# Impedance in lumped circuits

I was wondering, at high frequency circuits, when the lumped circuit model must be used, why does impedance depends on the position in the wire?

By the way, it's my very first post here =D

Averagesupernova
Gold Member
What is the definition of a capacitor? It would be: 2 conductors separated by an insulator. That in and of itself should give a clue for one of the reasons that wire position has an effect.

• jrmiranda
analogdesign
To follow on to Averagesupernova's reply, what is the definition of a resistor? A length of metal or similar conductive material that has some length and some resistance per unit length. At high frequencies do small resistors become more or less significant?

• jrmiranda
Averagesupernova
Gold Member
Many many things that are not significant at low frequencies become so at high frequencies. When starting out with simple dry cells, resistors, light bulbs, etc. we certainly were not told that there is a small capacitance or inductance that affects the circuit at the brief instant we switch the power on or off. It is real though, but generally of no consequence so in order to avoid confusing new students it is not mentioned. When we come around to AC though, it may be significant and sometimes it is downright difficult to train our minds to consider these things that have been in front of us all along and we simply ignored.

• jrmiranda
Many many things that are not significant at low frequencies become so at high frequencies. When starting out with simple dry cells, resistors, light bulbs, etc. we certainly were not told that there is a small capacitance or inductance that affects the circuit at the brief instant we switch the power on or off. It is real though, but generally of no consequence so in order to avoid confusing new students it is not mentioned. When we come around to AC though, it may be significant and sometimes it is downright difficult to train our minds to consider these things that have been in front of us all along and we simply ignored.
But why impedance oscillates? I understand how resistance is affected, but following this logic, capacitance and inductance should also increase with distance, but they don't, they vary sinusoidally.

Averagesupernova
Gold Member
But why impedance oscillates? I understand how resistance is affected, but following this logic, capacitance and inductance should also increase with distance, but they don't, they vary sinusoidally.
I think you have some things confused. I don't understand what you mean by impedance oscillates. Nor do I understand what you mean by saying that capacitance and inductance vary sinusoidally. Capacitance is fixed. So is inductance. The reactance presented by each will vary with frequency but that is pretty much a linear relationship.

Baluncore
2021 Award
I was wondering, at high frequency circuits, when the lumped circuit model must be used, why does impedance depends on the position in the wire?
This OP is like “what happens when an irresistible force acts on an immovable mountain”. Either the circuit should not be modelled as “lumped constants”, or the frequency of interest should not be so “high”.

If the dimension or shape of the circuit is important in determining performance, then the lumped circuit is not applicable and transmission line theory must be used. Impedance does not oscillate. Circuits may oscillate.

Impedance comes in two parts, resistance and reactance. Z = R + jX.
If the circuit is specified by lumped constants then the circuit may appear to be “resonant at some particular frequency”.
At a resonant frequency, a circuit has zero reactance. That resonant frequency is when X = XC + XL = zero.
If the resistance component, R, of the circuit impedance is positive then it will be damped resonance.
If the resistance component of the circuit impedance is negative then the circuit has gain and so may oscillate at some frequency.