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I've read and heard from knowledgeable people here that using an impedence EQ (Zobel) on a tweeter cleans up response. But doesn't it reduce output slightly as frequency goes up?The reason I'm asking:
I've kinda settled on the Audax HM210C0 (8" carbon fiber) and the Seas H881 (27mm chambered textile) for my next project. The woofer appears it could benefit from such a slight rolloff as it's freqency graph is flat to ~1.5k but with a slight incline going up with frequency. The tweet, however, has a beautifully flat response that I want to preserve. I've also heard that this is a very smooth and neutral tweeter, and so don't feel it would need to be "cleansed". From what I know at this point, I'm inclined to use a Zobel on the woofer and a series notch on the tweeter with a 2k L-R 2nd order. This will be in an aperiodic enclosure. Any thoughts on this project are welcomed.
I toke my Morel MDT40 T/S parameters:Re = 5.45ohm
Le = 0.05mH
fs = 700hz
f1 = 500hz
f2 = 1kHz
Zmin = 6.0ohm
Zmax = 9.9ohm
+---Cs---+
| |
0---+---Rs---+---Re---Le---0
| |
+---Ls---+
where:
Rs = Zmax - Re = 4.45ohm
Cs = 1/(Re*2*Pi*f2) = 29.2uF
Ls = Re/(2*Pi*f1) = 1.735mHI wired a notch filter but virtually nothing happened, which could be expected due to the small size of the impedence spike & the couple octaves distance away from the XO point. I then wired a Zobel of:
0---Cz---Rz---0
where:
Rz = Zmin = 6.0ohm
Cz = Le/Rz/Re = 1.529uFAnd, low & behold, a 2dB boost occurred between 5-10kHz, up & disappeared by installing a Zobel. Mind you, an 8kHz reasonant interplay between the XO cap & the voice-coil inductance was overted by the Zobel. In fact, the response curve resembles a unit Q 2nd-order XO roll-off knee.
where I have the tweeter's raw measured data imported & the spike is back. I need to do more tweeking.
Cs = 1/(2*(f2 - f1)*Pi*Rp*Sqrt[Re/(Re + Rs)]) = 96.41uF
Ls = ((f2 - f1)*Rp*Sqrt[Re/(Re + Rs)])/(2*f1*f2*Pi) = 0.5255mHbut still doesn't display much of a spike from the "fs" in the equivalent XO as Excel demos. However, each component's impedence was lower by a factor of 3.3. I then numerically solved for the "conjugate":
Cn = 17.5uF
Rn = 16.4ohm
Ln = 3.01mHbut it'll ring like a -%?+$%&*! at 2.8kHz which should only be down 5.5 dBels for a 1st-order XO @ 3.75kHz, because critical damping requires that "Rn + Re == 71 ohms". Even if I dump the "Cn" that still requires 68 ohms.
Rn = Re*Zmax/( Zmax - Re )Ln = Sqrt[Zmax*Re^3]/(2*(f2 - f1)*Pi*(Zmax - Re))
Cn = ((f2 - f1)*(Zmax - Re))/(2*f1*f2*Pi*Sqrt[Zmax*Re^3])
For those who aren't familiar with speaker building, f1 & f2 are the corresponding frequencies where the impedence spike has a value of Rx = Sqrt[Zmax*Re].
+---Cp---+
| |
0---+---Rp---+---Re---Le---0
| |
+---Lp---+
0-----Ln-----Rn-----Cn-----0
0-------Rz--------Cz-------0
where the driver is:
Rp = Zmax - Re
Cp = Sqrt[Zmax/Re]/( 2*Pi*(f2 - f1)*Rp)
Lp = (f2 - f1)*Rp*Sqrt[Re/Zmax]/( 2*Pi*f1*f2)
where the conjugate(notch) is:
Rn = Re * Zmax/(Zmax - Re)
Ln = Rn * Sqrt[Re/Zmax] /
( 2*Pi*(f2 - f1) )
Cn = (f2 - f1)/
(2*Pi*f1*f2*Rn*Sqrt[Re/Zmax])
Next will translate into T/S parameters (Qe,Qm,fs)
where the Zobel is
Rz = Zmin
Cz = Le/(Re*Rz)
+---Cp---+
| |
0---+---Rp---+---Re---Le---0
| |
+---Lp---+
0-----Ln-----Rn-----Cn-----0
0-------Rz--------Cz-------0
where the driver is:
Rp = Re*Qms/Qes
Cp = Qes/(2*fs*Pi*Re)
Lp = Re/(2*fs*Pi*Qes)
where the conjugate(notch) is:
Rn = ((Qes + Qms)*Re)/Qms
Ln = (Qes*Re)/(2*fs*Pi)
Cn = 1/(2*fs*Pi*Qes*Re)
where the Zobel is
Rz = Re + Rms
Cz = Le/(Re*Rz)
I can't seem to solve your generic conjugate exactly with any proceedure except numerically. The closest approximation I've come up with is:
0-----Lr-----Rr-----0
where:
Lr ~ Sqrt[Ln*Rn/w2]
Rr ~ Sqrt[Rn*Re]
eq1 =
0 == -((Rr^2 + Lr^2*w1*w2)*Zmax^2) +
Re^2*(Rr^2 + Lr^2*w1*w2 + 2*Rr*Zmax + Zmax^2)
eq2 =
0 == 2*Lr*Sqrt[Re^5]*w2*Sqrt[Zmax] +
Re^3*Zmax -
2*Lr*Sqrt[Re^3]*w2*Sqrt[Zmax^3] -
(Rr^2 + Lr^2*w2^2)*Zmax^2 +
Re^2*(Rr^2 + Lr^2*w2^2 + 4*Rr*Zmax + Zmax^2)
where of course:
w1 = 2*Pi*f1
w2 = 2*Pi*f2
The inductance of a tweter, as small as it is, will resonate to some extent with the series cap of even a first order crossover network. All higher order networks will also be prone to this problem. A 1" soft dome tweeter with an inductance of 75 uH will resonate to the tune of 1 to 1 1/2 dB without a Zobel, higher inductances to a greater degree, lower to a lesser degree.Technically, according to the textbooks, a Zobel will not cause a loss of HF due to it's presence, say, in a direct amp connection. However, if a tweeter were to have a relatively high inductance, then a suitable Zobel to make the Z flat at HF would exhibit a shelving response where it's impedance became significantly lower than that of the tweeter within the audio band.
This would not be likely to be an issue with most tweeters, but could become an issue for midranges. The inductance of many midranges is high enough to become a significant factor in the HF response. A Zobel for some nidranges WILL cut into the HF via the shelving action, but only for those with a relatively high inductance. You would be surprised at how many drivers have an electrical roll off due to the inductance and total series resistance, that actually rolls off a mechanical resonance in the top end of the driver, just like a moving magnet phono cartridge.
If you calculate the effective electrical -3 dB point, and examine the drivers FR curve, if the - 3 dB point does not correspond to the -3 dB point on the acoustic curve (it is higher in frequency), then the driver has a mechanical resonace aiding the top end. This is like a built in crossover EQ that is permanantly built-into the driver. If this -3 dB electrical roll off occurs low enough, adding a Zobel to flatten the Z curve will cause a shelved response above the inflection point.
You could try using an overdamped Zobel on the woofer to tame the slight rise, but an overdamped Zobel is much more succesful with a single HF peak or a mild peak at the top range of a driver, rather than a gentle slope. You could make the inductor bigger, and instead of a hard cap shunt, place a 1 to 3 ohm resistor in line, a highly overdamped Zobel instead of the cap, as opposed to in addition to a shunt cap. This will often tame a rising response as you describe.
Jon Risch
Zobel's will only attenuate HF output from current-sources like tube amps. A true voltage-source couldn't care less.
Granted, I'm no EE and am just starting to understand Zobels myself but your response is out in left field for hZ's question. What's he (or anybody) gonna do with your response. Please help the man with clear, simple answers.
... So, could you be more specific. I thought I was very direct & candid. In lieu of an explanation as to what you don't understand, I'll explain everything.Zobel corrective circuits try to change the high-frequency (HF) impedence of a dynamic driver, as seen by the cross-over (XO), into a purely resistive load, by counteracting the "Le" (voice-coil inductance) by a proper "Cz" (Zobel capacitor). As the "Le" increases the impedence of the driver, the "Cz" starts to reduce the parallel Zobel circuit impedence to the eventual "Rz" (Zobel resistor) value.
Most all Solid-State (SS) amps are voltage-sources. That means these amplifiers try to dictate the signal's electric potential (as measured in Volts). So, a Zobel circuit mearly helps make the XO work properly. In fact, it may decrease the HF range but so slighltly, it isn't worth considering. This would work by reducing the artificial boost made by using voice-coil reactance increasing the voltage-divider ratio. However minor this amount ( < 1dB) is at that HF range several octaves awy from the XO point.
Tubes are current-sources. That means these amplifiers try to dictate the signal's electric current (as measured in Amps). So, while a XO would still act much more appropriately with a Zobel, the Zobel, itself, robs the speaker of the current in HF range by its lower impedence. Maybe you've heard of the over-used addige that "current seeks the path of least resistance". This happens in a SS too, but unlike a SS, the tube doesn't supply extra current for the lowered impedence.
Hope this helps...
hz- A Zobel will not attenuate the response, it's used to equalize the impedance rise of speakers not using ferro fluid. This equalized impedance allows mid and low frequency crossovers to work properly.
Not so certain about several of your points. Speakers that use ferro fluid could also have their impedance curve "flattened out" also with the use of a Zobel. Also it will make any Lpad affect the output in a more linear way across the frequency range of the tweeter.Finally the response can be attenuated by the addition of a Zobel but not the same way a Lpad or resistor will. I would site the example in the fifth edition of the LDC as an example of zobel attenuating the upper portion of a SEAs (I think) tweeter. It is in the passive crossover chapter. I can get the page numbers if needed. I also found this to be true at least with the Focal Ti90TiO2 tweeter, but as you mentioned it is not fluid damped.
Edp- I mentioned ferro fluid tweeters because they won't benefit much from use of a Zobel. As for attenuation, I interpreted the original question to mean attenuation as in an "L" pad. I have the 4th edition of the LDC and I know of the section you are referring to and the tweeter in question is a Peerless 105DT.
In my experience, a tweeter with ferrofluid tends to make a conjugate superfluous, not the Zobel, which most will still need.Jon Risch
With most ferrofluid drivers, the resonance of the tweeter is all but completely damped by the ferrofluid. In fact, if you try to go by the Z curve with ferrofluid in the unit, and try to compensate the tiny remaining bump you see, often, the overall Z curve will get worse, as the actual resonance is not the little remaining bump you see!Jon Risch
To me, a conjugate is a specific network, designed and tuned to neutralize the fundamental resonance of a loudspeaker; it is a series network placed in aprallel with the driver. A notch filter is used to reduce an amplitude bump, and in order to prevent an imedance dip in the region of a nominal Z, it usually has to be a parallel circuit in series with the driver.Jon Risch
1) CONJUGATE
0---+-----driver----+---0
| |
+---L---R---C---+
2) NOTCH FILTER
+---L---+
| |
0---+---R---+-----driver----0
| |
+---C---+
I usually refer to them both as notch filters. I just stipulate that #1 is for a voltage-source & #2 is for a current-source. But then again, I can't keep the parallel & series XO straight either. I think it's:
1) PARALLEL
+---C---tweeter---+
| |
0---+ +---0
| |
+---L---woofer----+
2) SERIES
0--+--tweeter--+--woofer--+--0
| | |
+-----L-----+-----C----+
I just stipulate that once again #1 is for a voltage-source & #2 is for a current-source.
Do not comparmentalize the various topologies into voltage source and current source use, as in BOTH of these cases, it is incorrect and misleading. Undoubtedly, it would lead to confucsion when trying to analyze or think through the operation and action of a particualr topology or network in use.You do have the crossover names correct, and the proper diagrams associated with my prior post.
Jon Risch
The crossover capacitor in series with the tweeter will resonate with the voice coil inductance and cause a peak in the frequency response that is not on the published graph(because the graph is made without any crossover parts).The Zobel will neutralize this and thus restore the response of the tweeter to what you see on the graph.
To take the worst case scenerio & keep things simple :
Re Le
0----/\/\/\/----)()()(---0
| |
| |
+----/\/\/\/------| |----+
Rz Cz
Rz=Re
Cz=Le/Re^2Zz = Rz + 1/(s*Cz)
Ze = Re + s*LeZeff = Zz*Ze/(Zz + Ze) = Re
Resonate Loop:
Zz + Ze == 0
we = Re/Le
damp factor = 1 (critical)thus, there is no ringing.
That post looked very educational, but I didn't quite understand it. Could you clarify / explain the purpose of the circuit you demostrated and it's purpose?
a driver can be accurately aproximated by:
+---)()()()(--+
| |
| |
0---+---/\/\/\/---+---/\/\/\/\---)()()()(---0
| |
| |
+-----| |-----+
However, the left half approximates the speaker's LF near fs. Thus, we can shorten it to:
Re Le
0---/\/\/\/\---)()()()(---0
where "Re" & "Le" are among the common Thiel-Small parameters of the speaker:
Le : voice-coil inductance in Henries
Re : DC resistanceThis is the Zobel circuit:
Rz Cz
0---/\/\/\/\---| |---0
When the 2 are wired in parallel the effective impedence is purely resistive at the higher frequencies.
The preceeding post was talking about a resonant reactance current between the cap & choke. The frequency {fe} is defined as:
2*Pi*fe == 1/Sqrt[Le*Cz]However, in a LRC circuit the damping factor (del) is:
+---/\/\/\/\---+
| |
| |
| -----
|
| -----
| |
| |
+---)()()()(---+
del == R*Sqrt[C/L]/2
In our case
R = 2*Re
L = Le
C = Cz = Le/Re^2thus
del == 2*Re*Sqrt[Le/(Re^2*Le)]/2 == 1If del is less than one the circuit rings, above one the circuit is slow & makes the sound dull.
If you need more info, it's time to grab a basic electronics book.
That did help. Also reminded me that the only thing mathematical I really enjoy is electronics. I will have to take that "Foundation of Electronics" book off the shelf and open her back up. Thanks!
and open that book (while thumbing through your memorized cookbook). You'll understand both much better.
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