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Erschienen in:
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2013 | OriginalPaper | Buchkapitel

3. Fully Integrated Time References

verfasst von : Fabio Sebastiano, Lucien J. Breems, Kofi A. A. Makinwa

Erschienen in: Mobility-based Time References for Wireless Sensor Networks

Verlag: Springer New York

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Abstract

Measuring the time interval between two events requires the choice of a repetitive and regular phenomenon, such as the oscillation of a pendulum, and then counting how many times this phenomenon takes place between the two events. The science of timekeeping has evolved through the centuries by basically adopting more and more precise and reliable periodic phenomena to keep track of time. From the first attempts using evident astronomical events, such as the motion of the sun and the moon, chronometry evolved by employing periodic phenomena in man-made devices, such as sand motion in hourglasses, oscillations in pendulums, balance wheel rotations in mechanical clocks, electromechanical vibrations in quartz crystal oscillators and absorption or emission of radiations in atomic clocks.

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Vorheriges Kapitel Fully Integrated Radios for Wireless Sensor Networks
Nächstes Kapitel A Mobility-Based Time Reference
Fußnoten
1
x(t) is obtained using the Fourier series expansion of m(t), i.e. \(A(t) = S(t)\sqrt{{a}_{1 }^{2 } + {b}_{1 }^{2}}\), \(\phi (t) + \theta (t) = 2\pi {f}_{0}\epsilon (t) +\arcsin \frac{{a}_{1}} {\sqrt{{a}_{1 }^{2 }+{b}_{1 }^{2}}}\), where \({a}_{1} = \frac{2} {T}{\int \nolimits \nolimits }_{0}^{{T}_{0}}m(t)\cos (2\pi {f}_{0}t)\,\textrm{ d}t\), \({b}_{1} = \frac{2} {T}{\int \nolimits \nolimits }_{0}^{{T}_{0}}m(t)\sin (2\pi {f}_{0}t)\,\textrm{ d}t\).
 
2
Note that phase noise can in general also not be a stationary process, since its statistical property changes with time, such as, for example, its variance that can increase with time. The relation between its standard deviation and its PSD is then not well defined. However, defining jitter as a stationary process with parameter τ justifies the calculations presented in this section, even if not all of them are not formally correct, including the integration of S ϕ(f) to compute the jitter.
 
3
It can be proven, integrating by parts, that \({\int \nolimits \nolimits }_{0}^{+\infty }\frac{{\sin }^{2}x} {{x}^{2}} \textrm{ d}x ={ \int \nolimits \nolimits }_{0}^{+\infty }\frac{\sin x} {x}\textrm{ d}x\); the latter term can be proven to be equal to π ∕ 2 [7].
 
4
The linearity of passive components describes the variation of the component properties, i.e. resistance or capacitance, for a change in the voltage applied to the component. A high linearity is sign of robustness to voltage variation and consequently low sensitivity to supply voltage variations.
 
5
Reference capacitors can be constructed whose capacitance is only dependent on the permittivity and one dimension, such as the Thompson–Lampard capacitor [20, 21]. However, their implementation in an integrated circuit is unpractical.
 
6
This condition can be fulfilled by simply embedding in the oscillator tank all reactive components of the active circuit, such as the parasitic capacitances.
 
7
In order to fulfill this condition, the parasitic capacitances introduced by the active circuit must be minimized; those parasitic can be due to junction capacitances and MOS capacitances, which have different temperature coefficient than the tank capacitor and consequently can not be trimmed out by a temperature compensation.
 
8
A more efficient circuit could be employed by adding a cross-coupled pMOS pair in parallel with the tank and re-using the same bias current of the nMOS pair. This would result in a factor 2 for the lower bound for the bias current but it would not radically change the conclusions.
 
9
State-of-the-art CMOS temperature sensors can achieve an inaccuracy of the order of 0.1 ∘ C, as shown in [39] and as will be further discussed in Chap. 5.
 
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Metadaten
Titel
Fully Integrated Time References
verfasst von
Fabio Sebastiano
Lucien J. Breems
Kofi A. A. Makinwa
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Mobility-based Time References for Wireless Sensor Networks

Print ISBN: 978-1-4614-3482-5

Electronic ISBN: 978-1-4614-3483-2

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-3483-2_3

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