# Low pass filter [DELAY]

Ok guys, I can't understand a thing, why a low pass filter will delay only a signal with an high frequency?If I have a RC low pass filter, why the delayed band is only the band that has an high frequency though the bass frequency as a Tau=R*C?Why the tau "don't work" in low frequency?

• Who says it doesn't? Try plotting the delay of the filter in any of the available options for simulators, you'll see that the lower frequencies are actually delayed more, but the effect is, probably, more visible for higher frequencies (depends on the filter). – a concerned citizen May 6 '18 at 9:47
• @a concerned citizen Why high frequencis are more delayed? – user187959 May 6 '18 at 9:48
• Read carefully what I said. – a concerned citizen May 6 '18 at 9:49
• @a concerned citizen So the lower frequencis are more delayed that the higher, but the delay is more visibile in the high, but why?For example ins this filter s.hswstatic.com/gif/thx-crossover.gif – user187959 May 6 '18 at 9:53
• @a concerned citizen Is why high frequencies are move fast,so the delay comparated to them is more "visible"? – user187959 May 6 '18 at 9:59

The delay you are (probably) talking about is only apparent. Here is a lowpass RC with fc~34Hz, with a swept sine from 10Hz to 100Hz:

Visually, the delay for the lower frequencies seems less than for the higher ones, but if you look at the .AC analysis:

you can clearly see that the delay (dotted line) is more towards the lower frequencies, and drops as the frequency goes up.

Conclusion(s): the lowpass doesn't delay only the high frequencies, it delays all frequencies. If it does seem so, it's because the delay's value, compared to the period, is less at low frequencies than at higher ones. In rest, your question doesn't make much sense, so I cannot answer.

• @a concerned citizen thanks a lot hope that you'll have a nice day!!!! – user187959 May 6 '18 at 10:30

Tau always works but with filters with order n >1 you have more choices.

Here I compare Group Delay on right side for Butterworth n=1,2,3,4 then compare with Bessel filter ( Maximally flat group delay)

The same characteristics are true for LC filters and active RC filters which use C as an active L.

Notice for f=1kHz in each case group delay is related to order of filter and $$\\tau=\frac{2^{n-1}}{2\pi f}\$$ approx. for Butterworth ( my estimate)
Except for n>1 you can see the critically damped Butterworth filter actually has a peak group delay at the breakpoint, which wreaks havoc with data jitter (ISI) for data transitions with spectrum at the breakpoint. So wiser choices are Bessel or Raised Cosine.

See how flat the group delay is for Bessel 4th order compared to Butterworth? This group delay is TAU $$\\tau\$$ but it increases by the square root of 2 to the power of n-1.

Note also the attenuation scale is changing on each plot.

Note the group delay on the 4th order Bessel filter is less than Butterworth for the same LPF breakpoint.

Can you see why? (hint: look at Q)

in case you do not know , group delay= $$\\tau _{\theta} = -d\phi/d \omega\$$