Hello Ioan Gheorma, Thanks for the detailed and clear explaination. I am working on your inputs. I ended up seeing the paper "General Oscillator Characterization Using linear OPen-Loop S-PArameters" by Mitch RAndall and Terry Hock in IEEE Transcations on Microwave Th. and Techniques of 2001. The authors have come up with an expression for 90% rise time which also includes the gain term of the amplifier...higher the gain lesser is the startup time of oscillator....and direct relationship with the Q of the resonator. Sincerely Himanshu Arora --- Ioan Gheorma <igheorma@xxxxxxxxxxxx> wrote: > Hi Arora, > > I don't have SAW experience, however since nobody > answered to your question > I could tell you some very general relationships for > resonators. These work > for any type of resonators if their response can be > approximated with that > of a second order linear system - and at least near > resonance this > approximation should work well in most cases. > You find the Q of the resonator from the frequency > response of the system, > in this case Q= zeta/2, where zeta is the damping > factor. > Then you calculate the time domain response of the > system with a sinewave > excitation that starts at zero (use Laplace > transforms). This response > contains a transient and a permanent term. The > startup time is related to > the decay of the transient term, and this decay > should be of the exp(-a t) > form, with a=zeta*omega0. > If you take the 0-90% rise time tr=2.3/a=2.3Q/(pi > f0)=0.73Q/f0, where f0 is > the resonance frequency. Or if you want the 0 - 96% > rise time is approx = > Q/f0. > This makes sense, as the quality factor increases > the systems needs more > oscillations to stabilize, and higher resonance > frequency means the system > is faster - lower startup time. > > If the resonator's response cannot be approximated > with that of a second > order system you have to use more math, but the > steps are similar. I > noticed that SAW resonators are approximated by > equivalent circuits having 3 > reactive elements, and have both a resonance and an > anti-resonance; thus 3rd > order system calculations may be needed. Your > definition of bandwidth and Q > factor may be different (for some SAW resonators the > definition of bandwidth > may be the frequency separation between resonance > and anti-resonance). > However, if your application is limited to > frequencies very close and > centered to the resonance or to the anti-resonance > but does not include both > you can go with the 2nd order approximation. > The results apply only for the resonator, if you > include the resonator in an > oscillator you have to consider the whole system. > > Regards, > Ioan Gheorma > > > -----Original Message----- > From: si-list-bounce@xxxxxxxxxxxxx > [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of > Himanshu Arora > Sent: Tuesday, September 03, 2002 12:32 PM > To: si-list@xxxxxxxxxxxxx > Subject: [SI-LIST] Startup time of SAW Resonators > > > > Hello, > > I am doing research on satrtup time of SAW based > Resonators for Amplitude Shift Keying Applications. > In > literature it is mentioned that the high Q of SAW > resonators results in high value of start up time. > > Does there exist any mathemtical relationship which > gives startup time as a function of Q for SAW > resonators? > > Sincerely > > Himanshu Arora > > __________________________________________________ > Do You Yahoo!? > Yahoo! Finance - Get real-time stock quotes > http://finance.yahoo.com > ------------------------------------------------------------------ > To unsubscribe from si-list: > si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in > the Subject field > > or to administer your membership from a web page, go > to: > //www.freelists.org/webpage/si-list > > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the > Subject field > > List archives are viewable at: > //www.freelists.org/archives/si-list > or at our remote archives: > http://groups.yahoo.com/group/si-list/messages > Old (prior to June 6, 2001) list archives are > viewable at: > http://www.qsl.net/wb6tpu > > > __________________________________________________ Do You Yahoo!? Yahoo! Finance - Get real-time stock quotes http://finance.yahoo.com ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu