Lumped to distributed element conversion

[errikosgk]

Hello, I have designed an LC matching network and now I want to convert it into a distributed matching network using ideal transmission lines in ADS.
I know that I have to replace series inductors with series TLIN and shunt capacitors with open circuit stubs but I cannot find how to choose the right impedances and electrical lengths of the traansmission lines in order to have exactly the same match. I would like to find out if there is a specific procedure that will solve my problem.

 

[volker@muehlhaus]

I would try very narrow line width (not 50 Ohm) for the series L section and wide open stub (not 50 Ohm) for the shunt C.

 

[errikosgk]

I would try very narrow line width (not 50 Ohm) for the series L section and wide open stub (not 50 Ohm) for the shunt C.

I know that but I am wondering if there is an exact method to calculate the parameters and just assign approximate values

 

[biff44]

there is no "exact method". You pick a narrow band of frequencies you are interested (for instance near the cuttoff frequency of a filter), and pick a distributed element to simulate by a distributed one.

so as an example, you have a series L, shunt C, lowpass filter with a cuttoff frequency of 2 GHz.
Lets say ONE of the lumped elements in the lowpass prototype model is 2 nH.

You would simulate the above inductor of 2 nH, and see its impedance across its terminals, maybe its magnitued of S21 from 1 to 3 GHz, concentrating the most right at 2 GHz.

Then you would replace it in your simulator with a high impedance microstrip element.

Then you try to match the above to the response of the actual lumped inductor you previously simulated.

If you find something that kind of matches, you then add on a length of LOW impedance line to simulate the follow on lumped capacitor in the filter.

then keep going until the entire lowpass filter is made up of transmission line elements.

if you want to get fancy, you can add models for microstrip line width changes, that will model the parasitic shunt capacitances and series parasitic inductances. In this specific case (lowpass filter) those parasitic capacitances actually help you make the distributed sections look more lumped in nature.

the fringing capacitance adds to the shunt capacitance of the low impedance section

THIS will get you pretty close to the actual response.

at this point you either build the actual distributed element filter and measure it to optimize, OR do a full electromagnetic simulation of the structure to give it a final tweak. You might tweak this lowpass filter to have the exact cuttoff frequency you want. Or you might not like the return loss ripple, and want to improve that.

 

[errikosgk]

there is no "exact method". You pick a narrow band of frequencies you are interested (for instance near the cuttoff frequency of a filter), and pick a distributed element to simulate by a distributed one.

so as an example, you have a series L, shunt C, lowpass filter with a cuttoff frequency of 2 GHz.
Lets say ONE of the lumped elements in the lowpass prototype model is 2 nH.

View attachment 192216

You would simulate the above inductor of 2 nH, and see its impedance across its terminals, maybe its magnitued of S21 from 1 to 3 GHz, concentrating the most right at 2 GHz.

Then you would replace it in your simulator with a high impedance microstrip element.

View attachment 192217
Then you try to match the above to the response of the actual lumped inductor you previously simulated.

If you find something that kind of matches, you then add on a length of LOW impedance line to simulate the follow on lumped capacitor in the filter.

View attachment 192218

then keep going until the entire lowpass filter is made up of transmission line elements.

if you want to get fancy, you can add models for microstrip line width changes, that will model the parasitic shunt capacitances and series parasitic inductances. In this specific case (lowpass filter) those parasitic capacitances actually help you make the distributed sections look more lumped in nature.

View attachment 192219
the fringing capacitance adds to the shunt capacitance of the low impedance section

THIS will get you pretty close to the actual response.

at this point you either build the actual distributed element filter and measure it to optimize, OR do a full electromagnetic simulation of the structure to give it a final tweak. You might tweak this lowpass filter to have the exact cuttoff frequency you want. Or you might not like the return loss ripple, and want to improve that.

ok I understand, thank you

 

[Analog_Joe]

These formulas work fairly well: https://www.rfcafe.com/references/electrical/lumped-distributed-components.htm as long as you keep the electrical length as short as possible. If you want the distributed element to closely follow the lumped element response, you should strive for electrical lengths much shorter than the figures given in that webpage. This implies that you may have to either raise or lower Zo excessively, depending on the element you want to implement, which may result in either very thick or very thin lines which turn out to be impractical to implement. So you will probably have to compromise between line width vs electrical length. Discontinuities are also an issue and a full-wave EM simulation should be carried out to evaluate the design.