Circuit Theory/LC Tuned Circuits

There are no reviewed revisions of this page, so it may not have been checked for quality.

[edit] CL in Series

Z = Z L + Z C

$Z = j\omega L + \frac{1}{j\omega C}$

$Z = \frac{(j\omega)^2 LC + 1}{j\omega C}$

There is one frequency at which $Z L = Z C$

$j\omega L = \frac{1}{j\omega C}$

$(j\omega)^2 = \frac{1}{LC}$

$\omega = \frac{1}{\sqrt{LC}}$

The frequency $\omega = \frac{1}{\sqrt{LC}}$ is called The Resonant Frequency is denoted as ω_o

$\frac {1}{Z} = \frac{1}{Z_L} + \frac{1}{Z_C}$

$\frac {1}{Z} = \frac{1}{j\omega L} + j\omega C$

$\frac {1}{Z} = \frac{(j\omega)^2 LC + 1}{j\omega L}$

There is one frequency at which $Z L = Z C$

$j\omega L = \frac{1}{j\omega C}$

$(j\omega)^2 = \frac{1}{LC}$

$\omega = \frac{1}{\sqrt{LC}}$

The frequency $\omega = \frac{1}{\sqrt{LC}}$ is called The Resonant Frequency is denoted as ω_o