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Modeling >> Passive Devices >> Loaded Resonance Resistance of Crystal
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Message started by pancho_hideboo on Jul 21^st, 2010, 9:27am

Title: Loaded Resonance Resistance of Crystal
Post by pancho_hideboo on Jul 21^st, 2010, 9:27am

I have a trivial question about derivation of characteristic quantity of Crystal.

See http://www.yoketant.com.tw/yoketant/terms.htm

It is well known that Loaded Resonance Resistance(=RL) of Crystal can be approximated as RL≈R1*(1+C0/CL)².

R1 ; Motional Resistance(=Equivalent Series Resistance)
C0 ; Shunt Capacitance
CL ; Load Capacitance

Here my question is how to derive this approximated formula for RL.

Title: Re: Loaded Resonance Resistance of Crystal
Post by vp1953 on Aug 18^th, 2010, 12:03pm

I have not worked out the math but I think this is how it is derived: the network has two shunt arms - one with R1, C1 and L1 and the second with just C0. The loaded resistance term is just the series equivalent of the entire network with some approximations.