By Eric Vittoz
Electronic oscillators utilizing an electromechanical gadget as a frequency reference are irreplaceable parts of systems-on-chip for time-keeping, service frequency new release and electronic clock iteration. With their very good frequency balance and extremely huge caliber issue Q, quartz crystal resonators were the dominant resolution for greater than 70 years. yet new probabilities are actually provided through micro-electro-mechanical (MEM) resonators, that experience a qualitatively exact similar electric circuit.
Low-Power Crystal and MEMS Oscillators concentrates at the research and layout of crucial schemes of built-in oscillator circuits. It explains how those circuits should be optimized by way of top exploiting the very excessive Q of the resonator to accomplish the minimal energy intake appropriate with the necessities on frequency balance and section noise. the writer has forty years of expertise in designing very low-power, high-performance quartz oscillators for watches and different battery operated structures and has amassed lots of the fabric in this interval. a few extra unique fabric regarding section noise has been further. the reasons are in general supported via analytical advancements, while computing device simulation is restricted to numerical examples. the most half is devoted to crucial Pierce circuit, with a whole layout method illustrated by means of examples. Symmetrical circuits that grew to become renowned for contemporary telecommunication structures are analyzed in a final chapter.
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2 Qualitative example of the locus of Zc(1) (|Ic |). This corresponds to point 0, where Zc(1) is identical to the small-signal impedance Zc of the circuit. The real part of Zc should be negative (as is the case in this example) to be able to compensate the losses of the resonator. When the current is large enough to produce harmonic components of V (t), the amplitude |V(1) | of its fundamental component is normally progressively reduced, thereby reducing the negative real part of Zc(1) , as is the case for points 1 to 4.
For the particular case depicted in Fig. 4, there are two solutions labelled A and B. 2) for phase stability. 4 Loci of Zc (Gm ) and −Zm (p) in the complex plane. The only stable solution is at intersection A, for the particular value Gmcrit of Gm called critical transconductance for oscillation. 15) (as long as the circuit remains linear). A maximum amount of net negative resistance Rn0 + Rm is obtained for Gm = Gmopt , corresponding to a minimum value of time constant τ0 . If Gm is increased beyond Gmcrit , τ0 starts increasing again, until it becomes infinite at point B, for Gm = Gmmax .
11 Variation of the channel noise spectral density with increasing VDS = VD − VS. 61) SI 2 = 2qID (saturated weak inversion). nD In strong inversion, the noise for a given value of drain current is reduced, since Gms /ID is reduced. Flicker noise due to carrier trapping and mobility fluctuations is also important in MOS transistors. Since its spectral density is inversely proportional to the frequency, it dominates at low frequencies. It can be approximated by a noise voltage VnG added to the gate voltage, with a spectral density SV 2 given by nG Kf 1 .