I was just wondering if there were some upper frequency at which a field would not fully form in a transformer and the output would be clipped.
A few things to consider:
- skin effect: at very high frequencies, the conductors in your transformer become more and more lossy (because current ends up flowing only in the surface, not throughout the entire conductor).
- Core losses: the core material in the transformer (necessary to improve the coupling) introduces some losses that typically increase with frequency (eg eddy current loss). Some high frequency transformers use ferrite (a non-conductive ferromagnetic material) that try to give the "best of both worlds".
- At sufficiently high frequency the atoms in the core don't have time to align to the magnetic field, which means there will be some lag in "establishing the magnetic field" in a transformer with core
- In an air-core transformer, there is a point where the magnetic field lags due to transmission effects (the current in the coil emits an electromagnetic wave). When the scale of the diameter becomes large compared to the (quarter)-wavelength at the frequency of interest, the coupling efficiency decreases (because you will have magnetic fields of opposite signs in different part of the core)
In short - yes, transformers do "cut off" at high frequencies. Some techniques exist to extend the frequency range - but you do have to take care to get decent signal transfer and low losses at high frequency. These precautions primarily relate to geometry, core material, and choice of conductor.