Superior-Order Curvature-Correction Techniques for Voltage References

I2a D Vth ln n: I2b D So, the reference voltage will have the expression: The choosing of this factor with a under unitary value allows to obtain a reference voltage smaller than 1 V , for a low-voltage operation of the circuit. It is possible to replace diodes from Fig. Another current-mode approach of a voltage reference circuit is presented in Fig.

The current I can be expressed as follows: It is possible to write as follows: The current I2b has the following expression: The operational amplifier imposes equal potentials on its inputs, so: The AD analog device circuit presented in Fig. The adjustment of R4 —R5 resistors permits to obtain the desired value for reference voltage, the result being a precise and stable reference voltage with respect to temperature, supply voltage, or load current variations.

R2 R2 R2 3. Applying the condition for linear curvature-correction, the expression of reference voltage can be given as follows: The T10 transistor has an area of eight times larger than the area of T11 transistor. The structure of the voltage reference is classic, a PTAT voltage being summed with a voltage having a negative temperature coefficient.

There is a value of temperature at which the two tendencies are compensating; in the neighborhood of this temperature, the temperature coefficient of the voltage reference has very low values. The voltage across R7 resistor has the following expression: The second differential amplifier has as active load the T5 —T6 current mirror, being biased using T9 —T10 current mirror.

The T11 —T11 0 current mirror ensures the biasing of the two differential stages.

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The base—emitter voltages of T3 and T4 transistors are equal because transistors are identical and work at the same collector current owing to the T5 —T6 current mirror. The voltage across R3 resistor will have, therefore, the following expression: The expression of I biasing current is as follows: As a consequence of linear curvature-correction, the reference voltage will contain a constant term and a logarithmical dependent on temperature term [coming from the expression of VGS. D ln R1 R1.

Superior-Order Curvature-Correction Techniques for Voltage References

The expression of VS voltage will be as follows: Transistors T1 —T8 form a PTAT current generator, the cascode self-biasing and the biasing of T7 transistor strongly improving the power supply rejection ratio of the circuit. Because the expression of the reference voltage is as follows: The core of voltage reference is formed from T1 ; T3 ; T6 , and T7 transistors, operating in weak inversion region; T8 —T10 and T12 —T19 transistors form a self-biased multiple current source necessary for obtaining a good power supply rejection.

Considering that the transistors of voltage reference work in weak inversion, the drain currents of T3 and T4 transistors will have the following expression: Using the previous three relations and the temperature dependence of gate—source voltage for a weak inversion biased MOS transistor expressed by 2. There are several constructive versions for the threshold voltage extractor, the most representative of them being further on presented as constitutive part of a voltage reference circuit designed in CMOS technology.

The output voltage of the threshold voltage extractor is as follows: The simulation of the temperature dependence of threshold voltage is presented in Fig. In order to obtain 3. The OVF block is similar to that from previous example. The proposed method achieves the dividing ratio from the OVF block in three steps, the total dividing ratio being the result of the three individual ratios.

The circuit of the modified voltage reference is presented in Fig.

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The simulation of the reference voltage temperature dependence is presented in Fig. C ln R3 qR1 IS2 3. Considering the quadratic equation that characterizes the operation in saturation of the MOS transistor and also the temperature dependencies of mobility and of threshold voltage, respectively: It imposes the biasing of the MOS transistor at a drain current having the following temperature dependence: The cancellation of linear dependence on temperature term from the expression of reference voltage implies that: The temperature dependence of reference voltage is presented in Fig.

The temperature coefficient of the resulted voltage after applying the correction presents relatively high values as a consequence of the logarithmical term from the expression 2. A possible version for realizing this type of compensation is presented in Fig.

The reference voltage has the following expression: According to relations 3. Choosing R1 D 1: The simulation of the VREF. The simulation of VREF. Because for the circuit from Fig. T3 and T4 transistors form a current mirror biased by the current through T2 transistor, which is, in turn, controlled by the Zener voltage and by base—emitter voltages of T1 and T2 transistors.

As a result, the biasing current of the voltage reference will Fig. The current through R1 and R2 resistors has the following value: R1 C R2 The reference voltage can be expressed as follows: R1 1C R2 3. For this circuit, the sensitivity of reference voltage with respect to the supply voltage variations depends on the difference of Early voltages of T5 and T6 transistors. So, in the theoretical hypothesis of perfectmatched devices, it is possible to obtain a null dependence of the reference voltage on the supply voltage.

For comparison, for the voltage reference from Fig. The utilization of a Zener diode with positive temperature coefficient permits the compensation of temperature dependence of VZ. Consider the circuit from Fig. Choosing R2 D 1: The temperature dependence of reference voltage obtained following this linear curvature-correction is an exclusive consequence of the logarithmical term from expression 2. Changing successively the value of the R2 resistor at 0: Wiley, New York 3. Proceedings of the International Symposium on Circuits and Systems 1: International Conference on Microelectronics — International Symposium on Circuits and Systems 1: Fundamental Theory and Applications The 25th International Semiconductor Conference — Wiley, New York The 17th International Conference on Microelectronics 10—12 The International Symposium on Circuits and Systems 1: Popa C 0.

Prentice-Hall, New Jersey General principles for bipolar technology include correction of the base—emitter voltage nonlinear temperature dependence by using a proper biasing of bipolar transistor and compensation of the base—emitter voltage nonlinear temperature dependence by using a correction current or a correction voltage. For CMOS technology, superiororder curvature-correction techniques are based on correction of the gate—source voltage nonlinear temperature dependence by using a proper biasing of the MOS transistor and on compensation of the gate—source voltage nonlinear temperature dependence by using a correction current or a correction voltage.

Concretely, the linear curvature correction being implemented, the superior-order curvature correction presumes the cancellation of logarithmical dependence on temperature term from the expression 2. There is the possibility of biasing the bipolar transistor at a collector current having a polynomial dependence on temperature, IC. The reference voltage has the following expression VREF. The complete circuit of the voltage reference is presented in Fig. The condition for linear curvature correction implies: For the circuit from Fig.

Similarly, for the circuit from Fig. The operating principle of the circuits from Fig. For the first circuit the following equations are valid: For evaluating the temperature dependence of reference voltage, the general temperature dependence 2. The temperature dependence of reference voltage will be caused only by the superior-order terms disregarded in the limited Taylor series expansion, ln.

The voltage reference has the block diagram presented in Fig. The composing blocks are as follows: The concrete implementations of the component blocks are presented in Figs. The expression of reference voltage is obtained in four steps: The complementary of the two terms implies the theoretical cancellation of reference voltage temperature dependence in the hypothesis of the previous achievement of a linear curvature correction by a method proposed in Chap.

An alternative method refers to the achievement of this type of correction by summing the correction current having temperature dependence complementary to the VBE. The current-mode operation associates advantages mainly related to the capability of low-voltage operation. In addition, the improvement of power supply rejection can be achieved in the hypothesis of the existence of an enough high supply voltage by using a cascode current mirror for self-biasing the voltage reference core.

The current-mode circuit resulted from following these modifications, using the previously mentioned principle, is presented in Fig. I5 and I6 currents are equal because I5 D. In the expression of the reference voltage, two types of temperature dependencies can be identified: The condition of achievement of the linear curvature correction imposes the cancellation of the linear dependence on temperature term from expression 4.

R3 TO qR1 4. The expression of the I2 current is I2. Starting from the Taylor series expansion of the temperature dependence of base— emitter voltage, the circuit achieves the compensation of its superior-order terms by the correction of the PTAT I current, specific to the elementary voltage reference, using Icor: The main matter is the implementation of a generator of which output current contains superior-order nonlinear terms with amplitudes controllable by designing. Because drain currents of the T1 and T4 transistors are equal, and all MOS transistors work in weak inversion, it results in I.

The principle for the improvement of voltage reference temperature behavior is the summing of a Icor: R1 R1 T14 T9 Fig. Owing to the low value requested to the correction current, the circuit designed in order to obtain this current is based on the operation in weak inversion of a MOS transistor, T The drain current for this transistor can be expressed by Icor: Because temperature dependencies of the two terms are evaluated by different functions, the superior-order curvature correction imposes the Taylor series expansion of these functions in the neighborhood of TO central value and, on one hand, the adjustment of the condition 4.

The result will be the obtaining of a reference voltage temperature dependence containing exclusively terms having the order greater or equal to three, resulted from the Taylor series expansion of the two temperature functions, therefore, a very low value of the temperature coefficient for VREF: Following the applying of the exponential curvature correction, the nonlinearity of the voltage reference will be only a consequence of the superior-order error terms from the reference voltage expansion.

The implementation of this circuit leads to the experimental results presented in Table 4. The experimentally obtained temperature coefficient based on data from the Table 4. The reference voltage can be expressed as VREF. Considering the expression 2. A possible implementation in bipolar technology of the above-described principle is presented in Fig.

Replacing this temperature dependence in 4. If both linear and superior-order curvature corrections are implemented, the reference voltage will be approximately independent on temperature, VREF D EG0. The voltage reference presented in Fig. The simulation of the ID. In addition, the elimination of resistors from the circuit implies an important reduction of its area. After applying the linear curvature correction, the reference voltage will have the following expression lin VREF. Following to the previously presented curvature correction, the reference voltage will be expressed by sup VREF.

The complementary of these two terms implies a theoretical cancellation of the reference voltage temperature dependence, in the hypothesis of previous achievement of the linear curvature-correction, using a method proposed in Chap. The linear curvature correction of the reference voltage is achieved by summing a PTAT term with the expression of a VGS derived current. The minimization of the logarithmic dependence on temperature of the VGS voltage 4.

Because the aspect ratio of T4 —T6 transistors is chosen to be m times greater than the aspect ratio of the T1 —T3 transistors, it results in IR1. The superior-order curvature correction can be realized by summing the IR3. IO and I1 currents approximately independent on temperature and, respectively, of PTAT type are generated by an auxiliary current reference. The relation between gate—source voltages of transistors from Fig. The voltage reference implementation is presented in Fig. Particularizing the expression of gate—source voltage temperature dependence for VGS. Following the two corrections, the reference voltage will have the approximate expression: This term is obtained by considering the difference of two gate—source voltages, VSG2.

The additional fulfillment of the linear curvature correction implies VREF. A large bandwidth of the voltage reference improves the transient behavior of the circuit, implying also a good noise rejection. Referringtothe possibilities ofimplementinga voltagereferencecircuit,two d- ferent approaches could be identi?

Superior-Order Curvature-Corrected Voltage References Using Double Differential Structures

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Electronic Tap-changer for Distribution Transformers. The Design of Active Crossovers. Switching Power Supplies A - Z. Superior-Order Curvature-Correction Techniques for Voltage References is dedicated to the analysis and design of voltage reference circuits and evaluates improving their temperature behavior by implementing superior-order curvature-correction techniques. The author begins with the study of biasing current references with controllable temperature dependencies.

That is followed by examining simple zero-order and first-order curvature-corrected voltage reference circuits which leads into the final topic of the analysis of superior-order curvature-correction techniques. The material includes a number of simulations which validate the estimated results. Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support?

Voltage references represent important VLSI structures, having multiple appli- tions in analog and mixed-signal circuits: Operating as a subcircuit in a complex system, an important requi- ment for this class of circuits is represented by the possibility of implementation in the existing technology, using the available active and passive devices. The most important performances of a voltage reference circuit are represented by temperature behavior, power supply rejection ratio, transient response and, for the latest designs, by low-power low-voltage operation.

Depending on the load - quirements, the output of the circuit can be regulated or unregulated. In order to reduce the sensitivity of the reference voltage with respect to the supply voltage variations, modi? A large bandwidth of the voltage reference improves the transient behavior of the circuit, implying also a good noise rejection. Referringtothe possibilities ofimplementinga voltagereferencecircuit,two d- ferent approaches could be identi? Read more Read less.