Electronics Handbook/Circuits/High-pass Filter

High Pass Filter

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

RC Configuration

Vo / Vi

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

T = RC

Frequency Response

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

RL Configuration

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

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 .

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