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Main points on Resonant Circuit

By Applied Electronics - Monday, January 16, 2017 No Comments
A Resonant Circuit produces signal with high amplitude at a specific frequency than any other. The specific frequency is determined by the component of the circuit. For example in parallel LC circuit the resonant frequency is determined by the inductor and capacitor value. But resonance does not only occur with inductor or capacitor or when they are parallel. In fact, any circuit made of reactive component will resonant at a certain frequency, that is produces high signal amplitude at certain frequency. It can be resistor and capacitor in series for example but the peak amplitude(highest amplitude) is rather flat at the resonant frequency compared to other frequencies.

The aim in designing resonant circuit is to produce a circuit whose output signal has high amplitude at specific frequency called the resonant frequency. LC circuit is one good example. Once the circuit is designed the amplitude vs frequency is plotted and we can see how peakly the plot is at frequencies. Any values for L and C will give a peak but the designer will be interested in designing and obtaining L and C value for specific frequency in which he is interested in . That frequency is given by,
\[ fr=\frac{1}{\sqrt{LC}}\]

The above equation is approximately valid for circuit that has a resistor in series with the voltage source.

A parallel resonant circuit is a bandpass filter designed to resonant at a specific frequency. A parallel resonant allows a specific resonant frequency signal to pass through it and blocks all the others. A bandpass filter is designed to allow to pass a range of frequencies and block the others.

In the figure below a plot of attentuation vs frequency is shown for a typical bandpass filter.



 The passband is frequency band from f1 to f2. These f1 and f2 frequencies are cutoff frequencies. fc is the center frequency of the filter corresponding to resonant frequency of a filter.

The above figure helps us to describe or characterize a filters. Some of the characteristics notions are as follows.
  • Bandwidth
The difference between the upper and lower frequencies f2 and f1, that is, f2-f1 is called the bandwidth of the resonant circuit or the filter. The f1 and f2 frequencies are frequencies where the attentuation is 3dB lower than the maximum attenuation.
\[BW = f2-f1\]
  • circuit Q or design Q
circuit Q or sometimes called design Q is the ratio of the center frequency divided by bandwidth.

\[Q_{cir} = \frac {f_{c}}{BW}\]
  • Shape Factor
This is the ratio of 60dB bandwidth divided by 3dB bandwidth.
\[SF=\frac {60dB BW}{3dB BW}\]
  • Ultimate attenuation
From the figure above, ultimate attenuation is the attenuation from the top of the filter attenuation to the first sideband lobe attenuation.
  • Insertion Loss
Insertion loss is the loss of signal(magnitude) when the resonant circuit or the filter is inserted between the source and load.
  • Ripple
The ripple is the measure of flatness in the passband. If there are no ripple in the passband then the response is ideal. However in reality due to the reactive components of the resonant circuit there will be ripples in the attenuation vs frequency graph.

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