Fourth IEEE International Caracas Conference on Devices, Circuits and Systems, Aruba, April 17-19, 2002

CMOS ANALOG SINE FUNCTION GENERATOR USING LATERAL-PNP BIPOLAR TRANSISTORS

Murilo Pilon Pessatti and Carlos A. dos Reis Filho School of Electrical and Computer Engineering

State University of Campinas, UNICAMP Campinas, SBo Paulo - Brazil

E-mail: Carlos reis@,LPM.fee.unicamp.br

Abshuct - An implementation in CMOS technology of the ingenious analog sine hnction generator invented by Barrie Gilbert over two decades ago [ l ] is described in this paper. New in this circuit is the use of lateral-pnp bipolar transistors to build the core of the sine generator together with MOS transistors in saturation region making up the rest of the circuit. Experimental results from prototypes of the circuit fabricated in 0.8pm CMOS technology showed that the accuracy of the produced sine is lower than what has been reported from implementations in Bipolar and BiCMOS [2] technologies. The measured deviation from ideal sine over the ( 4 2 to +62) range is less than 0,5%. Total harmonic distortion measured for a fundamental frequency at 20KHz and the next four harmonics is approximately 1 %.

I. INTRODUCTION

There are at least three well known techniques for generating a sine wave: A sinusoidal continuous time oscillator, for instance a Wien-Bridge oscillator; a digital function synthesizer [3], which has been widely used in modem function generators; and analog sine shapers, which evolved from linear- segment approximation methods [4] and the use of a single differential BJT pair [5] to the ingenious circuit of Barrie Gilbert, which is based on a hyperbolic tangent series approximation using a group of differential BJP pairs [ 1,6]. Clearly, there is not one only technique which is absolutely better than the others, since it all depends on the envisaged application and its requirements. Sinusoidal oscillators produce quite accurate signals, but are not always adequate for integration - the need for large value capacitors, when operating at low frequencies, is one of those impediments. The digital synthesis, certainly provides the highest achievable accuracy and stability, but demands an expressive processing power, silicon area and energy consumption. The third alternative, analog sine shapers, are simpler to implement and occupy small area, but suffer from thermal drift, offset errors and other imperfections that are properties of any analog circuit. Despite all

these constraints, the hyperbolic tangent based sine shaper stands as an attractive option in those cases of “analog-compatible” accuracy and area-saving restrictions. In CMOS technology the hyperbolic tangent approach has been used to generate a sine wave with MOS transistors operating in weak inversion, since in this mode of operation MOS transistors show a current versus voltage characteristics that is similar to BJT‘s [7]. In this paper a similar circuit is described, which is also implemented in CMOS technology, but using lateral-pnp bipolar transistors instead and using less transistors in the sine generation cell than in the circuit described in [7].

11. PRINCIPLE

Gilbert’s sine shaper is based on the fact that there is a pair of exponential functions, whose series exhibit a very close fit to the sine [I]. One of those functions is the hyperbolic tangent. Coincidentally, this is exactly the function that relates the current difference at the output of a differential pair, AIc, of bipolar transistors with the differential base voltage AE.

AIc = 1. tanh- AE (Vt is the thermal voltage) 2.Vt

V

(1)

I1 12

Fig. 1: Gilbert’s sine shaper with six BJT’s

Applying this concept to one of Gilbert’s suggested circuits, shown in Fig.1, which uses six BJT’s, the current difference at the output is related to the input voltage Va according to the following equation:

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Where N is the number of transistors in the core and

(3)

111. CMOS IMPLEMENTATION

A simplified schematic of the new implementation is shown in Fig.2.

Vdd

Vr l

Va

lout

vss

Fig. 2: Lateral-PNP implementation of Gilbert's sine generator

A temperature-stable bias current, Ibias, derived from a bandgap reference, is replicated through a p- channel cascode current mirror to form the tail currents of the three pnp differential pairs. The amplitude of this current was adjusted to 50@, as an adequate compromise between error and efficiency. Efficiency should be understood in this context as the ratio of the output current to the tail current. The output signal, which is the difference between the altemated sum of the collector currents from the differential pairs, is obtained by mirroring the sum of collector currents from Q1, Q4 and Q5 against the sum of collector currents from the respective pair of each one of these transistors. Since the output current is to be converted into voltage through a transresistance stage (not shown in the schematic), whose input is referred to the ground, the collectors of Q1, Q4 and QS are tied to approximately zero voltage thanks to the Vgs voltages of M6 and M1. Transistors M5 and M3 improves mirror M2-M4 by forcing the voltage at the drain of M4 to be approximately near its Vgs. The input angle-equivalent voltage Va was chosen to vary from -100mV to +100mV in correspondence with 360*. As a result, voltages Vrl and Vr2 at the bases of Q1 and Q6, respectively, were fixed at

+100mV and -100mV, nominal values. Due to mismatches, and since these voltages are not adjustable, the extreme values of the input voltage Va were slightly adjusted in order to produce a complete period of the sine as illustrated in Fig.3.

Fig. 3: Input: Va from-100mV to +100mV. Output current: complete sine period

Measurements were done using a semiconductor parameter analyzer HP4 155A at a temperature controlled ambient. The temperature was monitored during the mesurements and showed to be stable at 18'C (_+I'C). A die photograph of the test chip is shown in Fig.4.

Fig. 4: Die photograph of the test chip

IV. TEMPERATURE DEPENDENCE

A point of concem in this circuit is the strong influence of the temperature. A solution to this problem, which was adopted for the implementation of a commercial product that is based on this principle, was the use of two identical sine generators connected to produce an output proportional to the quotient of their individual outputs [6]. Another simpler and less efficient yet satisfactory solution, is to force voltages E and Va to be temperature

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dependent according to the same fimction as Vt. if E and Va are proportional to the absolute temperature (PTAT), as is Vt, then both the amplitude and the argument of the sine will be temperature independent. These measures were not incorporated into the described circuit but are being considered for another implementation, which is currently under development.

V. EXPERIMENTAL RESULTS

The produced sine was compared with a numerically calculated sine for a complete range of 360". The obtained result is shown in Fig.5. Notice that the measured sine has a peak amplitude of approximately lo@. For better visualizing, the amplitude of the error is 10 times enlarged.

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-1.505 -0.09 -0.05 -0,Ol 0.03 0.07 0.11

Equivalent Angle Input Voltage M

Fig. 5: Comparing the produced sine with an ideal sine. Error increases rapidly at the extremes of the

range. The amplitude of the error is 10 times enlarged.

Referring to Fig.5, notice that the produced sine does not cross zero for zero input voltage due to offset errors. The produced signal sensitively departs from an ideal sine as the input angle approaches the extremes of the range. On the other hand, in the range ( 4 2 to M2) the measured error showed a peak that is less than 1%. The learning from these results is that it is more appropriate to use a triangle wave varying from the equivalent angle of 4 2 to W 2 instead of using the full sine period for generating a continuous time sinusoidal signal. Measured errors from a Bipolar implementation reported in [6] are less than the values we obtained in our lateral-pnp CMOS version. This is mainly because the lateral-pnp's in CMOS goes into high- injection [8] at relatively low current levels.

The high-injection effect in these transistors can be seen in Fig.6, which shows a plot of Log(1c) versus Vbe.

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Fig. 6: Measurement of Log (IC) versus Vbe, showing the high-injection effect.

The derivative if the Log(1c) curve was also plotted in order to better visualize the point where the coefficient of the exponential function that rules the Ic-Vbe relationship of the transistor departs from one. The derivative starts bending upwards when Vbe is approximately 600mV, as the mark point indicates. As a result, any transfer function that relies on the exponential characteristics of the involved transistors will be affected by this effect.

50mV lOOmV -1OOmV -5OmV ov 0 V ( E 1 2 ) - V ( B 1 ) 0 V(E121 - V ( B 2 ) V V ( E 3 4 ) - V ( B 3 ) A V ( E 3 4 ) - V ( B 4 ) 0 V ( E 5 6 1 - V ( B 5 ) + V ( E 5 6 ) - V ( B 6 )

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Fig. 7: SPICE simulation showing the variation of Vbe for all transistors in the sine generator core.

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Since the Vbe of the transistors cannot be directly measured in an integrated circuit, some SPICE simulations of the circuit were done, using the transistor model provided by the foundry. Simulation results, as illustrated in Fig.7, shows that the transistors operate in a region where the coefficient of its exponent is changing, that is, where the effect of high-injection is evident. Moving the transistors from this region into a high- injection-free region means to lower drastically the operating current. Unfortunately, other performance degrading effects arise, which, however, will be discussed in a future publication.

VI. CONCLUSIONS

This paper described a CMOS implementation using lateral-pnp bipolar transistors of the ingenious analog sine function generator invented by Barrie Gilbert. Prototypes of the circuit were fabricated in a 0 . 8 ~ CMOS technology and showed that the accuracy of the produced sine wave is slightly lower than those produced by circuits in Bipolar implementations. The main cause of errors is the high-injection effect in the pnp’s at relatively low currents, altering the exponential characteristics of the involved transistors, on which the functioning of the circuit relies. The measured deviation from an ideal sine wave of less than 0,5% in the -7rJ2 to + 6 2 range is appropriate for several applications, including the AC excitation of bridge-type sensors as a replacement for sinusoidal oscillators.

VII. ACKNOWLEDGMENTS

The authors are indebted to the Instituto de Pesquisas Eldorado for granting this project and to the lnstituto Nacional de Tecnologia da Informaciio, ITI, Campinas, S.P. Brazil for the manufacturing of prototypes through their multi-project wafer program.

VIII. REFERENCES

[ I ] B. Gilbert, “Circuits for the Precise Synthesis of the Sine Function,” Electronics Letters, Vol. 13,

[2] C. A. dos Reis Filho and F. Fruett, “A BiCMOS Analog Integrated Circuit for Vibration Anulysis,” Proceedings of 4“’ IEEE Intemational Conference on Electronics, Circuits and Systems, ICECS’97, Cairo, Egypt, December 1997.

[3] J.N. Lygouras, “ Memory Reduction in Look-Up Tables for Fast Symmetric Function Generators, “IEEE Transactions on lnstr-mientation and Measurenient, Vo1.48, No.6, December 1999.

[4] L. Bames, “Linear-Segment Approximations to a Sinewave,” Electronic Engineering, pp: 502-508, September 1968.

[ 5 ] R. G. Meyer, W. M. C. Sansen, S. Lui and S. Peeters, “The Differential Pair as a Triangle-Sine Wave Converter,” IEEE Journal of Solid-state Circuits, SC-11, pp:418-420, June 1976.

[6] B. Gilbert, “A Monolithic Mycrosystem for Analog Synthesis of Trigonometric Functions and Their Inverses,” IEEE Journal of Solid-state Circuits, SC- 17, No.6, pp: 1 1 79- 1 191, December 1982.

[7] 0. Ishizuka, Z . Tang and H. Matsumoto, “MOS Sine Function Generator Using Exponential-Law Technique,” Electronics Letters, Vol. 21, pp: 1937-1939, October 1991.

[SI R. S. Muller and T. I. Kamins, Device Electronics fo r Integrated Circuits, New York: John Wiley & Sons, 1977, chapter-6.

pp:506-508, August 1977.

pp: 1254-1258.

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