transmissionline is a distributed element

The difference is that in a lumped element resonator, the circuit's elements are localized together. In a distributed element resonator, they are spread apart.

lumped" means that the dimension of you ckt element is much smaller than the wavelength of the signal passing through it. Therefore, you can treat your ckt element as a lumped unit (against the wavelength), and do not have to worry about wave propagation phenomenon "within" your ckt element. The opposite of "lumped element" is "distributed network."

Typically, in low-frequency ckt/network, since the frequency is low, therefore, the wavelength is large (wavelength = propagation speed(usu. speed of light) / frequency ), so most elements can be treated as lumped. However, as frequency goes higher and higher, the wavelength becomes shorted and shorter, the wave propagation effect WITHIN the ckt element becomes more and more pronounced.

Using Lumped Element Modeling, Taking Energy & Co-energy and integrating them

Lumped systems are those systems in which electrical

properties like R, L, C etc are assumed to be located on a

small space of the circuit. these systems are applicable

for low frequency application.

On the other hand Distributed systems assume that

electrical properties R, L, C etc are distributed across

the entire circuit. these systems are applicable to for high

(microwave)

frequency application.

Unlike the lumped element model, it assumes non-uniform

current along each branch and non-uniform voltage along

each node.