Colpitts Oscillator Design

The Colpitts oscillator is a type of high frequency oscillator consisting of a LC tank within the feedback loop of a class-A common-emitter bi-polar junction transistor (bjt) circuit. The tank circuit usually consists of a pair of capacitors in series joining to an inductance coil. The simplest type of bjt circuit consists of a shunt-fed LC tank as shown above.

For this oscillator to start, the voltage gain must be equal to or greater than the Barkhausen criterion described by the following expression:

In this expression, A_v is the amplifier voltage gain, and beta is the feedback ratio. Usually engineers forget to use this part in their calculation, which is why their circuits do not work!

In this type of tank circuit the output voltage appears across C₁ and the feedback voltage across C₂ therefore, we get the above expression for beta:

This means that for the oscillator to start, the voltage gain A_v must satisfy the above condition in terms of capacitance ratios.

The antiresonant frequency of the Colpitts oscillator occurs when the reactance presented by the inductance, and total capacitance, are equal.

This is where C is the total capacitance consisting of C₁ and C_2.

Since the ratio of C₁ and C₂relate to beta, we can get an expression for C₂ in terms of C and beta. This formula helps to calculate individual capacitor values with proper ratios. If these ratios are not correct, then your oscillator will not start, hence this part is extremely important.

A high Q value is extremely important in this circuit as it maintains stable oscillations and produces near perfect sine waves when the transistor is driven beyond class A. In this formula, X_L is the resistance of the coil at the resonant frequency, and R_S is the DC resistance of the coil.

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