"For their part, transformers have long been known for their ability to inject both radiated and conducted noise into a system. Rather than being confined to the transformer's core, the radiation can be a source of hum. The electromagnetic field around the transformer isn't omnidirectional in its coverage, but rather directional. This minimizes interference to other components in the enclosure by locating the transformer in such a way that the radiation won't affect sensitive components.
An alternative has been to move the transformer to a section of the enclosure far enough away from these components to make interference in significant. Still, another option is to design a transformer with reduced EMI in mind. This is accomplished by designing the transformer with reduced flux density, which involves increasing the number of turns on the transformer or increasing its core area.
In addition, electrostatic shields placed between the primary and secondary windings of the transformer can be effective in reducing EMI. This technique is most often applied in noise- sensitive applications such as airframes, where suppressing EMI sources encompasses the design of the entire aircraft.
A Faraday shield is a type of electrostatic primary-to-secondary shield that's commonly
employed in transformers. The shield is usually one turn of thin copper foil that encircles the core and is attached to system ground. It prevents high-frequency current from coupling into the secondary windings. When left unshielded, this high-frequency current will more than likely find its way into the
entire system by means of inter-winding capacitance. The weight added by a Faraday shield is typically negligible. In low-power applications, the need for the isolation provided by a Faraday shield can be fulfilled with a split-bobbin transformer.
In extreme cases, one of several types of magnetic shielding can be applied. The shielding usually consists of an enclosure that surrounds the transformer, captures stray flux (radiation), and sends it to a solid system ground. It can be supplemented by another outer magnetic shield. This technique often is quite effective, but it's also expensive because the interior enclosures are made from high-nickel magnetic alloys and the exterior shields from mild steel. Together, they add considerable weight and complexity to the design. However, when the highest level of EMI protection is required, the magnetic enclosure is the first choice. "
so you can use a bigger transformer to lower flux density for a fixed power demand and therefor lower EMI, but >
"One thing that obviously confuses many people is the idea of flux density within the transformer core. While this is covered in more detail in Section 2, it is important that this section's information is remembered at every stage of your reading through this article. For any power transformer, the maximum flux density in the core is obtained when the transformer is idle. I will reiterate this, as it is very important ...
For any power transformer, the maximum flux density is obtained when the transformer is idle.
The idea is counter-intuitive, it even verges on not making sense. Be that as it may, it's a fact, and missing it will ruin your understanding of transformers. At idle, the transformer back-EMF almost exactly cancels out the applied voltage. The small current that flows maintains the flux density at the maximum allowed value, and represents iron loss (see Section 2). As current is drawn from the secondary, the flux falls slightly, and allows more primary current to flow to provide the output current. "
so as you increase xfmr size, you have two things fighting each other, flux will go down with the increase in core size, but flux will go up as you get closer to an unloaded condition,
see also as mentioned in the first quoted article that there is also bad stuff getting into the circuit thru the windings, so transformer construction is also important in the way of Farady shields and external cans.