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

 * $$\frac{v_o}{v_i} = (\frac{1}{1 + j\omega RC})(\frac{j \omega \frac{L}{R}}{1 + j \omega \frac{L}{R}})$$
 * $$\omega_2 - \omega_1 = \frac{R}{L} - \frac{1}{RC}$$