RL Filters

High pass filter[edit]

When the inductor is in parallel with the load while the resistor is in series with the inductor and load, this creates a high pass filter.

High pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {j\omega T}{1+j\omega T}}}$

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

Frequency response of High pass filter

${\displaystyle \omega =0.v_{o}=0}$

${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$

${\displaystyle \omega =00.v_{o}=v_{i}}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$

Low pass filter[edit]

When the resistor is in parallel with the load while the inductor is in series with the resistor and load, a low pass filter is created.

Low pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {1}{1+j\omega T}}}$

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

Frequency response of Low pass filter

${\displaystyle \omega =0.v_{o}=0}$

${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$

${\displaystyle \omega =00.v_{o}=v_{i}}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$

A single RL circuit creates a filter with a 20.0 dB/decade, or 6.02 dB/octave, slope.