Therefore, in our three stage RC network above the amplifier gain must be greater than 29.

Explanation: The physical size of the quartz crystal affects the final or fundamental frequency of oscillations. The fundamental frequency is generally called the crystals “characteristic frequency”. The crystals characteristic or characteristic frequency is inversely proportional to its physical thickness between the two metalized surfaces.

The oscillation frequency varies from few hertz to hundreds of GHz.

Explanation: In oscillators using positive feedback it is important that amplitude of the oscillator output remains stable. Therefore the closed loop gain must be 1 (unity). In other words, the gain within the loop; provided by the amplifier, should exactly match the losses (caused by the feedback circuit) within the loop.

The Nyquist plot combines gain and phase into one plot in the complex plane. It is drawn by plotting the complex gain g(iω) for all frequencies ω. That is, the plot is a curve in the plane parameterized by ω.

Explanation: The oscillator is a device which gives an AC output without any input. Oscillator needs an input signal for start. But once the capacitor is charged then, Oscillator can effectively start work without an input signal.

The lead-lag circuit in the Wien-bridge oscillator has a resonant frequency fr, at which the phase shift through the circuit is and the attenuation is 1/3.

Explanation: The slope of the crystals impedance suggests that as the frequency increases across its terminals. At a particular frequency, the interaction between the series capacitor and the inductor creates a series resonance circuit reducing the crystals impedance to a minimum and equal to Resistance.

This is resonant frequency, Oscillations can occur only at this frequency as the filter provides significant negative feedback at frequencies below or above the resonant frequency which is not good for oscillation.

Explanation: The applied negative feedback can improve its performance (gain stability, linearity, frequency response, step response) and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.