If crystal oscillator parameters are as follows: R = 5K Ohm, L = 0.5H, Cs = 0.06pF, Cp = 1.25pF, then what is the difference between two frequencies of oscillations?
Question
If crystal oscillator parameters are as follows: R = 5K Ohm, L = 0.5H, Cs = 0.06pF, Cp = 1.25pF, then what is the difference between two frequencies of oscillations?
Solution
To find the difference between two frequencies of oscillations, we first need to calculate the series and parallel resonant frequencies.
The formula for the series resonant frequency (fs) is:
fs = 1 / (2π√(LCs))
The formula for the parallel resonant frequency (fp) is:
fp = 1 / (2π√(L(Cp+Cs)))
Where: L = Inductance = 0.5H Cs = Series capacitance = 0.06pF = 0.06 * 10^-12 F Cp = Parallel capacitance = 1.25pF = 1.25 * 10^-12 F
First, calculate fs:
fs = 1 / (2π√(0.5 * 0.06 * 10^-12)) fs = 1 / (2π√(0.03 * 10^-12)) fs = 1 / (2π * 5.47722557505 * 10^-8) fs = 2.89827534924 * 10^9 Hz
Next, calculate fp:
fp = 1 / (2π√(0.5 * (1.25 + 0.06) * 10^-12)) fp = 1 / (2π√(0.5 * 1.31 * 10^-12)) fp = 1 / (2π * 5.09901951359 * 10^-8) fp = 3.12250225676 * 10^9 Hz
Finally, find the difference between the two frequencies:
Δf = fp - fs Δf = 3.12250225676 * 10^9 Hz - 2.89827534924 * 10^9 Hz Δf = 224226907.52 Hz
So, the difference between the two frequencies of oscillations is approximately 224.23 MHz.
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