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10th October 2012, 07:08 PM  #1391 
diyAudio Member
Join Date: Mar 2007
Location: California

Funny that I should find this thread now, and Gootee's post above. I've been working up a spreadsheet of my own in the past couple of weeks, to calculate power supply transformer capabilities and ripple voltage for a single pair of caps driven by a bridge rectifier from the transformer secondary. It seems to share many things with Bob's spreadsheet, but coming from a different angle. My spreadsheet tries to answer the question "for a given transformer, how much output power can a class AB amplifier deliver into a resistive load?".
You will need to enter data for a transformer. Data for the Antek AN2230 is provided currently. This is obtained from their datasheet. Take a look. Comments welcome. It's a work in progress... some screen shots are provided below. http://audio.claub.net/software/PS_d...lculations.xls Charlie 
11th October 2012, 05:12 AM  #1392  
diyAudio Member

Quote:
Welcome! Your work is impressive! Yes, we seem to be working two ends of the same problem, with the spreadsheets. This thread is about how much reservoir capacitance should be used. It's complicated. Since transformer effects and limitations couldn't be ignored, I included a transformer model in a spice simulation of a power supply and amplifier. It seemed natural to first try to find out how to determine a lower bound on the capacitance that could be used. Using simulations, with the condition that what you call the "output stage dropout voltage" could not be violated (which would cause gross distortion of the output waveform), we found that the maximum output power is first limited by the reservoir capacitance. As the reservoir capacitance is increased, the output power (without having the rail voltage gouge into the output stage's dropout voltage range) could be increased. For a given rated transformer output voltage, at power levels where there was plenty of difference between the rail voltage and the output voltage and the ripple voltage could be relatively large without causing a problem (and capacitance could be relatively low), my spreadsheet predicted the minimum capacitance fairly accurately. But it didn't take into account the sagging of the rail voltage caused by higher currents. So at higher power levels, relative to the rated transformer output voltage, the calculated capacitance values were too low and the ripple voltage would in fact impinge on the output stage's voltage range, causing gross distortion of the output waveform. My latest spreadsheet attempted to account for that effect, by dropping the peak rail voltage by the peak current times a constant that should represent all of the parasitic resistances, including the transformer secondary and the power and ground rails' parasitic resistances (I just stuck a constant in there and still need to make it a set of usersettable quantities.). But it still quickly goes off course as capacitance values get above a little less than 10000 uF. (Keep in mind too that I'm comparing the results from the spreadsheet to simulations that use square wave signals that have output levels that are equal to the peak output level for a sine wave, but deliver 2X as much power to the load (1.414X as much current). The problem might be that the capacitor charging and discharging are not modeled well. I used the same approximations that most people resort to, for that, which are only valid if there is less than 10% ripple (e.g. linear cap discharge). I also did not account for any parasitic inductances. And I also assumed that the rectifier diodes have a constant voltage drop. And I did not explicitly take into account the transformer VA rating. I plan to first just tabulate what happens to the rail voltage, when the output power, reservoir capacitance, and VA rating are changed, so that I'll at least know what I'm aiming for. I might be overlooking things that are obvious to you so please feel free to point out anything that could be improved. More later! Cheers, Tom Last edited by gootee; 11th October 2012 at 05:16 AM. 

11th October 2012, 06:12 PM  #1393  
diyAudio Member
Join Date: Mar 2007
Location: California

Quote:
Thanks for the kudos! I think what I am working on and the topic of this thread are very interrelated. As you explain below, there are many variables to consider regarding the rail voltage and the potential output power that can be generated from it. I will provide some details on how I do the calculation and what is considered. I think that my model of a "real world" transformer and what you are saying you do here: "dropping the peak rail voltage by the peak current times a constant"is essentially the same thing. My transformer model is just a voltage generator with an output resistance. In my calculation of transformer voltage sag, I use the peak current times this output resistance to obtain the voltage sag. But I get the peak current by back calculating what that should be from an output power level. I will detail all of this below. As far as how the capacitor values are involved in my spreadsheet, it's pretty simple  these are determined from the ripple voltage and the RMS current that will be required to reach the maximum power level that the transformer can support. The user enters the allowed ripple, and this changes the required capacitance AND the maximum power level, the latter because the ripple voltage is subtracted from the available rail voltage, which in turn is used to calculate the maximum power. I will outline the calculation method below, and then subsequently how the capacitor values are tied in to the rest of it. Please excuse this long post  it's not something that can be explained in brief! Quote:
Vsec, available > Vsec, req and sets the cell contents to empty set ("") otherwise. In cell B45, I survey column N for the maximum number (empty cells are ignored) and in this way I can find where Vsec, available = Vsec, req which is the maximum (peak) power output. In column N, rows 61120 I scan coarse increments of power level, and these are refined in rows 122132 and 134144 to give a more accurate number. So, what about the capacitors and the ripple voltage? I calculate the required capacitance using a formula for Vripple near the bottom of this web page: The Signal Transfer Company: Power Output (in fact I based everything in my spreadsheet on the formulas in this web page). These calculations can be found in cells P134P144. I rearranged the Vripple formula to calculate capacitance FROM Vripple, which is a user input. This formula is the typical one describing the discharge rate of a capacitor that is being recharged at twice the mains frequency and is discharging in between. The discharge rate depends on the average current (Irms), which I have already calculated. That's it! You can see how increasing ripple influences the required capacitance AND the maximum output power very easily by changing the Vripple value in the spreadsheet. There is a second set of calculations that incorporate the dissipated power and the crest factor to see if the total AVERAGE demand is greater than the rated transformer VA. Also, the number of channels in the amplifier is part of all these calculations. I won't describe these in detail at this point. Also, I should note here that: Cells that are in blue, bold text are intended for user input. All other cells are calculated output I have been building some power supplies in the last week for a couple of chip amps that I am putting into service. I am very happy to report that the numbers that I get out of my spreadsheet are EXACTLY what I measure in the real world power supply. I connect a dummy load (power resistor) to the amp and a small probe resistor. I use my computer sound card and REW to measure the percent distortion in real time. Using a pure sine wave input, I increase the power output until the point of clipping (e.g. 1% distortion) and then I measure the rail voltage and output power. It's exactly what is predicted by my spreadsheet model, given the data for the transformer that I am using, the total capacitance, etc. At this point, the user needs to enter the data to generate a model of the transformer. What I would like to do is survey an array of transformers from different manufacturers to come up with a relationship that will predict the typical series output impedance of my transformer model as a function of transformer VA. That way a user could check "typical" performance based on VA alone, OR enter the data for an actual transformer when and if it is available. Charlie Last edited by CharlieLaub; 11th October 2012 at 06:17 PM. 

12th October 2012, 01:46 AM  #1394 
diyAudio Member

Thanks, Charlie. I grok all of that.
I still need to figure out why my model craps out as the max possible power approaches the limit for a particular transformer output voltage. I don't think it will be too difficult. I just haven't had enough time to work on it yet. Depending on your intent, the following might not be significant, for your purposes: One thing that I see, offhand, that your model is probably not taking into account is the fact that the ripple voltage amplitude is not always constant, because your output is a sine rather than the assumed "DC at the sine's RMS level". Using the average or RMS output current gets you in the ballpark, and usually very close, actually, but, for LOWENOUGH frequencies it will give you a maximum possible output power level that is sigificantly too high, because it doesn't account for the relative timing between the signal and the charging pulses and ripple voltage waveform minima. Try it at 25 Hz, for example. To account for that, or test it, you would have to look at every possible phase angle of the sine, at the lowest frequency (or the worstcase frequency), and see if it happens to pull the ripple down farenough to bang into the output device's dropout region. I went to a lot of trouble to implement that in my spice simulation. Then I realized that a square wave of the same amplitude would cover all phase angles with only two simulation runs, 180 degrees apart. Also, music is not usually as simple as a single sine. Someone here found music that is very close to a square wave, and which basically went rail to rail. The square wave is not quite the "worst case" signal, but it is a much better worst case than a sine, since it draws current for much longer, at a time, giving much worse railvoltage sag, especially when its "on" portion lasts longer than the interval between charging pulses (or several of them). Anyway, I then also went to a lot of trouble to devise a way to measure the distortion of a square wave, in spice, ignoring the rise and fall portions with high precision, and also implemented measurements of things like the voltage difference between the rail and the high side of the load, and also ways to keep track of the actual minimum value of that difference over the entire time of a simulation run (since dropout/clipping might happen only once in a great while). I also have the simulation produce a calculated plot of the output voltage's error, based on the input signal. Essentially, from each simulation run I had at least three ways by which I was able to see if the dropout region was struck by the rail/ripple voltage, even just once, even for just a very short time, even by just a few tens of microvolts. Of course, the more accurate I wanted to be, the longer the process would take, for each scenario tested. I didn't really intend to be THAT meticulous about it. But once it was all in place I found that it could be made very accurate, especially if I took the time to calibrateout the calculated error's amplitude and DC offset, and then took the time plot the distotion, and to magnify the resulting waveforms for close inspection, etc. Your goal is probably different than mine (I hope so, for your sake, at least! <grin!> ). Mine was to find (or find a method to find) the absoluteminimum capacitance, for any output power level, given transformer output voltage rating, and VA rating, and load resistance, and mains frequency, such that it would literally be "impossible" to have ANY clipping, even just occasionally, that resulted in more than a 1 mV excursion of the output voltage waveform due to the rail voltage impinging on the output circuit's "dropout" voltage region. I can do that, now, fairly easily, with LTSpice, although it can be tedious if I calibrate each case, which I do when I am also interested in looking at the distortion and output error and other metrics, or when I want to compare results between scenarios, or if I just need to be very accurate for some other reason. Not everyone will want to, or would even be able to, use LTSpice in order to find out what capacitance is required for a system they wish to design and/or implement. And I was mostly just doing the simulations to try to get a better idea of what was "really" happening, while hoping that a simple rule of thumb or some simple equations would eventually be sufficient. I knew about all of the approximate methods that were already out there and hoped that after my spice model was wellenough refined and validated and verified, that then I could evaluate the accuracy and applicability of the usuallyused approximate equations, and possibly add a little to them if necessary, and end up with something relatively simple that would be accurateenough. I guess that's where I am, now. And I am finding that, so far, the equations appear to work well ONLY in the "comfortable, easy" regions, where the transformer's rated output voltage is highenough, relative to the desired maximum output power. Basically, for a transformer output voltage rating and a desired maximum output power level, my spreadsheet calculates (or SHOULD calculate) the absoluteminimum capacitance that is required to achieve it, without any possibility of "clipping" (as defined above). "Ideally", to give a true "guarantee" that there cannot possibly be any clipping at the desired max output power, the worstcase signal should be assumed, which would be a constant DC output at the maximum desired PEAK sine level (NOT the average or the RMS level). I used square waves (at 25 Hz), at that peak level, instead, in my simulations, and for the spreadsheet (or at least I intended to). Square waves do consume twice as much power as a sine would, if it had the same peak voltage. However, I do think that the square wave is morerepresentative of a worstcase scenario for a real music signal. Anyway, sorry to blatheron about all of that. I just wanted to give you the short version of what led up to my spreadsheet. Right now I am in the process of going over the equations for my spreadsheet (which so far was just slapped together, fairly quickly, without a lot of debugging or verification yet), with an eye toward verifying that it assumes a peaklevel square wave output, everywhere, and also that it accounts for as many significant parasitic effects as possible, and anything else that might be significant that I might have overlooked. Cheers, Tom 
12th October 2012, 02:17 AM  #1395  
diyAudio Member
Join Date: Mar 2007
Location: California

Hi Tom,
Thanks for the lengthy reply and explanation. I would love to grok all that you do in Spice, but I am alas only a sophomoric user... I will read over an digest what you write none the less. One note below, however. Quote:
Charlie 

12th October 2012, 10:27 AM  #1396 
diyAudio Member
Join Date: Jul 2004
Location: Scottish Borders

select a 35+35Vac transformer for a 100W amplifier.
It works. It works with a range of smoothing capacitance options. Now select a 34+34Vac transformer and ask it to deliver the same 100W. You will find that some of the very lowest cap options no longer work. Go even further, choose 33+33 & 32+32 transformers. As the transformer voltage goes down so the low end of the range of smoothing cap options gets higher and higher. Why is this happening. It's down to the minimum voltage available at the supply rail when the amplifier output is at it's highest. When the available supply voltage drops below a certain value the amplifier is incapable of delivering that unclipped peak at the top of the 100W sinewave. Gootee's sims are telling us exactly that. Ask for more power and the sim tells us to reduce the supply ripple by increasing the smoothing capacitance. But the sim like all sims relies on KNOWLEDGE of what the sim is doing to make sense of the predictions. I started by selecting a 35+35Vac transformer for a 100W amplifier. I know I would NEVER select a 40+40Vac transformer for a 100W amplifier. Not even when the sim says it works !!!!!!!!!!!!!!!!!!!!!!!!
__________________
regards Andrew T. Sent from my desktop computer using a keyboard 
12th October 2012, 10:43 AM  #1397 
diyAudio Moderator

why not? you can use a 40040ac traffo and still call your amp 100watts, who's to stop you? i know i wouldn't.....
__________________
the best advertisement for a good audio design is the number of diy'ers wanting to build it after all the years....never the say so of so called gurus.... 
12th October 2012, 11:28 AM  #1398 
diyAudio Member
Join Date: Feb 2001
Location: USA

"I know I would NEVER select a 40+40Vac transformer for a 100W amplifier. "
I guess David Hafler was an idiot for using a 44044 on the DH200? I guess Tom Holman was likewise on the APT amplifier? etc.
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Candidates for the Darwin Award should not read this author. 
12th October 2012, 04:49 PM  #1399  
diyAudio Member
Join Date: Mar 2007
Location: California

I have an update to post, so that my spreadsheet model is more flexible and you do not need to enter or measure the data for a transformer. I will give an example using AndrewT's post from above and show how my spreadsheet can be used to answer questions about the minimum capacitor size that can be used in a power supply.
For my latest revision, I went through a bunch of the Antek transformer datasheets, copied over the relevant parameters that were needed to model the transformer (as a voltage source with output resistance) and plotted the data. I used a range of both VA rating and secondary voltage. When I plotted Log(Zmodel) versus Log(VA) the data series were essentially linear. See below: Note the axes are loglog. I then created a separate linear regression for each secondary voltage (lines on plot above). It turns out the the slopes of the regression lines are almost identical, and I decided on an "average" slope. It was then a process of adjusting the intercepts to make things line up by eye. When plotted against the secondary voltage, the intercepts fell on a nice line (more or less) as shown below: These data regressions give me the ability to model the performance of ANY TRANSFORMER (based on the Antek data) having a VA between 50 and 1000 Watts and a secondary voltage between 12VAC and 60VAC. This pretty much covers the ranges used for audio power amplifiers. I also wanted to be able to know the lumped transformer losses (core and copper losses) for an arbitrary transformer. It turns out that this is mostly just a function of the VA rating. Again, data taken from Antek's datasheets is plotted versus VA  the trend wasn't linear as higher VA transformers have slightly lower losses, so I used a quadratic relationship (see line in plot below): So, what is this good for? Well, for instance, AndrewT's post above can be investigated using my spreadsheet: Quote:
[Edit: I will follow up with more on this in the next post] It's important to note that the required capacitance value will change with transformer VA as well as secondary voltage because the VA value influences the amount of "sag" or "stiffness" as current is drawn by the amplifier. This is why you can not just make claims about capacitance in your power supply without a good idea of how the transformer comes in to play. Hopefully this is not news to anyone. I hope that the example above shows how my spreadsheet can be used to investigate various questions about the power supply, minimum required capacitance, ripple, etc. With the new addition of the data regressions for the Antek transformers, the user can quickly check the result for a hypothetical transformer of arbitrary VA and secondary voltage. The only note of caution is that the Antek transformers are actually under rated by about 15% in terms of their VA rating compared to others. I have found this to be true when checking the calculations against some real world performance data that I measured. GET THE UPDATED SPREADSHEET (VERSION 2.0) HERE: Transformer_capability_calculations_VER2.0.xls I HAVE REMOVED THE PREVIOUS VERSION. Charlie Last edited by CharlieLaub; 12th October 2012 at 04:57 PM. 

12th October 2012, 05:23 PM  #1400  
diyAudio Member
Join Date: Mar 2007
Location: California

Continuing from above:
Quote:
So, Andrew is completely correct in his statements. Let's look into another thing he mentions: Quote:
There are certainly lots of tradeoffs that can be investigated! Edit: I just realized that for the 40V case and VA ratings below 200VA the transformer is limited by the VA rating itself (e.g. because of heating) and not from the rail voltage. I will explain this in the nest post, below. Charlie Last edited by CharlieLaub; 12th October 2012 at 05:42 PM. 

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