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14th March 2013, 01:36 AM  #1791 
diyAudio Member
Join Date: Jun 2009

Yes, little faith; steps are skipped and result is off by a scaling factor. It's not that big of an error3dBso if one chooses design based on the result anyway there's probably minimal harm done; going from the usual guesswork to a not bad approximation is significantly more design than happens in a lot of DIY. If one's trying to get that last few dB it's Spice, parameter sweeps, and a pile of RLCG parasitic models anyway.

14th March 2013, 02:05 AM  #1792 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

The spreadsheet I posted doesn't use that equation.
But yes, the capacitance values in the last spreadsheet I posted are 2X too high, due to a transcription error (and then me not checking carefullyenough). I am writing a post that includes that information, but which is not about that. I think you might find it interesting. 
14th March 2013, 02:43 AM  #1793 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

THIS seems interesting!!
ALL,
Someone tell me if I've gone mad (AFTER reading this, please ) This seems too good to be true. It seems like I have found the Holy Grail for reservoir capacitor calculations. I stumbled upon "an invariance", while playing with the last spreadsheet I posted... (LOOK at the attached thumbnails! Notice the wide variation in the output power ratings (et al), and NO variations in the required capacitances (or certain ratios)!) (By the way, the C values are 2X what they should be, in that spreadsheet. I will attach a new one, below.) I happened to set up a series of calculations (of the minimum capacitance to prevent clipping) that were based on the max rated RMS sine output power DIVIDED BY the theoretical maximum RMS sine output power. For the theoretical maximum output power, I just assumed that the ripple could be zero which meant that I used a peak output voltage of Vrail_unloaded  Vclip, instead of Vrail_unloaded  Vclip  Vripple, to calculate the "theoretical" max output voltage peak level and the RMS power. Then I set up Excel to calculate the ripple and Vpeak values needed, to set up a row of cases, for which I would have it calculate the minimum capacitances. i.e. I set up columns for fixedpercentage cases of "rated max power divided by theoretical max power", e.g. 97.5%, 95%, 90%, 80%, ..., 50%, so I could see how fast the capacitance went up as the voltage space for the ripple was squeezed toward zero. So I did all of that. The inputs were the usual things, like load R, Rail voltage, vclip, fmains, and the capacitor's voltage rating (since I was using the "ESR approximation" version of the equations, which, by the way, I got right when recapping earlier work at Finalizing TDA2050, LM3886 but somehow got wrong while finally figuring out how to eliminate all but one variable, at http://www.diyaudio.com/forums/chip...ml#post3403946 ). Anyway, I noticed that when I changed the rail voltage, none of the calculated capacitance values changed! NOTHING I CHANGED changed the capacitance values, except the load resistance. And that changed them only by the expected scale factor! For any amplifier from 2 Watts to over 1500 Watts (and more, I'm sure), if you want, for example, the maximum pp ripple voltage to be 7.59% of the peak output voltage, then the minimum capacitance required to prevent clipping, if your output is the worstcase DC at the peak level, is always the same (> 12896 uF). And for the same thing, except to prevent clipping for a DC output at the rated max RMS level instead of the peak level, then the capacitance required will always be the same, i.e. > 9119 uF (assuming, of course, that my calculations were correct). (There WILL be a slight change, of course, if the capacitor ESR changes. For the examples, I left it the same, just to make the point. But obviously, for 163V rails you wouldn't use 50V caps. But putting in 200V caps didn't change it all that much. And that's not the point, anyway, but I figured I needed to preemptively explain that, for the nitpickers who might also miss the main point. Please don't post about that.) So that got me really excited. I finally plotted the row of capacitances versus the row of Vripple/Vpeak values. And THEN I let Excel do a curve fit. Sure enough, it found a perfect fit: y = 109167 / x I was using, for x, 100 * Vripple_pp / Vout_pk (assuming rated max output). And y was the calculated minimum capacitance to prevent clipping (for DC output at Vout_pk, which is my chosen worst case). That gives: C_min(pk) = 1091.67 * Vout_pk / Vripple_pp (my "upper bound" minimum) for the "DC load at max rated peak" method. For the "Dc load at max rated RMS" method, I got: C_min(rms) = 771.92 * Vout_pk / Vripple_pp (my "lower bound" minimum) The spreadsheet will follow. Cheers, Tom Last edited by gootee; 14th March 2013 at 03:04 AM. 
14th March 2013, 03:24 AM  #1794 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

Spreadsheet for Calculating Reservoir Capacitance, et al
Attached is the spreadsheet mentioned in my previous post.
(P.S. I meant to quote 8.47% instead of 7.59%, in my last post.) Now I guess I need to derive the expressions for the coefficients that the curvefitter came up with. <grin> Cheers, Tom Gootee Last edited by gootee; 14th March 2013 at 03:38 AM. 
14th March 2013, 03:42 AM  #1795  
diyAudio Member
Join Date: Jun 2009

Quote:
If you do a more exensive analysis which accounts for additional factors there is a weak relation between ripple and supply, mainly with regards to the transformer's regulation interacting with the bridge's conduction angle. It's not usually worth worrying about as it's swamped by mains variability and easily mitigated by appropriate trafo choice. 

14th March 2013, 04:17 AM  #1796 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

Ah! Makes sense. And if I take i = C dv/dt, i.e. C = i / ( 2 f vripple) plus the second curvefitted equation above, C = 772 Vout_pk / vripple, so i /2f = 772 Vpk, and Vpk/sqrt(2) = i Rload, I can probably get close to the correct number for Rload.
By the way, what is the rectifier equation to which you referred? Last edited by gootee; 14th March 2013 at 04:26 AM. 
14th March 2013, 04:47 AM  #1797 
diyAudio Member
Join Date: Jun 2009

Rload ~= Vrail_average / Irms. Ohm's law and small signal approximation as usual.
I wouldn't say there's a rectifier equation per se, but a simple model of the system is an ideal transformer + effective source impedance along with an ideal voltage source for the bridge diode forward drop + equivalent diode resistance. It's only a few elements so turning the analytic crank to apply KCL/KVL is no big deal; series expansion and truncate the small terms. Kind of useful for a "hands on" kind of understanding, though it doesn't tell you anything a sweep in spice wouldn't do better. 
14th March 2013, 05:23 AM  #1798 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

I asked because I did what might be called "a deep dive" into the "simple" transformer/rectifier/capacitor power supply circuit. It's basically impossible to come up with a "nice" closedform solution, unless as you just mentioned you use a series expansion and truncate it. But I didn't want the approximations. I acquired and read most of the papers, back to the 1940s. Tried to relearn some of the mathematics and electronics that had rusted away, which was actually quite rewarding. I decided to do a numerical solution. I was worried about calculating when the rectifiers turn on and off, since that's normally a transcendental equation with no closedform solution, i.e. "where does an exponential meet a sinusoid?", and is where many authors used the series expansion to advantage (or the LambertW function). But I learned that one of the great things about solving differential equations numerically is that at every instant, you also have the derivatives available to use in any calculations.
I would have thought you had seen it, if you followed this thread. I did a PDF writeup (minus references), and wrote my first VBA macro for Excel. And it works! It's actually a prettyuseful tool. And most people won't bother with spice (although I did nothing but that, for several years, so I could no longer imagine why). Please have a look: PDF is at: Power Supply Resevoir Size Excel file is at: Power Supply Resevoir Size Also in that spreadsheet is a nifty scalable power transformer model, which I use to much greater advantage in LTSpice. The famous Terry Given had taught me about "perunitization", right here in this thread, not long before I did the spreadsheet. (Well, he's famous to me, at least.) Regards, Tom Last edited by gootee; 14th March 2013 at 05:30 AM. 
14th March 2013, 04:30 PM  #1799 
diyAudio Member
Join Date: Jun 2009

Thanks for the links; there are internet threads in the hundreds of pages where I've read all the posts but, I think, any on DIYA. Is there a schematic for the transformer model?

14th March 2013, 06:04 PM  #1800 
diyAudio Member
Join Date: Nov 2006
Location: Indiana

The schematic is in the linked Excel spreadsheet, on the first tab's sheet. It includes the leakage inductances and resistances of the windings.
An older LTSpice implementation is at the link below. It is a subcircuit, in this case, so I don't know if you'll be able to tell what settings come from elsewhere, or not. Power Supply Resevoir Size The basic idea for the nonideal parts of the transformer model originally came from AN1679D at onsemi.com, which I think was written by Christophe Basso. 
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