[SOLVED] output amplitude for a LC-tank oscillator

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palmeiras

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Hello everyone!


Considering a LC-tank oscillator, the single-ended output voltage amplitude is given by:

Vtank = ( Bias_current * Equivalent parallel resistance_tank) / PI

Hower, this equation is converted to the next one for high frequencies:

Vtank ~ bias_current * Equivalent parallel resistance_tank


Why? What did happen with "PI"?

Thank you very much
 

PI is coming from Fourier expansion of square wave signal.The textbooks assume that the transistors are either ON or OFF state so the their currents are presumed being as Square Wave.Therefore there is a PI multiplier.It's a rough approximation and it's been assumed that the frequency is relatively low.This current becomes more sinusoidal rather than square and PI term disappears at high frequencies due limited slew rate of the transistors.But the reality is not as stated.( you should check it how much it is..)
 
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