Zaph's L18 design, notch filter---Do I miss something?

[Jay_WJ]

I consider building Zaph's L18/27TBFCG 2 way (http://www.zaphaudio.com/audio-speaker17.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

[sreten]

Originally posted by Jay_WJ

Do I miss something here?
I would appreciate any help.
Jay

Hi,

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.

[jimangie1973]

Originally posted by Jay_WJ
I consider building Zaph's L18/27TBFCG 2 way (http://www.zaphaudio.com/audio-speaker17.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

The LC notch filter works because the capacitor has an impedance phase of -90 degrees, and the inductor has an impedance phase of +90 degrees. At the specific notch frequency, the capacitor and inductor have the same impedance magnitude, but since the impedance phases of the two are opposite, the net impedance of the two in series is 0.

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.

[Jay_WJ]

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!

[Jay_WJ]

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?

[jimangie1973]

Originally posted by Jay_WJ
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?

The LCR parallel circuit will notch the load impedance when it is placed in series with the load. At the resonance (notch) frequency, the LCR will have an impedance of R, so the value of R relative to the load impedance at the notch frequency determines the attenuation of the notch.

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.

[Jay_WJ]

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?

[jimangie1973]

Originally posted by Jay_WJ
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?

Your in luck. I do all my simulations using Matlab as well. I'm an EE doing mostly DSP work so I am naturally most comfortable with Matlab. I have M files for a few crossover designs. PM me and I will send you one on Monday (they're on my work PC) to use as a reference. I do individual driver frequency response measurements in baffle using a Behringer DEQ2496 RTA with an ECM8000 mic, then use the crossover simulation to get a desired response. It's not the ideal method since room reflections impact the response, but I've gotten very good results.

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 x-axis the real component, and the y-axis the imaginary component. This vector will have a magnitude and phase.

[Jay_WJ]

You have some m-files 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 RS180---more cost-effective 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.

[augerpro]

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