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

["Ioan Gheorma" <igheorma@xxxxxxxxxxxx>]

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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