Transformer Loading: Relationships & Calculations

[temujin]

dear all,

When loading the secondary winding of a transformer, my textbook gives the following relationships:
$$\frac{V_{sec}}{V_{pri}}=\frac{N_{sec}}{N_{pri}}\\$$
and
$$\frac{I_{sec}}{I_{pri}}=\frac{N_{sec}}{N_{pri}}\\$$

Do these relationships hold also when the diameter of the windings are different?
I suspect they don´t...If they do not, are there any other relationships I can use to calculate I and V in the secondary winding?


regards
t.

 

[berkeman]

Those are the simple first-order relationships, and as you suspect, they ignore parasitic inductance, capacitance and resistance, as well as core material issues. I did a quick google search, and pages like this one are pretty common:

http://www.beigebag.com/case_xfrmer_2.htm

Depending on lots of stuff, you can make your model a lot more accurate by including at least the leakage inductance and winding resistance (both are in series with the magnetizing inductance), and also the inter-winding capacitance of each winding (put in parallel with the magnetizing inductance of each winding). The N1:N2 transformation only applies to the magnetizing inductance components of this model.

Hope that helps, -Mike-

 

[ravenprp]

Dear T,

Thank you for bringing up this question about transformer loading relationships and calculations. The relationships you have mentioned are known as the turns ratio and they do still hold true even when the diameter of the windings are different. This is because the turns ratio is a fundamental property of the transformer and is independent of the physical dimensions of the windings.

However, in practical applications, the diameter of the windings can affect the transformer's performance and loading. In this case, there are other relationships that can be used to calculate the secondary voltage and current. One such relationship is the transformer's impedance ratio, which is given by:

\frac{Z_{sec}}{Z_{pri}}=\left(\frac{N_{sec}}{N_{pri}}\right)^2

This relationship takes into account the impedance of the windings and can provide a more accurate calculation of the secondary voltage and current. Additionally, the transformer's load also affects its performance, so it is important to consider the load when calculating the secondary voltage and current.

I hope this helps clarify the relationships and calculations involved in transformer loading. Thank you for your question and all the best in your studies.