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

Circuit Configuration

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

Z_L - Z_C = 0 .

Z = Z_R + Z_L + Z_C = Z_R + 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

ω	I
0	0
$\omega ={\sqrt {\frac {1}{LC}}}$	${\frac {V}{R}}$
00	0

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

Tuned Resonance Selected Band Pass Filter

Operation

RLC eries

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 $\omega _{1}-\omega _{2}$