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3rd March 2012, 07:52 AM  #31  
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Join Date: Nov 2005
Location: San Antonio

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For the primary bypass cap Cb = 50/pi*fc "Here fc represents the unitygain crossover frequency of the op amp and generally represents the upper limit of the amplifier's useful frequency range." For the secondary bypass cap Cb2 = Lbp1 "Thus simply making the magnitude of the Cb2 capacitance equal to that of Cb1's parasitic inductance transfers line impedance control from Zcb1 to Zcb2 at the 1ohm level."
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It is error only, and not truth, that shrinks from enquiry.  Thomas Paine 

3rd March 2012, 08:50 AM  #32  
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Join Date: Nov 2009
Location: Los Angeles

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*gasp* Useful EDN article on tantalum caps  sci.electronics.design  Google Groups John's company is Highland Technologies in San Francisco. G² 

3rd March 2012, 03:02 PM  #33  
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Quote:
I haven't read Graeme's stuff, yet. I had received Henry Ott's EMC book just after I started the decoupling explorations at the link I gave, so I drew heavily on his work and on some others found on line. They are all mainly worried about highfrequency digital circuits on multilayer PCBs but I tried to apply their methods (and some verybasic math) to highcurrent audio amplifier circuits on one or two sided PCBs (or pointtopoint), with mainly throughhole/leaded parts, since that is what most DIYers can implement most easily, and also seems morelikely to be difficult to get right. Interestingly, the equation from Graeme that you gave, Cb = 50/pi*fc, looks closelyrelated to an equation that Ott provided for bandwidth versus rise time, i.e. f = 1 / (π trise), which can be rearranged as trise = 1 / (π f), which is very similar to Graeme's 50 / (π f), implying that he uses Cb = 50 x trise. I'm not sure how the physical "units" work out, there, without seeing how he got the "50". But it's interesting. Ott basically started with the worstcase current range that would need to be slewed through (call it dI), along with a chosen maximum railvoltage disturbance (call it dV) to try to have, and the worstcase (shortest) rise time (call it dt) based on the max slew rate. With those, you can find a "target impedance" across the decoupling points, Zt = dV / dI, which must not be exceeded up through at least the frequency implied by f = 1 / (π trise). That gives enough constraints to solve for C in two different ways and we can just use the larger result: C ≥ 1 / (2 π f Zt) (from the standard capacitor impedance equation) and C ≥ dI dt / dV (from the standard differential equation for capacitor behavior) So far, the parasitic inductance problems have been left out. But since V = L dI/dt (the standard inductor equation), I think that we can use our previouslyestablished dV, dI, and dt and find that L ≤ dV (dt / dI) is the maximum total inductance that can be tolerated, in the decoupling capacitance plus its connections. (That's not quite the whole story, so please see the posts indicated, at the link I gave, if interested.) For an example with 10 Amps in 2 μs, with 0.1 Volts or less raildisturbance amplitude, that comes out to needing L ≤ 20 nH, which is on the order of one inch of combined trace/wire length plus capacitor lead spacing, maximum! That could be very difficult to implement on a one or twosided PCB with an LM3886 layout, especially since the capacitance would be at least 200 uF or more, for that example. So, for practical DIY applications, the main problem to solve seemed to have become finding ways that could be used to "get around" the parasitic inductance problem. Obviously, a professional PCB designer would immediately decide to use multilayer boards with separate power and ground planes. And we could DIY several versions of that, by using thin PCB laminates and gluing them together (which I am going to try, since the easeoflayout benefits would also be so great). But I also wanted to see how far we could get with the easiest and moretraditional DIY construction types. One way to get lower inductance is to use several smaller decoupling caps in parallel. But note that the total inductance won't fully reduce (like total resistance reduces when paralleling resistors) UNLESS there is no mutual inductance, which, I think, means that the connections could not share conductors, i.e. the connections would also have to be paralleled, all the way to the decoupling points if possible (which would be much easier with power/gnd planes, but is also why even with planes the cap placement geometries do matter, as does the distribution geometry for injecting power into the power planes, i.e. the currents should ideally use separate paths, on the planes, so there is less mutual inductance involved). An extension of that might be to use multiple parallel power and ground rails, all the way from the PSU to the device, with each set of filter and decoupling capacitances basically having their own pair of power/ground rails. That seems like a very promising approach and is where I have gotten, so far (having been interrupted by demands from my real job and some other stuff). That approach should be able to give one of the main benefits of power and ground planes, but when using simple PCBs or pointtopoint wiring. Theoretically, we would be able to make the PSU impedance, as seen by the device pins, as small as desired, by adding more parallel paths from the PSU to the device, since the total parasitic inductance and parasitic resistance would be divided by the number of conductor pairs that were used, while the total filter and decoupling capacitances would be multiplied by the number of conductor pairs that were used. There will probably be limits that appear quickly for practical implementations. But at least all of the variables we were worried about move in the right directions. Sorry to have blatheredon for so long about all of that. I don't want to take this thread too far away from what the OP intended. Maybe we can consider an LM3886 to be an overgrown opamp. Last edited by gootee; 3rd March 2012 at 03:22 PM. 

5th March 2012, 08:09 AM  #34  
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Join Date: Dec 2010
Location: North, lakes region

Quote:
But I have a couple of those old stilish big cerafine 1000uF 35V around, I'm tempted to swap nichicon for these 

8th March 2012, 03:54 AM  #35  
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Quote:
The more caps you can fit in parallel, physically, the better it should be, since the overall ESL (equivalent series inductance) and probably also the overall ESR (equiv ser resistance) should be divided by the number of paralleled caps that are used, especially if their leads share as little conductor length as possible (except don't incur too much extra lead or conductor length trying to achieve that). And if the smaller caps have a smaller LS (lead spacing), then they should start out with lower inductance (than the larger original cap) and the benefit should be even greater. Last edited by gootee; 8th March 2012 at 03:56 AM. 

8th March 2012, 07:59 AM  #36 
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Join Date: Dec 2010
Location: North, lakes region

This method could be right just to reduce ESL, not the ESR
The smaller (physically) the cap, the higher the ESR, so paralleling more smaller caps doesn't give any real advantage about ESR But it does about ESL, because while the ESR is inversely proportional to cap dimension, the ESL is directly proportional 
8th March 2012, 08:13 AM  #37 
diyAudio Member
Join Date: Nov 2005
Location: San Antonio

The ESR's are in parallel, which effectively reduces the total resistance. I'm under the impression that some resistance can be beneficial as it dampens the LC resonance.
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It is error only, and not truth, that shrinks from enquiry.  Thomas Paine 
9th March 2012, 04:01 AM  #38  
diyAudio Member

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