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A Novel Ultra-Low-Power, Low-Voltage, Ultra-High Output Resistance and Uniquely High Bandwidth Femto-Ampere Current Mirror

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Abstract

In this paper, a novel ultra-low-power, low-voltage, ultra-high output resistance and uniquely high bandwidth (BW) femto-ampere current mirror is proposed. Pre-layout results with HSPICE in TSMC 0.18 \({\upmu }\hbox {m}\) CMOS technology are given at 1.2 v power supply that prove such exceptional features of the proposed current mirror as: ultra-low consumed power of 1.56 \({\upmu }\hbox {w}\), ultra-high output resistance of 1.98 \(\hbox {T}\Omega \), very low output voltage of 91 mv and most exceptionally, the extra high BW of 26.5 MHz that is, so far, unique at such extra low minimum output current of 1.8 fA. Also, post-layout plus Monte Carlo simulation results are performed with CADENCE in the same abovementioned technology. Most favorably, this study also proves the same exceptional quality of the features as: the same ultra-low consumed power, fairly the same output voltage of 92 mv, ultra-high output resistance of 1.45 \(\hbox {T}\Omega \) and still uniquely high BW of 17.5 MHz but at extra low output current of 5.5 fA. Good robustness of the proposed current mirror against PVT non-idealities is also proved by Monte Carlo simulations.

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Acknowledgements

The authors would like to greatly appreciate Dr. Abrishamifar and, PhD student Naghavi for the helpful discussions, respectful reviewers for the productive remarks and Mrs Fateme Abdi, the MSC graduate of this school, for her valuable input at the beginning of this work.

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Authors and Affiliations

  1. Iran University of Science and Technology, Tehran, Iran

    Seyed Javad Azhari & Ghader Nickhah

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  1. Seyed Javad Azhari
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  2. Ghader Nickhah
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Correspondence to Seyed Javad Azhari.

Appendix

Appendix

$$\begin{aligned} {{a}}_\mathrm{{{1}}}= & {} C_\mathrm{ds{2}A}C_\mathrm{A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( C_\mathrm{gs{1}A}C_\mathrm{ds{1}}+C_\mathrm{s}C_\mathrm{ds{1}}+C_\mathrm{s}C_\mathrm{gs{1}A} \right) \end{aligned}$$
(47)
$$\begin{aligned} {{a}}_\mathrm{{{2}}}= & {} C_\mathrm{ds{2}A}C_\mathrm{A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&+\,C_\mathrm{s}C_\mathrm{A}\left[ C_\mathrm{ds{2}A}g_\mathrm{ds{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) +\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{1}A}+g_\mathrm{ds{4}A} \right) \left( C_\mathrm{ds{1}} +C_\mathrm{gs{1}A} \right) \right. \nonumber \\&\left. +\,C_\mathrm{ds{2}A}(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A})(C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}) \right] \nonumber \\&+\,C_\mathrm{ds{2}A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \left[ C_\mathrm{s}g_\mathrm{dsC{1}}+C_\mathrm{A}\left( g_\mathrm{dsN{1}}+g_\mathrm{dsC{1}} \right) \right] \nonumber \\&+\,C_\mathrm{A}C_\mathrm{ds{1}}C_\mathrm{gs{1}A}\left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) +C_\mathrm{ds{2}A}(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}) \right] \nonumber \\&+\,C_\mathrm{ds{2}A}C_\mathrm{gs{1}A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left[ C_\mathrm{ds{1}}g_\mathrm{dsC{1}}+C_\mathrm{A}\left( g_\mathrm{m{1}}+g_\mathrm{ds{1}} \right) \right] \end{aligned}$$
(48)
$$\begin{aligned} {{a}}_\mathrm{{{3}}}= & {} C_\mathrm{ds{2}A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{dsC{1}}g_\mathrm{ds{1}} \right] \nonumber \\&+\,C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \left( g_\mathrm{ds{2}}+\,g_\mathrm{m{2}} \right) \left[ C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right] \nonumber \\&+\,C_\mathrm{s}C_\mathrm{A}\left[ g_\mathrm{ds{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+\,g_\mathrm{ds{4}A}\right) +g_\mathrm{ds{1}}C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}\right. \right. \nonumber \\&\left. +g_\mathrm{m{3}A} \right) \left. +\,(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}{)(}g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A}{)(}C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}) \right] \nonumber \\&+\,\left[ C_\mathrm{s}g_\mathrm{dsC{1}}+C_\mathrm{A}g_\mathrm{dsN{1}}+C_\mathrm{A}g_\mathrm{dsC{1}} \right] \left[ C_\mathrm{ds{2}A}g_\mathrm{ds{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \right. \nonumber \\&\left. +\,\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( C_\mathrm{ds{1}}\right. \right. \nonumber \\&\left. \left. +\,C_\mathrm{gs{1}A} \right) +C_\mathrm{ds{2}A}{(}g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}{)(}C_\mathrm{ds{1}A}+C_\mathrm{gs{1}A}) \right] \nonumber \\&+\,C_\mathrm{ds{2}A}g_\mathrm{dsN{1}}g_\mathrm{dsC{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \nonumber \\&+\,C_\mathrm{gs{1}A}C_\mathrm{ds{1}}C_\mathrm{A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \nonumber \\&+\,C_\mathrm{ds{2}A}C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{m{1}}+g_\mathrm{ds{1}} \right) \nonumber \\&+\,C_\mathrm{gs{1}A}\left[ g_\mathrm{dsC{1}}C_\mathrm{ds{1}}+C_\mathrm{A}{(}g_\mathrm{m{1}}+g_\mathrm{ds{1}}) \right] \left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right. \nonumber \\&\left. +\,C_\mathrm{ds{2}A}{(}g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}) \right] \end{aligned}$$
(49)
$$\begin{aligned} {{{a}}_\mathrm{{4}}}= & {} C_\mathrm{ds{2}A}g_\mathrm{ds{1}}g_\mathrm{dsC{1}}\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) +\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right. \nonumber \\&\left. +\,C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{ds{1}}g_\mathrm{dsC{1}} \right] \nonumber \\&+\,C_\mathrm{A}\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \nonumber \\&+\,g_\mathrm{mP{1}}g_\mathrm{m{1}A}g_\mathrm{m{4}A}C_\mathrm{A}C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}\right. \nonumber \\&\left. +\,g_\mathrm{ds{4}A} \right) \left[ C_\mathrm{ds{1}}g_\mathrm{dsC{1}}+C_\mathrm{A}\left( g_\mathrm{m{1}}+g_\mathrm{ds{1}} \right) \right] \nonumber \\&+\,C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}\left( g_\mathrm{m{1}}+g_\mathrm{ds{1}} \right) \left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) +C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \nonumber \\&+\,C_\mathrm{s}C_\mathrm{A}g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \nonumber \\&+\,\left[ C_\mathrm{s}g_\mathrm{dsC{1}}+C_\mathrm{A}g_\mathrm{dsN{1}}+C_\mathrm{A}g_\mathrm{dsC{1}} \right] \left[ g_\mathrm{ds{1}}\left( C_\mathrm{B}\right. \right. \nonumber \\&\left. \left. +\,C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right. \nonumber \\&\left. +\,g_\mathrm{ds{1}}C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) +(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A})(g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A}{)(}C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}) \right] \nonumber \\&+\,g_\mathrm{dsN{1}}g_\mathrm{dsC{1}}\left[ C_\mathrm{ds{2}A}g_\mathrm{ds{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) +\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \right. \nonumber \\&\left. +\,C_\mathrm{ds{2}A}{(}g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}{)(}C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}) \right] \end{aligned}$$
(50)
$$\begin{aligned} {{a}}_\mathrm{{{5}}}= & {} g_\mathrm{ds{1}}g_\mathrm{dsC{1}}\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \nonumber \\&+\,\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{ds{1}}g_\mathrm{dsC{1}} \right] \nonumber \\&+\,g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left[ C_\mathrm{s}g_\mathrm{dsC{1}}+C_\mathrm{A}g_\mathrm{dsN{1}}+C_\mathrm{A}g_\mathrm{dsC{1}} \right] \nonumber \\&+\,g_\mathrm{dsC{1}}g_\mathrm{dsN{1}}\left[ g_\mathrm{ds{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) +C_\mathrm{ds{2}A}g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right. \nonumber \\&\left. +\,(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}{)(}g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A})(C_\mathrm{ds{1}}+C_\mathrm{gs{1}A}) \right] \nonumber \\&+\,g_\mathrm{mP{1}}g_\mathrm{m{1}A}g_\mathrm{m{4}A}\left[ g_\mathrm{dsC{1}}C_\mathrm{ds{1}}+C_\mathrm{A}{(}g_\mathrm{m{1}}+g_\mathrm{ds{1}}) \right] \nonumber \\&+\,C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A})(g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A})(g_\mathrm{m{1}}+g_\mathrm{ds{1}}) \end{aligned}$$
(51)
$$\begin{aligned} {{a}}_\mathrm{{{6}}}= & {} g_\mathrm{dsC{1}}\left[ g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \right. \nonumber \\&\left. +\,g_\mathrm{dsN{1}}g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right. \nonumber \\&\left. +\,g_\mathrm{mP{1}}g_\mathrm{m{1}A}g_\mathrm{m{4}A}{(}g_\mathrm{m{1}}+g_\mathrm{ds{1}}) \right] \end{aligned}$$
(52)
$$\begin{aligned} {{b}}_\mathrm{{{1}}}= & {} C_\mathrm{ds{1}}C_\mathrm{ds{2}A}C_\mathrm{A}{(}g_\mathrm{ds{2}}+g_\mathrm{m{2}}{)(}C_\mathrm{B}+C_\mathrm{ds{1}A}) \end{aligned}$$
(53)
$$\begin{aligned} {{b}}_\mathrm{{{2}}}= & {} C_\mathrm{ds{2}A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{ds{1}}g_\mathrm{dsC{1}} \right] \nonumber \\&+\,C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \right. \nonumber \\&\left. +\,C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \nonumber \\&-\,C_\mathrm{ds{2}A}C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&-\,C_\mathrm{gs{1}A}C_\mathrm{A}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&-\,C_\mathrm{gs{1}A}C_\mathrm{ds{2}A}C_\mathrm{A}{(}g_\mathrm{ds{1}A}+g_\mathrm{m{3}A}{)(}g_\mathrm{ds{2}}+g_\mathrm{m{2}}) \end{aligned}$$
(54)
$$\begin{aligned} {{b}}_\mathrm{{{3}}}= & {} C_\mathrm{ds{2}A}g_\mathrm{ds{1}}g_\mathrm{dsC{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&+\,\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ \left( C_\mathrm{B}+\,C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) +C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \nonumber \\&\left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{ds{1}}g_\mathrm{dsC{1}} \right] \nonumber \\&+\,C_\mathrm{ds{1}}C_\mathrm{A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&-\,C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}\left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&-\,C_\mathrm{gs{1}A}C_\mathrm{ds{2}A}g_\mathrm{dsC{1}}(g_\mathrm{ds{1}A}+g_\mathrm{m{3}A})(g_\mathrm{ds{2}}+g_\mathrm{m{2}}) \end{aligned}$$
(55)
$$\begin{aligned} {{b}}_\mathrm{{{4}}}= & {} g_\mathrm{ds{1}}g_\mathrm{dsC{1}}\left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ \left( C_\mathrm{B}+C_\mathrm{ds{1}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) +C_\mathrm{ds{2}A}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \right] \nonumber \\&+\,\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \left[ C_\mathrm{A}\left( C_\mathrm{ds{1}}+C_\mathrm{gs{1}A} \right) +g_\mathrm{ds{1}}g_\mathrm{dsC{1}} \right] \nonumber \\&-\,C_\mathrm{gs{1}A}g_\mathrm{dsC{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) \left( g_\mathrm{ds{2}}+g_\mathrm{m{2}} \right) \nonumber \\&-\,g_\mathrm{mP{1}}g_\mathrm{m{1}A}g_\mathrm{m{4}A}C_\mathrm{A}{(}g_\mathrm{ds{2}}+g_\mathrm{m{2}}) \end{aligned}$$
(56)
$$\begin{aligned} {{b}}_\mathrm{{{5}}}= & {} g_\mathrm{dsC{1}}{(}g_\mathrm{ds{2}}\nonumber \\&+\,g_\mathrm{m{2}})\left[ g_\mathrm{ds{1}}\left( g_\mathrm{ds{1}A}+g_\mathrm{m{3}A} \right) \left( g_\mathrm{ds{2}A}+g_\mathrm{ds{4}A} \right) -g_\mathrm{mP{1}}g_\mathrm{m{1}A}g_\mathrm{m{4}A} \right] \end{aligned}$$
(57)

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Azhari, S.J., Nickhah, G. A Novel Ultra-Low-Power, Low-Voltage, Ultra-High Output Resistance and Uniquely High Bandwidth Femto-Ampere Current Mirror. Circuits Syst Signal Process 36, 3527–3548 (2017). https://doi.org/10.1007/s00034-016-0482-5

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