Circuit LLC

A circuit LLC is a Electrical circuit containing a winds ( L ) and a condensing ( C apacity). A circuit LLC is used in the filters, the tuners and the mixers of Fréquence S.

Frequency of resonance

The own pulsation or of Résonance of a circuit LLC (in Radian S a second) is:

\ omega_0 = \ sqrt {1 \ over LLC}

What gives us the Eigen frequency or of Résonance of a circuit LLC in Hertz:

f_0 = {\ Omega \ over 2 \ pi} = {1 \ over {2 \ pi \ sqrt {LLC}}}

Impedance

LLC series

The impedance of a circuit series is given by the sum of the impedances of each one of its components. Maybe in our case:

$Z = Z_ {L} + Z_ {C} \,$

With $Z_ {L} = I \ Omega L \,$ impedance of the reel and $Z_ {C} = \ frac {- I} {\ Omega C} \,$ impedance of the condenser.

$Z = I \ Omega L + \ frac {- I} {\ Omega C}$

What gives us once reduced to the same denominator:

$Z = \ frac {(\ omega^ {2} L C - 1) I} {\ Omega C}$

It will be noticed that the impedance is null at the frequency of resonance $\ omega_0 = \ sqrt {1 \ over LLC}$ but not elsewhere. The circuit thus behaves like a Filtre band pass.

Parallel LLC

The impedance of the circuit is given by the formula:

$Z= \ frac {Z_ {L} Z_ {C}} {Z_ {L} +Z_ {C}}$

After substitution of $Z_ {L} \,$ and $Z_ {C} \,$ by their literal formulas, one obtains:

$Z= \ frac {\ frac {L} {C}} {\ frac {(\ omega^ {2} LC-1) I} {\ Omega C}}$

Who is simplified in:

$Z= \ frac {- L \ Omega I} {\ omega^ {2} LC-1}$

It is noticed that $\ lim_ {\ omega^ {2} LLC \ to 1} Z = \ infty$ whereas the impedance is finished for the other frequencies. Parallel cicuit LLC thus acts like a Filtre band suppressor.

Selectivity

Circuits LLC are often used as filters. It is the ratio L/C which determines their selectivity.

Applications

Oscillating
Filters
Tuners

See too

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