Electronics/Electronics Formulas/2 Port Network

RL

$\frac{v_o}{v_i}=\frac{j\omega L}{R+j\omega L}$

$\frac{v_o}{v_i}=\frac{j\omega T}{1+j\omega T}$

$T=\frac{L}{R}$

LR

$\frac{v_o}{v_i}=\frac{R}{R+j\omega L}$

$\frac{v_o}{v_i}=\frac{1}{1+j\omega T}$

$T=\frac{L}{R}$

RC

$\frac{v_o}{v_i}=\frac{\frac{1}{j\omega C}}{R+\frac{1}{j\omega C}}$

$\frac{v_o}{v_i}=\frac{1}{1+j\omega T}$

$T=RC$

CR

$\frac{v_o}{v_i}=\frac{R}{R+\frac{1}{j\omega C}}$

$\frac{v_o}{v_i}=\frac{j\omega T}{1+j\omega T}$

$T=RC$

LR - CR

$\frac{v_o}{v_i}=(\frac{1}{1+j\omega \frac{L}{R}})(\frac{j\omega RC}{1+j\omega RC})$

${\omega }_2-{\omega }_1=\frac{R}{L}-\frac{1}{RC}$

CR - LR

$\frac{v_o}{v_i}=(\frac{1}{1+j\omega RC})(\frac{j\omega \frac{L}{R}}{1+j\omega \frac{L}{R}})$

${\omega }_2-{\omega }_1=\frac{R}{L}-\frac{1}{RC}$