Hi all, was hoping someone could confirm that my calculations for sizing transformers for small dc loads is correct.
Im building a dc power supply with three available voltages, 5, 12 and -12 and have used the following equation

Vac= vdc+vreg+vrec+vrip/0.9*vnom/vlow*1/√2
Vdc= output of voltage regulator
Vreg= voltage drop of regulator
Vrec= voltage drop across diodes on rectifier
Vrip= ripple voltage @ 10% of vdc
0.9= rectifier efficiency
Vnom= 230v in uk
Vlow= 190 in uk
Iac= Idc*1.8conversion factor

For 5v dc @ 0.5a
Vac= 5+2+1.25+0.5=8.75/0.9= 9.7*230/190*1/√2= 8.3vac
Iac= 0.25*1.8= 0.45vac
Transformer va= 8.3*0.45*2= 7.47va
Note I will be using a dual rail PCB mount transformer, this is reason for *2 on va calculation. Plan to connect output rails in parallel to obtain Max current output of around 0.5a

For +12 and -12vdc @ 0.5a
Vac= 12+2+1.25+1.2= 16.5/0.9= 18.3*230/190*1/√2= 15.6v
Iac= 0.5*1.8= 0.9a
Transformer va= 15.6*0.9*2= 28.08va
Going by my calculations I have decided to select two transformers rated @ 10 and 30va
Appreciate if anyone could confirm that this is the best method to select transformers for a dc power supply using l78 and l79 voltage regulators, also that my results are correct, thanks.

 

Maybe this'll help you decide how to proceed.

 

If Vreg is the *minimum* voltage drop across the regulator, then your calc will return the minimum AC needed.

The ripple voltage positive peak is the peak voltage into the regulator. The ripple voltage negative peak is what you have to watch in terms of the minimum voltage across the regulator.

I don't know what rectifier efficiency is. At the peak secondary current there will be a peak Vf across the rectifiers that can be assumed to be a constant at all output currents.

I usually break this up into two calculations, one to determine the secondary voltage, and one to modify that based on primary voltage conditions. Makes it easier to see what's what and adjust when parameters change.

ak

 

You did a lot of math, but I think you made it too complicated.

Transformers come in standard values, with 6.3, 12.6, 18, and 25.2 VAC RMS being typical from my experience. Rectified, filtered DC will be 1.414 * RMS.

For your 5V supply, a 12.6V transformer work (6.3 would be cutting it a bit close for low line/high load conditions). For your +/-12V supplies, something around 18V or 36V CT would work.

Current rating of the transformer depends on the filtering you use. Since capacitor filtering is most common, current rating needs to be 1.4X the desired output current.

 

Hi Gerty, I already have that PDF, thanks anyway. Think the equation is more accurate compared to PDF, just wanted to double check with someone on here that my answers are correct before ordering transformers. Could you let me know if you think calculations are correct, thanks

 

As already mentioned, I think you're over complicating the math. Unless you're buying custom wound transformers I don't think you'll find a 15.6 v transformer. And if you did, your nominal voltage would/could vary enough to mess up all your calculations.

 

Due to the high RMS current drawn by a rectifier/capacitor filter, the transformer RMS current rating should be at least 1.7 times the maximum DC output current.

 

Hi guys, thanks for replys. Got equation from another site, thought it useful as I could factor in v drops specific to my regulators.
Have seen the 1.414. * RMS before, if its tried and tested think I'll use it. As its a cap filtered circuit then 1.4*Iac is suitable.
With these factors, new values should be
12*1.414= 16.9vac 18v tran is nearest available size
0.5*1.4= 0.7Iac

Trans va= 18*0.7*2= 25.2va, think it will be 30va tran

5*1.414= 7.07vac 9v tran is nearest available size
0.25*1.4=0.35Iac

Trans va= 9*0.35*2= 6.3va go to next available size

Appreciate if someone could confirm that these calculations are now correct, thanks

 

Having checked over calculations can see I've gone wrong. Can't multiply 12v dc by 1.414 as it has to be rms, as already stated. Problem now is how do you calculate vac, when using dc values.
Does anyone have equation that converts dc into ac.?

 

The Vac calculation in your first post will do it (I think); too many terms with no grouping to make it easier to read...

The only thing you need to do is round up Vac if it isn't a standard value.

 

Hi dennis, will go with original equation got it from transformer corporation web site. Lot of good information on it if interested about power supplys.

 

A factor of 1.4 * Idc for the transformer AC RMS current rating is too low for continuous operation of a transformer as that will likely cause it to overheat.
That value sounds suspiciously like someone used the ratio between peak and RMS voltage of a sinewave for the conversion factor, but the current de-rating factor is unrelated to that.
If you do a calculation (or simulation) of the RMS transformer current for a given capacitor rectified DC current you will find that the factor is more like about 1.7 or greater (DC current no more than about 60% of the transformer RMS current rating).

 

Hi crutschow, im going to use my original equation that includes a factor of 1.8 for calculating dc current. Having checked over original calculations again I think they are best to use when sizing for a transformer.
Going to order 18v 30va and 12v 10va.