Step input to loaded transformer

In summary, the conversation discusses the calculation of the response of a loaded ideal transformer to a step input. The ideal assumption is that there are no resistance losses except for the load on the secondary coil and the ability to pass infinite magnetic flux. The equations used in this scenario reduce to a normal DC circuit, but if instantaneous DC values are desired, Maxwell's Equations must be solved.
  • #1
Ambforc
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I am trying to calculate the response of a loaded ideal transformer to a step input. For example a step input in voltage from zero on the primary coil with a resistor connected across the secondary coil.

I already understand that with the second coil disconnected (for all practical purposes not existing) and the resistor connected in series with the voltage source over the primary coil a first order response in primary coil current will be observed. Now I am trying to simulate the response when the resistor is placed over the secondary coil. Of course, with no resistor over either the primary coil and the second disconnected you get an unbounded response in current (pure integrator).

The ideal assumption includes no resistance losses in any part except the load on the secondary coil and the ability to pass infinite magnetic flux.

This is as far as I have come:

Assuming the inductance of both coils to be equal with perfect coupling:

[itex]V_{1} = L \left(\frac{di_{1}}{dt} - \frac{di_{2}}{dt} \right)[/itex]
[itex]V_{2} = L \left(\frac{di_{2}}{dt} - \frac{di_{1}}{dt} \right)[/itex]
[itex]V_{2} = i_{2}R_{2}[/itex]

However this set of equations reduce to:

[itex]V_{1} = -i_{2}R_{2}[/itex]

and therefore fails to say anything about the transient response of the current in the primary coil [itex]i_{1}[/itex] and appears to reduce to a normal DC circuit.

Any help will be appreciated.
 
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  • #2
Your problem statement is unclear. If you want answers for an integer number of whole cycles, use the transformer equivalent circuit.

If you want instantaneous DC values, then you must solve Maxwells Equations. Circuit analysis is inadequate for that case.
 

1. What is a step input to a loaded transformer?

A step input to a loaded transformer refers to a sudden change in the input voltage of the transformer while it is connected to a load. This change in voltage can be either an increase or decrease and can be caused by external factors such as fluctuations in the power supply.

2. How does a step input affect a loaded transformer?

A step input can cause the transformer to experience a surge in current, which can lead to an increase in temperature and stress on the transformer's components. This can potentially damage the transformer or shorten its lifespan.

3. What are the possible consequences of a step input on a loaded transformer?

The consequences of a step input on a loaded transformer can include overheating, insulation breakdown, and even complete failure of the transformer. In extreme cases, it can also cause damage to other connected electrical equipment.

4. Can a transformer handle a step input?

Transformers are designed to handle a certain amount of voltage and current fluctuation, but excessive and sudden changes in input voltage can exceed their capabilities. It is important to choose a transformer with the appropriate capacity and to monitor and regulate the input voltage to avoid damaging the transformer.

5. How can the effects of a step input on a loaded transformer be reduced?

To reduce the effects of a step input on a loaded transformer, it is recommended to use surge protection devices, such as surge suppressors or voltage regulators, to regulate and stabilize the input voltage. Additionally, using a transformer with a higher capacity than the required load can also help mitigate the impact of a step input.

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