By analyzing the pulse transformer and ideal drive electric current wave, we try to improve the rate of changing-over, discuss the damped oscillation, point out existing circuit design error, and working a new circuit design which can reduce the common circuit circulation and switch loss.

The mathematical essence of damped oscillation is researched with the qualitative theory of differential equation from the odd characters of the plane autonomous system.

The damped oscillation wave is expressed to harmonics in the Fourier series,the loss resistance of inductor and capacitor are measured when the first harmonic and the harmonics which replacing the damped oscillation wave are applied to the RLC series circuit.

The critical damping characteristics of a linear oscillator was analyzed based on energy method and the conclusion obtained is that the linear oscillator at critical damping state can pass the balance site once under specific condition,the force of the oscillator possesses the“critical property”and the energy E(t) curve of the oscillator is the fastest convergent.

After analyzing the damped motion of vibrator, the paper derives additional conditions for critical damping.

This article analyses its irregular attenuated movement in the condition of over damping and critical damping.

In this paper, it is pointed out that the accuracy of measurement must be considered for the discussion about the restitution time of damped vibration, and it is in the “critical state of weakly damped vibration” defined by this paper, not the critical damping state, that the restitution time is the shortest.