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20th July 2018, 01:39 PM  #1 
diyAudio Member
Join Date: Jul 2010

Delays created by first order crossover component.
Anyone explain this. Using a first order LP filter winisd/ Xsim correctly show the group delay ramping evenly up as frequency decreases.
When "connected" to a real driver, even when it's impedance is flattened with a series notch network to provide a virtually flat impedance and no more than +/ 5 degrees phase variation at the original Fs, the group delay rises to a peak and then falls as the frequency decreases?! Observations? 
21st July 2018, 06:36 PM  #2 
The one and only

Group delay is mathematical construct, defined by of the rate of change of phase with frequency.
It doesn't always look like what you might think. 
21st July 2018, 11:37 PM  #3 
diyAudio Member
Join Date: Jul 2010

Hi Nelsen, thanks for the reply. What baffled me is how a first order lp filter (created in winisd, say, and at line level therefore ) has an increasing gd with decreasing frequency and this rise increases at an even rate, whereas a choke/inductor selected for the same crossover point, the gd rises to a peak before dropping rapidly at Lf.
I need to investigate further....! 
22nd July 2018, 12:28 AM  #4  
diyAudio Member
Join Date: Apr 2011

Quote:
at low frequencies, where fo is the corner frequency in Hz. This is because the phase response, having the form of an arctangent function, has a maximum slope at f=0Hz. This causes the group delay, being the negative derivative of the phase, to reach a maximum peak at 0Hz. For frequencies << fo, the phase response is nearly linear since arctan(x) ~ x for small x. In that region there is nearly a constant delay (near the peak of the group delay curve). Last edited by rayma; 22nd July 2018 at 12:48 AM. 

22nd July 2018, 02:11 PM  #5 
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Join Date: Jul 2010

Thanks....but for a first order value choke (180hz, 3dB point ) the gd peaks around 80 100Hz before dropping again? Simulated in Xsim....with a series notch filter to level the driver impedance and flatten phase. True, a simulated first order "line level" filter in winISD does indeed perform as you state. And this is what is confusing me!!

22nd July 2018, 05:10 PM  #6 
diyAudio Member
Join Date: Apr 2011

Can you post the complete circuit that does this?
Last edited by rayma; 22nd July 2018 at 05:12 PM. 
22nd July 2018, 06:22 PM  #7 
diyAudio Member
Join Date: Jul 2010

Hi rayma,
Yes, happy to post the circuit. As you can see the GD peaks then drops off. When modelled as a line level first order filter (in WinISD), the GD "gradient" remains linear. You will note the RCL network is successful in flattening the impedance at driver resonance and with the zobel actually remains very flat up to around 10kHz where there is a small rise. Observations very welcome! 
22nd July 2018, 06:34 PM  #8  
diyAudio Member
Join Date: Apr 2011

Quote:
If so, can you extend the plot of the group delay for that LR circuit down to a very low frequency, like 0.1Hz? It should start to level out. 

22nd July 2018, 06:58 PM  #9 
diyAudio Member
Join Date: Jul 2010

Rayma, thanks. Been very helpful....cheers.

22nd July 2018, 07:33 PM  #10 
diyAudio Member
Join Date: Apr 2011

Here is a plot of a first order low pass filter. It's an RC type, but it has the
same curves as an LR type does with the same time constant (where RC = L/R). See the top set of curves, which are for a first order low pass filter. The group delay increases at lower frequencies, leveling out eventually to having a nearly constant group delay value approaching 0Hz. https://i.stack.imgur.com/4pm1R.jpg Last edited by rayma; 22nd July 2018 at 07:38 PM. 
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