Editing Electronic oscillator (section)

===Frequency stability===
Temperature changes, other environmental changes, aging, and manufacturing tolerances will cause component values to "drift" away from their designed values.<ref name="Stephan1">{{cite book
 | last1  = Stephan
 | first1 = Karl 
 | title  = Analog and Mixed-Signal Electronics
 | publisher = John Wiley and Sons
 | date   = 2015
 | location = 
 | pages  = 192–193
 | language = 
 | url    = https://books.google.com/books?id=cDAABwAAQBAJ&pg=PA192
 | doi    = 
 | id     = 
 | isbn   = 978-1119051800
 }}</ref><ref name="Vidkjaer">{{cite web
  | last = Vidkjaer
  | first = Jens
  | title = Ch. 6: Oscillators
  | work = Class Notes: 31415 RF Communications Circuits
  | publisher = Technical Univ. of Denmark
  | date = 
  | url = http://rftoolbox.dtu.dk/book/Ch6.pdf
  | doi =
  | access-date = October 8, 2015}} p. 8-9</ref> Changes in ''frequency determining'' components such as the [[tank circuit]] in LC oscillators will cause the oscillation frequency to change, so for a constant frequency these components must have stable values. How stable the oscillator's frequency is to other changes in the circuit, such as changes in values of other components, gain of the amplifier, the load impedance, or the supply voltage, is mainly dependent on the [[Q factor]] ("quality factor") of the feedback filter.<ref name="Stephan1" /> Since the ''amplitude'' of the output is constant due to the nonlinearity of the amplifier (see Startup section below), changes in component values cause changes in the phase shift <math>\phi\;=\;\angle A\beta(j\omega)</math> of the feedback loop. Since oscillation can only occur at frequencies where the phase shift is a multiple of 360°, <math>\phi\;=\;360n^\circ</math>, shifts in component values cause the oscillation frequency <math>\omega_0</math> to change to bring the loop phase back to 360n°. The amount of frequency change <math>\Delta \omega</math> caused by a given phase change <math>\Delta \phi</math> depends on the slope of the loop phase curve at <math>\omega_0</math>, which is determined by the <math>Q </math><ref name="Stephan1" /><ref name="Vidkjaer" /><ref name="Huijsing">{{cite book
 | last1  = Huijsing
 | first1 = Johan
 | last2  = van de Plassche
 | first2 = Rudy J.
 | last3  = Sansen
 | first3 = Willy
 | title  = Analog Circuit Design
 | publisher = Springer Scientific and Business Media
 | date   = 2013
 | location = 
 | pages  = 77
 | language = 
 | url    = https://books.google.com/books?id=B8fSBwAAQBAJ&pg=PA77
 | doi    = 
 | id     = 
 | isbn   = 978-1475724622
 }}</ref>
<ref name="Kazimierczuk">{{cite book
 | last1  = Kazimierczuk
 | first1 = Marian K. 
 | title  = RF Power Amplifiers, 2nd Ed.
 | publisher = John Wiley and Sons
 | date   = 2014
 | location = 
 | pages  = 586–587
 | language = 
 | url    = https://books.google.com/books?id=-U7YBAAAQBAJ&pg=PA587
 | doi    = 
 | id     = 
 | isbn   = 978-1118844335
 }}</ref>
:<math>{d\phi \over d\omega}\Bigg|_{\omega_0} = -{2Q \over \omega_0}\,</math> &nbsp;&nbsp;&nbsp;&nbsp; so &nbsp;&nbsp;&nbsp;&nbsp;  <math>\Delta \omega = -{\omega_0 \over 2Q}\Delta \phi \,</math>
RC oscillators have the equivalent of a very low <math>Q</math>, so the phase changes very slowly with frequency, therefore a given phase change will cause a large change in the frequency. In contrast, LC oscillators have [[tank circuit]]s with high <math>Q</math> (~10<sup>2</sup>).  This means the phase shift of the feedback network increases rapidly with frequency near the [[resonant frequency]] of the tank circuit.<ref name="Stephan1" /> So a large change in phase causes only a small change in frequency.  Therefore, the circuit's oscillation frequency is very close to the natural resonant frequency of the [[tuned circuit]], and doesn't depend much on other components in the circuit.  The quartz crystal resonators used in [[crystal oscillator]]s have even higher <math>Q</math> (10<sup>4</sup> to 10<sup>6</sup>)<ref name="Kazimierczuk" /> and their frequency is very stable and independent of other circuit components.