Electronics Handbook/Circuits/High-pass Filter

High Pass Filter
Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency

Vo / Vi

 * $$\frac{V_o}{V_i} = \frac{Z_R}{Z_R + Z_C} = \frac{R} = \frac{j\omega CR}{1 + j\omega CR}= j \omega T \frac{1}{1 + j \omega T}$$


 * T = RC

Frequency Response

 * {| class="wikitable"

! ω = 0 !! ω = $$\frac{1}{RC}$$ !! ω = 00
 * $$V_o = 0$$ || $$V_o = V_i/2$$ || $$V_o = V_i$$
 * }
 * }

Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency


 * [[Image:Bode_High-Pass.PNG|200px]]

Vo/Vi

 * $$\frac{V_o}{V_i} = \frac{Z_L}{Z_R + Z_L} = \frac {j \omega L}{R + j\omega L} = j \omega T \frac{1}{1 + j\omega T}$$.
 * $$T = \frac{L}{R}$$

Frequency Response

 * {| class="wikitable"

! ω = 0 !! $$\omega =\frac{R}{L}$$ !! ω = 00
 * $$V_o = V_i $$|| $$V_o = V_i$$ || $$V_o = 0$$
 * }
 * }

''Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency. ''


 * Bode_High-Pass.PNG

Summary

 * High Pass Filter Circuit has stable voltage at High Frequency and increasing voltage at Low Frequency
 * High Pass Filter can be constructed from RC or RL
 * High Pass Filter has a general formula
 * $$\frac{V_o}{V_i} = j\omega T \frac{1}{1 + j\omega T}$$
 * T = RC = R / L


 * Angle Difference Tan θ = j ω T