A Modified Method for Compensating the Base-Emitter Voltage Used in Bandgap References

Transcription

1 IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9 7 A odified ethod for ompensating the Base-Emitter Voltage Used in Bandgap eferences Vahideh Sadat Sadeghi and Hossein iar Naimi Electrical Engineering department, Babol Noshirvani University of echnology Babol, Iran Summary In this paper after a survey on base structure of band gap references, the nonlinear property of V and its effect on thermal dependency in bandgap references has been discussed. Furthermore, one of the main methods of curvature correction has been investigated by using mathematical computations. he mathematical and circuit simulations have been implemented in ALAB7 and ADS6, respectively. A corrected modified criterion has then been suggested to minimize the curvature of V by using the best available resistors according to the thermal variations of the collector currents. Accuracy of the introduced criterion has been confirmed by applying circuit simulations. Key words: ompensating, Bandgap eferences. Introduction. Basic Structure of Bandgap eferences As we now, V is a voltage reference with negative thermal coefficient called A (complementary to absolute temperature[6], therefore it is reasonable to add it to a voltage reference with positive thermal coefficient or PA (Proportional to absolute temperature,this voltage is obtainable using the relation. V ( V V I ln I ln( r S V I ln I ln( r K PA his PA voltage is added to the A voltage using the relation which illustrated in Fig. [7]. S ( Voltage and current references with low dependence on thermal situation have been used in many analogue circuits. he more necessity of accuracy in these circuits the more thermal stability is in needed []. Since the second order non linearity of the function V ( is generally the main limitation on the accuracy of bandgap references, it is necessary to minimize this nonlinearity. In [] thermal dependency of resistors has been used to generate a temperature dependence collector current to compensate the nonlinearity of V. In [] the resistors with negative thermal coefficient have been suggested to linearize V. Some of the researchers have suggested using the exponential currents to linearize the V. [4], [5]. In this paper after a survey on nonlinearity of V as the most important reason that decreases the accuracy in bandgap references, a new criterion will be introduced that minimizes the nonlinearity of V using the selection of the best available resistors. V out V Figure. Basic structure of a bandgap reference V ( V B V B a. PA A V As a result by proper selection of a according to the proper adjusting of resistor proportions, the voltage reference with thermal stability can be obtained. However since PA is completely linear and A is nonlinear Vref has a nonlinear curvature. AP Vout ( anuscript received April 5, 9 anuscript revised April, 9

2 forth nonlinear error when Ic is constant(mv third error when Ic is constant(mv V when Ic is constant(mv V-V V when nonlinear Ic is constant(mv error when Ic is constant(mv nonlinear error when Ic is constant(mv V when Ic is constant(mv V when Ic is constant(mv 8 IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9. Nonlinearity of V According to the relevance between V and physical parameters of transistor, different uantitative relations has been extracted which one of them is eijer relation which described in euation [8]. K I V ( I, Ln IS ( ( I ( S e V K his paper simulations have been done according to this relation. Fig. illustrates the V variations when the temperature changes a Assuming I independent from temperature, the aylor polynomial of V around can be written as relation 4. V ( V N n I ln ( n ( n( n ln n n Using the different error relations such as Lagrange error relation and also Fig.-b to Fig.-d shows that the second order nonlinear error is the most important reason of V nonlinearity [8]. In order to study V characteristics, different thermal ranges have been investigated until now [9].In this research, thermal range between -5 to 95 centigrade has been considered. Fig.5 shows the PA and A voltage according to the simulation of circuit shown in Fig.. he bipolar transistor used in the simulation has been implemented using Gummel-Poon parameters [] Quadratic: norm of residuals =.9 b a ubic: norm of residuals =.5455 c b Figure. a- A voltage graph with obviously nonlinear curvature b- Linear PA voltage graph t d Figure. a-v vs temperature, b-second order nonlinear error of V, c- hird order nonlinear error of V, d- forth order nonlinear error of V As clearly extracted from Fig.-a, the difference between V and linear curve fitted on it is little. For more clarity, Fig.-b shows second order nonlinear error of V, Fig.-c and Fig.-d shows third and forth nonlinear error of V. As Fig. shows, A is nonlinear while PA is linear; therefore, the aim is to overcome the problem of A nonlinearity. 4. urvature orrection of V According to the previous sections the aim is to minimize the nonlinearity of V. he dependency of collector

3 dv/d IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9 9 current to temperature can be used to overcome this problem. First of all the approach described in [8] is discussed briefly. Assuming the possibility of temperature dependent collector current, euation 5 has been considered. K I ( V ( I, Ln (5 IS ( eanwhile the second order derivation of V as the most important reason of total nonlinearity has been obtained as relation 6. ( I V ( ( * I I ( I I * Furthermore, it has been described that the difference of two base-emitter voltage related to two proportional collector currents remains PA even under thermal dependency of collector currents. Afterwards, he V and its curvature have been studied for collector current as euation 7. he current of euation 7 can be obtained by applying a linearly temperature dependence voltage to a linearly temperature dependence resistor. V[ ( ] I (7 [ ( ] In fact, if the V ( is linear A, according to linearity of PA it is possible to choose the proper coefficients in order to achieve a reference voltage without temperature dependency. If it is possible to mae zero the second order derivation of V (, the nonlinearity of V ( will be eliminated. herefore according to relations 6 and 7 the relation 8 is as following: V( ( ( his term will be made zero if the euation 9 is true. ( ( Keeping in the mind that or the thermal coefficient of V ( the transistors are nown to us, (6 (8 (9 that is a parabola of will be made zero if we could realize euation., ( In order to have real values for, it is necessary to have relation. or ( For instance if and 7, it is necessary to have 44 / ppm / ( or 96 /8ppm / In other words for all satisfying the above conditions, it V ( is possible to select some maing zero. Plotting the curves by using ALAB, this issue has been illustrated in Fig x -6 increasment of s from 6ppm to 46ppm termal coefficient of voltage[ppm/] Figure 4. variation of second order derivation of V with α,dashed line showes the place that second order derivation of V gets zero and dotted showes the place that second order derivation of V minimizes when β changes from 6ppm/ to46ppm/ he available resistors cannot satisfy our reuirement to V ( mae zero and this term always remains negative. onsidering as a constant, the minimum value V ( of occurs when as shown below. V ( ( Setting means that applied voltage to the resistor corresponding to must be in the form of V V or PA and therefore the current of the transistor must be PA/ and using PA/ current had been noteworthy [8].

4 IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9 5. Selection of the Best resistor for urvature orrection 7 x A Survey on Present criterion As discussed in the previous sections, resistors with V ( that mae zero are not available. herefore it is necessary to loo for the resistors that V ( minimize. Since PA/ current is typically used in most applications, by setting we have V ( (4 V ( herefore to mae has to be established. zero, the following euation (5 he ordinary method used is to select the resistor with that minimizes criterion d defined as follows [8]. d min, (6 5.. New ecommended riterion he criterion d mentioned in the last section cannot minimize V ( strictly and some other resistors may V ( exist that lead to smaller values of and also there may some resistors that lead to eual d but V ( different. In other words, the variation of d according to relation 6 has been illustrated in Fig x 4 Figure 5. variation of d vs β according to relation 6 herefore it is necessary to use more exact euations. In fact, assuming that we have different and according to relation 4 and Fig. 6, it is obvious that those have the best performance that the differences between V ( resulted from them and V ( resulted from are minimums. hat is the criterion d must be defined as relation 7. d V ( ( V ( ( (7 herefore minimizing d by the new criterion described in relation (8 leads to minimum value of d Where min(( ( ( V ( (,,. (8 It is noticeable that this new criterion confirms the example discussed in [8]. In other words as table implies, both previous and new criterions confirm that the best result among the first to the forth group of resistors is achieved if the collector current is generated by applying a PA voltage to a resistor of the fourth group.

5 nonlinear error nonlinear error our defind minimum of d IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9 ABLE I. DEEINAION OF d IN ODE O SELE HE S ESISO, WHEE / AND ppm/ inimum of d according to relation 6 inimum of new defined d according to relation 8 ppm/.4.9 6ppm/ ppm/ ppm/ ppm/.. 6 4ppm/..4 Fig.6 shows the nonlinear curvature corresponding to 5 ppm/ and 6 4ppm/. Attention to this figure confirms the efficiency of new commended d. in fact as table implies, the previous criterion led to similar result for both 5 and 6 while Fig.6,clearly shows that this inference is not true. However, the new defined d (relation 8 predicts the difference between s very well and selects 5 as better selection. However, base-emitter voltage cannot be linear completely even in use of. his problem is because of higher order derivations existence. According to the simulations shown in Fig.6, it is obvious that minimizing d is euivalent to minimizing the nonlinear curvature. In general, simulations are in agreement with corresponding new d. hat is the difference from linear state about 5 and 6 are.5mv and.79mv respectively that confirms suitability of when beta is set to -4 Linear: norm of residuals =.5 linear temperature a When beta is set to -4ppm/ Linear: norm of residuals =.798 linear temperature b Figure 6. nonlinear curvature of V a-corresponding to 5 ppm / 6 4ppm /,b-corresponing to It is noticeable from Fig. 7 that a range of β can be assigned through applying the new d leading to a predetermined error by using a simple scale changing..4 x beta=-5857 X: 5 Y: 4e-5 beta=5 beta=544 beta= [ppm/] x 4 Figure 7. Variation of d with β using new commended d to determine the ranges of β that lead to given nonlinear error. 6. onclusion In this paper, after a survey on nonlinear property of V and its effect on thermal dependency of bandgap references, a new criterion has been introduced to select optimal thermal coefficient to reach the minimum curvature in V by using the thermal changing of collector current. he accuracy of commended criterion has been confirmed by using circuit simulations. 7. eferences [] N. Azemard, and L. Svensson (Eds.: PAOS 7, LNS 4644, 7. Springer-Verlag Berlin Heidelberg, pp. 7 4, 7. [] J.L. Doorenbos, ethod of curvature correction, offset compensation and capacitance trimming of a switched capacitor bandgap reference,us Patent 6,6,874,. [] J.. Sundby, Low voltage OS bandgap with new trimming and curvature correction methods, US Patent 5,5,45,994. [4] D.. acquigg, OS voltage reference with post-assembly curvature trim, US Patent 6,8,8,. [5] J.L. Doorenbos, D.. Jones, Bandgap reference curvature correction circuit, US Patent 6,55,87,. [6] Y.K. eha, etal, "Design of adaptive supply voltage for subthreshold logic based on sub-v bandgap reference circuit,"icroelectronics Journal,No.9, pp. 4 9, 8. [7] B. azavi, Design of Analog OS Integrated ircuits,pp.84-87,. [8].Falconi, et al.," Low cost curvature correction of bandgap references for integrated sensors," Sensors and Actuators A 7, pp. 7 6, 5. [9] L.Xinuan, et.al, A OS piecewise curvature-compensated voltage...," icroelectron. J (8, doi:.6/ j. mejo [] Gummel-Poon oolit B9_APPEN.WPS 7.4., Franz Sischa

6 IJSNS International Journal of omputer Science and Networ Security, VOL.9 No.4, April 9 Vahideh Sadat Sadeghi received her B.Sc in electronics from Isfahan University of echnology; Iran in and her.sc in electronics from University of Semnan. She is currently a PhD student in electronics,babol University of echnology. Her interests include analog designs and image processing. Hossein iar-naimi received the B.Sc. from Sharif University of echnology in 994 and.sc. from arbiat odares University in 996 and Ph.D. from Iran University of Science and echnology in all in electrical engineering respectively. Since He has been member of Electrical and Electronics Engineering Faculty of Babol University of echnology. His research interests are analog OS design, Image processing and Evolutional Algorithms.