Circuit Theory/Introduction to Filtering

Filter is a circuit constructed from Resistor and Capacitor or Inductor in order to pass certain range of frequencies. The range of frequencies that make the circuit stable

Let examine the following circuits

RC Circuit
A circuit with one resistor in series with the input and one capacitor parallel to the load
 * $$V_o = V_i \frac{\frac{1}{j\omega C}}{R + \frac{1}{j\omega C}}$$


 * {| class="wikitable"

! ω = 0 !! $$\omega = \frac{R}{L} $$!! ω = Infinity
 * $$ V_o = V_i $$|| $$V_o = V_i$$ || $$V_o = 0$$
 * }
 * }

The RC circuit is more stable at frequencies from zero up to the response frequency :$$\frac{1}{RC}$$. This circuit is ideal for Low Pass Frequency Filter.

CR Circuit
A circuit with one capacitor in series with the input and one resistor parallel to the load


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


 * {| class="wikitable"

! ω = 0 !! ω = $$\frac{R}{L}$$ !! ω = Infinity
 * $$V_o = 0$$ || $$V_o = V_i$$ || $$V_o = V_i$$
 * }
 * }

The CR circuit is more stable at frequencies from the response frequency $$\frac{1}{RC}$$ up to infinity. This circuit is ideal for High Pass Frequency Filter.

RL Circuit
A circuit with one resistor in serires with the input and one inductor parallel to the load


 * $$V_o = V_i \frac{j\omega L}{R + j\omega L}$$


 * {| class="wikitable"

! ω = 0 !! $$\omega = \frac{R}{L}$$ !! ω = Infinity
 * $$V_o = 0$$ || $$V_o = V_i$$ || $$V_o = V_i$$
 * }
 * }

The RL circuit is more stable at frequencies from the response frequency $$\frac{R}{L}$$ up to infinity. This circuit is ideal for High Pass Frequency Filter.

LR Circuit
A circuit with one inductor in serires with the input and one resistor parallel to the load

$$V_o = V_i \frac{R}{R + j\omega L}$$

The LR circuit is more stable at frequencies from zero up to the response frequency $$\frac{R}{L}$$. This circuit is ideal for Low Pass Frequency Filter.

In Conclusion, Resistor and Capacitor or Inductor can be used for constructing a Filter


 * For Low Pass Filter use LR or RC
 * For High Pass Filter use RL or CR