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What determines the minimum/maximum frequency an AC transformer will work at?

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Beamin:
I was quite surprised to learn that after shutting off a transformer there is still measurable current that can be seen on "human" time scales, I believe 10's or 100's of milliseconds. Is this actually capacitance and not the same principle as "stepping up/down current" and it just seems like it is storing charge? If so what's the lowest frequency you can transfer current between two coils and what determines this speed? Size/distance? What happens as you make the frequency higher and higher is there an equivalent transformer that uses mm waves, IR, or even light somehow?

bjbb:
All hail the search lords of duckduck/bing/google.

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19660001049.pdf

Core construction, core and wire material, and voltage determine applicable frequency.

The excitation energy takes much time to decay, depending on core size and material.

bob91343:
On the low frequency side, the limiting factor is the core saturation.  In order not to draw excessive current, the source must have a minimum frequency and voltage combination.  If the frequency is lowered, the voltage must also be lowered in proportion.  So a 120 V 60 Hz transformer primary can be operated safely at 60 V and 30 Hz.

On the high frequency side, the situation is entirely different.  Basically there is no upper limit other than that posed by the distributed capacitance of the windings and the inductance of the leads.  However, the hyteresis and eddy current losses in the core increase wirh frequency so there is heating just from the excitation.  At some point it becomes impractical to use the device.  Typically the upper frequency limit is very roughly ten times the design frequency.

Transformer design is nearly a black art.  Without decades of experience, it's simple to screw up a design.  That's why there are experts to consult and established companies to manufacture.  Even the relatively mundane factors such as winding patterns become important for certain applications.

Beamin:
So my question (like most of my questions) is more theoretical then practical. I'm not interested at say 30hz, or building one, but rather what happens at 1Hz or a gigantic transformer at less then 1hz. When does AC cease to become AC and just turn into pulsed DC with no transfer of energy? What kind of magic happens at the extreme ends of the spectrum. IR/Light is just high frequency why can't it work in a transformer (If you think this is a stupid /easy question then you are not thinking about it hard enough i.e. why is glass an insulator of EMF at lower frequencies but a good one at high frequencies if we go past the simple answer of: refraction down fiber optics make it work, or what happens between light and RF)?   

Imagine a magic DC to daylight signal gen what would the outputs on the back look like assuming you started at 1hz and cranked it up to 1000THz and noted what happens to your transmission lines as you went up in small 10hz steps.

Gyro:
Any time you have a change in current (no matter how small) then you have a change in magnetic flux - translate small change as a larger change over a longer period. It is a matter of whether the core is large enough to couple it to the secondary.

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