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5th April 2007, 02:52 PM  #1 
diyAudio Member
Join Date: Mar 2006
Location: Indiana

Zaph's L18 design, notch filterDo I miss something?
I consider building Zaph's L18/27TBFCG 2 way (http://www.zaphaudio.com/audiospeaker17.html). Looking at his XO design, I got a question.
He said he used a series notch filter in the woofer XO to reduce most of breakup garbage peaks at 7 kHz and above. I don't understand why he used an LC notch filter in this case instead of just a capacitor only. According to my calculation, a capacitor only reduces the woofer's higher frequency response more greatly than the LC notch filter because of a steeper decreasing slope. Do I miss something here? (perhaps phase issue?) I would appreciate any help. Jay 
5th April 2007, 03:49 PM  #2  
diyAudio Member RIP
Join Date: Nov 2003
Location: Brighton UK

Re: Zaph's L18 design, notch filterDo I miss something?
Quote:
Indeed you do. Research Cauer or Elliptical filters. Basically a single capacitor cannot implement the "precision strike". At near 7khz the LC notch attenuates far more than a capacitor. /sreten. 

5th April 2007, 04:05 PM  #3  
diyAudio Member
Join Date: Jan 2007

Re: Zaph's L18 design, notch filterDo I miss something?
Quote:
In Zaph's design, the woofer impedance is in parallel with only the resistor (R4) impedance at the notch frequency (since the inductor and cap impedances cancel). At this frequency the series inductor (L0) must have a much higher impedance than the resistor (R4) for the notch to provide adequate attenuation. A parallel cap by itself can only attenuate 6 dB per octave. 

5th April 2007, 08:41 PM  #4 
diyAudio Member
Join Date: Mar 2006
Location: Indiana

Thank you so much for your reply. Yes, I didn't take into account the phase characteristics of the components. Simply used inductive/capacitive reactance formula's to calculate summed impedance. How ignorant!

6th April 2007, 07:43 PM  #5 
diyAudio Member
Join Date: Mar 2006
Location: Indiana

Now I understand how a series notch filter works. Then my question is how an LCR parallel notch works. Can I still take into account the phase characteristics of inductor and capacitor to calculate the total impedance of a parallel notch filter? Or could I simply use inductive/capacitive reactance formulas and calculate a parallel resistance of them (including a resistor)?
Can anyone explain to me? 
6th April 2007, 11:17 PM  #6  
diyAudio Member
Join Date: Jan 2007

Quote:
Here's why: Using the Laplace transform, the cap has an impedance of 1/jwC (magnitude of wC with angle of 90 degrees), and the inductor has an impedance of jwL (magnitude of wL with angle of +90 degrees), where j=sqrt(1) and w=2*pi*frequency. The cap and inductor in parallel have an impedance of: Z = 1 / ((1 / jwL) + (1 / (1/jwC))). This simplifies to: Z = jwC / (1(w*w*L*C)) The notch frequency is the frequency where the term (1(w*w*L*C)) equals 0. At this frequency, the parallel L and C form an infinite impedance. So at this frequency, you have R in parallel with an infinite impedance, which results in a total parallel impedance of R.  By the way, the Seas TBFC/G is a fantastic sounding tweeter. I made a pair of the AR.com kit design a few years ago and was never quite happy with the sound. I replaced the Peerless 812687 tweeter with the Seas, coupled with the Peerless 850122 woofer, and the improvement was huge. The crossover adjustments were only minor as well. 

7th April 2007, 12:15 AM  #7 
diyAudio Member
Join Date: Mar 2006
Location: Indiana

Thanks a lot again. This is really educational! The reason why I'm asking how to calculate the impedance of different alignment of components is that I think I can easily simulate XO performance using my computer language (Matlab). I know I can use an XO design software like Speaker Workshop, but I just want to do it myself for fun. I'm a cognitive scientist and do some mathematical/computational modeling in my research. So math/statistics is not a problem to me, but not being an EE or physicist, I don't have much knowledge about this stuff.
One thing I still don't understand is how to use phase properties of caps and inductors to compute the final voltage and phase across a driver unit in an XO network. Maybe a simple explanation is not possible. In that case, I think I need patience to learn things slowly. Also I want to know how to simulate a driver unit (woofer/tweeter) in a circuit. BTW, in the above equations why did you use j=sqrt(1)? Apparently this does not affect the impedance calculation of the notch filter itself. In what situation will it be useful? 
7th April 2007, 01:09 AM  #8  
diyAudio Member
Join Date: Jan 2007

Quote:
The j=sqrt(1) term is the imaginary component of a complex number. Impedance is represented as a vector on a two dimensional plane, with the xaxis the real component, and the yaxis the imaginary component. This vector will have a magnitude and phase. 

7th April 2007, 01:54 AM  #9 
diyAudio Member
Join Date: Mar 2006
Location: Indiana

You have some mfiles for XO designs! That's great. I'll give you a reminder to send me those.
I don't have a measurement setup and won't bother to have one for my first DIY speakers. That's why I chose Zaph's design and wanted to tweak from there if I need something a bit different. Actually I want to swap its L18 Seas woofer with Dayton RS180more costeffective and better distortion performance than the L18 according to people's measurement. I know the two woofers are not interchangeable without XO redesign but actually they are not far different from each other, either, in many aspects. So I'll try. 
7th April 2007, 04:25 AM  #10 
diyAudio Member
Join Date: Aug 2006

I have a question concerning notches. When does one use the parallel LCR versus the series LCR shunt?

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