Coupling Transformers in a Bus Line

transformer

I'm trying to figure out how to model a transformer in order to estimate the number of transformers on a bus line. Each transformer is connected in parallel and may or may not have a connected load. I've been able to collect some empirical data from an available device, but I'm having trouble formulating an equation to satisfy that data.

I would assume that, ignoring hysteresis and eddy currents for simplification, calculating a bus like this would be a simple matter of combining the primary-side resistance/reactance with any referred secondary-side resistance/reactance and then adding these resistances in parallel with all other transformers connected in the bus. But when I perform actual measurements, my calculated numbers are off. When testing a circuit with this setup (transformers are a simple 1:1 ratio), the measurement is closer to 75 ohms rather than approximately 71-72 ohms (adding 13.52k + 5k + 3k + 75 in parallel). The measurement will also continue to stay relatively close to 75 ohms rather than dropping to the low 70s/high 60s that I would expect when introducing lower load values.

What exactly am I missing here?

Best Answer

Just examining the 75 ohm and transformer connected to the 3k load, the combined impedance (assuming perfect transformers) is: -

75 ohms // (3k + 53.6 + 53.6) = 73.23 ohms

Clearly as you add more parallel transformers this number is going to drop so how do you account for the actual reading being a little higher: -

  • The transformer dc winding resistances will add a little
  • The tranformer leakage inductances will add a little impedance

Given what you have shown there can be no other reason other than your measurement accuracy is poor.

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