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# KU EECS 622 - Oscillator Stability

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3/7/2005 Oscillator Stability.doc 1/3 Jim Stiles The Univ. of Kansas Dept. of EECS Oscillator Stability In addition to noise, spurs, and harmonics, oscillators have a problem with frequency/phase instability. I.E., a better model for the oscillator signal is: ()()0cc rvtAcost tωφ=+⎡⎤⎣⎦ where ()rtφ is a random process ! Note then the frequency will likewise be a random process: ()()()()000rrrdt ttdtdtdttωφωφωωω+⎡⎤⎣⎦==+=+ In other words, the frequency of an oscillator will vary slightly with time. We refer to these random variations as oscillator instability, and these instabilities come in two general types: The derivative a random process is likewise a random process!3/7/2005 Oscillator Stability.doc 2/3 Jim Stiles The Univ. of Kansas Dept. of EECS 1) Long term instabilities – These are slow changes in oscillator frequency over time (e.g., minutes, hours, or days), generally due to temperature changes and/or oscillator aging. For good oscillators, this instability is measured in parts per million (ppm). Parts per million is a similar to describing the instability in terms of percentage change in oscillator frequency. However, instead of expressing this change relative to one one-hundredth of the oscillator frequency 0ω (i.e., one percent of the oscillator frequency), we express this change relative to one one-millionth of the oscillator frequency 0ω! A more direct way of expressing “parts per million” is “Hz per MHz”—in other words the amount of frequency change rω∆ in Hz, divided by the oscillator frequency expressed in MHz. For example, say an oscillator operates at a frequency of 0100fMHz= . This oscillator frequency will can (slowly) change as much as 10rfkHz∆=± over time. We thus say that the long-term stability of the oscillator is: ()()010 000100100rfHz,ppmfMHz∆±==± 2) Short-term instabilities - The short-term instabilities of oscillators are commonly referred to as phase noise—a result of having imperfect resonators!3/7/2005 Oscillator Stability.doc 3/3 Jim Stiles The Univ. of Kansas Dept. of EECS With phase noise, the random process ()rtφ has very small magnitude, but changes very rapidly (e.g., milliseconds or microseconds). This is equivalent to narrow-band frequency modulation (FM), and the result is a spreading of the oscillator signal spectrum. Phase-noise is a very complex phenomenon, yet can be critical to the performance (or lack thereof) of a radio receiver. As such, it deserves its very own

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