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