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- W4360606717 abstract "Startup time <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$(mathrm{t}_{mathrm{s}})$</tex> and energy <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$(mathrm{E}_{mathrm{S}})$</tex> of crystal oscillators (XO) determine the efficiency of ultra-low-power duty-cycled loT radios. MHz-range X0s take a few milliseconds to reach the steady state without any startup aid [1–6], limiting the latency and average power of the radios. Injecting energy into the crystal can raise its motional current <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$(mathrm{i}_{mathrm{M}})$</tex> for <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{t}_{mathrm{s}}$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{E}_{mathrm{S}}$</tex> reduction, but only if the injection source's frequency <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$(mathrm{f}_{text{inj}})$</tex> is close to the crystal's series resonant frequency <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$(mathrm{f}_{mathrm{s}})$</tex> . The two-step injection technique, which calibrates the injection source using the XO's signal after the 1 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>st</sup> injection, can safeguard <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{f}_{text{inj}}$</tex> for the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$2^{text{nd}}$</tex> injection [2], [3]. Unfortunately, the phase-locked loop takes>1,000 cycles to calibrate in a closed-loop fashion, opposing the reduction of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{t}_{mathrm{s}}$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{E}_{mathrm{S}}$</tex> ." @default.
- W4360606717 created "2023-03-24" @default.
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- W4360606717 date "2023-02-19" @default.
- W4360606717 modified "2023-10-16" @default.
- W4360606717 title "3.6 A 12/13.56MHz Crystal Oscillator with Binary-Search-Assisted Two-Step Injection Achieving 5.0nJ Startup Energy and 45.8μs Startup Time" @default.
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- W4360606717 doi "https://doi.org/10.1109/isscc42615.2023.10067401" @default.
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