# Low-Cost and High-Precision Inverse Sine Function Circuit

## Keywords:

Inverse sine function circuit, Operation transconductance amplifier, Hyperbolic tangent circuit, Numerical approximation## Abstract

This paper proposes a new estimation method of the inverse sine function transformation. By taking the approximation of the hyperbolic tangent function, the inverse hyperbolic tangent function and mathematic manipulation determine the appropriate signal gains with the numerical computer program. The inverse sine function comes with small errors and high accuracy when compared to the previous methods. The proposed inverse sine function circuit is synthesized from an operational transconductance amplifier (OTA) with a bipolar transistor differential-pair front end circuit and the appropriate configuration of the input signal and bias current. With an inverting summing amplifier circuit, it amplifies the signal according to the specified gain. The proposed circuit is compact. It consists of two amplifier circuits (Op-Amp) and two conductivity amplifiers (OTA) with some resisters. The results of a circuit simulator show the error of approximately 1.2 degrees and a Root Mean Square Error (RMSE) of the weighted frequency component 0.8%.

## References

M. Benammar, L. Ben-Brahim and M. A. Alhamadi, “A novel resolver-to-360 linearized converter,” IEEE Sensors Journal., vol.4, no. 1, pp. 96–101, 2004, doi: 10.1109/JSEN.2003.820317.

S. L. Kwok, “Sine wave to triangle wave convertor,” U.S. Patent No. US4415860A, 1981.

M. Karray, J. K. Seon, J. -J. Charlot and N. Nasmoudi, “VHDL-AMS modeling of a new PLL with an inverse sine phase detector (ISPD PLL),” in Proc. 2002 IEEE International Workshop on Behavioral Modeling and Simulation, Santa Rosa, CA, USA, Oct. 08, 2002, pp. 80–83, doi:10.1109/BMAS.2002.1291062.

Y. Chiu, B. Jalali, S. Garner and W. Steier, “Broad-band electronic linearizer for externally modulated analog fiber-optic links,” IEEE Photonics Technology Letters, vol. 11, no. 1, pp. 48–50, 1999, doi: 10.1109/68.736386.

M. J. Narasimha, K. Shenoi and A. M. Peterson, “The arcsine transform and its applications in signal processing,” in IEEE International Conference on Acoustics, Speech, and Signal Processing, Hartford, CT, USA, May 09–11, 1977, pp. 502–505, doi: 10.1109/ICASSP.1977.1170346.

S. Nandi, S. Prasad, C. M. Ananda and S. S. Rekha, “Fixed point implementation of trigonometric function using Taylor's series and error characterization,” International Conference on Advances in Computing, Communications and Informatics (ICACCI), Jaipur, India, Sep 21–24, 2016, pp. 442-446, doi: 10.1109/ICACCI.2016.7732085.

S. Dyer, N. Ahmed and D. Hummels, “Computation of the discrete cosine transform via the arcsine transform,” Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 1980, pp. 231–234, doi: 10.1109/ICASSP.1980.1170904.

B. Gilbert, “A monolithic microsystem for analog synthesis of trigonometric functions and their inverses,” IEEE Journal of Solid-State Circuits, vol. 17, no. 6, pp. 1179–1191, 1982, doi:10.1109/JSSC.1982.1051878.

M. Benammar, “Precise, wide-range approximations to arc sine function suitable for analog implementation in sensors and instrumentation applications,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 2, pp. 262–270, 2005, doi: 10.1109/TCSI.2004.840287.

M. Abdellaoui, B. Gassara and N. Masmoudi, “A new model of an inverse sine phase detector to design ISPD PLL demodulator without using any filters,” AEU-International Journal of Electronics and Communications, vol. 61, no. 1, pp. 10–21. 2007, doi: 10.1016/j.aeue.2006.01.007.

J. -K. Seon, “A fully integrated CMOS inverse sine circuit for computational systems,” International Journal of Electronics, vol. 97, no. 8, pp. 867–882, 2010, doi:10.1080/00207211003646886.

A. Kaewpoonsuk, W. Petchmaneelumka, A. Rerkratn, S. Tammaruckwattana and V. Riewruja, “A novel resolver-to-DC converter based on OTA-based inverse-sine function circuit,” in SICE Annual Conference, Chofu, Japan, Aug 20–22, 2008, pp. 609–614, doi: 10.1109/SICE.2008.4654729.

P. Apisitticharoonlert, W. Petchmaneelumka, and V. Riewruja, “Inverse sine function circuit with temperature compensation,” Proc. International MultiConference of Engineer and Computer Scientists (IMECS), Hong Kong, Mar 16–18, 2016, pp. 616–619.

J. Tongcharoen, W. Petch maneelumka, T. Cheypoca, and V. Riewruja, “Resolver-to-Triangular Wave Converter,” in SICE2014, Nagoya, Japan, Sep. 9–12, 2014, pp. 1181–1184.

P. Prommee, K. Angkeaw and K. Karawanich, “Low-Cost Linearity Range Enhancement for Linear Variable Differential Transformer,” IEEE Sensors Journal, vol. 22, no. 4, pp. 3316–3325, 2022, doi: 10.1109/JSEN.2022.3142195.

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*Eng. & Technol. Horiz.*, vol. 39, no. 4, pp. 52–62, Dec. 2022.

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