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S11 changes as the same transmission line structure gets longer
Posted 24.06.2020, 02:43 GMT-4 RF & Microwave Engineering Version 5.5 2 Replies
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Hi,
I am trying to use COMSOL to simulate some lumped-element based transmission line structure (modified CPW line by increasing series inductance and shunt capacitance) by having lumped ports on both ends. While I could sweep the shunt capacitance and obtain a 50 Ohm transmission line with a certain configuration (a certain shunt capacitance for instance), I realize that if I simulate the same structure with a longer length by repeating the unit cell, I obtain a different result. That is, the shunt capacitance needed to give a 50 Ohm structure is different for different TL length.
My original goal was to obtain an equivalent LC-ladder for the lumped-element TL, it will be critical to obtain a consistent and accurate S11 from the simulation. Your advice will be much appreicated.
PS: More details on the structure: The lumped-element transmission line is formed by having series inductance along a CPW, and in between the lumped inductors, there are 1 to 2 open-ended stubs to provide shunting capacitance. By sweeping the shunt capacitance, I meant sweeping the length of these open stubs.
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If or when you see a reflection coming back from the end of a transmission line (TL), then that termination (port, if you prefer) is not perfectly matched to the TL in terms of its impedance. In general, the phase of the resulting reflection (as detected wherever you are looking) will depend on the distances traveled by the wave in going back and forth. See https://en.wikipedia.org/wiki/Transmission_line#Input_impedance_of_transmission_line . Now, although I may not fully understand your question, it seems to me that you simply aren't terminating your cpw line properly. If you terminate it with an excellent impedance match, then you should not see a significant reflected wave, regardless of the length of the line.
By the way, I would expect that your termination will need to be equivalent to a R=50 Ohms resistor, rather than to some LC combination, at least assuming that your line has a "characteristic impedance" of 50 ohms (as opposed to some other resistance). L's and C's, if properly chosen, may be appropriate for modeling the line in terms of a circuit model (alhough personally, if I were doing that, I would use a traditional circuit modeling code like SPICE (https://en.wikipedia.org/wiki/SPICE) , instead of Comsol Multiphysics). But regardless, you'll need a resistor to model the (in effect, ideally lossy) infinite length of it, when you get to the end of the TL. Is that where you are having trouble? Are you trying to terminate the line in L's and C's alone, when you need to be using an R?
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If or when you see a reflection coming back from the end of a transmission line (TL), then that termination (port, if you prefer) is not perfectly matched to the TL in terms of its impedance. In general, the phase of the resulting reflection (as detected wherever you are looking) will depend on the distances traveled by the wave in going back and forth. See https://en.wikipedia.org/wiki/Transmission_line#Input_impedance_of_transmission_line . Now, although I may not fully understand your question, it seems to me that you simply aren't terminating your cpw line properly. If you terminate it with an excellent impedance match, then you should not see a significant reflected wave, regardless of the length of the line.
By the way, I would expect that your termination will need to be equivalent to a R=50 Ohms resistor, rather than to some LC combination, at least assuming that your line has a "characteristic impedance" of 50 ohms (as opposed to some other resistance). L's and C's, if properly chosen, may be appropriate for modeling the line in terms of a circuit model (alhough personally, if I were doing that, I would use a traditional circuit modeling code like SPICE (https://en.wikipedia.org/wiki/SPICE) , instead of Comsol Multiphysics). But regardless, you'll need a resistor to model the (in effect, ideally lossy) infinite length of it, when you get to the end of the TL. Is that where you are having trouble? Are you trying to terminate the line in L's and C's alone, when you need to be using an R?
Thanks for getting back to me, in fact I have lost this post and couldn't come back to reply until I saw your email.
I realized my question was very vagued, and later on I have found the issues of my model which came largely from my lack of understanding on how COMSOL works. With the help of your reference, I can now obtain results much closer to the theoretically predicted values for the artificial transmission line.