How do I calculate the maximum load on a center-tapped AC/AC transformer for a bi-polar linear power supply with full wave rectification?

I have a 24 VCT AC to AC step-down transformer, which has three wire leads on the secondary. I'll call the secondary leads X, Y, and C, where C is the center tap. With a DMM, the voltage between X and Y is about 24 VAC (actually slightly higher), and the voltage between X and C is 12 VAC, and the voltage between Y and C is 12 VAC. The manufacturer rates the transformer as 24 VCT, 10 amps.

Putting aside safety factors, overhead, and load types for a moment (for clarity):

1. If we ignored the secondary wire, C, and connected an AC load across X and Y, we could have a maximum load on the transformer of 10 amps @ 24 volts, which is 240 watts. Correct?

2. Let's say we have an AC load that's designed to run at 12 volts. We should be able to run a maximum of 10 amps @ 12 volt load from X to C, at the same time as we are running a maximum load of 10 amps @ 12 volts from Y to C. In other words, we can now power 20 amps of 12 volt load because halving the voltage doubles the ampacity while power (240 watts) remains constant. Is that correct? This is assuming that we put no more than 10 amps on each 12 volt set. ie. two balanced 10 amp, 12 volt AC loads.

3. Now let's say we have a full-wave bridge rectifier on the secondaries X and Y, and we use the center tap C as circuit ground. We run both the + and - outputs of the rectifier past a smoothing cap(s), and through a 7912 voltage regulator (7812 on the positive rail). We now have three connections; the ground (which is the center tap), a +12 rail (relative to ground, ) and a -12 volt rail (relative to ground). Can we run a 12 volt, 10 amp DC load from the positive rail to ground at the same time as we run another 10 amp, 12 volt load from the ground to the negative rail? For a total of 20 amps load at 12 volt DC? Remember, this question is about the AC to AC transformer's rating when used in this context.

4. Now, for the title question. Let's say we have the same setup as question #3. But, instead of having perfectly balanced loads, let's say that we really only want the negative rail for op amps and there's not going to be much draw on the negative rail. Are we still limited to 10 amps @ 12 volts from the positive rail to ground? Or does using full-wave rectification allow us to "borrow" spare ampactiy from the negative rail to ground (that isn't needed) and use it on the positive rail instead? For example, could we have 12 amps @12 volts on positive to ground and 8 amps @ 12 volts on the negative to ground? Could we have 18 amps @ 12 volts on the positive to ground and 2 amps @ 12 volts on the negative to ground?

Or to put it another way, if a transformer is rated for 24 volts at 10 amps, can you use any combination of load on the positive and negative rail (in a bi-polar, full-wave rectifier scenario) as long as the total does not exceed 20 amps @ 12 volts?

For the purposes of this question, let's assume that "maximum load" on the transformer means either the point at which a fuse should blow (if fuses are sized properly) and/or the point at which the transformer would be damaged, become dangerous, or perform incorrectly due to overloading or unbalanced loading.

• what kind of 7812 allows 10A? re 4: no, you can't "borrow" power, not for very long at least. Also, is that measured 12v w/o any load? If so, that's going to droop well under 12v well before 10A are drawn. Commented Jun 25, 2021 at 19:46
• re: 1-3; basically yes, yes, yes. Keep in mind VA and how that (slightly) differs from W. Also keep in mind the several sources of loss along the way. to wit, you can't make a very strong 12v DC supply using a 12v AC transformer; you'll want to use a 14v or even a 16v one to compensate for BR and LDO losses. Commented Jun 25, 2021 at 20:00
• @dandavis: The purpose of the question is about transformer loading, balancing, and rating, not the whole circuit design. So it's a theoretical 7812 that can handle infinite current because it's not really part of the question, other than to illustrate that we're dealing with 12 volts and not the 24 at the transformer output. :)
– Nick
Commented Jun 25, 2021 at 20:31
• There is a good explanation that was posted here about 10 years ago, try this link: electronics.stackexchange.com/questions/16276/…
– Gil
Commented Jun 25, 2021 at 20:33
• @dandavis: The most likely scenario is that there would be a bunch of voltage regulators in parallel, and that each +/-12v device (around 200mA or so) would be on it's own voltage regulator to prevent the load from influencing the voltage to other loads. The load in my case would be voltage-controlled oscillators for an analog audio synthesizer. Each oscillator must have the same precise voltage from + to ground, because the voltage controls (pitch) tuning. So I'm trying to determine the transformer sizing first, with a goal of driving a large bank of individually small 12v loads.
– Nick
Commented Jun 25, 2021 at 20:44

1.&2. are correct given load current proportional to voltage at every instance - resistive.

3.&4. are wishful thinking.

For a "balanced 2×half voltage load", the ideal centre tap current was zero.
In reference to this cheat-sheet, you can expect about 6 Amperes at (just incidentally!) about 12 Volts (with real diodes) at the charging capacitor for each rail when loaded symmetrically, 10 A from a single rail with the other loaded insignificantly.
Assuming the "negative" peak of ripple .5 V, allowing for 100-10% line voltage and a regulator drop-out of 2.5 V, it's "difficult" to get more than 7.5 V regulated.

Few loads operate from pulsating DC/unbuffered (single-phase) rectifier output just as well as from buffered DC.
By no means all DC loads profit from the supply voltage being stabilised/constant/defined exactly.
Some profit from supply voltage being well filtered, e.g. audio amplifiers (voltage amplification stages, which get additional filtering internally).

can you use any combination of load on [both rails of a bridge rectifier on a centre-tap secondary]
as long as the total does not exceed [double the secondary current rating]?

No, on two accounts:

• there is a derating to about 60% of the secondary's current rating with a "capacitor input filter" (90% with a (costly) DC choke input)
• total current decreases further with load(ing) imbalance - Hammond suggests down to (two times) 50% (72% with choke input).
Note that, if the secondary was two-part, really, you could connect the halves in parallel instead of in series and use a regular bridge configuration and (2×) 60% of rated current (almost 190% (?!) with choke), but suffering one "diode drop" more.

In real life, things like (frequency dependant) ESR and "wiring"/PCB layout make a significant difference (e.g. in ripple voltage).

Since a bulk Cap with 10%V ripple needs a pulse of current to charge it for the 90% decay time with 10%Vpp ripple the current ripple is a pulse just 10% before peak to peak at 10x the load current, so the transfer of power is poor and can saturate the core, so the VA rating must be reduced significantly. A more efficient method is to use an active PFC and buck regulator and the negative side is same with a small cap. Old BJT LDO’s will drop 1.5 to 2V so you get 10V, maybe if the Vpp ripple is <10%. The XFMR should give you 12Vac at full load and 10% higher with no load per tap.
FET LDO’s are much less.

• re: "10% higher"; the E/R/toroids that i've dabbled with seem to put out more like 50% higher under open circuit (18v on a 12v, 24v on a 16v). Is that 10% figure after smoothing/regulation (you said vac)? Commented Jun 25, 2021 at 19:51
• It’s a standard 90% efficiency for low cost/power transformers. No load is 10% above full. 50% would be very lossy or resonant or very poor mutual coupling. Commented Jun 25, 2021 at 21:32
• That n umber reduces to 2% on 10kVA types and <1% on 10MVA types Commented Jun 25, 2021 at 21:37
• @Tony I've seen 30% regulation on cheap wallwart transformers. Though that was a decade back when I last played around that way with them. Some were 10%. I considered those to be the really good ones! Of course, the OP's transformer is very substantial. Nothing like a wallwart transformer. A handy 24V@5A here on my shelf in a cardboard box weighs about 6-8 lbs (just hefting it for feel.)
– jonk
Commented Jun 26, 2021 at 0:57

Transformer load current ratings have mostly to do with the dissipation in the windings. The windings and the core have a lot of thermal mass, so they don't mind pulsed current as long as the RMS power rating of the transformer is not exceeded.

The transformer may have a VA rating. As long as the load attached to the rectifier output doesn't consume, in the RMS sense, more than that VA rating, you should be OK.

Or the transformer may have output current rating. That is, again an RMS rating. As long as the RMS rectifier current is below that, you're OK.