So, imagine you have a big box filled with different types of toys. Now, if you shake the box, you will hear different sounds depending on the type of toys inside.
Similarly, in electrical engineering, we have big boxes called systems that have lots of different parts (like circuits, wires, and antennas) and are used to do different things. And just like the toy box, if we shake these systems in different ways, we can hear different sounds (in this case, signals).
Characteristic mode analysis is just a fancy way of studying these sounds of a system by identifying certain patterns in the way it reacts to different types of shaking (called excitations). These patterns are called characteristic modes and they give us information about how the system will behave in different situations.
For example, say we want to design an antenna for a radio. We can use characteristic mode analysis to help us figure out how the antenna will receive different frequencies of radio waves. By shaking the antenna in different ways (like moving it up and down, left and right), we can identify its characteristic modes and use them to optimize its performance for different types of radio waves.
So, characteristic mode analysis is like listening to the different sounds a system makes when we shake it in different ways, so we can better understand how it works and optimize its performance.