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In Reply to: RE: Yes, but... posted by Al Sekela on April 23, 2010 at 14:40:56
I am struggling with the use of parallel networks instead of one multiply bypassed cap and one resistor.At the frequencies that are passed by more than one of the caps in parallel, the resistors will also be in parallel and the total resistance will thus decrease greatly in value, following the rules for adding resistors in parallel. So, if you have a network with three 10ohm resistors in parallel, you will have only 3.33ohms of resistance in the circuit at the frequencies passed by all three caps. I checked this with my Escort LCR meter set to measure R at 10kHz and found that for a 5.6uF cap in parallel with a 0.39uF cap (just what I had around) connected in series with one 51ohm resistor, the R = 51 ohms, but when I connected it as two separate parallel networks (5.6uf-51ohms in parallel with 0.39uF-51ohms) the resistance dropped to 32 ohms.It seems to me that the impedance of such a setup will decrease as the frequency increases as the various caps either block, partially pass or fully pass the RF, making it impossible to closely match the characteristic impedance of the cable over the full range of RF we are concerned with.
On the other hand, having multiple caps bypassing each other, all connected to one resistor of value equal to the characteristic impedance should allow much closer matching of the network to the cable.
What am I missing? Is there something else that makes the parallel networks desirable even with the changing impedance? Do we want the impedance to drop as the frequency increases?
I realize that many here have had good results with the parallel networks, but I am trying to understand how the theory squares with the reality - just the scientist in me coming out, I guess.
Edits: 04/24/10 04/24/10Follow Ups:
Your analysis is correct as long as the goal is only to match the cable impedance to the resistor.
However, as I mentioned below, the capacitors also have their own self-resonance issues.
By experience, I've found it better to isolate the multiple capacitors from each other by placing each one in series with two resistors, one on each side. The sum of the two resistors is the "R" to which we are attempting to load the output circuit of the amplifier and cable.
This does raise the additional question of whether the self-bypassed capacitor designs suffer from intractable internal resonances. I don't know.
Keep in mind the large difference between typical cable impedance and the ten ohms Walker uses in the High Definition Links. The lower impedance may be better in cases of amps with marginal stability at ultrasonic frequencies. If the tweeters do not provide a resistive load over a frequency range well above that in which the amp's feedback network is active, the R-C filters would give a great benefit by stabilizing the amp, and the actual resistance value would not be that important. However, if the amp is stable and cable resonances are the main issue, then matching cable impedance would be more beneficial.
There is plenty of opportunity here for further investigation.
Here's my question...If you parallel multiple RC filters (whether or not you connect a resistor on either side of each cap) the paralleled capacitors "add" but the resistors would "divide" and = (R1 x R2) / (R1 + R2)...right? So if we parallel an RC = (.10uf + 10R) with an RC = (.01uf + 10R) the equivalent RC filter would be RC(eq) = .11uf + 5R. Or is there some more complex calculation needed?Thanks...
Edits: 04/25/10
only well above the corner frequencies of both capacitors. There is a frequency dependence that needs to be taken into account. That is why I measured 32 ohms in my test setup (in the post above) instead of the calculated 25.5 ohms (51/2) - the 0.39uF cap still had a significant impedance to the test signal at the 10kHz test frequency. At a higher frequency it would have measured 25.5ohms.
What that shows is that the impedance will vary non linearly with frequency in a multiple parallel RC network - at audio frequencies it will be very large, then it will decrease to that of the resistor in series with the largest cap in the filter as the largest cap passes its corner frequency. Impedance should be stable for a range of frequencies, then it will begin to decrease non-linearly as the second cap begins to pass the RF, then it will decrease again as the third cap begins to pass the RF signal, and so on. Add to that the fact that somewhere in there the caps will reach their resonant frequency and the impedance will then increase again. It becomes quite complicated to figure out what impedance the filter is presenting at any particular frequency.All that said, folks here do report good results with the parallel networks, so maybe sometimes we can analyze ourselves to death. It's the age-old struggle between the theorist and the experimentalist - and the best approach probably lies somewhere in the middle...
Edits: 04/26/10
RC filters using the following values: .1uf + .012uf in series with a single 10R resistor. It will be interesting to hear the results of your experiments with values "theoretically" matching the characteristic impedance of your speaker cables.
BTW...the resistor values in the following link seem incorrectly sized "if" the goal was to have an R(eq) of 10R.
I wouldn't say they are "incorrect", but the impedance will be lower than 10ohms and as low as 3.33ohms at some frequencies. If that works, then it's fine, but if you need 10ohms at all frequencies it is not fine.
I've been testing over years both single and multiple R-C arrays. I can tell you unequivocally that the multiple R-C arrays do work better.
Second, I've also compared the multiple R-C array to the multicap R-C and the multiple array still sounds better.
Also, I've used Al's R-C-R formula too in my multiple array filters, but only in my AC filtering system, which uses safety rated X and Y caps. Yes, this works better there, but I have no idea if it works as well on the speaker cables as I have not yet tried it there.
Have you tried using separate cascaded RF-friendly capacitors in parallel with only one resistor for the lot? For example, .01uF +.001 uF +.0001uF silver mica in series with one 10ohm resistor. In that way you would get the benefits of cascaded caps (shifting resonance to a higher frequency) but still keep the impedance constant.
On both speaker cabling and on AC filters. It does not work as well as the R-C or R-C-R multiple arrays.
You are welcome to try these recipes sequentially yourself. I did it by simply using wirenuts to tie the pieces together, including lead wires until I found the best formulae. This makes it cheap and easy to try out the combos to your heart's content.
Then I solder those final versions, which sounds better yet, as it doesn't engage the metal in the wirenuts (which may be ferrous).
I have an array of silver mica values on order, and I already have .01uF and .001uF Multicaps on hand. I have lots of different values of PRP resistors, and I just ordered some 71ohm Texas Components TX2575 Z-foil resistors as well, to match the characteristic impedance of my speaker cables. Texas Components will make any value of resistor you want at no extra cost, but the resistors are pricy (~$10 each), so multiple parallel arrays can get $$$ fast!The Z-foil resistors are especially well-suited to this job as they have a very low self-inductance. I measured a 100ohm PRP resistor at 10kHz and found 3.3uH of inductance, meaning the 100ohm PRP thus has a -3dB point of only 4.8MHZ. Since I'll be using a value of 71ohm, this could be a significant issue.
I'll post my results when I'm done - it will take 2 weeks for me to get the TX2575 resistors.
Edits: 04/26/10
It seems to me that the impedance of such a setup will decrease as the frequency increases
Yep, it's called capacitive reactance.
Capacitive reactance (Xc) is inversely proportional to the signal frequency (f) and the capacitance (C).
I understand that the resistance of the capacitors will decrease with frequency as the frequency moves above the corner frequency for each of the paralleled capacitors, but I'm talking about the added series resistance decreasing as each capacitor in turn begins to pass signal, since more resistors are being added to the circuit in parallel.
Compared to a circuit with three capacitors in parallel connected to one series resistor, a circuit with three capacitor-resistor pairs in parallel will end up with lower resistance as each capacitor begins to pass signal. Since I'm attempting to match the impedance of the RC network to the characteristic impedance of the speaker cable, wouldn't I be better off with the single resistor circuit? The perplexing part to me is that others have reported that the multiple RC parallel circuit sounds better, so I'm wondering if I'm missing something obvious in the theory.
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