a bipolar transistor which varies negatively with temperature.

This addition of two inverse direction of variation voltages is carried out for example by the circuit of the figure 2 : the left part of the figure 2 exactly resume the circuit of the figure 1 and constitutes a PTAT current generator. The current 12 is copied by a PMOS transistor Q3 mounted in current mirror of the transistors Q1 and Q2 (same source potential Vdd, same gate potential provided by the output of amplifier A1). The transistor Q3 is preferably identical to the transistors Q1 and Q2 but it is not mandatory; if it is not identical to them, it must be taken into account in the calculations.

A resistor R3 is connected between the drain of Q3 and the emitter of a PNP transistor T3 diode-mounted like T1 and T2, having its collector and base grounded. The series assembly Q3, R3, T3 is thus mounted as the set Q2, R2, T2 and the current flowing through the resistor R3 is identical to the current I2 which flows through R2.

The potential of the junction point of Q3 and R3 is thus the sum of the base-emitter voltage Vbe3 of T3 and of the voltage drop R3.I2 which has the value R3.I2 = (kT / q) (LogN) R3 / R2. It will be noted that only the ratio of the resistors plays a role in the value of the voltage drop R3.12, this ratio being practically independent of the temperature. The coefficient of positive variation with temperature is (k / q) (LogN) R3 / R2.

The negative variation of the base-emitter voltage Vbe3 of the transistor T3 depends on the technological parameters of the transistor. It is linear in the first order, and the order of magnitude of the coefficient of variation is, for example, -2mV / ° C. It can be determined experimentally for a given technology. Therefore, by correctly choosing the resistor R3 and adding the voltage R3.I2 and the voltage Vbe of the transistor T3, it is possible to obtain a voltage having a zero overall coefficient of variation at the first order. The value chosen for R3 for this purpose obviously depends on the values chosen for N and for R2 as well as on the emitter surface of transistor T3.

The circuit of the figure 2 is a circuit that can be called "heart bandgap circuit" and the voltage EG (T) = R3 (kT / q) (LogN) / R2 + Vbe3 that appears between the output of this circuit and the ground is a voltage that , at the first order, is independent of the temperature.

However, there are second- or third-order effects that cause the EG (T) voltage to exhibit some manufacturing dispersion and is not completely constant with temperature; this is all the more true as the quality of the PNP transistors is worse. However, in many MOS technology circuits, only PNP transistors of poor quality are available (low beta transistors, ie low gain transistors). while running). The input offset voltage of the differential amplifier A1 is also a factor which deteriorates the constancy of the output voltage EG (T).

Another example of embodiment is shown in the figure 3 ; this circuit works in a very similar way to that of the figure 2 and it is shown here because it is easier to use in the architecture of the present invention. In this example, instead of adding two voltages Vbe3 and R3.12 in a branch Q3, R3, T3 as was the case in the figure 2 , two currents are added before converting the sum of these currents into a voltage EG (T). A very similar result is obtained in terms of the addition of voltages, one of which varies positively and the other of which varies negatively. Elements identical to those of the figure 2 have the same references and play the same role; it is mainly the PTAT generator which establishes a current 12 = (kT / q) (LogN) / R2 from the transistors T1 and T2 of different emitter surfaces.

A differential amplifier A2 controls the gate of a PMOS transistor Q4 which is in series with a resistor R4, so as to pass in the resistor R4 a current such that the voltage drop in this resistor is equal to the base-emitter voltage Vbe2 of transistor T2. For this, the differential amplifier A2, at high gain, receives the difference between the voltage across R4 and the base-emitter voltage Vbe2; the current in transistor Q4 automatically adjusts to a value 14 such that R4.I4 = Vbe2. This assembly therefore converts the voltage Vbe2 into a current Vbe2 / R4 in the resistor R4 and in the transistor Q4. A PMOS transistor Q5 copies the current Vbe2 / R4 passing through Q4 (same gate voltage as Q4, same source voltage Vdd); another PMOS transistor Q6 copies the current 12 which passes into the transistor Q2 (same gate voltage as Q2, same source voltage Vdd). The currents of Q5 and Q6, respectively equal to Vbe2 / R4 and 12 = (kT / q) (LogN) / R2 are summed in a load resistor R6. On the diagram of the figure 3 the load resistor is connected between the combined drains of Q5 and Q6 and the mass. It will be seen that the load resistor can also be an input resistor or a loopback resistor of an operational amplifier.

The output voltage EG (T) across the resistor R6 is then: EG (T) = R6 (kT / q) (LogN) / R2 + Vbe2.R6 / R4. The result is therefore substantially identical to that provided by the diagram of the figure 2 .

The figure 8 represents the principle of the present invention.

As has been said, the PNP transistors may be of poor quality and in particular they may have a gain in low beta current and highly dispersed. This is particularly the case when the voltage reference circuit is made in a CMOS technology where the only available bipolar transistors are PNP transistors formed between the P-type substrate, the N-type wells and the source and drain diffusions. PMOS formed in these boxes. These transistors are of poor quality. That is why it is preferable to provide a compensation circuit of the PTAT current generator, which will be described with reference to the figure 8 .

The circuit represented at figure 8 includes, on its right side, the PTAT current generator of the figure 1 and on its left side the compensation circuit whose function is to inject into the emitter of the transistor T1 and into the emitter of the transistor T2 a current equal to the base current Ib which flows through these transistors when the resistor R2 is traveled. by the current 12 proportional to the absolute temperature. By injecting these currents, it is ensured that the equal currents flowing through Q1 and Q2 and thus the current I2 passing through the resistor R2 are not the emitter current of the transistors T1 and T2 but are the collector current Ic. When it is the emitter current, there are inaccuracies because the operating equations of the PTAT generator are based on the calculation of the collector currents of the transistors T1 and T2 of different size. This does not matter when the current gain is high because the difference between the collector current and the emitter current is insignificant. This is more important when the gain is low. With the compensation introduced, the PTAT generator is actually operated from collector currents even if the gain is small.

To achieve this result, the current I2 in Q1 is copied into a branch Q10, T10. The transistor Q10 is identical to Q1 and has its gate and its source at the same potentials as the gate and the source of Q1. Transistor T10 is identical to T1 and has its emitter connected to ground like T1. The base of T10, however, is not connected directly to the mass as that of T1, it is connected to ground by means of a NMOS transistor Q11 mounted diode. This transistor Q11 is therefore traversed by a current Ib which is the basic current of T10, identical to the basic current of T1.

• à l'identique par un transistor Q14 qui injecte son courant égal à Ib dans le point de jonction entre les transistors Q1 et T1.
• à l'identique par un transistor Q15 qui injecte un courant Ib dans le point de jonction entre les transistors Q2 et T2.

The current in Q11 is copied identically in a branch with two transistors Q12 NMOS), Q13 (PMOS diode mounted); from there, this current Ib is still recopied

• identically by a transistor Q14 which injects its current equal to Ib in the junction point between the transistors Q1 and T1.
• identically by a transistor Q15 which injects a current Ib into the junction point between the transistors Q2 and T2.

Finally, a transistor Q16 copies the current Ib of the transistor Q13 to inject it at the junction point of the transistors Q10 and T10.

As a result, the current I2 in the transistors Q1 and Q2 is indeed a collector current of the transistors T1 and T2.

With this scheme, the result is an operation in which the current proportional to the temperature is a transistor collector current and not an emitter current as in the conventional diagrams, so that it is insensitive to the fact that the current gain of PNP transistors are small and scattered. We could also make a diagram on the same principle if the transistors were NPN.

This current gain compensation of the PMOS transistors of the PTAT generator can be applied to a more complex voltage reference circuit in which it is sought to compensate for the curvatures of the reference voltage variation as a function of the temperature towards the highest temperatures. or the lowest.

The diagrams that will now be described use PTAT generators which are represented in simplified form, that is to say without the basic current compensation represented in FIG. figure 8 so as not to weigh down the representation, but it will be understood that these PTAT generators are made in practice as in the figure 8 . However, it should be noted that the schemes which will be described can be used also with PTAT generators which do not incorporate the basic current compensation of the figure 8 because they allow in themselves to improve the stability from the reference voltage to high temperatures and low temperatures.

The figure 4 represents the principle of obtaining a stable reference voltage. In this diagram we use a heart circuit C1 bandgap such as that of the figure 2 or the figure 3 that is to say, using the summation of a voltage Vbe and a voltage proportional to the absolute temperature and giving a reference voltage (or a current) stable in the first order; and we add to the sum EG (T) thus obtained two other voltages, one of which, denoted by E2 (T), comes from a circuit C2 called "thermometer circuit" and the other, denoted by E3 (T) is derived from a circuit C3 of elevation squared which raises squared voltage from the thermometer circuit. By thermometer circuit is meant a circuit capable of establishing a voltage proportional to the difference T-Tr between the absolute temperature T and a reference temperature Tr; the temperature Tr can be the standard ambient temperature of 25 ° C. The squaring circuit is, in turn, capable of establishing a voltage proportional to (T-Tr) ² from a voltage supplied by the thermometer circuit.

An adder ADD performs a linear combination of the three voltages EG (T), E2 (T) and E3 (T), i.e., it adds them with respective weighting coefficients G1, G2, G3 to establish an output voltage Vref = G1.EG (T) + G2.E2 (T) + G3.E3 (T).

The weighting coefficients are chosen to make the output voltage of the summator as constant as possible in the presence of temperature variations. The coefficient G1 can be chosen arbitrarily equal to 1, adjustment parameters such as the value of R6 making it possible to adjust the level of EG (T).

For the circuit C1, which is a basic circuit of the bandgap type, it has been noticed that the output voltage can be considered as being generally of the form: $$\mathrm{EG}\left(\mathrm{T}\right)\mathrm{=}\mathrm{EG}\left(\mathrm{Tr}\right)\mathrm{+}\mathrm{at}\mathrm{.}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)\mathrm{+}\mathrm{b}\mathrm{.}{\left(\mathrm{T}\mathrm{-}\mathrm{<figure-callout\; id="2"\; label="Tr"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">Tr</figure-callout>}\right)}^{\mathrm{2}}$$

This means that the output voltage of the circuit C1 is not constant with the temperature but tends to vary along a curve that can be approximated by a parabola.

The coefficients a and b can be determined experimentally and depend on the scheme used and the technology. EG (Tr) is a value fixed, which is the theoretical value that one would like to have at all temperatures but that in fact only has the reference temperature Tr.

The thermometer circuit C2 and the squaring circuit C3 are intended to compensate for these output voltage variations of the circuit C1. The thermometer circuit should produce a voltage E2 (T) = k2 (T-Tr) to compensate for the term a (T-Tr) and the squaring circuit should produce a voltage E3 (T) = k3. (T-Tr) ² to compensate for the term b (T-Tr) ² . The coefficients G2 and G3 of the linear combination EG (T) + G1.E2 (T) + G3.E3 (T) performed by the adder ADD will have to be adjusted so that k2.G2 = -a and k3.G3 = -b so that the weighted summation of the output voltages of the three circuits C1, C2, C3 results in a voltage Vref = EG (Tr) as independent as possible from the temperature T.

If the circuit C1 supplies an output current rather than a voltage EG (T), this current is converted into voltage in a resistor of the adder ADD. Same note for the outputs of circuits C2 and C3.

The coefficients G2 and G3 are negative if a, b, k1 and k2 are positive. But it must be provided in particular that the signs of a and b may be arbitrary, and it will be provided that the coefficients G2 and G3 may be of negative sign (or alternatively that the outputs E2 (T) and E3 (T) may be have an inverted sign if necessary).

The figure 5 is a practical diagram taking up the heart of the bandgap circuit of the figure 3 and showing how one can perform the desired linear combination using an operational amplifier and several summing resistors. In the case shown, the circuit C1 supplies an output current which is the sum of the currents flowing in the transistors Q5 and Q6: (kT / q) (LogN) / R2 + Vbe2 / R4

The combined outputs of transistors Q5 and Q6, constituting the output of circuit C1, are not applied to a resistor R6 as to the figure 3 but they are applied, which amounts to the same, to an input E1 of an operational amplifier AO looped by a loopback resistor Rs1.

The other input E2 of the amplifier is brought to a reference potential VG (which may be the ground GND or preferably the midpoint between the low supply GND and the high supply Vdd). The potential VG is, as will be seen, the reference with respect to which the thermometer circuit C2 provides a voltage proportional to T-Tr, and the circuit C3 provides a voltage proportional to the square of T-Tr. That is why this potential must also serve as a reference in the adder ADD placed at the output of the circuit C1.

The loopback resistor Rs1 converts the current passing through it into voltage (like the resistor R6 of the figure 3 ). The current flowing through it is such that the sum of the currents entering on the node E1 is zero. This sum comprises the currents originating from transistors Q5 and Q6 (currents Vbe2 / R4 and 12), the current in resistor Rs1 and two currents injected, through a resistor Rs2 and a resistor Rs3 respectively, by the voltage outputs of the thermometer circuit. C2 and squaring circuit C3.

The resistor Rs2 defines the weighting coefficient G2 corresponding to the circuit C2. This resistor Rs2 is placed between the output of the circuit C2 and the input E1 of the operational amplifier AO. Similarly, a third resistor Rs3, placed between the output of the circuit C3 and the input E1, defines the weighting coefficient G3. The circuits C2 and C3 provide low output impedance voltages and impose their output potential on the resistors Rs2 and Rs3.

The circuits C2 and C3 provide referenced voltages with respect to the voltage VG. The circuit C2 provides a voltage E2 (T) which is equal to k2 (T-Tr). The circuit C3 provides a voltage E3 (T) which is equal to k3 (T-Tr) ² .

The operation of the operational amplifier is conventional: the sum of the currents arriving at its input E1 is zero, and the voltage at this input is equal to the voltage at the input E2, that is to say at VG.

$$\mathrm{Vref}\mathrm{=}\mathrm{-}\mathrm{Rs}\mathrm{1}\left[\mathrm{I}\mathrm{2}\mathrm{+}\mathrm{Vbe}\mathrm{2}\mathrm{/}\mathrm{R}\mathrm{4}\right]\mathrm{-}\mathrm{E}\mathrm{2}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\mathrm{-}\mathrm{E}\mathrm{3}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}$$

If we call Vref the output voltage (referenced with respect to the reference potential VG) of the amplifier AO, then we can write: $$\mathrm{Vref}\mathrm{/}\mathrm{Rs}\mathrm{1}\mathrm{+}\mathrm{E}\mathrm{2}\left(\mathrm{T}\right)\mathrm{/}\mathrm{Rs}\mathrm{2}\mathrm{+}\mathrm{E}\mathrm{3}\left(\mathrm{T}\right)\mathrm{/}\mathrm{Rs}\mathrm{3}\mathrm{+}\mathrm{Vbe}\mathrm{2}\mathrm{/}\mathrm{R}\mathrm{4}\mathrm{+}\mathrm{I}\mathrm{2}\mathrm{=}\mathrm{0}$$

$$\mathrm{Vref}\mathrm{=}\mathrm{-}\mathrm{Rs}\mathrm{1}\left[\mathrm{I}\mathrm{2}\mathrm{+}\mathrm{Vbe}\mathrm{2}\mathrm{/}\mathrm{R}\mathrm{4}\right]\mathrm{-}\mathrm{E}\mathrm{2}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\mathrm{-}\mathrm{E}\mathrm{3}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}$$

Therefore $$\mathrm{Vref}\mathrm{=}\mathrm{-}\mathrm{Rs}\mathrm{1}\left[\mathrm{I}\mathrm{2}\mathrm{+}\mathrm{Vbe}\mathrm{/}\mathrm{4}\right]\mathrm{-}\mathrm{E}\mathrm{2}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\mathrm{-}\mathrm{E}\mathrm{3}\left(\mathrm{T}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}$$

Or, if we call EG (T) the value -Rs1 [I2 + Vbe2 / R4], imperfect voltage of the bandgap circuit C1, equal to EG (Tr) at the reference temperature Tr. $$\mathrm{Vref}\mathrm{=}\mathrm{EG}\left(\mathrm{T}\right)\mathrm{-}\mathrm{k}\mathrm{2}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\mathrm{-}\mathrm{k}\mathrm{3}{\left(\mathrm{T}\mathrm{-}\mathrm{<figure-callout\; id="2"\; label="Tr"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">Tr</figure-callout>}\right)}^{\mathrm{2}}\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}$$

Ou $$\mathrm{Vref}\mathrm{=}\mathrm{EG}\left(\mathrm{Tr}\right)\mathrm{+}\left[\mathrm{a}\mathrm{-}\mathrm{k}\mathrm{2.}\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\right]\mathrm{.}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)\mathrm{+}\left[\mathrm{b}\mathrm{-}\mathrm{k}\mathrm{3}\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}\right]\mathrm{.}{\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)}^{\mathrm{2}}$$

Since the second order approximation is that EG (T) is equivalent to the sum EG (Tr) + a (T-Tr) + b (T-Tr) ² , we find that $$\mathrm{Vref}\mathrm{=}\mathrm{EG}\left(\mathrm{Tr}\right)+\mathrm{at}\mathrm{.}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)+\mathrm{b}{\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)}^{\mathrm{2}}-\mathrm{k}\mathrm{2}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}-\mathrm{k}\mathrm{3}{\left(\mathrm{T}\mathrm{-}\mathrm{<figure-callout\; id="2"\; label="Tr"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">Tr</figure-callout>}\right)}^2\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}$$

Or $$\mathrm{Vref}\mathrm{=}\mathrm{EG}\left(\mathrm{Tr}\right)\mathrm{+}\left[\mathrm{at}\mathrm{-}\mathrm{k}\mathrm{2.}\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{2}\right]\mathrm{.}\left(\mathrm{T}\mathrm{-}\mathrm{Tr}\right)\mathrm{+}\left[\mathrm{b}\mathrm{-}\mathrm{k}\mathrm{3}\mathrm{Rs}\mathrm{1}\mathrm{/}\mathrm{Rs}\mathrm{3}\right]\mathrm{.}{\left(\mathrm{T}\mathrm{-}\mathrm{<figure-callout\; id="2"\; label="Tr"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">Tr</figure-callout>}\right)}^{\mathrm{2}}$$

The value of Rs1 is set in principle according to the value that it is desired to give to the reference voltage Vref at the reference temperature Tr. This value is -Rs1 [I2 + Vbe2 / R4] measured at the reference temperature and which is EG (Tr) according to the notation previously used.

If the coefficients k2 and k3 of the circuits C2 and C3 are not adjustable, then the ratio Rs1 / Rs2 is adjusted such that Rs2 / Rs1 = k2 / a and the ratio Rs3 / Rs1 such that Rs3 / Rs1 = k3 / b, which makes it possible to eliminate the weighting coefficients of the terms T-Tr and (T-Tr) ² and to arrive at a reference voltage which has the value EG (Tr) over the whole range of temperatures for which the approximation EG ( T) = EG (Tr) + a (T-Tr) + b (T-Tr) ² remains valid for the bandgap circuit C1 used.

Thermometer circuit

The thermometer circuit C2 can be constituted for example as follows, as shown in FIG. figure 6 it comprises a current generator proportional to the absolute temperature (PTAT); this generator can be the one used in the circuit C1 to establish the current or the constant voltage to the first order. It is therefore composed of PNP transistors T1, T2, differential amplifier A1, resistor R2, and current sources constituted by PMOS transistors Q1, Q2 whose gates are connected to the output of differential amplifier A1. .

The current I2 proportional to the absolute temperature is copied by a PMOS transistor Q7 and a PMOS transistor Q8 which both have the same source and gate potential as Q1 and Q2. Transistor Q7 supplies a resistor R7. The resistor R7 is connected between the drain of the transistor Q7 and the output of a differential amplifier A3. Transistor Q8 feeds a diode-mounted bipolar transistor T8 having its emitter connected to the drain of Q8 and its collector and base connected to the reference potential VG. The differential amplifier A3 has a first input connected to the point of junction of R7 and Q7 and a second input connected to the junction point of Q8 and T8.

As a result, the differential amplifier A3 establishes a voltage which is the difference between the base-emitter voltage of this bipolar transistor (traversed by a current proportional to the temperature) and the voltage drop across the resistor (traversed by a current proportional to the temperature).

It can be shown and verified experimentally that if the resistor R7 is adjusted so that the output voltage of the differential amplifier A3 is equal to VG for the reference temperature Tr, then the output voltage of the amplifier for any absolute temperature T is a voltage E2 (T) that is practically proportional to T-Tr and that we can write E2 (T) = k2. (T-Tr)

This approximate proportionality results in particular from the curve of variation practically in (T-Tr) of the base-emitter voltage Vbe8 of the transistor T8 when it is traversed by a current I2 proportional to the absolute temperature.

The resistor R7 is adjustable to adjust the thermometer circuit such that the output voltage E2 (T) is zero for the reference temperature Tr, that is to say that the output of the amplifier A3 is equal at VG for this temperature.

If it is estimated that the coefficient a of the variation curve of EG (T) with the temperature can be either positive or negative, an additional operational amplifier mounted in an analog inverter can be provided at the output of the amplifier A3. The output of the additional amplifier or the output of the amplifier A3 will be used according to the sign of a, the choice being made during the circuit test; the adjustment of the resistance R7 is also done during the test.

Elevation circuit squared

To produce a signal proportional to (T-Tr) ² the thermometer circuit is used, and its output voltage E2 (T) is applied to a squaring circuit which uses the same potential reference VG.

The squaring circuit can be that of the figure 7 . It has two sources of current input and output SC1 and SC2 value arbitrary 2.lo each; the first source, SC1, supplies to the incoming current a group of two differential branches identical to one resistor and three transistors each (a resistor R21, a PMOS Q21 and two NMOS Q22 and Q23, all in series, in the first branch, a resistor R24 = R21, a PMOS Q24 and two NMOS Q25 and Q26 in series in the second branch); the second source SC2 feeds outgoing current a pair of two identical NMOS transistors Q27 and Q28 having their sources together. These combined sources are connected to the gate of a NMOS transistor Q30 fed by an incoming power source SC3 of value Io (thus half the value of each of the other sources). The PMOS transistors of the two identical differential branches respectively receive on their gate a potential E2 (T) coming from the thermometer circuit and the reference potential VG. It can be shown that the current flowing through the transistor Q30 is equal to Io + [E2 (T)] ^2/4 (R21) ² .io

A current equal to the difference between the current of the source SC3 and the current of the transistor Q30 is extracted from the junction point between the source SC3 of value Io and the drain of transistor Q30. This difference is equal to [E2 (T)] ² /4.(R21) ² .Io

It is converted into a voltage in a differential amplifier A4 whose input is brought to the reference voltage VG and the other input, which receives the current [E2 (T)] ² /4.(R21) ² .Io, is connected by a loopback resistor R30 at the output of the amplifier.

The voltage that appears at the output of the amplifier is then a voltage E3 (T) equal to R30. [E2 (T)] ² /4.(R21) ² .Io + VG

The voltage E3 (T) is practically proportional to the square of E2 (T), therefore to the square of T-Tr, provided, however, that Io is approximately independent of the temperature. To obtain this result, it is arranged to realize the current sources of value Io and 2Io from the ratio between a voltage approximately independent of the temperature and a bias resistor Rpol. The voltage approximately independent of the temperature is preferably the output voltage EG from the bandgap circuit core.

Io is then of the form Io = Eg / Rpol and it may be noted that the voltage E3 (T) then involves a ratio RpoI.R30 / (R21) ² . This ratio is also approximately independent of the temperature, all the resistances varying in the same way.

Again, if the coefficient b of the variation curve EG (T) has any sign, an inverting operational amplifier can be placed at the output of the amplifier A4. The output of one or the other of these amplifiers will be chosen on the test.

Claims (6)

1. A voltage reference circuit, comprising a first circuit of bandgap type (C1) providing a first-order temperature-stable voltage or current, on the basis of a PTAT current generator providing a current proportional to absolute temperature, this generator comprising, between a power supply (Vdd) and a ground (GND), two parallel branches, one comprising a first MOS transistor (Q1) in series with a diode-mounted bipolar transistor (T1), the other branch comprising a second MOS transistor (Q2) identical to the first bipolar transistor, the PTAT current generator further comprising a resistor (R2) and a second bipolar transistor (T2) having an emitter area N times as large as the emitter area of the first, with a differential amplifier (A1) which controls the MOS transistors and which establishes in the resistor a voltage drop equal to the difference of the base-emitter voltages of the two bipolar transistors, characterized in that there are provided means for injecting, at the junction point between the first bipolar transistor (T1) and the first MOS transistor (Q1), a current which is equal to the base current of the first bipolar transistor (T1) and means for injecting, at the junction point of the second bipolar transistor (T2) and of the resistor (R2), a current which is equal to the base current of the second bipolar transistor (T2), in such a manner that the output current of the generator of current proportional to temperature is equal to the collector current and not to the emitter current of the second bipolar transistor.
2. The reference circuit as claimed in claim 1, characterized in that the first circuit of bandgap type provides a temperature-stable voltage or current on the basis

   - of a bipolar transistor base-emitter voltage (T3) having a negative slope of variation as a function of temperature

   - and of the current (I2) arising from the PTAT generator.
3. The circuit as claimed in claim 1, characterized in that it comprises a differential amplifier (A2) and a third MOS transistor (Q4) controlled by this differential amplifier, for establishing in a resistor (R4) of value R4 a current equal to Vbe2/R4, where Vbe2 is the base-emitter voltage of the second transistor.
4. The circuit as claimed in claim 3, characterized in that it comprises at least one fourth and one fifth transistor (Q5, Q6) for copying over the current in the resistor of value R4 and the current in the resistor of value R2.
5. The reference circuit as claimed in one of the preceding claims, characterized in that it comprises a summator (ADD) for establishing a linear combination, with respective weighting coefficients, of three values which are respectively

   - the output voltage or current (EG(T)) of the first circuit of bandgap type (C1),

   - the output voltage or current of a second circuit (C2) providing a voltage (E2(T)) or a current proportional to the difference between the absolute temperature T and a reference temperature Tr,

   - the output voltage or current (E3(T)) of a third circuit (C3) providing a voltage or a current proportional to the square of this difference.
6. The circuit as claimed in claim 5, characterized in that the second circuit (C2) providing a voltage proportional to the difference T-Tr comprises a generator of current proportional to absolute temperature, means for applying this current to a resistor of value R7 and to a bipolar transistor (T8), and a differential amplifier for establishing a voltage which is the difference between the base-emitter voltage (Vbe8) of this bipolar transistor and of the voltage drop across the terminals of the last mentioned resistor (R7).

Images