The transformer rules
An ideal transformer's voltage ratio equals its turns ratio: Vs ÷ Vp = Ns ÷ Np. The current goes the other way, so the power stays the same. The impedance ratio is the turns ratio squared, which is why a 1:3 winding gives a 1:9 impedance transformation, as in the 9:1 unun used for random wire antennas, and 1:2 gives 4:1. Real transformers lose a little to winding resistance and core losses.
RF transformers
At RF, the same rules apply to transmission-line and conventional transformers wound on ferrite. The turns must give enough inductive reactance at the lowest frequency, usually at least four times the impedance, and the core must not saturate or overheat at your power. The unun calculator and balun calculator handle that side.
Mains and audio
For mains transformers, the secondary voltage is quoted at full load and rises a little when lightly loaded. For audio, an output transformer matches a speaker to a valve or amplifier stage, using the impedance ratio. Always treat mains wiring with care.
Questions
What is the impedance ratio of a transformer?
The square of the turns ratio. 1:3 turns gives 1:9 impedance.
How many turns does a 4:1 balun need?
A 1:2 turns ratio. The number of turns depends on the core and lowest frequency.
Does a transformer change power?
No. An ideal transformer passes the same power. Voltage goes up as current goes down.
Why is my measured voltage higher than calculated?
Mains transformers are rated at full load, so they read higher with little or no load.