Looking for a Model of Transformer when it is used in a Pure Sinewave Inverter - Page 1
Forum section: electronics / projects

author: KerimF
author_rank: Frequent Contributor
timestamp: July 04, 2023, 08:41:06 pm
content: I used hearing of pure sinewave inverters which use conventional two-winding iron core transformers.Their transformer is driven by a MOSFET bridge which, in turn, is driven by a sinewave PWM (for 60/50 Hz) whose frequency could be 16 KHz, for example.This means that the transformer, with or without load, can also act as an effective low pass filter (perhaps with a very small ripple on its output voltage).I think the transformer’s leakage inductances play the main element(s) in its function as LPF. But there must be another element to complete the LPF. Is it the stray capacitances, the core losses or both?In vain, I have searched a model which could be used in simulating a transformer in such application.So, I hope that someone here had the chance to hear of an equivalent RLC circuit of a transformer that shows, if implemented in a simulation, its LPF function.Regards,Kerim

author: moffy
author_rank: Super Contributor
timestamp: July 05, 2023, 08:32:33 am
content: I can only suggest a ferroresonant filter as a possibility, but I am not sure that is what you are asking about:https://www.snaptec.com.au/sa-slc-series-line-conditioners.html

author: RoGeorge
author_rank: Super Contributor
timestamp: July 05, 2023, 09:50:54 am
content: Any integrator is a low pass filter. Either L or C can be seen as analog integrators:- Any coil is an integrator. If a constant voltage is suddenly applied to a coil, the current will start to increase linearly.- Any capacitor is an integrator. If a constant current is suddenly applied to a capacitor, the voltage will start to increase linearly.A single coil will be enough to see the LP filtering effect, by looking at the coil current. However, if you want to simulate in LTspice an ideal transformer, use two coupled L1 and L2, with coupling factor k=1. Each coil for a transformer turn. You can couple more than two coils if needed. First search result for "LTspice transformer":https://www.analog.com/en/technical-articles/ltspice-basic-steps-for-simulating-transformers.htmlhttps://www.analog.com/en/education/education-library/videos/5579254291001.html

author: KerimF
author_rank: Frequent Contributor
timestamp: July 05, 2023, 10:31:17 am
content: Quote from: moffy on July 05, 2023, 08:32:33 amQuote from: RoGeorge on July 05, 2023, 09:50:54 amThank you for replying.I was surprised when I tested a ready-made inverter, its no-load HV output (of a conventional iron core transformer) was sinewave even without a capacitor as a load!In general, knowing an equivalent circuit of a device (here a transformer) is enough for making a suitable model for a simulator, as LTspice.But none of the actual various equivalent circuits of a transformer seems being able to simulate its function as a stand-alone LPF!

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 05, 2023, 10:42:12 am
content: Yes. Most generally, a transformer is a transmission line structure; or -- well,mostgenerally it's a pile of wires and fields -- but, it often happens that the wires, being, you know, long and parallel, can well exhibit meaningful transmission line characteristics.For transformers of typical mains-frequency construction, the multiple layers required per winding means that the transmission line characteristics are rather muddied (you get groups of resonant modes from each of the per-turn, per-layer and per-section geometries), but we can still model the lowest such mode as the overall capacitance and inductance (leakage) of the given winding(s).This is an example 2nd order model for two windings. A more realistic model might have many more LC elements, and various crosswise connections thereof, to accurately model all the resonant modes -- but we're only interested in the lowest one, so we can solve for Cp, LL, etc. accordingly.Since the transformer may still transform at higher frequencies, this should be read as a cutoff frequency (above which, ratios and impedances vary strongly), not necessarily the LPF that this model suggests. Again, it's only a model valid up to the first resonant mode!We can read some things off this with ease:- Cutoff is of order Fc = 1 / (2 pi sqrt(Cp LL)), or using Ciso or various combinations thereof- Bandwidth is maximized for Zsystem = Zo = sqrt(LL / Cp)- LL is measured by shorting the secondary and reading primary inductance (this reads LLp + LLs (Np/Ns)^2)- Cp, Cs can be measured by resonant frequency, additive shift (put a known capacitor in parallel and measure the change in Fc), Zo, etc.- Ciso (and Cp and Cs to some extent depending on geometry) can be measured at low frequencies (e.g. any old C meter)Oh, and T1 has some (magnetizing) inductance (Lm), and k = 1. This form (with series LL's and a shunt Lm) is effective when k ~= 1, but the nonideal tee/pi equivalent circuit should be used when k <~ 1.Trivia: leakage inductance is essentially given by winding geometry (especially wire length), and is independent of magnetic core in well-coupled (k ~= 1) designs. (Simply put: the leakage doesn't leak out beyond the windings, into the core!)Tim

author: KerimF
author_rank: Frequent Contributor
timestamp: July 05, 2023, 11:41:16 am
content: Quote from: T3sl4co1l on July 05, 2023, 10:42:12 amThank you.It seems that, in this model, Cs only (besides the series impedances) has a role in the LPF (in case of no load).Don't you think that Rm, equivalent of core losses at the high frequency of PWM (not included in this model) could also act as a shunt (after LLp) at a high frequency? If this is the case one will need to find out a rather simple test to measure, even approximately, Rm at the PWM frequency.

author: KerimF
author_rank: Frequent Contributor
timestamp: July 05, 2023, 03:56:47 pm
content: Quote from: T3sl4co1l on July 05, 2023, 10:42:12 amIn your opinion, does the flux leakage increase with frequency due to the decrease of the core magnetic permeability?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 05, 2023, 09:40:29 pm
content: Quote from: KerimF on July 05, 2023, 11:41:16 amBoth are involved in the general case i.e. some given Zin and Zout. Whether one or both elements is shorted out depends on mismatch from the given case (Zs ~ Zo).Core loss is at most equal to inductance (in the eddy current / skin effect region where Z ~ sqrt(F)) so I would not say it's an effective filter element. It may be a significant power loss. (You may find a PWM filter is desirable.)If leakage varied with frequency, it would have to be expressed by other elements. Inductance increasing with frequency can only be achieved through approaching resonance with a capacitor, which peaks and then inverts the impedance. That is, it can only increase relatively quickly, up to some maximum point, not forever.k however can fall with increasing frequency, due to the mentioned effect!The usual approach for your application would be simply a capacitor on the secondary, and preferably an R+C across that, and maybe additional line filter hardware (DM/CM choke, another 'X' cap, 'Y' caps to GND, etc.) to reduce emissions. The transformer would be designed to give desired leakage, so that the PWM filter looks like any old buck converter, transformed appropriately (i.e. inverter split into push-pull configuration, transformer ratio in the middle).Oh BTW, speaking of PP -- if you are using this, you must have minimal leakage between the two halves of the primary. Preferably this should be, not just bifilar wound, but multiple pairs in parallel. Since the impedance will be quite low. Leakage between primary halves incurs peak switching voltages due to current flow and dI/dt, and ringing with Coss. This can be R+C snubbed or diode clamped, but at some expense to power dissipation, thus keeping it low is paramount. (It is possible for it to be "too" low, in that Cp will dominate instead, incurring excess peak currents and ringing; the best case is around the impedance-matched condition, taking the ratio of the inverter's peak voltage and current at turn-on/off to be a kind of impedance.)Tim

author: PCB.Wiz
author_rank: Super Contributor
timestamp: July 05, 2023, 11:29:23 pm
content: Quote from: KerimF on July 04, 2023, 08:41:06 pmYes, but keep in mind that the losses in an iron core increase rapidly with frequency.So you need to de-rate a transformer that you are asking to do two tasks : work at 50Hz and act as a inductor at 16kHz.That, plus EMC considerations, is why most good designs have an upstream start to filtering, usually a ferrite core choke, before the iron core transformer.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 06, 2023, 03:42:49 am
content: Quote from: PCB.Wiz on July 05, 2023, 11:29:23 pmYou'll find that it's not actually all that much. Tube audio output transformers are designed for power limit at, well, some lower limit -- maybe 20Hz, maybe lower for flatter response, maybe higher for weight savings. And in this case, with most of the HF dropped across leakage, very little will actually go into the core.You may need a configuration like a side-by-side banked winding to get enough leakage, which will put some leakage flux into the core -- the windings aren't right on top of each other to cancel out 100% then. So the losses may be higher for that reason. But given the frequency ratio, it's probably fine.Last time I characterized an iron core transformer, the losses looked like a small shorted turn, basically resistance in parallel with the magnetizing inductance. Easily measured as a square wave current for a square wave voltage. With a capacitor on the secondary, it should measure as a much lower inductance, with some amount of resistance depending on how much leakage gets into the core versus shared between windings. And the wire of course (AC resistance), which about limits the Q factor to like, 20 ballpark maybe..? Hm, I suppose you'll need quite a lot of inductance at 16kHz. Also it'll be whiny...Tim

author: johansen
author_rank: Super Contributor
timestamp: July 06, 2023, 05:19:58 am
content: Typical 750 watt rated APC sine wave back up power supply was iirc 1.3 amps at 24v no load, with most of that wasted in the transformer.My attempts at using blue green iron powder cores as an inductor did not decrease loses.A rather large, 1 inch diameter ferrite core (as in actual diameter of the core cross section) with a paper thin air gap and only 8 turns of copper reduced the no load losses to .9 amps.Decreasing the 20uf output capacitor to 10uf made little difference. Also the test isnt particularly valid because the capacitor is passed through a current transformer and the ripple current is used to change the pwm frequency. So adding the inductor drops the freq.Actual core losses are going to depend on construction.I bet welding the core together (like a mot) would triple your hf losses.

author: PCB.Wiz
author_rank: Super Contributor
timestamp: July 06, 2023, 05:20:16 am
content: Quote from: T3sl4co1l on July 06, 2023, 03:42:49 amI found a paper on PWM added losses, and they certainly cannot be ignored. See attached graph.It seems PWM frequency itself is not so critical on the iron-loss component, but I'd still tend to use an upstream inductor, so as not to expect too much from the transformer, and also actually pass EMC tests.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 06, 2023, 05:39:27 am
content: Quote from: PCB.Wiz on July 06, 2023, 05:20:16 amDid I say "ignored"? Pretty sure I implied low quantity, not none...I also provided explanation how it could be further lowered (reducing HF in core by shunting it at the secondary etc.), and, generally about justdoingthe analysis and characterization, rather than looking up papers and working on supposition (or worse, superstition..). These aren't complex systems, AC steady state analysis will do, and with a function generator, scope, and maybe  power amp, and a handful of passives, all parameters can be fully characterized.Tim