Practical Electronics/Circuits Analysis/Two Port Network

RC

 * $$\frac{V_o}{V_i} = \frac{\frac{1}{j\omega C}}{R + \frac{1}{j\omega C}} = \frac{1}{1 + j\omega T}$$
 * $$T = RC$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$
 * This circuit has Stable voltage at low frequency therefore suitable for filtering low frequency therefore the name Low Pass Filter

CR

 * $$\frac{V_o}{V_i} = \frac{R}{R + \frac{1}{j\omega C}} = \frac{j\omega T}{1 + j\omega T}$$
 * $$T = RC$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$
 * This circuit has Stable voltage at high frequency therefore suitable for filtering high frequency therefore the name High Pass Filter

LR

 * $$\frac{V_o}{V_i} = \frac{R}{R + j\omega L} = \frac{1}{1 + j\omega T}$$
 * $$T = RC$$
 * $$\omega_o = \frac{j\omega L}{R + j\omega L} = \frac{1}{1 + j\omega T}$$
 * This circuit has Stable voltage at low frequency therefore suitable for filtering low frequency therefore the name Low Pass Filter

RL

 * $$\frac{V_o}{V_i} = \frac{R}{R + \frac{1}{j\omega C}} = \frac{j \omega T}{1 + j\omega T}$$
 * $$T = \frac{L}{R}$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$
 * This circuit has Stable voltage at high frequency therefore suitable for filtering high frequency therefore the name High Pass Filter

LC - R

 * $$\frac{V_o}{V_i} = \frac{R}{R + j\omega L + \frac{1}{j\omega C}}$$
 * Tuned Resonance Selected Band Pass Filter

R - LC

 * $$\frac{V_o}{V_i} = \frac{j\omega L + \frac{1}{j\omega C}}{R + j\omega L + \frac{1}{j\omega C}}$$
 * $$T = RC$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$
 * Tuned Resonance Selected Band Reject Filter

LC// - R

 * $$\frac{V_o}{V_i} = \frac{R}{R + j\omega C + \frac{1}{j\omega L}}$$
 * Tuned Resonance Selected Band Pass Filter

R - LC//

 * $$\frac{V_o}{V_i} = \frac{j\omega C + \frac{1}{j\omega L}}{R + j\omega C + \frac{1}{j\omega L}}$$
 * Tuned Resonance Selected Band Pass Filter


 * Tuned Resonance Selected Band Pass Filter

LR + CR
Transfer Function
 * $$\frac{V_o}{V_i} = (\frac{1}{1 + j\omega \frac{L}{R}}) (\frac{j\omega RC}{1 + j\omega RC}) $$

Band Pass or band of frequencies that has a stable voltage
 * $$\frac{R}{L} - \frac{1}{RC}$$ provided that $$\frac{1}{RC} > \frac{R}{L} $$

Band Pass Filter

RC - RL
Transfer Function
 * $$\frac{V_o}{V_i} =  $$

Band Pass or band of frequencies that has a stable voltage
 * $$\frac{1}{RC} - \frac{R}{L}$$ provided that $$\frac{R}{L} > \frac{1}{RC} $$

Band Pass Filter

Low Pass Filter

 * Low-pass_filter.png


 * $$\frac{V_o}{V_i} = \frac{\frac{1}{j\omega C}}{R + \frac{1}{j\omega C}} = \frac{1}{1 + j\omega T}$$
 * $$T = RC$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$

High Pass Filter

 * High-pass_filter.png


 * $$\frac{V_o}{V_i} = \frac{R}{R + \frac{1}{j\omega C}} = \frac{j\omega T}{1 + j\omega T}$$
 * $$T = RC$$
 * $$\omega_o = \frac{1}{T} = \frac{1}{RC}$$