i) The parameters of a crystal oscillator equivalent circuit are L;= 0.5 H, C;= 0.1 pF, R3 = 5 kn and CM= 10 pF. Determine the series resonant frequency, fs and the parallel resonant frequency, fp.

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i) The parameters of a crystal oscillator equivalent circuit are L;= 0.5 H, C;= 0.1 pF,
R; = 5 kn and CM= 10 pF. Determine the series resonant frequency, fs and the
parallel resonant frequency, fp.
ii) Prove that = (1+)
Is
2CM-
Hint: Use the following binomial series definition to simplify your equation.
(1+ x)“ = Ek=o) x*=1+ ax +
α(α-1)
+
%3D
2!
Transcribed Image Text:i) The parameters of a crystal oscillator equivalent circuit are L;= 0.5 H, C;= 0.1 pF, R; = 5 kn and CM= 10 pF. Determine the series resonant frequency, fs and the parallel resonant frequency, fp. ii) Prove that = (1+) Is 2CM- Hint: Use the following binomial series definition to simplify your equation. (1+ x)“ = Ek=o) x*=1+ ax + α(α-1) + %3D 2!
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