# How to determine the frequencies in which the L&C model of an artificial transmission line works?

I want to model an artificial transmission line with L & C. So far I used the following circuit and used the values of L=400 pH and C=0.16 pF so that Z=sqrt(L/C)=50 ohms. So, expected S21 and S31 could have a 3dB or 6dB drop from 1 to 2 and 1 to 3. (power divider).

But I am getting S21 and S31 as the following:

The gain is lower than 0 dB which I am not worried as of now as I will put some transistors in future (adjust the L values as well) and correct the gain.

But I am worried about the frequency independent behaviour. Well, I see that the input power flows from 1 to 2,3 well from 5-20 GHz. If I change the value of L to 1nH and C to 0.4 pF, then I see that it works at a different range.

During my design with transistors, I can figure out the capacitor parasitics that I would be getting (C_total) per node and then figure out the L depending upon the same formula Z=sqrt(L/C_total). But how can I be sure that the L value which I found works?

Am I missing something?

• It's not clear to me what physical structure you are trying to model. Each line has capacitance to another line but no capacitance to ground, which is probably unrealisable. You also have three inductors and but only two capacitors per line. What is the intended function? Oct 30 '18 at 0:00
• @Steve Hubbard My function is a power divider and combiner. Oct 30 '18 at 1:22

How to determine the frequencies in which the L&C model of an artificial transmission line works?

Since you're using ADS, simulate the s-parameters of one and simulate the s-parameters of the other.

The frequencies where the results are the same (to whatever accuracy you choose) are the ones where you can use the LC model and get the same results as using a more complete model.

As mentioned in comments, the LC model you presented doesn't look much like we'd normally expect an LC transmission line model to look.

Also, you can always extend your LC model to work at higher frequencies by splitting it up into more pi or T sections. Here are two models for the same transmission line, but the one on the right will remain accurate to a higher frequency:

simulate this circuit – Schematic created using CircuitLab

• So, the trick is to increase the orders - got it. Oct 30 '18 at 6:05