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The term
"resonance"
literally translates to "to vibrate with". In physics,
resonance is the phenomenon wherein two systems are vibrating within
the same frequency range, creating order. In electronics,
resonance is a state wherein a tuned circuit's capacitive reactance
is equal to its inductive reactance.
A
series LC
circuit
that is in resonance, i.e., excited by a signal at its resonant
frequency, exhibits zero reactance. On the other hand, a
parallel
LC circuit
exhibits infinite reactance at its resonant frequency. Series
and parallel LC circuits may therefore be combined to form either a
band-pass filter or a
band-stop filter.
The
frequency at which resonance in a tuned LC circuit occurs is given
by the following formula:
fr = 1 / [2π(sqrt(LC))]
where
fr =
resonant frequency (Hz);
L = the
inductance (H); and
C = the
capacitance (F).
Using the
equation above, one can calculate either the value of the inductance
L or capacitance C that will result in resonance at a given
frequency fr:
L =
1 / [4π2fr2C]
or
C = 1 /
[4π2fr2L].
The ratio
of the reactance of the tuned circuit to its resistance is called
the
"quality
factor",
or Q factor, or simply Q. Thus, Q is the ratio of the energy
stored to the energy dissipated in the circuit per cycle.
The
reactance of an inductance L is equal to 2πfL while that of a
capacitance C is equal to 1/2πfC. Thus, for a series RL
circuit, the quality factor Q is given by the equation:
Q = 2πfrL / R.
On the other hand, the quality factor Q for a series RC circuit is
given by the equation:
Q = 1 / 2πfrCR.
The
quality factor Q of a tuned circuit is given by the equation:
Q = fr
/ B
where B is the bandwidth of the circuit in Hz. The bandwidth of a
circuit is the frequency interval between its half-power points f2
and f1, or
B = f2
- f1.
Thus,
Q = fr / (f2 - f1).
Since Q
is the ratio of the resonant or center frequency fr to the bandwidth
B, Q is a measure of the 'sharpness' of the response of the tuned
circuit to the resonant frequency. Thus, a circuit with a
high Q
will exhibit a higher amplitude at the resonant frequency, but will
decay more quickly as the frequency moves away from the resonant
frequency.
See Also:
Band-Pass Filter;
Band-Stop Filter; More
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