Parameters
Inductance L
10.0 μH
C1
100 pF
C2
100 pF
Resistance R
10.0 kΩ
Q Factor
50
Loop Gain A
3.0
Barkhausen Criterion
—
Frequency f₀
—
Feedback Ratio β
—
Loop Gain |Aβ|
—
Q Factor
—
Gain Margin [dB]
—
Phase Noise [dBc/Hz]
Nyquist Plot — Loop Gain Aβ(jω)
Oscillation Frequency Formulas
Colpitts: $f_0 = \dfrac{1}{2\pi\sqrt{L\cdot\frac{C_1 C_2}{C_1+C_2}}}$
Wien Bridge: $f_0 = \dfrac{1}{2\pi RC}$, gain condition $A \geq 3$
RC Phase Shift: $f_0 = \dfrac{1}{2\pi\sqrt{6}\cdot RC}$, $A \geq 29$
Barkhausen criterion: $|\mathbf{A\beta}| \geq 1$ and $\angle A\beta = 0°$
Applications: Colpitts/Hartley are used for RF local oscillators and PLL references. Wien Bridge produces low-distortion audio signals for test equipment. Crystal oscillators provide precision clock references for CPUs, GPS, and communications systems.