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reflected impedance of a transformer

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PG1995

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Hi

Could you please help me with the query included in the attachment? Thank you for the help.

Regards
PG
 
Hi,


With an ideal transformer, we say that the secondary load is reflected to the primary. Since there is a turns ratio more typically not equal to 1, the equivalent primary parallel resistance is usually different than the secondary parallel resistance.

The primary series resistance however comes in when we start to work with a non ideal transformer that actually has some primary and secondary resistance in the winding itself, without even yet considering the load. The primary series resistance then reflects into the secondary as more series resistance in the secondary. Doing this little transformation would allow us to draw all the resistances on the secondary of the transformer instead of having them all over the place.
For example, with a transformer with a 2:1 primary to secondary turns ratio (a step down transformer) with 1 ohm primary series resistance, 0.25 ohms secondary series resistance, and a 2.5 ohm load, and with a 12v primary input voltage source, we could draw it exactly like that with one series resistor in the primary and one in series with the secondary and one parallel for the load, or we could 'reflect' the primary 1 ohm series resistance to be in series with the secondary and combine that with the already present secondary series resistance and that would allow us to draw the circuit with only one secondary series resistance and one parallel load resistance and nothing in the primary. Since the primary series resistance is 1 ohm and the turns ratio is 2:1 (which means the turns ratio is 0.5), the series resistance reflected from the primary to the secondary is 1 ohm times 0.5^2 which equals 0.25 ohms reflected. Combining that with the already present secondary series resistance of 0.25 we get a total of 0.5 ohms and that includes both the original secondary series resistance and the reflected primary series resistance so now we can draw the circuit with only two resistors on the secondary and none on the primary. This makes it a little easier to analyze by simple inspection.

Just to note, the resulting output across the parallel load resistance of that example would be 5 volts either way.

We can also reflect the primary parallel input impedance to the secondary which allows us to obtain the equivalent impedance looking into the secondary.
 
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Thanks a lot, MrAl. It's very kind of you.

MrAl said:
For example, with a transformer with a 2:1 primary to secondary turns ratio (a step down transformer) with 1 ohm primary series resistance, 0.25 ohms secondary series resistance, and a 2.5 ohm load, and with a 12v primary input voltage source, we could draw it exactly like that with one series resistor in the primary and one in series with the secondary and one parallel for the load, or we could 'reflect' the primary 1 ohm series resistance to be in series with the secondary and combine that with the already present secondary series resistance and that would allow us to draw the circuit with only one secondary series resistance and one parallel load resistance and nothing in the primary.

I don't get that why would you say that the load resistance is a parallel one? Even if it is, then it's parallel to what? I would say load resistance and secondary winding resistance are in series. Where am I going wrong? Please help me with it. Thank you.

Best wishes
PG
 
Hi,

The load itself is usually considered to be in parallel to the secondary winding. It's a little more convenient like that so that we can easily distinguish between the series resistances of the windings and the input or output impedances. Yes the load is in series with the secondary series resistance, but that's not the way it is referred to usually, it is usually said to be in parallel with the secondary without mentioning the series resistance of the secondary.
It's easier to think of it in parallel also because the series resistance drops voltage and looses power and thus efficiency while the voltage that appear at the very output is what delivers the power to the external circuit. So we always have to distinguish between the Rs and the Rp (or RL).

So although the load is in series with the secondary series resistance, it is usually referred to as being in parallel with the secondary.
If there was a load in the primary circuit and in the secondary circuit the two loads would be in parallel, not in series.
Also, if the load was polarized we would be connecting the positive to the positive which makes it seem sort of like a battery charger where the output connects to the battery and we certainly dont say that we connect the battery in series with the output of the battery charger.

By contrast, the secondary series resistance is always considered to be in series with the secondary.

So if you see or hear about some primary series resistance or secondary series resistance you know it's not the load, it's the resistance of that winding respectively.
 
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