In some medical equipment like CT we find that the voltage entering the equipment is around 380 V, but then it's increased to be around 70 kV to 140 kV.
To increase voltage we use more turns on the secondary than the primary, but that will make the transformer's size way to big and it won't be practical.
In order to use less turns on the secondary coil we increase the frequency, but I don't get what that means or how it is applied.
How do we increase the frequency in this case?
Increasing the frequency allows you to use smaller inductors or transformers, typically. The way I look at it is that the amount of magnetic energy that can be stored in an iron core depends on the core volume and saturation field of the material. Higher frequency delivers the stored energy more times per second. So all else being equal, raising the frequency increases the power transmission capability of a transformer.
It is not really about turns count per-se.
How do you increase the frequency? Well, one way would be to rectify the incoming AC from 380 VAC up to about 530 VDC, then use a DC-DC converter, or a small transformer to boost up the voltage. For high boost ratios, you would definitely want to use a transformer or auto-transformer rather than a simple inductor. Note that this is outside my area of expertise but should be mostly correct (I am just ignoring a lot of important details to avoid making the answer too confusing).
High-voltage power supplies are a challenge to design. They stress the limits of materials and components, and so require some specialized knowledge.
That said, a very common high-voltage supply in the multiple tens of kV range can be found in every CRT: the anode supply. This varies from 10 to 50kV depending on the tube size.
TV anode supplies use three key elements:
At each step, the circuit topology is carefully balanced to avoid stressing each element beyond the voltage it can handle. TV flybacks work at the horizontal scan rate (15kHz or so), outputting a medium-voltage pulsed waveform to the tripler built from a diode stack and capacitors.
I can’t speak to how to make a 140kV supply, but I would bet that like a TV flyback it uses some combination of step-flyback followed by a voltage multiplier.
X-ray power supplies also need to have current limiting and safety interlocks.
To increase voltage we use more turns on the secondary than the primary, but that will make the transformer's size way to big and it won't be practical.
No, that doesn't makes sense. The person who said that is unfamiliar with transformer design, and is assuming you continue onward with the same size wire, just making more turns of it. That's not true.
Transformers have a fixed amount of power which both primary and secondary must handle. Watt's Law says when voltage increases by factor X, current decreases by factor X also. Ohm's Law says since the current changed, the wire size can change in proportion as well!
Get it? If you use 10 times the windings, you are using 1/10 the wire cross-section, which means, the total amount of copper/aluminum remains the same regardless of secondary voltage! The varnish insulation takes some small amount of space, so finer wire is slightly larger, but not by a whole lot.
With transformers, the mass of copper/aluminum is decided by the total power of the transformer.
In order to use less turns on the secondary coil we increase the frequency, but I don't get what that means or how it is applied.
No, that too is nonsense. This person "knows a little bit" about transformers but it's jumbled so-called knowledge and they are wrong.
What frequency does is change the mass of the iron core of the transformer. Higher frequencies greatly shrink it. That's why electric locomotives (for whom mass is a virtue) use 16.667 Hz, and airplanes (for whom mass is a curse) use 400 Hz.
They still need about the same amount of copper/aluminum for a transformer of a given power rating.
