@rg1Explaining that the base is the same for both sides of the transformer makes sense. Base power or say Base VA remains same throughout!!! Not the base Voltage, currents and impedance.
But, if you are transferring voltage across the transformer why do they use the "a (turns ratio)" and not "a^1 (inverse turns ratio)". Once a ratio is there, it is there. For example if a transformer transforms 1 Volt on one side (side A) to say 10 Volts on another side ( side B), it always does it with same ratio. So if you apply 2 Volts on side A, you get 20Volts on side B for 5 Volts you get 50Volts............. The BASIC formula for transformation are - Volts on side1/Volts on side2=Number of turns on side1/Number of turns on side 2 and for currents it is I1*N1=I2*N2. You call it anything, turns ratio or inverse turns ratio is your choice. I generally pickup things from basics to avoid confusion of nomenclature. Did it make some sense!!! Transformer is a both way device, so primary and secondary changes depending on how it is used. The side where power enters is Primary and so is the ratio.
One explanation I read online is to use intuitive reasoning to determine if the voltage is going from high potential to low potential, or visa versa. Intuitive reasoning comes from my explanation above.
I just don't like how vague that concept sounds even though I do understand the intent.
Best regards,
Brip