Magnetics Question; is the Answer Really as Obious as it Might Seem?

[Keasy]

TL;DR

This is what seems like a simple magnetics question involving a transformer, but the answer could have potentially important implications for advanced circuit design. The answer to the question may appear obvious, but is it really?

We have an ideal electrical transformer, 1:1 turns ratio. We can ignore winding resistance, core losses, hysteresis, core saturation, etc.
Call the primary P and the secondary S. The secondary is connected to a programmable voltage generator and to a resistance R in a simple series circuit.

The voltage generator is initially set to provide a constant 1 A current through the secondary S and the resistor R.

Now we use a voltage source to provide a changing voltage and current across and through the primary. But at the same time we vary the voltage across the secondary S (adding approximately the negative of the primary voltage to the secondary voltage source) so that the secondary current stays constant at 1A. I can see nothing that would prevent us from doing this.

Now the question : Is the time varying input impedance seen by the voltage source supplying P any different than if the secondary S had been open, rather than having the constant 1 A current?

Comment: It seems to me the 1A current in S establishes a constant magnetic flux in the transformer core. The current variations in P due to the voltage source adds to and subtracts from the magnetic flux in the core. But so long as the 1 A secondary current does not change it is unclear why the primary input characteristics should be different than if the S output terminals were open.

 

[Baluncore]

I think you need to identify which currents and voltages are AC and which are DC.

A 1 amp DC secondary current, delivered by a DC supply in series with a resistor to the secondary, will appear to be a resistive load across the secondary when seen from the primary, so it is not the same as an open circuit secondary.

 

[berkeman]

Summary:: This is what seems like a simple magnetics question involving a transformer, but the answer could have potentially important implications for advanced circuit design. The answer to the question may appear obvious, but is it really?

The voltage generator is initially set to provide a constant 1 A current through the secondary S and the resistor R.

Now we use a voltage source to provide a changing voltage and current across and through the primary. But at the same time we vary the voltage across the secondary S (adding approximately the negative of the primary voltage to the secondary voltage source) so that the secondary current stays constant at 1A. I can see nothing that would prevent us from doing this.

If you really want to discuss whatever this is that you have in mind, please draw a proper schematic for each of the pieces so we can understand what you are trying to do. Thank you.

 

[Keasy]

I think you need to identify which currents and voltages are AC and which are DC.

A 1 amp DC secondary current, delivered by a DC supply in series with a resistor to the secondary, will appear to be a resistive load across the secondary when seen from the primary, so it is not the same as an open circuit secondary.

What I am proposing is that the secondary current is always 1 A DC. No matter what happens in the primary we manipulate the circuitry attached to the secondary so the current is always 1 A. Under those conditions is the response of the primary to input voltage/current (dynamic impedance) any different than if the secondary were an open circuit? I would point out that in both cases there are no magnetic flux variations in the core caused by the secondary.

 

[Keasy]

If you really want to discuss whatever this is that you have in mind, please draw a proper schematic for each of the pieces so we can understand what you are trying to do. Thank you.

I cannot easily do that for this post, but I will try to make my future posts more explicit. Thanks, Keasy

 

[Baluncore]

The only connection to the secondary is an ideal 1 amp DC current source.
The ideal source is quite independent of the induced secondary voltage.
An ideal current source has an infinite impedance.
It would appear to the primary, as though the secondary was open-circuited.

 

[Keasy]

The only connection to the secondary is an ideal 1 amp DC current source.
The ideal source is quite independent of the induced secondary voltage.
An ideal current source has an infinite impedance.
It would appear to the primary, as though the secondary was open-circuited.

That is my view also. But it does result in what I consider a rather interesting issue, that I will discuss in another post.

 

[hutchphd]

That is my view also. But it does result in what I consider a rather interesting issue, that I will discuss in another post.

I also agree but with a caveat. No part of the core can be driven out of linear response by the DC offset.

 

[Baluncore]

I also agree but with a caveat. No part of the core can be driven out of linear response by the DC offset.

That is right.
My analysis was based on a long term response of the operating circuit, it did not consider the switching transients that set up the steady state.

If the AC voltage is applied first to the primary, that potential will appear at the secondary.
If the 1 amp ideal current sink is then connected to the secondary that 1 amp step current will appear immediately in the primary, (a transformer is a reciprocal device).

Since the primary is driven by an AC voltage source, with a very low output impedance, that 1 amp current step will appear as a voltage across the output impedance of the AC voltage source.

The primary 1 amp offset will eventually decay, even though the secondary current continues to flow. During that period, the V/I characteristic of the voltage source will be changing.