# Thread: DC to AC power conversion formula

1. Member
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## DC to AC power conversion formula

I need to calculate the AC power required to serve telecommunications equipment. The data I have on the equipment is given with its DC value (i.e. 40A at -48VDC). How can I convert this DC load to AC (say 240VAC single phase)?

2. ## Re: DC to AC power conversion formula

If you are asking what amount of AC power is the same as the DC you have described, then that is simple. Power is power. 40 amps times 48 volts (we can safely ignore the negative sign) equals 1920 watts. Now divide that by 240 VAC and you get 8 amps. But I think that what you really need to know is what type of power converter you need to accomplish your desired conversion. I can't help you with that, as electronics and I do not get alone.

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## Re: DC to AC power conversion formula

Actually, your first response was the one I was looking for. I've seen the formula AC=DC/.636 tossed around--Is this perhaps used for equating AC and DC voltages (not power)?

4. ## Re: DC to AC power conversion formula

120v AC / .707 = DC. In otherwords 170v AC (Peak Value) is the equivalent of 120 v DC.

Is that what you were asking?

edited to clarify my wording

Roger

[ August 10, 2005, 11:29 AM: Message edited by: roger ]

5. ## Re: DC to AC power conversion formula

I tried to play around with the "0.636" number, without success. I can't figure out its origin. It does not appear to help in the conversion of DC power to AC power, for any of the commonly used voltage levels (12 VDC, 24 VDC, 48 VDC, 120 VAC, 208 VAC,240 VAC, etc.).

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## Re: DC to AC power conversion formula

0.636 is the average value of a sine wave.
0.707 is the RMS value of a sine wave.

Steve

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## Re: DC to AC power conversion formula

My mistake, .636 is the average value of a "rectified" sine wave. The average of a sine wave would be zero, since the negative half equals the positive half.

Steve

8. ## Re: DC to AC power conversion formula

I did notice earlier that 0.636 was approximately equal to 2 divided by pi. I didn't think it was worth mentioning. But based on steve66's statement, I just did the integration, and confirmed that the average value of a rectified sine wave is 2/pi. But I still don't see how anyone would say that to convert DC power to AC power, you divide by that number. I think the "rule of thumb" that msteiner had been told is nonsense.

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## Re: DC to AC power conversion formula

Reading between the lines, the question seems to be, "How much alternating current at 240V is required to operate a 40A, 48Vdc telephone power supply?"

If that is the case and assuming 75% efficiency,

Irms = 40Adc x 48Vdc/(240Vrms x 0.75) = 11A

Sounds like a 20A, 240V circuit to me.

One would have to see the specs on the equipment to be absolutely sure though.

Oops, had to correct some typos.

[ August 10, 2005, 05:26 PM: Message edited by: rattus ]

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## Re: DC to AC power conversion formula

The last post by rattus is essentially what I was looking for--thanks for the reminder to incorporate efficiency.

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