Why Size of transformer/motor reduces as frequency of operation increases ?

[gkraju]

In aircraft the frequency of operation of electrical systems used is mostly is 400hz. The reason given is that the size/weight of the equipment reduces as the frequency increases. can anyone please explain me the theory behind this with some formula, please do not stop with formula. How and why the size reduces ?

 

[uart]

- The amount of "iron" that you need increases as the peak magnetic flux increases.

- The peak magnetic flux is proportional to the time integral of voltage. \Delta \Phi = \int v \, dt

Essentially this means that the amount of iron you need is directly related to the area under each half cycle of the voltage/time graph.

 

[KingNothing]

Uart, could you provide some references for this?

 

[uart]

Ref :

1. The definition of flux density.
2. Faraday's Law of Induction.
3. The Fundamental Theorem of Calculus.

 

[uart]

BTW. The above relates more to transformers, why you can get roughly the same voltage and current ratings with less "iron" (or other soft magnetic material) section.

With respect to motors the operating speed is very significant. Here the maximum torque is related to the flux and the current linkage (ampere turns), so that tends to be fixed for a given size machine. Power being the product of torque times speed means that you can get more power in a smaller AC machine if it operates at higher frequencies.