Electronics Handbook/Circuits/Tuned Resonance Selected Band-pass Filter

Analysis

 * At ω = 0, Capacitor opens circuit . Therefore, I = 0


 * At Resonance Frequency, Impedance of L and C cancel out.
 * $$\omega L = \frac{1}{\omega C}$$
 * $$\omega = \sqrt{\frac{1}{LC}}$$

Therefore, the Impedance of the circuit is R and at minimum value and Current will be at its maximum value
 * ZL - ZC = 0.
 * Z = ZR + ZL + ZC = ZR + 0 = R
 * $$I = \frac{V}{R}$$


 * At ω = 0, Inductor opens circuit . Therefore, I = 0

From three paired value ω and I graph of I - ω can be plotted. From graph
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! ω !! I
 * 0 || 0
 * $$\omega = \sqrt{\frac{1}{LC}}$$ || $$\frac{V}{R}$$
 * 00 || 0
 * $$\omega = \sqrt{\frac{1}{LC}}$$ || $$\frac{V}{R}$$
 * 00 || 0
 * 00 || 0


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At resonance frequency $$\omega = \sqrt{\frac{1}{LC}}$$, current is at its maximum value $$I = \frac{V}{R}$$. If the current is reduced to half the resonance value $$I = \frac{V}{2R}$$ then the circuit is respond to a bandwidth of frequencies $$\omega_1 - \omega_2$$. Further reduce or increase the value of the current below or above $$I = \frac{V}{2R}$$ the circuit will respond to a Wider or Narrower Bandwidth

In conclusion, RLC series can be used as a Resonance Tuned Selectede Band Width Filter by Tuning L or C into Resonance Frquency to have a maximum value. Increasing or Descreasing the value of R to yield a desired bandwidth

Summary

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! Tuned Resonance Selected Band Pass Filter!! Operation
 * RLC eries [[Image:RLC series circuit.png|left|100px]]|| 1) Tune L or C into Resonance Frquency$$\omega_o = \sqrt{\frac{1}{LC}}$$ . Current is at its mmaximum value$$I = \frac{V}{R}$$ 2) Reduce Current by increasing R . Current value at $$I = \frac{V}{2R}$$ voltage is stable over a band width $$\omega_1 - \omega_2 $$ . Current under the value I < $$\frac{V}{2R}$$ Current is stable over a wide band width $$\omega_1 - \omega_2 $$ . Current over the value I > $$\frac{V}{2R}$$ Current is stable over a narrow band width $$\omega_1 - \omega_2 $$
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