Draw and explain colpitts oscillator, Electrical Engineering

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Q. Draw and explain Colpitts oscillator?

Colpitt's oscillator is a superb circuit which is used widely in commercial signal generations of  frequency of 100 Mhz . It consists of  a single state inverting amplifiers and an (phase shift network). The two series capacitors C1 and C2 form the potential divider for providing the feedback voltage ie. Voltage developed across the capacitor C2 provides the regenerating feedback.If you consider positive feedback is applied to compensate for the losses in the tuned circuit, the amplifier and feedback circuit create a negative resistor. When Z1 and Z2 are capacitive, the impedance across the capacitors can be estimated from a formula I won't lay on you here because it includes beta, hie, as well as XC1 and XC2. Suffice to say it can be shown that the input impedance is a negative resistor in series with C1 and C2.  And the frequency is in accordance with:

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