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almikel

filter delays and phase

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I wasn't sure where to put this thread, but it's about electronics, so it ended up here..

..I'm hoping the smart people on SNA can help me better understand...

 

I struggle with the phase lead introduced by a high pass filter...

 

This is the phase response of a complementary high and low pass 1st order filter at 1kHz

2117434432_1storderlowandhighpass.JPG.ced025ec178f31af3e4d0920fb6a618b.JPG

Image copied from the Rane paper "Linkwitz-Riley Crossover: A Primer" https://www.rane.com/note160.html

 

The top curve is the high pass phase response and the lower curve is the low pass phase response of a 1st order filter.

 

A piece of wire would have no phase change.

 

I can't get my head around the high pass phase lead response - it seems non-causal.

How does the high pass response get 90 degrees in front of the input?

 

cheers

Mike

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33 minutes ago, almikel said:

it seems non-causal

Heh, it does (but it's not).   You have asked a reasonably complex question.

 

https://en.wikipedia.org/wiki/Leading_and_lagging_current   This may help a little...  Keeping in mind that the chart you posted is of voltage (what we typically think of as the 'input signal') ... but what actually moves the speaker is the current.

 

As to the 'causal' nature of this.   What might help you as well, is if you take the chart you posted... and rename "100" (ie. the top of the Y axis) as "zero".    ie. consider t=0 to be the top of the Y axis.

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Cheers Dave,

43 minutes ago, davewantsmoore said:

This may help a little...

I'm completely comfortable with the lead/lag of voltage and current with reactive loads with continuous signals...

5 minutes ago, davewantsmoore said:

What might help you as well, is if you take the chart you posted... and rename "100" (ie. the top of the Y axis) as "zero".    ie. consider t=0 to be the top of the Y axis.

This is the crux - so a piece of wire would be a flat phase response at the top of the high pass phase response? ie +90 degrees?

So they plot the high pass response starting at +90 degrees similar to wrapped phase so it fits on the graph more easily?

I've been pondering this for a while, and that was the only answer I could get to fit...

...if this is the case my paradigms haven't been dented :thumb:

 

cheers

Mike

 

 

 

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Good on you for engaging your brain! So good questions.

 

First, the answers are not simple without grounding in undergraduate level physics/maths.

 

However, from a physical point of view note that the phase plots, and just about all plots as function of frequency are for 'steady-state' fields. What I mean by this is that, when you switch on a source, and stuff happens over time and fields build up, this is non-steady state, but eventually you reach a stable, constant time-harmonic (periodic variation at the source frequency) situation... this is steady-state. 

 

The phase plot you are referring to is a steady state result frequency-domain plot. Most plots with frequency as the parameter you will are steady-state solutions (as opposed to time-domain results, were instead you have plots of fields versus time). If one field leads/lags another in a steady-state plot it does not mean that one field existed first/last, as the fields built up over-time in the non-steady state regime, of course originating causally from the originating field. Now in the steady-state regime, yes, some component can end up apparently in front of the originating source or some other apparently weird things, but this lead/lag in steady-state really only tells you about direction of energy flow (i.e. which field drives which, e.g. you know caps charge up on one half a cycle and discharge on the other half of cycle providing current, while inductors do exactly the same but half a cycle later, while the current the wire connecting them has phase in between the two) The phase is all about energy flow.

 

Sorry, that is a bit of a physicsy response, but this is physics. If you want to learn more about it, you can grab a physics text book and study pendulum or spring systems. Any resonant system will exhibit the same behaviour as the crossover circuits... they are just resonators and this is why they have this phase response in general (with phase of driven field shifting 180deg either side of resonant frequency with respect to driving force). As a most common analogy you can consider pushing someone on a swing (where you push periodically (with fixed period) providing a driving force to a field (amplitude of swing motion).

 

HAVE FUN

 

PS. I know I've made some simplifications here. I'm just trying to break it down to be understandable. FWIW I'm a PhD in physics dealing with causality of fields and simulations in time and freq domain of electromagnetic fields, in resonant and non-resonant structures.

 

PPS. Perhaps a simpler way to approach to accepting the causality it is to realize that the phase at a given frequency corresponds to the phase not of a complex signal but of a sine wave (sine waves are steady-state waves, periodic but infinitely long in duration) at single frequency. Now imagine a plot of two infinitely long (in time) sine waves, with different phase (i.e. one leading, the other lagging). You can really 'say' the one that the sine wave with leading phase 'got there first', as both sine waves exist throughout all time. You can only say the peaks or troughs of one arrive periodically earlier (or later, depending on your point of view)...but this does not mean the signal/energy was there earlier... both waves exist throughout time. In reality there is no such thing as a steady-state system, but it's a good approximation and mathematically convenient. In practice the incident field will build up the other fields over time in a resonant system, following causality. Much as the energy of a person pushing a swing always flows to the motion of the swing, depending on phase relationship, the swing can later kick back on the person pushing...

Edited by Smurfer
Giving additional/alternative approach

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Heh. I couldn’t think how to write that without being in danger of “confusing not helping” :D

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13 hours ago, Smurfer said:

Now in the steady-state regime, yes, some component can end up apparently in front of the originating source or some other apparently weird things, but this lead/lag in steady-state really only tells you about direction of energy flow

:thumb:

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