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Bandwidth

As already mentioned, a series resonant circuit can be used to filter out certain signal frequencies. This type of circuit is also termed a notch filter or more usually a band-stop filter. The diagram below shows a filter circuit with an input voltage Ue and output voltage Ua.

Electric Resonant Circuits !

This circuit acts as a frequency-dependent voltage divider where the output voltage is tapped via the reactance X = XL - XC. At very low frequencies, the capacitor behaves like a very high resistance, so that the output voltage is nearly identical to the input voltage. The same applies at very high frequencies, due to the correspondingly high inductive reactance. At the resonant frequency fr, the total reactance is zero, so that the output voltage is also zero in this instance. The greater the difference between the input voltage frequency and resonant frequency, the higher the reactance and the output voltage. The diagram below shows the amplitude response (i.e. ratio between output and input voltages) of a band-stop filter near the resonant frequency (resonance peak).

Electric Resonant Circuits !

Another characteristic parameter of a resonant circuit of this kind is its bandwidth B which indicates the breadth of the frequency range blocked by the filter. The bandwidth is the range between the sub-resonance frequency at which the output voltage has dropped to 0.707 (i.e. 1/Ö2) times the maximum value and the corresponding frequency above the resonance level. The diagram above demonstrates how to determine bandwidth from amplitude response. The narrower the bandwidth, the steeper the drop in the characteristic near the resonant frequency, i.e. the more accurate the filter. The quotient of the resonant frequency and bandwidth is equivalent to the quality Q of the circuit, i.e.

Electric Resonant Circuits !

The higher an oscillating circuit's quality, the steeper and narrower the resonance peak.

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