Electromagnetic Interference in Converter
How can the derivation of the current and voltage affect the EMI production?



dv/dt


If a node of your circuit couples into another through capacitance, the amount of current injected via the parasitic capacitance will be proportional to dv/dt. This is simply due to the current in a capacitor being \$ C dv/dt \$. If the impedance of the victim node is known, then a voltage will develop on it proportional to this impedance and current through the parasitic cap.

=> If a node has high di/dt it should not have a large area which forms  large parasitic capacitances with everything nearby.

This is why it would be a very bad idea to have, say, the heatsink of your power MOSFET connected to the drain without insulation. A large heatsink with large voltage swings and high dv/dt will couple into anything nearby through parasitic capacitance. Likewise, nearby traces carrying fast signals will crosstalk depending on edges dv/dt.


di/dt


A current loop creates a magnetic flux which is proportional to current. This flux will induce a voltage in nearby loops (pcb traces, etc). This voltage is proportional to the derivative of the flux (and thus the derivative of the current). Thus the amount of magnetic coupling is proportional to di/dt in the source loop. 

=> if a loop has high di/dt then it should be as tight as possible, since the radiated flux (and thus EMI) is proportional to loop area.

Also, remember some features of your circuit are loop antennas, slot antennas, dipole antennas, etc. These will get much better at transmitting noise at certain frequencies, depending on how they resonate, their dimensions versus wavelength of signal, etc. High di/dt or dv/dt means your signal will contain many more high frequency harmonics, thus it will have a higher likelihood of exciting some resonance somewhere and turning some innocent looking part of your circuit into a tuned antenna.