1、Oscillator harmonics generation causes

The reference source for all electronic products originates from the oscillator. Oscillator from nothing to produce a frequency stable signal, for wireless signals to provide benchmarks, for digital signals to provide timing, so the oscillator is actually the heart of electronic products. Reference frequency generation circuits generally use feedback oscillator circuits, such as quartz crystal oscillator circuits, LC oscillator circuits, etc. This oscillator circuit generally includes a resonator, amplifier and phase shifter.

The loop below includes a holding amplifier with a gain of 𝐴 to compensate for the loss of the resonant circuit at a given frequency ω₀. In order to satisfy the positive feedback condition and the continuous amplification of the signal, the phase angle 𝐴β(𝑗ω) of the loop at ω = ω₀ must be zero or an integer multiple of 2π.

The phase and amplitude conditions that allow a complex signal to oscillate in steady state are called Barkhausen conditions:

It follows that integer multiples of harmonics also satisfy the Barkhausen condition and can also oscillate, so this is why an oscillator produces harmonics.

2. Strong odd harmonics of an oscillator

Oscillator initial power-up is no signal, the work of the oscillator starts with noise or a turn-on transient. For this random spectrum signal, there is only a very small amount of energy at the beginning. To achieve stable oscillation, the loop gain |𝐴β(ω₀)| > 1 at ω = ω₀ must be satisfied for small signals.When the loop gain is > 1, the oscillatory energy of the frequency signal that satisfies the phase condition grows exponentially and reaches the saturation value of the amplifier rapidly. If the oscillator does not take control measures of variable gain, the output signal will be limited and the situation shown in the figure below will occur.

If the input power increases further, the gain at ω₀ will decrease and the additional power is pushed into the higher harmonics at multiples of ω₀. Since the limiting is symmetrical, the even harmonics are greatly reduced, so the odd harmonics gain enhancement. This is why oscillators tend to produce strong odd harmonics. For example, a 100M thermostatic crystal oscillator has much stronger harmonics at 300M than at 200MHz.

Summary

Oscillators generate harmonics because integer multiples of the nominal frequency also satisfy the starting conditions, while the saturation of the amplifier leads to an increase in harmonic power, and the symmetry of the waveform makes the odd harmonics stronger.