Do I analyse a current source with transformer as a closed circuit in superposition?

[gauthamtechie]

If I have a two current sources in a circuit: Both coupled via 1:1 Transformers. Let's say one of them is a high frequency low ampere sinusoidal current source; And the other is a 50 Hz, 12 amp sinusoidal current source. With a number of Resistors in series in the circuit, LTspice is showing the superimposition of the high frequency current over my 50 Hz current sine wave. When I remove the transformer though, from the 50 Hz source and connect directly, I get no superimposition of the current. This makes sense with superposition theorem since it is replaced by an open circuit and hence analytically, this high frequency current doesn't add to the 50 Hz current.

Why then does the 1:1 transformer create a change by giving a closed path in the secondary and allowing the high frequency current to superimpose with the 50 Hz current? Isn't a 1:1 transformer connected in series electrically equivalent to a series current path, and hence should act as open circuit even in the secondary side?

 

[crutschow]

Post your .asc circuit.

 

[gauthamtechie]

Post your .asc circuit.

View attachment finalCurrentsource.asc

The transformer coupling the 6 amps if removed, doesn't have the current of the high frequency source superimposed in the series circuit when simulated.

 

[crutschow]

Post the .asc circuit for both configurations so I can better understand what you are referring too.

 

[gauthamtechie]

here is the .asc circuit without the transformer:
View attachment finalCurrentsourceW.asc

You see there is no superimposition. And my question is that a 1:1 transformer should ideally not have any effect electrically right? So when I open the Current source according to superposition theorem for analysis, I should open the secondary of the transformer as well right? This means no current can flow and no superimposition must occur. Is this theoretically right? ANd should I just treat this case as an issue because of my winding inductances?

Here are the images:

 

[MrAl]

Hello,

An idea transformer with a current source input would go open circuit on the secondary if the current source was disconnected, but that doesnt look like what you have drawn there. It looks like you'll see inductance and that is what you would see with a real transformer because either winding represents an inductor to ground if it is energized independently from the other winding. So it really depends what you are trying to analyze here. Do you need the total theoretical result without the transformer or do you really need to know what happens in a real life circuit?

 

[gauthamtechie]

I want to know why this is going on with the transformer. You mentioned Inductances. Can you elaborate? I am asking this because If I use the transformer, it is acting as a short for current source. Is this an application of 1:1 Transformers - So that super imposition of current occurs? Is this Supposed to happen ideally or not?

 

[MrAl]

Hello again,

With a transformer you have to specify what it is you are trying to find out. If it is what happens in the real life circuit for any possible condition then you have to consider the inductance looking into the primary and the inductance looking into the secondary. That's because the transformer has windings that wind around a core and that creates an inductance in itself. So even with the primary open, if you apply a signal to the secondary you will see some inductance to ground. That inductance depends on the transformer winding and core type.

What kind of current source are you talking about? Is it DC, or is it AC, and is it a constant current and you want to know what it does many seconds after it is turned on?
For a DC current that exits over all time, the transformer secondary or primary will act as a short if there is no winding resistance, but because a real life transformer always has winding resistance there will usually be some resistance. For an AC current, the winding resistance and winding inductance comes into play, so it looks like a resistor in series with an inductor.

The only time it looks like a short is for DC and when the winding series resistance is being ignored.

All of the AC discussion above assumes that the winding voltage does not cause saturation of the core. If that happens then we would see the impedance decrease and it could be so significant we consider it almost a short even for AC.

 

[gauthamtechie]

I get your explanation, but this is an issue I have with a current source which is sinusoidal.

So even with the primary open, if you apply a signal to the secondary you will see some inductance to ground. That inductance depends on the transformer winding and core type.

I need some basic understanding: By "inductance to ground" you mean that inductance will close the circuit in the secondary, so in my analysis I cannot open out the secondary because otherwise I'd just open out terminals in a current source to make analysis simpler as learnt in superposition theorem which in a nutshell says "Current source- open it. Voltage source -Short it." So even when i open out the primary, the non ideal nature of transformer does present an inductance. Also I wasn't aware of the role saturation plays until I read your answer. I did my research and now it makes sense.

From my understanding, since we are dealing with a current source, my open circuit current or magnetizing current might already be so large and in saturation. Is this why the secondary now behaves like it is looking at a DC and thus my transformer secondary makes way for current to flow, just like in the .asc diagrams I've posted in one of the previous replies?

 

[MrAl]

Hello again,

If i understand you correctly, that sounds right. Lets assume that the primary is now completely open circuited so only the secondary is connected. It is entirely possible that the rest of the circuit connected to the secondary can generate AC voltages high enough to saturate the core and thus lower the impedance of the secondary winding. But what you would do here is you would analyze for that operation point. If the secondary can take say 100 volts and you only see 50 volts with the normal secondary resistance and inductance, then it is not saturated. However if you see 200 volts then you might be concerned about saturation.
So you would first analyze it assuming everything is ok before the analysis and then actually check to see if is ok after you see some analysis results. If it is not ok you'll have to look into it further.
You might also note that superposition assumes a linear network, and saturation is not considered linear. However, if you find that it is not in saturation by the first analysis, then you might assume it is linear.

So when you think about it, this is almost the same as any other analysis. If you have a simple single standard 1/4 watt resistor being powered by a current source and you analyze the circuit and find that there is 1000 volts across it, you'll have to modify something somewhere because that little 1/4 watt resistor can not handle a voltage that high (normally they are rated for 200 or 300 volts no matter what the resistance is). This is even more immediately apparent with a capacitor. If you have a 1uf, 25v capacitor in a circuit and analyze the voltage across the capacitor and it comes out to 50 volts, you know it's not going to work. You either have to raise the voltage rating of the cap or modify the circuit in some way.