Mathematically speaking, it is a kind of free oscillation that appears in some nonlinear systems.
A typical example is the system described by Vanderbilt equation, whose form is MX-f (1-x2) x-kx = 0 (m >; 0，f & gt0，k & gt0)。
Where x and x are the first and second derivatives of the variable x.
The analysis shows that when the value of x is small, the damping f is negative, so the motion diverges; When the value of x is large, the damping f is positive, so the motion is attenuated.
Extended data:
1. Conditions for self-excited oscillation
1, amplitude balance condition |AF|= 1
2. Phase balance condition φ a+φ f = 2nπ (n = 0, 1, 2, 3 ...) where A refers to the gain (open-loop gain) of the basic amplifier circuit.
F means that the feedback coefficient of the feedback network must meet the initial condition that |AF| is slightly greater than 1. The basic amplifier circuit must be composed of multistage amplifier circuits to achieve high open-loop amplification.
However, if negative feedback is added between the stages of the multistage amplifier circuit, the phase shift of the signal may make the negative feedback amplifier circuit unstable and produce self-excited oscillation.
The fundamental reason of self-excited oscillation of negative feedback amplifier circuit is the additional phase shift of AF (loop amplification factor). Single-stage and two-stage amplifier circuits are stable, and three-stage or more negative feedback amplifier circuits are stable.
As long as there is a certain feedback depth, self-excited oscillation may occur, because frequencies satisfying 180 degree phase shift (satisfying the phase condition) can be found in the low frequency band and the high frequency band respectively. If the amplitude condition |AF|= 1 is satisfied at this time, self-excited oscillation will occur.
Therefore, for the negative feedback amplifier circuit with three or more stages, correction measures must be taken to destroy the self-excited oscillation and achieve the purpose of stable operation of the circuit.
Second, the composition of sine wave oscillation circuit
From the above analysis, it can be seen that the sine wave oscillation circuit must have the following four basic links.
(1) amplifier circuit: The process from initial vibration to dynamic balance of the circuit is to obtain a certain amplitude of output and realize energy control.
(2) Frequency selection network: determine the oscillation frequency of the circuit to make the circuit generate single-frequency oscillation, that is, ensure the circuit to generate sine wave oscillation.
(3) Positive feedback network: introducing positive feedback to make the input signal of the amplifier circuit equal to the feedback signal.
(4) Amplitude stabilization link: nonlinear link, which is used to stabilize the amplitude of the output signal.
In many practical circuits, frequency selection network and positive feedback network are often combined into one; Moreover, for the discrete component amplifier circuit, the amplitude stabilization link is no longer added, but depends on the nonlinearity of transistor characteristics to stabilize the amplitude.
Sine wave oscillation circuits are often named according to the components used in frequency selection networks, and are divided into three types: RC sine wave oscillation circuits, LC sine wave oscillation circuits and timely crystal sine wave oscillation circuits.
The oscillation frequency of RC sine wave oscillation circuit is low, generally below 1MHz; The oscillation frequency of LC sine wave oscillation circuit is relatively high, generally above 1MHz; The synchronous crystal sine wave oscillation circuit can also be equivalent to LC sine wave oscillation circuit, which is characterized by very stable oscillation frequency.
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