Lumped v. distributed parameter

[Cyrus]

This was mentioned casually in my controls book concerning differential equations.

Using simple english please describe to me what the two are. Please avoid any and all equations unless absolutely necessary.

Thanks!

 

[atyy]

When you have a long metal cylinder, each little bit of cylinder has some resistance and some resistance.

If you don't need a good model, you can lump all the little bits of resistance into one resistor, and all the little bits of capacitance into one capacitor. That's lumping.

If you need a really good model, then you should treat all the little bits of resistance and capacitance as little bits connected to each other. That's distributed.

 

[f95toli]

Another example would be a transmission line of some sort, e.g. a cable.
If the cable is much shorter than the wavelength of the signal passing through it you can model the influence of the cable (e.g its attenuation) using lumped element parameters, i.e th impedance Z is a simple function of R, C, L and S.
However, if the frequency is so high that the length of the cable is of the same order of magnitude as the wavelength of the signal this obviously won't work, simply because phenomena like standing waves (and more generally impedance missmatch) etc become important.
You then have to use disitributed parameters to describe the cable and properites like the impedance is now a function of postion Z(x), i.e. the parameters are distributed.