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Two Quadrant Analog Voltage Divider and Square-Root Circuits Using OTA and MOSFETs

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Abstract

In this communication, two novel architectures of voltage mode analog divider circuit and square-root circuit using an operational transconductance amplifier (OTA) have been presented. The proposed divider circuit employs an OTA and two MOSFETs, while the square-root circuit requires one OTA along with one MOSFET. The proposed divider circuit can also be configured as inverse voltage function generator. The performance of the proposed circuits has been validated through Cadence Virtuoso simulations using 0.18 µm CMOS technology parameters. The total power consumption for analog divider circuit is 821 µW, while for square-root circuit, it is 442 µW with ± 0.9 V power supply. Experimental results have also been provided to validate the theory.

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Acknowledgements

The authors gratefully acknowledge Professor Raj Senani, Department of Electronics and Communication Engineering, Netaji Subhas University of Technology, New Delhi, India, for his help and valuable suggestions in the preparation of this manuscript. The authors also wish to thank the anonymous reviewers for their constructive comments and suggestions in improving the quality of the manuscript.

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  1. Department of Electrical Engineering, Delhi Technological University, New Delhi, Delhi, India

    Ajishek Raj, D. R. Bhaskar & Pragati Kumar

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  1. Ajishek Raj
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Appendix

Appendix

1.1 Variation in VP Due to Changes in VDD

For generation of external voltage VP, we have used a voltage divider circuit with three matched MOSFETs (operating in saturation region) (Fig. 25).

Fig. 25
figure 25

Voltage divider circuit

Full size image

The current flowing through each MOSFET is same and is equal to:

$$ I_{{{\text{D}}1}} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{1} \left( {V_{{{\text{GS}}1}} - V_{{{\text{TH}}1}} } \right)^{2} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{1} \left( {V_{\text{DD}} - V_{x} - V_{{{\text{TH}}1}} } \right)^{2} $$
(23)
$$ I_{{{\text{D}}2}} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{2} \left( {V_{{{\text{GS}}2}} - V_{{{\text{TH}}2}} } \right)^{2} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{2} \left( {V_{x} - V_{P} - V_{{{\text{TH}}2}} } \right)^{2} $$
(24)
$$ I_{{{\text{D}}3}} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{3} \left( {V_{{{\text{GS}}3}} - V_{{{\text{TH}}3}} } \right)^{2} = \frac{1}{2}\mu_{n} C_{\text{ox}} \left( {\frac{W}{L}} \right)_{3} \left( {V_{P} - V_{{{\text{TH}}3}} } \right)^{2} $$
(25)

Solving Eqs. (23–25), assuming equal threshold voltages, we get:

$$ V_{P} = \frac{{\sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}} \left( {V_{\text{DD}} - V_{\text{TH}} } \right)}}{{1 + \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}} + \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{3} }}} }} \cong \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}} \left( {V_{\text{DD}} - V_{\text{TH}} } \right)\left( {1 - \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}} - \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{3} }}} } \right) $$
(26)

Now, in Eq. (26), if a deviation is introduced in VDD by a value of ± ΔVDD, then Eq. (26) becomes:

$$ V_{P} \cong V_{P} + V_{P}^{{\prime }} $$
(26)
$$ {\text{where}}\;V_{P}^{{\prime }} = \pm \frac{{\Delta V_{\text{DD}} }}{{\left( {1 + \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{1} }}} + \sqrt {\frac{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{2} }}{{\left( {{\raise0.7ex\hbox{$W$} \!\mathord{\left/ {\vphantom {W L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)_{3} }}} } \right)}} $$
(27)

Therefore, from Eq. (27), the effect of changes in VDD may be made negligible small, if (W/L)2 ≫ (W/L)1 and (W/L)2 ≫ (W/L)3.

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Raj, A., Bhaskar, D.R. & Kumar, P. Two Quadrant Analog Voltage Divider and Square-Root Circuits Using OTA and MOSFETs. Circuits Syst Signal Process 39, 6358–6385 (2020). https://doi.org/10.1007/s00034-020-01454-2

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