FreeLists / si-list / [SI-LIST] Re: Startup time of SAW Resonators

[Himanshu Arora <ha324005@xxxxxxxxx>]

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
> 
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