A transformer has a maximum volts per turn. You need to have sufficient number of turns on the primary so that the primary voltage you apply, divided by the number of turns, does not exceed this volts per turn.
The maximum voltage per turn for a transformer is controlled by three things.
- the operating frequency
- the core cross section
- the maximum core flux you can use
Taking the last item first, the limitation on core flux depends on the core material. If it's iron for a mains transformer, then the maximum is given by saturation, 1.5 T to approaching 2 T, depending on cost and quality of the iron. If it's a high frequency ferrite transformer, then core heating will probably limit you to less than the DC saturation level of typically 400 mT, operating figures of 50 mT to 200 mT are common. If it's air core, then obviously neither saturation nor core heating play any role, and the flux will be limited by primary inductance, primary I2R heating, or the primary current you are able to deliver.
Assuming a sinusoidal waveform for both voltage and flux (other waveforms can be used with a change in details, square voltage and triangular flux is the other common one), then as the flux swings through zero, its rate of change is maximum, and it generates the maximum voltage in the primary (and any other winding sharing the core).
The rate of change will be affected by the frequency. You can draw a single cycle and put slopes on it, or just accept the formula that swinging between fields of B and -B at a frequency f,
max rate of change = 2πfB
The magnitude of the voltage per turn is just the rate of change of flux in Webers/s. One Weber is one Tesla operating over an area of 1 m2. Now we know the maximum voltage per turn when we have a core area of A
max volts per turn = 2πfBA
To give a concrete example, let's say we have an iron core, 12 mm by 25 mm cross section, operating at peak 1.5 T, at 50 Hz.
The maximum volts per turn = 2π x 50 x 1.5 x 0.012 x 0.025 = 0.141 V
If we are going to connect this to standard 240 V mains, then we first need to calculate the maximum voltage that will produce. 'Standard' 240 V mains can exceptionally go up to 265 V. It's also an RMS figure, so we need to multiply by 1.414 to get to peak voltage, which is 375 V. Finally we can compute the primary turns as 375/0.141 = 2657 turns.