9.9 : 频率响应

Consider a radio transmitter unit that incorporates an RLC series resonance band-pass filter.

This circuit's frequency response indicates that the current magnitude initially increases, peaks at the resonance frequency, and decreases as the frequency increases.

The power dissipation, corresponding to the maximum current value, is highest at resonance.

At the half-power frequencies, the current is 0.707 times the maximum current, and the power dissipated is half the maximum.

The resonant frequency is the geometric mean of these half-power frequencies.

The bandwidth, defined as the frequency range between the half-power frequencies, equals the ratio of resistance to inductance.

The quality factor, representing the sharpness of the resonance curve, relates the maximum energy stored in the circuit to the energy dissipated per oscillation cycle.

At resonance, reactive energy oscillates between the reactive elements, yielding an expression of the quality factor in terms of reactances.

This factor can be expressed as the ratio of the resonant frequency to the bandwidth.

A higher quality factor implies a narrower bandwidth, thereby increasing selectivity.