How to understand if circuit can be conosidered lumped?

Hallo everyone.

I would like to understand if there is a way to understand if a complex structure (which I modeled in HFSS) can be considered lumped or not, and up to which frequency it can.

I can make some approximated calculations myself, but I suppose there is some more precise data I can get out of simulations? Maybe from S11?
In particular I have an equivalent lumped model of my structure, but I have doubts up to which frequency I can consider this model to be valid.

I thank you all in advance :-D

In general, the electromagnetic structure must be small enough relative to the wavelength that applying circuit theory makes sense. When size approaches the wavelength, the wave nature needs to be accounted for and lumped circuits are less valid and less useful.

rrumpf said:

In general, the electromagnetic structure must be small enough relative to the wavelength that applying circuit theory makes sense. When size approaches the wavelength, the wave nature needs to be accounted for and lumped circuits are less valid and less useful.

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Thank you for your answer.
My structure is though complex and I cannot apply such a general concept easily. This is why I was asking for a quantification of the issue.

A popular rule of thumb says distributed circuits with length < λ/10 can be described as lumped.

FvM said:

A popular rule of thumb says distributed circuits with length < λ/10 can be described as lumped.

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Problem with this is that I have different topologies on my circuit and it is not possible to define a lambda for the whole structure

Why not trying yourself? Compare lumped and distributed model results.

giangriff88 said:

Problem with this is that I have different topologies on my circuit and it is not possible to define a lambda for the whole structure

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The problem is that we don't know what you have done, and you don't provide enough detail to answer your question.

In general, distributed circuits can be approximated by lumped elements if we divide them into pieces. Every piece then has to be electrically small, as FvM has described. Example: transmission lined modelled by cascaded RLGC elements. The same applies to your circuit/model.

Ok sorry. Let me give you some more details.

Let´s say we have a chip with a resistor and two pads to connect both its pins. Then we bond to those pads two bondwires and we connect the wires with a probe thanks to an additional small PCB.
The simplified equivalent circuit of this would be a RL serie, but let´s say the bondwire gets longer and longer and at some point we cannot use the lumped equivalent model anymore. Same would happen if the PCB gets longer.

I know I can in this simple case divide the structure in two and check if both parts are to be considered lumped. Still I wonder if there is a way to quantify the phenomenon with simulation tools.

FvM said:

Why not trying yourself? Compare lumped and distributed model results.

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what do you mean? I just have the simulation results out of HFSS

Thank you all again

If the bond wires become long relative to your wavelength, you will have to account for the extra phase. You will need three lumped circuit models, on R and two L's, and two phase networks between the R and L's.

giangriff88 said:

Still I wonder if there is a way to quantify the phenomenon with simulation tools. (...) I just have the simulation results out of HFSS

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You can compare S11 and S21 of your lumped model to the simulated S-params, and see how good the fit is vs. frequency.
For the model that you described (with pads) I would expect that you need to add shunt capacitors for a good fit at higher frequencies.