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

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In summary, the frequency of operation of electrical systems in aircraft is typically 400hz because higher frequencies result in smaller, lighter equipment. This is due to the amount of iron needed being directly related to the area under the voltage/time graph, which is proportional to the peak magnetic flux. This is supported by concepts such as flux density, Faraday's Law of Induction, and the Fundamental Theorem of Calculus. Additionally, for motors, higher operating speeds allow for more power in a smaller machine due to the relationship between torque, flux, and current linkage.
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gkraju
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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 ?
 
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- 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. [itex]\Delta \Phi = \int v \, dt [/itex]

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.
 
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  • #3
Uart, could you provide some references for this?
 
  • #4
Ref :

1. The definition of flux density.
2. Faraday's Law of Induction.
3. The Fundamental Theorem of Calculus.
 
  • #5
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.
 

1. Why does the size of a transformer or motor decrease as the frequency of operation increases?

This phenomenon is known as the "skin effect" and is due to the way that alternating current (AC) behaves. As the frequency of the AC increases, the current tends to flow on the outer surface of the conductor, rather than evenly throughout the entire cross-section. This means that the conductor can be made smaller without affecting its performance, resulting in a smaller overall size for the transformer or motor.

2. How does the skin effect affect the performance of a transformer or motor?

The skin effect causes an increase in resistive losses, which can lead to decreased efficiency and potentially damage the equipment. This is why it is important to consider the frequency of operation when designing transformers and motors.

3. Are there any other factors besides frequency that affect the size of a transformer or motor?

Yes, the size of a transformer or motor is also influenced by the amount of power it needs to handle and the desired level of efficiency. Higher power and efficiency requirements may result in a larger size, even at higher frequencies.

4. Can the size of a transformer or motor be decreased indefinitely by increasing the frequency of operation?

No, there are practical limits to how high the frequency can be increased before other factors, such as eddy currents and dielectric losses, become significant and limit the size reduction. Additionally, the size reduction may not be justified if the cost of higher frequency components outweighs the benefits of a smaller size.

5. Are there any disadvantages to using higher frequencies in transformers and motors?

In addition to the limitations mentioned above, using higher frequencies may also lead to increased electromagnetic interference (EMI) and higher costs for specialized components and materials that can handle the higher frequencies. It is important to carefully consider the trade-offs and determine the optimal frequency for a given application.

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