Electronics Handbook/Circuits/Low-pass Filter

Low-pass Filter

A low-pass filter has a stable voltage at low frequencies and increasing voltage at high frequencies.

Low-pass Filter , LR Configuration

Picture

V_o/V_i

${\frac {V_{o}}{V_{i}}}={\frac {Z_{R}}{Z_{R}+Z_{L}}}={\frac {R}{R+j\omega L}}={\frac {V_{o}}{V_{i}}}={\frac {1}{1+j\omega T}}$

$T={\frac {L}{R}}$

Frequency Response

ω = 0 . $V_{o}=V_{i}$

ω = ${\frac {R}{L}}$ . $V_{o}=V_{i}/2$

ω = 00 . $V_{o}=0$

LR has a stable voltage at low frequencies and increasing voltage at high frequencies.

Low-pass Filter , RC Configuration

V_o/V_i

${\frac {V_{o}}{V_{i}}}={\frac {Z_{C}}{Z_{R}+Z_{C}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{1+j\omega CR}}={\frac {1}{1+j\omega T}}$ với

$T=CR$

Frequency Response

$\omega =0$	$\omega ={\frac {1}{RC}}$	$\omega =\infty$
$V_{o}=V_{i}$	$V_{o}=V_{i}/2$	$V_{o}=0$

RC has a stable voltage at low frequencies and increasing voltage at high frequencies.

Summary

1. Low-pass filters have a stable voltage at low frequencies and increasing voltage at high frequencies.
2. Low-pass filters can be constructed from RC or LR.
3. Low-pass filters have a general formula:

${\frac {V_{o}}{V_{i}}}={\frac {1}{1+j\omega T}}$ . T = RC = ${\frac {L}{R}}$