ohm is correct for dc, but don't forget the complex numbers when dealing with ac.
The error is you thought we were dealing with impedance when actually we're dealing with .... Impedance!
You'll laugh too in a moment, once it becomes clear.
Where you are stuck is thinking of inductive reactance of the transformer's primary (or secondary, or whichever). The reactance (measured in ohms) varies with frequency and being inductive, gets bigger as frequency increases. The transformer's winding
does have inductance, and its value may limit how low a frequency the transformer can handle without a reduction in level.
But so far, we've looked at a transformer as though it were just a coil; coils are nice frequency-dependent resistors, but a coil alone can't couple a signal the way a transformer does. Which brings up an important property...
When you have at least 2 coils sharing a common core, something interesting happens. If you apply a voltage across one of the coils, it will induce a voltage in the other coil. Let's say your coils are 200 turns and 50 turns, and you apply 100vac to the 200-turn coil. The transformer will cause the same number of volts-per-turn to be induced in the 50-turn coil.
100v / 200 turns = 0.5v per turn
0.5v * 50 turns = 25 v
This example conveniently showed how 1/2-turns arrives at 1/4 voltage output, but also legitimately shows how a transformer couples from one winding to another. The fundamental property is
volts-per-turn among all coils is equal.
Now transformers have another fundamental property observed by the original experimenters:
power in equals power out.
Because volts steps up or down in direct proportion to the number of turns of each coil, if power in equals power out then the current steps down or up in inverse proportion to the number of turns. And using the third fundamental electrical property, if current stepped down in a given coil while voltage stepped up, then
impedance must have stepped up in direct proportion to the voltage.
So a transformer winding will have a d.c. resistance, and will have a reactance due to its inductance, and the vector-sum of these is indeed impedance... but no one cares about these facts first.
Rather, the more useful property is how the transformer steps up/down voltage,
solely based on the turns ratio of the transformer. And the transformer doesn't have any set impedance in this respect until a load is attached to the secondary. After all, you can know exactly how much voltage will be induced in the secondary by the applied primary voltage and turns ratio, but you don't know how much current flows in the secondary or primary until you define the load attached to the secondary.
Ex:Using the same 200-turn/50-turn transformer as above, with 100v applied to the 200-turn primary, a 25Ω load attached to the secondary results in:
- 100v / 200 turns * 50 turns / 25Ω = 1A of secondary current.
- 100v / 200 turns * 50 turns * 1A = 25w of secondary power
- And power in = power out, so 25w / 100v = 0.25A primary current
-
Calculate primary impedance as 100v / 0.25A = 400Ω
Where did 400Ω come from?
Reflected impedance, the one we typically care about in an output transformer. We calculated it based on a knowledge of power in = power out, the number of turns on each coil, the voltage applied to the primary and the load attached to the secondary. But we could have gone a shorter path.
Topic: Simple (?) output transforer question (Read 6751 times)