11-12-2021, 12:15 AM
It might help to think about the transformers that you find in switched-mode power supplies.
How can they be so very small compared to a conventional 50Hz type that passes similar powers?
It's because they are dealing with much higher frequencies. Simply put, a switched-mode power supply turns 50Hz into DC, then turns it back into AC, but at 50kHz or 100kHz or more.
Power is energy over time; joules per second. When you run 50Hz mains through a transformer you have 50 cycles per second; whereas for a 50kHz switched-mode power supply you have 50,000 cycles per second.
So you can see that a 50Hz transformer has to transfer 1000 times as much energy per cycle to achieve the same power throughput.
And that means that the higher the frequency, the smaller the core of the transformer can be, because it has to store less energy during each cycle.
Conversely, if you slow down to 25Hz, then you've doubled the energy per cycle needed to maintain the same power throughput. That means the core will need to store double the flux than it did at 50Hz. Or 4 times for 12.5Hz. If it's not big enough to do this, it will saturate. And bear in mind that standard mains transformers are designed to be just starting to saturate at 50Hz. To bring the flux down to a level that the core can cope with, you must reduce the voltage by basically the same factor you reduced the frequency by.
When thinking about all this and trying to convey a "hand-waving" understanding of the basic idea, I don't find it helpful to consider the DC resistance or inductance of a transformer. Just think of it as an energy storage device. Though the DC resistance is basically what you're left with when you hit saturation, as it is no longer an inductor at that point.
Another way to approach this might be to think about audio. The signal level at which a transformer will saturate depends on frequency, for all the reasons discussed to far. Analogue tape is another possible "angle" that might help to get a handle on this, perhaps. Depends on what you've done before - analogies are only useful if you know the thing being used.
Sorry if all that is a bit simplistic, but hopefully it'll help you get to the nub of the question.
Mark
How can they be so very small compared to a conventional 50Hz type that passes similar powers?
It's because they are dealing with much higher frequencies. Simply put, a switched-mode power supply turns 50Hz into DC, then turns it back into AC, but at 50kHz or 100kHz or more.
Power is energy over time; joules per second. When you run 50Hz mains through a transformer you have 50 cycles per second; whereas for a 50kHz switched-mode power supply you have 50,000 cycles per second.
So you can see that a 50Hz transformer has to transfer 1000 times as much energy per cycle to achieve the same power throughput.
And that means that the higher the frequency, the smaller the core of the transformer can be, because it has to store less energy during each cycle.
Conversely, if you slow down to 25Hz, then you've doubled the energy per cycle needed to maintain the same power throughput. That means the core will need to store double the flux than it did at 50Hz. Or 4 times for 12.5Hz. If it's not big enough to do this, it will saturate. And bear in mind that standard mains transformers are designed to be just starting to saturate at 50Hz. To bring the flux down to a level that the core can cope with, you must reduce the voltage by basically the same factor you reduced the frequency by.
When thinking about all this and trying to convey a "hand-waving" understanding of the basic idea, I don't find it helpful to consider the DC resistance or inductance of a transformer. Just think of it as an energy storage device. Though the DC resistance is basically what you're left with when you hit saturation, as it is no longer an inductor at that point.
Another way to approach this might be to think about audio. The signal level at which a transformer will saturate depends on frequency, for all the reasons discussed to far. Analogue tape is another possible "angle" that might help to get a handle on this, perhaps. Depends on what you've done before - analogies are only useful if you know the thing being used.
Sorry if all that is a bit simplistic, but hopefully it'll help you get to the nub of the question.
Mark
