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General Asylum General audio topics that don't fit into specific categories. |
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In Reply to: Let's try another approach. posted by Al Sekela on May 2, 2006 at 14:26:10:
Visualize a transformer with the primary connected to a 120 volt DC, current-limited power supply through a switch, and with the secondary left open-circuit. The current limit on the power supply is set for one ampere to keep from blowing things up.Well, your example is somewhat irrelevant because you're asking me to analyze the step response of a simple RL circuit and not the steady state sine wave response of a transformer, but I'll play along.
At time t = 0 the switch is closed. What is the time response of the current in the primary?Below your arbibrary 1 amp hard limit on the current, it's a simple RL response:
I(t) = 120 * R * (1 - e^(-L*t/R))
where L, R are the series inductance and resistance of the primary. Once it reaches your hard limit of 1 amp, it will obviously be 1 amp.
It will not rise immediately to one ampere, but will do so after the core is saturated.That depends on R & L. It could reach 1 amp before saturation.
The core switches its magnetization to provide the back-emf that prevents short-circuit current from flowing.In the case of steady state AC, the effect of the back-emf you are referring two is called inductive reactance. Inductive reactance is frequency dependent, X_L = 2*pi*f*L. For steady state AC, it's a constant.
For steady state DC, it's zero, and nothing but the series resistance prevents short circuit current from flowing.
For a step response, it exponentially decays to zero, so the impedance is initially larger but then decays to just the series resistance once the core saturates.
The product of 120 volts and the time it takes to saturate the core should be greater than the integral under the half-wave sine curve if the transformer is to work properly at the sine wave frequency, whatever it is (25 Hz, 50 Hz, 60 Hz, 400 Hz).Yes, and the frequency dependence you speak of is captured in the inductive reactance.
I've greatly oversimplified here to get the basic point across. Transformers are designed to avoid core saturation for maximum expected primary voltage at some particular frequency. The lower the frequency, the more magnetic flux the core must contain without saturating.I don't think you're making a technical error, but I do think that the point you're making is largely irrelevant in this application. For power supply transformers in consumer electronics, the inductive reactance is generally insignificant compared to impedance of the load reflected from the secondary side to the primary. In fact, with transformers designed for this application, manufacturers usually don't even bother to specify the series inductance.
Also, the change in frequency is pretty insignificant too in this case. We're talking about a difference between 50 Hz and 60 Hz, not 60 Hz and 400 Hz.
Finally, the most relevant point is that the input voltage and load impedance are far more important than the mains frequency in determining whether the core is going to saturate. In any reasonable linear power supply, a reduction in frequency from 60 Hz to 50 Hz is going to produce a much smaller increase in VA than will typical variations in mains voltage from place to place.
This is why the transformers in switching power supplies are so small.No, transformers in switching power supplies are smaller because they are used in a different way. In a switching power supply, the transformer follows the switching circuit, so it is operating at a very high frequency. Not to mention it's impedance looks totally different than a transformer used in a linear power supply.
This is only the beginning of the design. The maximum current determines the size of the wire, which determines the size of the coils, and on and on. It may be cheaper to just design the thing for 50 Hz and sell it into both the 50 Hz and 60 Hz markets (so-called "World" transformers as carried by Mouser, etc.), so a device that uses one of these would be perfectly safe to use in either area. However, this is not guaranteed.I didn't say it was guaranteed. However, in the vast majority of cases, probably 99.9%, it won't be a problem. And if there are designs out there which are so close to the edge that a small frequency change causes a problem, these same designs won't be able to handle small changes in mains voltage either. So they would generally be considered defective by most designers.
Dave
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Follow Ups
- Re: Let's try another approach. - Dave Kingsland 19:13:20 05/02/06 (2)
- The transformer looks nearly like an open-circuit - Al Sekela 19:20:13 05/03/06 (1)
- Re: The transformer looks nearly like an open-circuit - Dave Kingsland 05:35:00 05/04/06 (0)
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